Structural, Electronic, and Physical Properties of Solid

Chapter 302

Structural, Electronic, and Physical Properties of Solid-State Rare-Earth Boride Carbides Volodymyr Babizhetskyy*,1, Josef Bauer†,2, R egis Gautier†, ‡,3 § Kurt Hiebl , Arndt Simon and Jean-Franc¸ ois Halet†,1 *

Department of Inorganic Chemistry, Ivan Franko National University of Lviv, Lviv, Ukraine Universit e de Rennes 1, Ecole Nationale Sup erieure de Chimie de Rennes, CNRS, ISCR—UMR6226, F-35042 Rennes, France ‡ € Festkorperforschung, € Max-Planck-Institut fur Stuttgart, Germany § € Physikalische Chemie der Universitat, € Wien, Austria Institut fur 1 Corresponding authors: e-mail: [email protected]; [email protected] †

Dedicated to Roald Hoffmann on the occasion of his 81st birthday.

Chapter Outline 1 Introduction 2 Synthesis Techniques 3 Ternary Systems—Compounds and Phase Relations 3.1 Sc–B–C System 3.2 Y–B–C System 3.3 La–B–C System 3.4 Ce–B–C System 3.5 Pr–B–C System 3.6 Eu–B–C System

146 147 148 148 160 161 162 163 164

3.7 Gd–B–C System 3.8 Ho–B–C System 3.9 Er–B–C System 3.10 Th–B–C System 3.11 U–B–C System 3.12 Peculiarities of the Interactions Between Components in the Ternary R–B–C Phase Diagrams

164 166 167 168 169

169

2. Deceased August 9, 2016. 3. Deceased December 17, 2017. Handbook on the Physics and Chemistry of Rare Earths, Vol. 53. https://doi.org/10.1016/bs.hpcre.2018.05.001 © 2018 Elsevier B.V. All rights reserved.

145

146 Handbook on the Physics and Chemistry of Rare Earths 4 Crystal Chemistry, Bonding, and Physical Properties 4.1 Two-Dimensional Boron–Carbon Networks 4.2 Infinite Boron–Carbon Chains

174 178 198

4.3 Coexisting Infinite and Finite Boron–Carbon Chains 4.4 Finite Linear Chains 5 Covalent Metal-to-Nonmetal Bonding in RxByCz Compounds 6 Conclusions References

205 212 257 258 260

1 INTRODUCTION Though boron and carbon are neighbors in the periodic table and have some conspicuous electronic differences, they behave rather similarly when combined together in more or less equal concentrations with rare-earth or actinide metals. The result is the formation of ternary boride carbide (generally called borocarbide) compounds RxByCz, where R ¼ rare-earth or actinide element, and throughout this review R refers not only to lanthanides and actinides but also to Sc and Y. Borocarbide chemistry, pioneered by Nowotny and others in Austria [1], has blossomed over the last 50 years or so, offering today a broad diversity of original crystallographic topologies, most of which are unique due to the much greater than boron and carbon sizes of R atoms and peculiar bonding within the nonmetal atom frameworks, and physical properties. Indeed, boron and carbon have a particular affinity with rare-earth and actinide elements. The R elements supply electrons to stabilize the boron– carbon frameworks, whereas their d- and/or f-electron shells afford attractive physical properties like electrical conduction or magnetism, for example. The skill and vision of the original researchers in this area over many years and, lately, improvements in synthetic methods and analytical techniques have shaped the borocarbide chemistry we know at present. Its progress has been charted periodically in several review papers, covering certains aspects of their chemistry and showing the all-important links between composition, structure and properties [2–8]. Borocarbide chemistry is now mature, and in this review, we offer a complete survey of the rare-earth and actinide borocarbides discussing their synthesis, their crystal structures, their bonding analysis, and, where relevant, pertinent physical properties. In the interest of brevity, we restrict our scope to ternary borocarbides where boron and carbon are present in roughly the same amounts. For information regarding other ternary or quaternary boron/carbon-containing solid-state compounds, the reader is directed to other reviews and surveys [9–13]. Since the authors have been working many years in the field of structural and chemical investigations of ternary rare-earth and actinide borocarbides, it is obvious that issues such as phase stability, phase diagrams, and crystal structures as well as physical properties of borocarbides constitute the main body of the chapter. Methods of synthesis are reviewed in Section 2. In Section 3, we focus on ternary systems containing rare earths and actinides. Each phase diagram and its isothermal section, if studied, are accompanied

Solid-State Rare-Earth Boride Carbides Chapter

302 147

by a brief comment. Information is also included on synthesis procedures of borocarbides and on their crystal structure as reported in the literature. Since in some cases published data are controversial, we have tried to make objective and critical comments to the best of our knowledge. Crystal chemistry, bonding, and known physical properties of ternary borocarbides containing rare earths and actinides are reviewed and discussed in Section 4. Brief comments about the bonding properties are given in Section 5. Section 6 summarizes the main features of these fascinating compounds and contains concluding remarks.

2

SYNTHESIS TECHNIQUES

Boron melts much higher than rare-earth metals or actinides, and carbon (graphite) is a common refractory that sublimes between 3600°C and 3750°C at the atmospheric pressure; hence the synthesis of ternary rare-earth and actinide metal boride carbides, RxByCz, requires very high temperatures. R-borocarbides can be prepared using different methods: (1) Repeated arc melting of compacted powder mixtures of high purity elements under argon, turning the arc-melted buttons over several times to obtain uniform compositions. Arc melting works well only for those R that have high boiling temperatures, e.g., La, Nd, and Gd, but for those that evaporate easily, e.g., Sm or Eu, repeated arc melting may result in substantial losses of R. (2) Repeated arc melting of compacted powder mixtures of high purity elements and boride master alloys prepared from borothermic reduction of metal oxides under argon. Once again, this technique may be unsuitable for low-boiling temperature R. (3) Reactive sintering at >1600 K in vacuum using compacted mixtures of spectroscopically pure graphite with rare-earth oxides and prereacted binary rare-earth borides. (4) Reaction of mixtures of elements at high temperatures up to 1500°C in sealed Mo containers under a protective atmosphere. (5) Carbothermal and borothermal reduction reactions of precursor materials if the evaporation pressure of R is high. Metal oxides such as boron and carbon powders are mixed and then heated in boron nitride crucibles in vacuum or arc melted. (6) Melting for long time in a high-frequency furnace under a protective atmosphere on a water-cooled copper support or in a boron nitride crucible in vacuum using graphite susceptor. Annealing of the arc melted ingot in a high-frequency furnace using the graphite crucible at the temperatures 2000°C under vacuum. Preparation of the rare-earth metal powders is generally performed by filing in a nitrogen or an argon-atmosphere glove box to prevent oxidation. The arcmelted buttons are always turned over and remelted two or three times to ensure homogeneity. Usually, to avoid any contamination the arc-melted ingots are

148 Handbook on the Physics and Chemistry of Rare Earths

wrapped in molybdenum foils, sealed in evacuated silica ampoules, annealed at different temperatures depending on the composition, and subsequently quenched in cold water. Annealing at high temperatures in TiB2 crucibles under a protective atmosphere can be carried out [14]. Typical annealing times are 10 days up to 4 weeks. In general, polycrystalline ingots have to be kept under vacuum or dry inert atmosphere to prevent hydrolysis, and when possible, single crystals suitable for X-ray analysis are isolated by mechanical fragmentation of the samples. The floating zone technique can also be employed using a double halogen-lamp image furnace as well as melting in high-frequency furnace under temperature control to obtain single crystalline samples [15]. Another method that has so far only scarcely been used for the synthesis of single crystals of boron-rich ScxByCz phases is silicon and tin flux [16], a method, which is successfully used for the growth of phosphide and arsenide crystals [17]. This technique has a great potential and could certainly be used for other boron-rich RxByCz compounds.

3 TERNARY SYSTEMS—COMPOUNDS AND PHASE RELATIONS In order to provide basic information about the phase equilibria, compatibility, composition, and structural chemistry of ternary rare-earth borocarbides, partial or complete investigations of ternary R(Ac)–B–C phase diagrams were established for quite a few rare-earth elements and actinides (R(Ac) ¼ Sc, Y, La, Ce, Pr, Eu, Gd, Ho, Er, Th, and U). More than 140 ternary equilibrium phases have been reported to date, the compositions of which often determined by a combination of electron probe microanalysis (EPMA) and X-ray diffraction. The main results are discussed here and the crystal data of these ternary phases are listed in Table 1 including the boron-rich rare-earth borocarbides discussed in Ref. [12] (in the order of increasing atomic number of the rare-earth elements).

3.1 Sc–B–C System The phase relations in the ternary system scandium–boron–carbon were fully investigated within an isothermal section at 1970 K [15]. Figs. 1 and 2 show the phase relations of the Sc-rich (Sc–ScB2–B4C) and the B-rich (ScB2–B– B4.1C) sections, respectively. Seven ternary compounds were identified with the following stoichiometries: Sc2BC2, Sc3B0.75C3, Sc2B1.1C3.2, ScB2C2, ScB17C0.25, ScB15C0.80, and ScB15C1.60. The compound ScB2C [20] is stable only at very high temperatures. It can be synthesized by arc melting. However, after annealing at 1970 K for more than 20 h, it decomposes to ScB2 and ScB2C2. No homogeneity regions in the Sc-rich section, except ScB2 have been established. Lattice parameters of ScB2xCx are different from ScB2, which has

TABLE 1 Crystallographic Data for Ternary Rare-Earth and Actinoid Metal Boride Carbides Unit Cell Parameters (A˚) Compound

Space group

Structure Type

a

ScB17C0.25

P6/mmm

ScB17C0.25

14.550

ScB13C

Imam

ScB13C

5.6829

ScB15C1.6

orth. I

—

ScB2C2

Pbam

ScB2C

b

c

References

8.454

[16]

8.0375

10.0488

[18]

10.027

8.0138

5.6668

[15]

ScB2C2

5.175

10.075

3.440

[19]

P4/mbm

YB2C

6.651

6.763

[20]

Sc2B1.1C3.2

P-3m1

Sc2B1.1C3.2

23.710

6.703

[21]

Sc2BC2

I4/mmm

Sc2BC2

3.3259

10.6741

[15,22]

Sc3B0.75C3

P4/mmm

Sc3B0.75C3

3.3315

7.6737

[23]

YB25C5

I2/m

YB25C5

16.024

5.641

[24]

56.887

[25]

5.860

[24]

3.5458

[26]

21.758 b ¼ 90.18°

YB28.5C4

R-3m

YB28.5C4

5.645

YB25C

I2/m

YB25C

8.278

10.327 b ¼ 90.46°

YB2C2

P4/mbm

DyB2C2

5.3327

YB2C

Pbam

LuB2C

6.7815

6.7904

3.7535

[27]

Y2B3C2

Cmmm

Gd2B3C2

3.405

13.765

3.631

[28] Continued

TABLE 1 Crystallographic Data for Ternary Rare-Earth and Actinoid Metal Boride Carbides—Cont’d Unit Cell Parameters (A˚) Compound

Space group

Structure Type

a

b

c

References

Y10+xB7C10x (x 0.1)

C2/c

Tb10B7C10

11.273

11.159

23.566

[29,30]

b ¼ 98.15° Y5B2C6

P4/ncc

La5B2C6

8.068

11.668

[31]

Y5B2C5

P4/ncc

Sm5B2C5

8.079

10.938

[32]

Y15B4C14

P4/mnc

Tb15B4C14

8.0503

16.041

[33]

LaB2C2

P4/mbm

DyB2C2

5.4020

3.9587

[34,35]

LaB2C4

hex

—

4.500

9.428

[36]

La15B14C19

P21/c

La15B14C19

8.640

19.823

[37]

25.689

[38]

8.636 b ¼ 94.28°

La10B9C12

P41212

Ce10B9C12

8.6678

LaBC

P212121

LaBC

8.646

8.691

12.479

[39]

La5B4C5x (x ¼ 0.15)

Pna21

Ce5B4C5

24.657

8.6051

8.6540

[40]

La5(BC)x (5.6 x 8.8)

P4/ncc

La5B2C6

8.584–8.598

12.315–12.730

[35,41]

CeB2C2

P4/mbm

DyB2C2

5.3943

3.8625

[42]

CeB2C

R-3m

ThB2C

6.6218

11.255

[36,43]

CeB2C4

hex

—

4.491

9.301

[36]

Ce10B9C12

P41212

Ce10B9C12

8.480

25.367

[44]

CeBC

P212121

LaBC

8.5021

8.5217

12.3834

[39,45]

Ce5B4C5

Pna21

Ce5B4C5

24.536

8.504

8.521

[46]

Ce5(BC)x (7.8 x 9.0)

P4/ncc

La5B2C6

8.421–8.363

11.883–12.578

[32,43]

Ce5B2C5

P4/ncc

Sm5B2C5

8.5676

10.978

[47]

PrB2C2

P4/mbm

DyB2C2

5.38486

3.8148

[34]

Pr10B9C12

P41212

Ce10B9C12

8.4365

25.468

[48]

PrBC

P212121

LaBC

8.4478

8.4719

12.325

[45]

Pr5B4C5x (x ¼ 0.15)

Pna21

Ce5B4C5

24.592

8.4563

8.4918

[49]

Pr15B6C20

P1

Nd15B6C18

8.34317

9.24927

8.35817

[50]

a ¼ 84.72°

b ¼ 89.68°

g ¼ 84.23°

8.4243

8.4095

30.828

[51]

Pr25B14C26

P21/c

Nd25B14C26

b ¼ 105.879° Pr5(BC)x (7.5 x 9.3)

P4/ncc

La5B2C6

8.407–8.403

11.969–12.637

[52]

Pr5B2C5

P4/ncc

Sm5B2C5

8.448

10.970

[53]

Pr2BC

C2/m

Nd2BC

13.088

9.488

[52]

3.6748 b ¼ 131.03°

NdB2C2

P4/mbm

DyB2C2

5.3823

3.7761

[54]

Nd10B9C12

P41212

Ce10B9C12

8.3834

25.352

[48]

NdBC

P212121

LaBC

8.370

12.253

[45]

8.392

Continued


Space group

Structure Type

a

b

c

References

Nd5B4C5

Pna21

Ce5B4C5

24.301

8.3126

8.3545

[49]

Nd15B6C20

P1

Nd15B6C20

8.284

9.228

8.309

[50]

a ¼ 84.74°

b ¼ 89.68°

g ¼ 84.17°

8.3404

8.3096

30.599

[51]

[51]

Nd25B14C26

P21/c

Nd25B14C26

b ¼ 106.065° Nd25B12C28

P1

Nd25B15C26

8.3209

8.3231

29.888

a ¼ 83.73°

b ¼ 83.29°

g ¼ 89.76°

Nd5(BC)x (7.5 x 9.2)

P4/ncc

La5B2C6

8.3439–8.3495

11.946–12.461

[32,55]

Nd5B2C5

P4/ncc

Sm5B2C5

8.4583

10.923

[47]

Nd2BC

C2/m

Nd2BC

12.732

9.398

[56,57]

3.6848 b ¼ 130.43°

SmB2C2

P4/mbm

DyB2C2

5.366

3.690

[58]

Sm10B9C12

P41212

Ce10B9C12

8.245

25.167

[59]

SmBC

P212121

LaBC

8.252

12.241

[39]

Sm5B2C6

P4/ncc

La5B2C6

8.213–8.240

11.879–11.971

[31,59]

Sm5B2C5

P4/ncc

Sm5B2C5

8.331

10.926

[47]

8.281

EuB2C2

P42/mmc

YB2C2

3.801

7.602

[14]

GdB2C2

P4/mbm

DyB2C2

5.3746

3.649

[26]

Gd2B3C2

Cmmm

Y2B3C2

3.445

3.710

[60]

Gd7B9C4

tetr. P

—

3.613

3.733

[61]

Gd10B9C10

P21/n

Tb10B9C10

7.9404

11.1887

[62]

23.683

[30]

[63]

13.733

23.811 b ¼ 133.74°

Gd10B7C10

C2/c

Tb10B7C10

11.567

11.451 b ¼ 98.46°

Gd4B3C4

P1

Gd4B3C4

3.9376

3.674

11.850

a ¼ 93.34°

b ¼ 96.77°

g ¼ 90.24°

Gd5(BC)x (7.5 x 9.3)

P4/ncc

La5B2C6

8.1493–8.154

11.799–12.338

[31,64]

Gd5B2C5

P4/ncc

Sm5B2C5

8.2455

10.855

[47]

Gd15B4C14

P4/mnc

Tb15B4C14

8.2103

16.096

[33]

TbB2C2

P4/mbm

DyB2C2

5.3550

3.5888

[34]

TbB2C

Pbam

LuB2C

6.7844

6.7907

3.7883

[27]

Tb2B4C

Immm

Dy2B4C

3.2877

6.569

7.593

[65]

Tb2B2C3

Cmmm

Tb2B2C3

3.412

13.699

3.669

[66]

Tb10B9C10

P21/n

Tb10B9C10

7.937

23.786

11.172

[62]

[30]

b ¼ 133.74° Tb4B3C4

P1

Gd4B3C4

3.6066

3.630

11.813

a ¼ 92.99°

b ¼ 96.77°

g ¼ 90.14° Continued


Space group

Structure Type

a

b

c

References

Tb10B7C10

C2/c

Tb10B7C10

11.310

11.276

23.583

[30]

b ¼ 98.28(1)° Tb5(BC)x (8.3 x 9.2)

P4/ncc

La5B2C6

8.102–8.054

11.568–12.335

[67,68]

Tb5B2C5

P4/ncc

Sm5B2C5

8.1381

10.861

[47]

Tb15B4C14

P4/mnc

Tb15B4C14

8.1251

15.861

[33]

DyB2C2

P4/mbm

DyB2C2

5.3433

3.5567

[34]

DyB2C

Pbam

LuB2C

6.7893

6.7776

3.7254

[27,69]

Dy2B4C

Immm

Dy2B4C

3.2772

6.567

7.542

[65]

Dy2B2C3

Cmmm

Tb2B2C3

3.396

13.694

3.627

[70]

DyBC

Cmmm

YBC

3.384

13.727

3.647

[71]

Dy4B3C4

P1

Gd4B3C4

3.5545

3.599

11.739

[30]

a ¼ 93.23°

b ¼ 96.74°

g ¼ 90.16°

11.387

11.147

23.715

[30]

Dy10B7C10

C2/c

Tb10B7C10

b ¼ 98.06° Dy5(BC)x (7.5 x 9.0)

P4/ncc

La5B2C6

8.012–8.0220

11.499–12.193

[31,70]

Dy2BC2

tI

—

3.598

10.794

[71]

Dy5B2C5

P4/ncc

Sm5B2C5

8.0987

10.795

[32]

Dy15B4C14

P4/mnc

Tb15B4C14

8.0882

15.884

[33]

HoB28.5C4

R-3m

YB28.5C4

5.638

56.881

[25]

HoB2C2

P4/mbm

DyB2C2

5.3414

3.5361

[34]

HoB2C

Pbam

LuB2C

6.7753

6.7856

3.6963

[27,72]

Ho2B4C

Immm

Dy2B4C

3.266

6.551

7.462

[65]

Ho2BC3, HT

tetr. I

—

3.561

12.455

[73]

Ho2BC3, LT

tetr. P

—

3.567

24.514

[73]

HoBC, LT

tetr.

—

3.546

46.40

[73]

HoBC, HT

Cmmm

YBC

3.384

13.697

3.594

[73]

Ho4B3C4

P1

Gd4B3C4

3.525

3.595

11.736

[30]

a ¼ 93.10°

b ¼ 96.62°

g ¼ 90.14°

11.206

11.099

23.509

[30]

Ho10B7C10

C2/c

Tb10B7C10

b ¼ 98.47° Ho5B2C6

P4/ncc

La5B2C6

7.990

11.396

[32]

Ho5B2C5

P4/ncc

Sm5B2C5

8.051

10.650

[32]

Ho15B4C14

P4/mnc

Tb15B4C14

7.9980

15.854

[33]

ErB28.5C4

R-3m

YB28.5C4

5.639

56.867

[25]

ErB2C2

P4/mbm

DyB2C2

5.3329

3.5065

[34]

ErB2C

Pbam

LuB2C

6.7515

3.6585

[27]

6.7806

Continued


Space group

Structure Type

a

b

c

References

Er2B4C

Immm

Dy2B4C

3.2528

6.5462

7.4048

[65]

Er2BC3, HT

tetr. I

—

3.62

12.19

[6]

Er2BC3, LT

tetr. P

—

3.62

24.92

[6]

ErBC, HT

Cmmm

YBC

—

—

—

[6]

Er4B3C4

P1

Gd4B3C4

3.4862

3.5582

11.806

[30]

a ¼ 92.85°

b ¼ 96.37°

g ¼ 90.15°

11.163

10.939

23.650

[30]

Er10B7C10

C2/c

Tb10B7C10

b ¼ 98.30° Er5(BC)x (8.0 x 9.0)

P4/ncc

La5B2C6

7.976–7.958

11.071–11.305

[31,74]

Er5B2C5

P4/ncc

Sm5B2C5

7.9892

10.740

[47]

Er15B4C14

P4/mnc

Tb15B4C14

7.9325

15.685

[33]

Er15B4C16

P4/mnc

Sc4C3

7.946

15.822

[75]

TmB28.5C4

R-3m

YB28.5C4

5.622

56.648

[25]

TmB2C2

P4/mbm

DyB2C2

5.3265

3.4743

[34]

TmB2C

Pbam

LuB2C

6.7323

6.7452

3.6383

[27]

Tm4B3C4

P1

Gd4B3C4

3.4855

3.5232

11.698

[76]

a ¼ 92.87°

b ¼ 96.43°

g ¼ 90.12°

Tm5B2C6

P4/ncc

La5B2C6

7.890

11.270

[32]

Tm5B2C5

P4/ncc

Sm5B2C5

7.925

10.814

[32]

Tm15B4C14

P4/mnc

Tb15B4C14

7.9214

15.751

[33]

YbB2C2

P4/mbm

DyB2C2

5.3387

3.5675

[77]

YbB2C

Pbam

LuB2C

6.7212

6.7304

3.6268

[27]

Yb4B3C4

P1

Gd4B3C4

3.4609

3.5100

11.749

[30]

a ¼ 92.70°

b ¼ 96.27°

g ¼ 90.22°

Yb5B2C5

P4/ncc

Sm5B2C5

7.882

10.774

[78]

Yb15B4C14

P4/mnc

Tb15B4C14

7.8601

15.504

[33,79]

LuB2C2

P4/mbm

DyB2C2

5.3212

3.4471

[34]

LuB2C

Pbam

LuB2C

6.7429

6.7341

3.5890

[27]

Lu4B3C4

P1

Gd4B3C4

3.4373

3.491

11.735

[30]

a ¼ 92.80°

b ¼ 96.07°

g ¼ 90.14°

5.010

15.670

[80]

Lu3BC3

Cmcm

Lu3BC3

4.978

Lu15B4C14

P4/mnc

Tb15B4C14

7.8225

15.603

[33]

ThB2C

R-3m

ThB2C

6.676

11.376

[81]

Th3B2C3

P2/m

Th3B2C3

3.703

9.146

[82]

3.773 g ¼ 100.06

ThBC

P4122

ThBC

3.762

25.246

[83]

ThScB6C3

P6/mmm

UScB6C3

6.60296

3.58421

[84] Continued


Space group

Structure Type

a

b

c

References

aUB2C

Pmma

aUB2C

6.0338

3.5177

4.1067

[85]

bUB2C

R-3m

ThB2C

6.5348

10.780

[86]

UBC

Cmcm

UBC

3.5899

3.3474

[87,88]

U5B2C7

tetr. P

—

7.84

23.58

[86]

UScB6C3

P6/mmm

UScB6C3

6.5096

3.4265

[84,89]

NpB2C

R-3m

ThB2C

6.532

10.769

[90,91]

NpBC

Cmcm

UBC

3.5913

12.0566

3.3803

[90,92]

PuB2C

R-3m

ThB2C

6.509

10.818

[90,91]

PuBC

Cmcm

UBC

3.5890

12.0210

3.3910

[92]

11.978


302 159

FIG. 1 Subsolidus phase relations in the Sc-rich (Sc–ScB2–B4C–C) section of the Sc–B–C system.

FIG. 2 Phase relations in the boron-rich (ScB2–B–B4C) section of the Sc–B–C system (the dotted lines represent hypothetical equilibria).

been explained in Ref. [15] by carbon substitution of boron atoms in the binary boride. The homogeneity range for ScB2xCx was, however, not established and is not shown in Figs. 1 and 2. Chemical analyses indicate a small homogeneity range for Sc3B0.75xC3+y (x 0.03, 0.02 < y < 0.1).


Concerning the boron-rich phases, ScB15C0.80, ScB15C1.60, and ScB17C0.25, they are in equilibrium with B4C. The latter has a homogeneity region from ScB16C0.20 to ScB18.7C0.64 [93]. For the boundary compound B4C a small solubility of Sc was found [15,94].

3.2 Y–B–C System No isothermal section at a specific temperature for the ternary Y–B–C system is available. Four ternary compounds were early identified by Bauer and Nowotny [1], namely YB2C2, YB2C, YBC, and Y2BC2, all characterized by X-ray single-crystal and powder diffraction techniques. Reckeweg and DiSalvo later performed a single-crystal X-ray diffraction refinement for YB2C2 [26]. The tentative phase relations of the ternary Y–B–C system obtained from as-cast alloys are shown in Fig. 3, which are mainly based on the experimental data published by Bauer and Nowotny [1], as well as supplementary investigations of constituent binary systems [6,12,95]. From a single-crystal structure determination of the phase labeled early as Sc15C19 and now identified as Sc3C4 [96], the earlier Y15C19 phase [1] has therefore to be described as Y3C4. The yttrium- and gadolinium-containing compounds “R3C4” are stabilized only by additions of small amounts of boron to the binary R3C4 compositions, whereas pure binary Ho3C4 and R3C4 for R ¼ Sc, Er–Lu are known [96]. The crystal structures of the isostructural phases R15B4C14 (R ¼ Y, Gd– Lu) were found as ordered true ternary compounds [33]. Rogl and Bouree [28] reinvestigated the structure of the so-called YBC phase, which was reformulated as Y2B3C2 on the basis of new X-ray single-crystal and neutron powder diffractometry data and, therefore, is analogous to Gd2B3C2. The structure of

FIG. 3 Tentative partial section of the Y–B–C system with approximated phase relations.


302 161

FIG. 4 Phase relations in the boron-rich (YB12–B–B4C) section of the Y–B–C system (the dotted lines represent hypothetical equilibria).

the earlier reported composition “Y2BC2” was reinspected by Bidaud et al. [47] and Oeckler et al. [32] and reformulated as Y5B2C5. The compound Y5B2C6, slightly richer in carbon, was also prepared by arc melting of the elements [31]. Finally, the monoclinic phase Y10+xB7C10x synthesized by floating zone crystal growth [29] is isotypic with the Tb10B7C10-type structure [30]. To sum up, seven well-characterized ternary YxByCz compounds are reported to date in the Y-rich section (Fig. 3). Additionally, somewhat analogous to Sc, three boron-rich compounds, YB25C, YB25C5, and YB28.5C4, were synthesized by solid-state reactions at high temperatures in the B-rich (YB12– B–B4C) part of the Y–B–C system (Fig. 4). Single crystals of these compounds could also be obtained from tin and copper flux. YB25C and YB25C5 can be considered as solid solutions of carbon in YB25 [24].

3.3 La–B–C System Fig. 5 depicts the isothermal section of the La–B–C phase diagram at 1270 K [35]. It was investigated by means of X-ray or neutron powder diffraction, microstructure, and EPMA analyses. In this system eight ternary compounds were found. For six of them, namely La5B2C6, La5B4C5, LaBC, La10B9C12, La15B4C14, and LaB2C2, the crystal structures have been established. The phase with the La5B2C6 structure type has a broad homogeneity range described by the formula La5(BC)x (5.6 x 8.8). The lanthanum sesquicarbide La2C3


FIG. 5 Isothermal section of the La–B–C phase diagram at 1270 K. Dashed tie-lines correspond to equilibria in the solid state below 1190 K. La15B14C19 (8) and LaB2C4 (9) are observed in samples prepared at higher temperatures. Adapted from V. Babizhetskyy, A. Simon, J. Bauer, Interaction of lanthanum with boron and carbon: phase diagram and structural chemistry, Monatsh. Chem. 145 (2014) 869–876 with permission of Springer.

forms an extended solid solution in the ternary domain La2BxC3x (x ¼ 0.4). The compositions of two new compounds, La4B3C12 and La4B5C18, were identified via wavelength-dispersive X-ray spectroscopy (WDX) analysis. The compound La15B14C19 [37] is stable only at high temperatures. It can be synthesized by arc melting, but after annealing at 1270 K for more than 100 h it decomposes in agreement with the isothermal section of the La–B–C phase diagram. Finally, the compound LaB2C4 was also found at temperatures higher than 1270 K [36].

3.4 Ce–B–C System The solid-state phase equilibria in the Ce–B–C system were characterized by X-ray diffraction, metallography and EPMA [43]. The region up to 60 at.% of Ce was studied at 1270 K, whereas the Ce-rich corner, due to generally lower melting points, was investigated at 970 K (Fig. 6). Nine ternary compounds have been detected. The existence of CeB2C2, Ce5B2C5, Ce5B4C5, Ce5B2C6, CeBC, and Ce10B9C12 was confirmed. The phase near Ce5B2C6 stoichiometry has a broad homogeneity range, described by the formula Ce5(BC)x (7.8 x 9.0).


302 163

FIG. 6 Isothermal section of the Ce–B–C phase diagram at 1270 and 970 K. CeB2C4 (10) is observed in samples at higher temperatures.

In addition, two new ternary compounds were found, namely Ce4B3C13 and Ce7B9C34, which could not be crystallographically characterized. Similar to LaB2C4, the compound CeB2C4 mentioned by Bauer et al. [36] was found at higher temperature.

3.5 Pr–B–C System Eleven ternary compounds were found in the ternary Pr–B–C system (Fig. 7). For nine of them, namely PrB2C2, Pr5B2C5, Pr5B4C5, Pr5B2C6, PrBC, Pr10B9C12, Pr15B6C18, Pr25B14C26, and Pr2BC, the crystal structures could be characterized by X-ray powder and single-crystal techniques. The isothermal section of the Pr–B–C phase diagram at 1270 and 1070 K was investigated by Babizhetskyy et al. [52], using X-ray diffraction, microstructure analysis, and EPMA. The phases Pr15B6C20 and Pr25B14C26 exist above 1270 K, and after annealing at this temperature for 1 month, they decompose in agreement with the isothermal section of the Pr–B–C phase diagram. The phase with approximate stoichiometry Pr5B2C6 has a broad homogeneity range described as Pr5(BC)x (7.5 x 9.3). For the boundary compounds of the Pr–B and Pr–C systems, no extensions into the ternary domain were found. The compositions of two new compounds Pr4B3C13 and Pr7B9C34 were localized via EPMA.


FIG. 7 Isothermal section of the Pr–B–C phase diagram at 1270 and 1070 K. Pr15B6C20 (10) and Pr25B14C26 (11) are observed only in arc-cast samples, decomposing after heat treatment at 1270 K.

3.6 Eu–B–C System The phase relations in the ternary system Eu–B–C were investigated within an isothermal section at 1770 K by Schwetz et al. [14]. Two ternary compounds, EuB2C2 and Eu2BC2, were identified. According to this investigation, another moisture-sensitive phase in the samples EuB6 + C with more than 3 mass% C annealed at T 2270 K is formed. This new phase was characterized from X-ray powder data and reportedly was not identical to EuB2C2. Fig. 8 presents the phase relations in the ternary Eu–B–C system at 1770 K with small changes to comply with the accepted binary systems. A solid solution EuB6xCx (0 x 0.25) was found by Schwetz et al. [14]. For the boundary compounds of the Eu–C system, no extensions into the ternary domain were found.

3.7 Gd–B–C System First information about the phase relations in the Gd–B–C ternary system was published by Smith and Giles [97] and is based on as-synthesized compositions, chemical analyses, and X-ray diffraction studies of samples quenched in an arc-melting apparatus. Five ternary compounds were found: GdB2C2 (A), Gd0.35B0.19C0.36 (B), Gd30B40C30 (C), Gd40B35C25 (D), and Gd35B45C20 (E). Building upon these investigations, an isothermal section at 1270 K was


302 165

FIG. 8 Isothermal section of the Eu–B–C phase diagram at 1770 K.

FIG. 9 Isothermal section of the Gd–B–C phase diagram at 1270 K.

determined by Bidaud [61]. Eleven ternary compounds were then found. Among them, the compositions of five compounds observed in the early work of Smith and Giles was confirmed [97] (Fig. 9). During these investigations, these five compounds, i.e., GdB2C2 (corresponding to phase A), Gd3B2C3 (corresponding to phase C), Gd5B2C6 (phase B), Gd10B9C6 (phase D), and Gd2B2C (phase E) [97] were fully characterized with respect to their crystal structure. A rather large homogeneity region for the ternary compound Gd10B9C6


FIG. 10 Tentative partial section of the Gd–B–C system.

suggested by Smith and Giles [97] was not confirmed during two subsequent reinvestigations of the Gd–B–C ternary phase diagram [61,64]. A solid solution GdB6xCx (0 x 0.013) was found in as-cast alloys. For ternary alloys annealed at 1270 K for 250 h the lattice parameters remain unchanged reflecting a small, if any, solubility of carbon in the hexaboride. For the boundary compounds of the Gd–C system, no extensions into the ternary domain were found. In addition to the ternary diagram proposed by Bidaud [61] (Fig. 9), Ruiz et al. [98] using EPMA measurements of arc-cast and annealed samples at 1270 K found 11 additional ternary compounds. A tentative phase diagram is shown in Fig. 10. Some phase regions of the ternary system could not be investigated, as the alloys rapidly hydrolyzed. They are presented with dashed tie-lines. This tentative phase diagram includes the already structurally characterized phases GdB2C2 [97], Gd5B2C6 [31], Gd5B2C5 [47], Gd2B3C2 [60], and Gd4B3C4 [63]. The new compositions Gd3B2C3 and Gd15B4C15 are in good agreement with the compounds Gd10B7C10 [30] and Gd15B4C14 [33], which were characterized later.

3.8 Ho–B–C System Phase equilibria for the ternary Ho–B–C system were established within an isothermal section at 1770 K by Bauer et al. [73] (Fig. 11). Eight ternary phases were inially identified, namely HoB2C, HoB2C2, HoBC, Ho2BC3, Ho5B2C5, Ho5B2C6, Ho15B2C17, and Ho3B2C3. The partially structurally characterized phases HoB2C2 [99], HoB2C [100], and Ho5B2C6 [32] were more recently fully characterized by Onoyama et al. [34], Bidaud et al. [31], and van


302 167

FIG. 11 Isothermal section isothermal section of the Ho–B–C system at 1770 K. Ho2B2C3 (10), Ho2B4C (11), and HoB28.5C4 (12) are observed at higher temperatures.

Dujin et al. [72]. HoBC shows two modifications [73]. From arc-melted samples the YBC structure type was proposed [1], but after annealing at 1770 K, a more complex structure with a tetragonal cell appears. The new proposed composition Ho15B2C17 is in a rather accordance with the compound Ho15B4C14 which was characterized later [33]. The powder pattern of the as-cast samples with the composition Ho2BC3 shows a body-centered tetragonal cell. After annealing at 1770 K, this compound transforms into a primitive tetragonal lattice with a doubled c-parameter [73]. The phase Ho2B4C [65] exists above 1270 K, and after annealing for 1 week, it decomposes in agreement with the isothermal section of the Ho–B–C phase diagram. The composition Ho3B2C3, initially found by Bauer et al. [73], is in good agreement with the compound Ho10B7C10, which was characterized later by Babizhetskyy et al. [30]. Additionally, the boron-rich compound HoB28.5C4 was synthesized by a solid-state reaction at high temperature from copper flux [25].

3.9 Er–B–C System The solid-state phase equilibria in the Er–B–C system have been investigated by means of X-ray diffraction, metallography, and EPMA at 1270 K [74] (Fig. 12). In this system, a total of 10 ternary compounds have been found. The existence of ErB2C2, Er5B2C6, ErB2C, Er2B4C, Er10B7C10, Er5B2C5, and Er15B4C14 was confirmed. The compositions of two other ternary compounds were also established, namely Er2BC3 and Er4B5C18. The new compound Er4B5C18 shows strong Bragg peaks which can be derived assuming metal


FIG. 12 Isothermal section of the Er–B–C system at 1270 K. Two ternary borides, ErBC (11) and ErB28.5C4 (12), are observed at higher temperatures.

intercalation into the graphite matrix. The phase adopting La5B2C6 structure type has a wide homogeneity range, described by the formula Er5(BC)x (8.0 x 9.0). The equiatomic ErBC phase with the YBC structure type exists in arc-melted samples but decomposes after annealing [6]. The high-temperature form of the ternary boron carbide Er2BC3 crystallizes in body-centered tetragonal lattice and the low-temperature form crystallizes in a primitive tetragonal lattice [6]. Additionally, the boron-rich compound ErB28.5C4 was synthesized by a solid-state reaction at high temperature from copper flux [25].

3.10 Th–B–C System The phase relations in the ternary Th–B–C system were investigated at 1670 K and 1270 K by Toth et al. [101] (Fig. 13). Indeed, the region delineated by Th–ThB4–“ThC” triangle refers to the isotherm at 1070 and 1270 K, while the region enclosed between the ThB4–“ThC”–B–C quadrangle represents the phase relation at 1670 K. Corrections have been made concerning the compound Th3B2C3 (earlier formulated as Th2BC2) [82]. The crystal structures of ThBC, ThB2C, and Th3B2C3 were determined from single-crystal X-ray data (Table 1). That of ThBC2 is still unknown. Mutual solid solubilities for Th borides and Th carbides were reported to be small [101].


302 169

FIG. 13 Isothermal section of the Th–B–C phase diagram at 1270 and 1670 K.

3.11 U–B–C System The phase relations in the ternary U–B–C system were studied by Toth et al. [87] and Rogl et al. [86] as four isothermal sections at 1270, 1670, 1870, and 2070 K. They are practically identical, and the isothermal section at 1870 K is shown in Fig. 14. Three ternary compounds were found in the investigated temperature range, namely UB2C, U5B2C7, and UB1xC1+x [86,87]. UB2C is observed in two polymorphic modifications (at low and high temperature, LT and HT) with a phase transition at 1945 K. The HT bUB2C polymorph is isotypic with ThB2C and the LT aUB2C form crystallizes in its own type of structure [85]. The crystal structure of U5B2C7 remains unknown, but it appears closely related to that of La5B2C6. In contrast to the fully ordered stoichiometric UBC compound, random occupation by carbon and boron atoms is observed on the boron site at the (off-stoichiometric) composition UB0.78C1.22 [88]. Mutual solid solutions of uranium carbides and uranium borides in the temperature range from 1270 to 2070 K were found to be very limited. The compounds UB2C and UBC melt congruently at 2550 and 2410 K, respectively [86].

3.12 Peculiarities of the Interactions Between Components in the Ternary R–B–C Phase Diagrams Altogether, 11 isothermal sections of the 21 possible phase diagrams for the R–B–C systems (R ¼ Sc–Lu, Th–Pu) in the whole concentration ranges are known at present. Moreover, isothermal sections were investigated in the region


FIG. 14 Isothermal section of the U–B–C phase diagram at 1870 K.

of high B content for three systems. Additional ternary compounds, which are stable over a limited temperature range, may also exist. In total, about 140 ternary rare-earth and actinoid borocarbides have been synthesized. For 131 compounds the crystal structures were studied, which belong to 38 structure types. Table 2 shows a survey of isotypic series of compounds found in ternary R–B–C systems. Some aspects of the interactions between components in the ternary systems R–B–C were considered by Bauer et al. [5] and Rogl [6]. The compositions with established crystal structure are summarized in Fig. 15. Phase diagrams are known for only 11 ternary systems, namely {Sc, Y, La, Ce, Pr, Eu, Gd, Ho, Er, Th, U}–B–C. Other systems were investigated for the synthesis and existence of ternary boron carbides with specific stoichiometries (Table 1; Figs. 1–14). Based on the data available, it is relatively easy to see that both the number and the stoichiometry of compounds that have been characterized are different and depend on the nature of the R element. Scandium, like Y, has no f-electrons, but it is unique in that it is the smallest among the rare earths ˚ . For this reason ternary and actinides with its effective metallic radius of 1.64 A scandium borocarbides as well as its binary borides and carbides are often different compared with other rare earths and actinides. Obviously, the electronic structure, electronegativity, and atomic radii are all important parameters to either observe or not a specific ternary compound. Indeed, the number of compounds formed is 7 in the Sc–B–C and Y–B–C systems, 9, 10, and 11 in the La– B–C, Ce–B–C, and Pr–B–C systems, respectively, but only 2 borocarbides form in the Eu–B–C system. For the smaller R, 11 compounds are found in the Ho–B–C system, whereas Gd seems quite unique since as many as 22 compounds are characterized in a small temperature interval. For the majority of

TABLE 2 Isotypic Compounds in the Ternary R–B–C Systems Compound

Type

RB25C5

YB25C5

RB28.5C4

YB28.5C4

RB25C

YB25C

RB17C0.25

ScB17C0.25

RB13C

ScB13C5

RB2C2

DyB2C2

RB2C2

ScB2C2

RB2C

YB2C

RB2C

LuB2C

RB2C

ThB2C

R2B4C

Dy2B4C

R2B3C2

Gd2B3C2

R2B2C3

Tb2B2C3

R15B14C19

La15B14C19

R10B9C12

Ce10B9C12

RBC

LaBC

Sc

Y

La

Ce

Pr

Nd

Sm

Eu

Gd

Tb

Dy

Ho

Er

Tm

Yb

Lu

Continued

TABLE 2 Isotypic Compounds in the Ternary R–B–C Systems—Cont’d Compound

Type

RBC

YBC

R10B9C10

Tb10B9C12

R5B4C5

Ce5B4C5

R4B3C4

Gd4B3C4

R15B6C20

Pr15B6C20

R10B7C10

Tb10B7C10

R25B12C26

Nd25B14C26

R25B12C28

Nd25B12C28

R5B2C6

La5B2C6

R2B1.1C2

Sc2B1.1C2

R2BC2

Sc2BC2

R5B2C5

Gd5B2C5

R3BC3

Lu3BC3

R3B0.75C3

Sc3B0.75C3

R15B4C14

Tb15B4C14

R2BC

Nd2BC

Sc

Y

La

Ce

Pr

Nd

Sm

Eu

Gd

Tb

Dy

Ho

Er

Tm

Yb

Lu


302 173

FIG. 15 Ternary compounds with established crystal structure in the R–B–C systems.

Ac–B–C systems, no systematic investigations were performed. Usually, only samples with specific stoichiometric compositions have been examined when searching for isostructural compounds found in related ternary systems (see Table 1). Ternary R–B–C systems can be divided into a few subgroups. As mentioned earlier, Sc system represents a subgroup on its own. Another one consists of systems with light lanthanides (R ¼ La–Nd). A third subgroup is made of systems with heavy lanthanides (Gd–Lu) and yttrium. The europium system is less studied. Nevertheless, even from the available limited data, probably related to experimental difficulty of sample preparation, it may be concluded that this system also represents a separate group due to likely divalent or intermediate oxidation state of europium in ternary borocarbides which are formed. Generally, among the 38 structure types known for R–B–C borocarbides, light and heavy rare earths adopt different structures, but there are several examples of structures observed practically for all rare earths, such as DyB2C2, La5B2C6, and Gd5B2C5 types. In the investigated R–B–C systems detectable homogeneity ranges are found only for the compounds crystallizing in the La5B2C6 type of structure. For the compounds Y10+xB7C10x and R5B4C5x (R ¼ Ce, Pr) a small deficiency


of carbon was detected, whereas other isostructural compounds R10B7C10 and R5B4C5 show full occupancies of carbon positions in the crystal structure. The nearly negligible homogeneity ranges can be assumed for these compounds. Fig. 15 illustrates the distribution of stoichiometric compositions of ternary rare-earth and actinide borocarbides with known crystal structures. Interestingly, almost all of them lie within a limited concentration triangle (the lightgray area in Fig. 15) delineated by B–R2C3–R2C. Such a narrow distribution indicates a large influence of the nature of the binary carbides and borides on the formation of ternary borocarbides. A small number of ternary compounds are reported for actinoid elements, 4, 3, 2, and 2 for Th, U, Np, and Pu, respectively. For 10 ternary and 2 quaternary actinoid borocarbides the crystal structures were studied, which belong to 6 structure types. As it is seen in Table 2 a number of morphotropic series are observed in the discussed systems. A brief description follows: (i) The RB2C2 compounds. The Dy2B2C2 type of structure is adopted with all rare earths from Y to Lu. With Sc, the ScB2C2 type of structure is observed. (ii) The RB2C compounds. YB2C shows its own type of structure. For heavy lanthanides the DyB2C type of structure is observed. The CeB2C and AcB2C compounds with Ac ¼ Th, Np, Pu have the ThB2C type of structure. UB2C is dimorphic. The HT form, aUB2C, exists above 1670 K and at lower temperature crystallizes in the ThB2C type of structure. (iii) The RBC compounds. Light ternary lanthanide borocarbides (R ¼ La, Ce, Pr, Nd, Sm) crystallize in the LaBC type of structure, whereas the heavy lanthanides (R ¼ Dy, Ho, Er) adopt the YBC type. AcBC (Ac ¼ U, Np. Pu) compounds crystallize in the orthorhombic UBC type of structure, whereas ThBC has its own type of structure. (iv) The R3BC3 compounds. The Lu3BC3 compound crystallizes in its own type of structure, while the scandium compound Sc3B0.75C3 exhibits a minor deficiency of boron and crystallizes in one original type of structure.

4 CRYSTAL CHEMISTRY, BONDING, AND PHYSICAL PROPERTIES Although more than 140 ternary rare-earth and actinide metal boron carbides have been structurally characterized (Table 1), not all of them have been studied with respect to their chemical and physical properties. The available data are discussed in this section together with their structural peculiarities. Most of the ternary rare-earth borocarbides are light metallic gray in color in the polycrystalline form. Single crystals have metallic luster. In contrast to the ternary rare-earthtransition-metal borides [9], many of the ternary rare-earth borocarbides are sensitive to moisture. Consequently, handling and storage of these compounds should be performed in inert gas-filled glove boxes or Schlenk flasks.


302 175

In general, X-ray structure determination and structural characterization of rare-earth metal borocarbides often proved to be rather difficult as the crystals are often twinned or consist of intergrown fragments with different compounds. Coherent twinning and intergrowth are much more frequently observed than incoherently intergrown fragments. Among the rare-earth boride carbides, which were crystallographically characterized, those with tetragonal or pseudotetragonal metal atom arrangements exhibit a tendency to form twins and coherently intergrown domains of different phases. This tendency is due to structural elements (motifs) common to all intergrown phases [102,103]. These motifs form (nearly) planar square nets of R atoms or even sandwich-like slabs, which are present in different orientations and constitute the interfaces between different domains. While reasonable structure determinations from “single-crystal” X-ray data can be obtained from twinned and/or intergrown crystals, some fine details of the structures can only be revealed from single-crystal data obtained from true single crystalline specimens. The results of the structure determinations, therefore, should be considered carefully. A compilation of the structural arrangements of the metal-rich RxByCz compounds listed in Table 3 indicates that various boron–carbon substructures are

TABLE 3 Relationships Between the Structural Arrangements and VEC for RxByCz Rare-Earth and Actinide Borocarbides That Have Been Structurally Characterized Compound

VEC

B/C Net

at % R

B/C

Two-dimensional networks RB2C2 (Y, Ce–Sm, Tb–Lu)

4.25

2/∞-[B2/3C2/3B4/3C4/3]

20

1

ScB2C2

4.25

2/∞-[B2/3C2/3.2B5/3C2/3]

20

1

RB2C (Sc, Tb–Lu)

4.33

2/∞-[B2/3C3/3B4/3C3/3]

25

2

ThB2C (Np, Ce, U (HT))

4.33 (4.67)

2/∞-[B6/6B6/3C3/2]

25

2

UB2C

4.33 (4.67)

2/∞-[B6/3C2/2]

25

2

R2B4C (Tb–Er)

4.40

2/∞-[B6/3C4/2B2/2]

28.6

4

R2B3C2 (Y, Gd)

4.60

2/∞-[B6/3C4/2B2/2]

28.6

1.5

Tb2B2C3

4.80

2/∞-[B6/3C4/2B2/2]

28.6

0.66

RBC (Dy, Ho, Er)

5.00

1/∞-[B2C2]

33.3

1

ThBC

5.00

1/∞-[B2C2]

33.3

1

UBC (Np, Pu)

5.00 (5.50)

1/∞-[B2C2]

33.3

1

Infinite branched chains

Continued


TABLE 3 Relationships Between the Structural Arrangements and VEC for RxByCz Rare-Earth and Actinide Borocarbides That Have Been Structurally Characterized—Cont’d Compound

VEC

B/C Net

at % R

B/C

UB0.78C1.22

5.11 (5.61)

1/∞-[B2C2]

33.3

0.64

Th3B2C3

5.00 (5.50)

1/∞-[B2C2] [C]

37.5

0.66

R10B9C10 (Tb, Gd)

5.10

1/∞-[B18C18] [C]

34.5

0.90

R4B3C4 (Tb–Lu)

5.29

1/∞-[B2C2] [BC2]

36.4

0.75

R10B7C10 (Y, Gd–Er)

5.35

1/∞-[B2C2] [BC2] [C]

34.4

0.90

La15B14C19

4.94

[B4C7] [B5C6]

31.0

0.74

RBC (La–Sm)

5.00

[B5C5]

33.3

1

R10B9C12 (La–Nd)

5.00

[B5C8] [B4C4]

32.2

0.75

R5B4C5 (La–Nd)

5.22

[B4C4] [B3C3] [BC2] [C]

35.7

0.8

Nd25B12C28

5.50

[B2C4] [BC2] [BC3]

38.5

0.43

R25B14C26 (Nd, Pr)

5.57

[B2C4] [B3C3] [BC2] [C]

38.4

0.53

R5B2C6 (Y–Sm, Gd–Tm)

5.63

[BC3] [C]

38.4

0.33

R15B6C20 (Pr, Nd)

5.62

[B3C3] [B4C4] [BC2]

38.4

0.33

Sc2BC2

5.67

[BC2]

40.0

0.5

R5B2C5 (Y, Ce, Pr–Tm)

5.86

[BC2] [C]

41.6

0.4

R3BC3, (Sc, Lu)

6.00

[BC2] [C]

42.8

0.33

R15B4C14 (Gd–Lu)

6.15

[BC2] [C]

45.5

0.28

R2BC (Nd, Pr)

6.50

[B2C2]

50.0

1

Finite linear chains

The VEC is calculated with n ¼ 3, in brackets for n ¼ 4.

encountered ranging from 2D to 1D to 0D networks embedded in the metal atom sublattices [5,7,8]. In the first family, 2D layers of boron and carbon atoms alternate with sheets made of metal atoms. In the second category, the nonmetal atoms form infinite 1D nearly planar ribbons based on zigzag chains of boron atoms to which carbon atoms are attached running in metallic channels. Finally, in the third family finite quasimolecular and nearly linear entities of


302 177

different lengths are trapped in metallic cavities. It turns out that the dimensionality of these anionic nonmetal substructures is strongly dependent on the valence electron concentration (VEC) per main group atom considering a Zintl–Klemm approach [104,105], which assumes that the metal atoms transfer completely their valence electrons (usually three, sometimes four) to the B/C framework [106]. VEC values are obtained by adding these electrons to those brought by the boron (three) and carbon (four) atoms, divided by the number of light atoms, i.e., VEC ¼ (nx + 3y + 4z)/(y + z), with n ¼ 3 or 4 depending on the metal oxidation state. VEC increases as the dimensionality of the nonmetal framework decreases. Compounds with 2D boron–carbon layers have a VEC slightly larger than 4. With a VEC around 5, 1D ribbons are found, whereas compounds with a VEC larger than 5 contain finite (0D) units. Indeed, the augmentation of the VEC corresponds to the formal population of antibonding orbitals of the B/C network, which leads to the breaking of bonds and thus diminishes its dimensionality. Of course, such an ionic approach to “rationalize” the B/C sublattice in these compounds must be considered as only approximate since, as we will see later, the metals need not always be fully oxidized to fulfill the electronic requirements of the anionic B/C network. However, existence of compounds with identical stoichiometry, but different B/C substructures as well as coexistence of nonmetal atom subsystems of different dimensionalities [63], indicates that this approach is rather qualitative and not sufficient to fully understand the bonding in these compounds. Other parameters such as the size of the rare-earth metal atom and the nonmetal-to-nonmetal bond order are obviously important as well, in determining the dimensionality of the boron–carbon networks. Moreover, calculating the VEC does not provide any information about the exact topology of the B/C subsystems as well as the local environment of the boron and carbon atoms in these compounds. Therefore, a deeper insight is necessary to get details about their bonding and physical properties. We will see later that the structures of these compounds are of interest and furthermore that exciting physical properties have been found. Superconductivity for YB2C2 as well as the isostructural LuB2C2 compound with Tc ¼ 3.6 and 2.4 K, respectively, was reported as early as the beginning of the 1980s [107,108] and confirmed later [109,110]. A lot of experimental attention has also been paid to the magnetic properties of ternary rare-earth metal boron carbides. For instance, unusual antiferroquadrupolar ordering is observed in the isostructural magnetic DyB2C2 and TbB2C2 compounds. The interesting magnetic properties of HoB2C and DyB2C may originate from the frustrated nature of the magnetic lattice containing triangular interactions between rare-earth metal atoms. For these RB2C compounds the magnetic ordering temperatures do not obey the de Gennes scaling, and the fluctuating ground states result from the complex spin–spin interactions or spin–quadrupole interactions. More details are given in the following sections.


4.1 Two-Dimensional Boron–Carbon Networks Layered compounds formed by alternating boron–carbon and metal atom layers constitute a substantial class among the R–B–C structures. They are generally characterized by a small VEC in the range from 4.25 to 4.8.

4.1.1 The RB2C2 Phases 4.1.1.1 Structural Properties of RB2C2 The first diboride dicarbides were produced by Post et al. [111] during an attempt to prepare lanthanoid borides by the reduction of sesquioxides with boron and carbon. An yttrium compound with the same stoichiometry was reported the same year by Binder [112]. These phases with tetragonal symmetry were initially believed to be pure borides RBx, but in later publications, it was suggested that carbon was needed to stabilize them. This was proved to be the case in the thesis work of Smith [113] who characterized a number of these phases with neodymium, gadolinium, terbium, dysprosium, holmium, erbium, and ytterbium and established the correct chemical formulae as RB2C2. At the same time, Nordine et al. [114] prepared the isostructural compound LuB2C2. Subsequent investigations performed by Fishel and Eick [115], Bauer and Nowotny [1], Bauer and Debuigne [71], Bezruk and Markovskii [116], and Schwetz et al. [14] established that all the lanthanides and yttrium form diboride dicarbides with tetragonal symmetry. In addition, Breant et al. [117] showed that CaB2C2 belongs to this series as well. X-ray powder diffraction patterns were indexed for these diboride dicarbides by all these authors on the basis of a small tetragonal unit cell containing one RB2C2 formula unit. Both powder and single-crystal diffraction data for TbB2C2, for instance, indicated clearly the metal position at 0, 0, 0, and the B/C network located at z ¼ 1/2. As pointed out by Hoard and Hughes [118], the geometry of the B/C network can easily be derived from the cubic hexaboride CaB6 arrangement. Indeed, a three-dimensional boron network consisting of fused four- and eight-membered rings (B4 squares and regular B8 octagons) is present in the CaB6 structure (Fig. 16). By selecting a single layer and eliminating the connecting interlayer B atoms—those that convert the B4 squares into B6 octahedra—one obtains a stratified (hypothetical) RB4 structure whose symmetry is lowered from cubic to tetragonal, and which contains infinite twodimensional flat boron layers (sheets) made of alternating four- and eightmember boron polygons. Substitution in an alternating pattern of C atoms for half the B atoms in the sheets then gives the B/C network and the structure of these rare-earth metal boride carbides RB2C2. There are two or more possible ordered substitutions in this structure, if one doubles the c-axis, as also illustrated in Fig. 16. When this structure was first reported, the accuracy of the structure determination using photographic techniques was insufficient to determine the ordering of the B and C atoms, and because no superstructure Bragg reflections were observed, the unit cell was doubled in a rather speculative way with an …ABAB… stacking of the B/C sheets.


302 179

€ FIG. 16 Barnighausen tree for the group–subgroup relationships CaB6 and RB2C2.

On the basis of general bonding considerations, bond distances, electronic requirements, and similarities with boride and carbide structures, Smith and Gilles [97] proposed a new unit cell with a ¼ a√ 2 and c0 ¼ c, space group P4/mbm, which allows a first step toward an ordered distribution without homoatomic bonds in the B/C network and …AAA… stacking along c. Interestingly, Bauer and Nowotny [1] proposed another model for YB2C2 with BBCC atomic distribution in the octagons (space group P-42c). In this case, the unit cell is doubled in the c-direction with subsequent B/C nets rotated by 90°, preserving the same a-axis as in the original small tetragonal cell. The situation is more complicated than expected. Fig. 16 shows the € Barnighausen tree [119] for group–subgroup relationships of CaB6 and RB2C2 phases. Four different B/C ordering schemes can be envisioned. The first one corresponds to that in the LaB2C2 structure as found on the basis of a singlecrystal X-ray study by Bauer and Bars [99]. This is the same as the model initially proposed for YB2C2. However, the space group P-42c is not the highest possible symmetry. It was later corrected into P42/mmm symmetry by


Cenzual et al. [120]. The second model proposed by Smith and Gilles [97] was modified on the basis of neutron powder diffraction results by Yamaouchi et al. [121], Onimaru et al. [42,54], and van Duijn et al. [122] studying DyB2C2. Indeed, the authors observed superstructure peaks arising from the enlarged unit cell in the ab-plane with a ¼ a0 √ 2 and c ¼ c0 (space group P4/mbm). X-ray single-crystal investigations on SmB2C2 performed by Babizhetskyy et al. [58] confirm previous studies on DyB2C2 with the B and C atoms alternating in the eight-membered rings (Fig. 17). The atomic parameters of SmB2C2 are given in Table 4. Even though Ca is not a member of the rare-earth elements, it is worth mentioning the existence of CaB2C2. As said earlier, this compound was first observed by Breant et al. [117] and was initially believed to be isostructural to the other rare-earth diboride dicarbides. A reinvestigation of CaB2C2 with much improved experimental and computational techniques by Albert and Schmitt [123] revealed another boron–carbon ordering scheme, corresponding € to the third subgroup in the Barnighausen family (Fig. 16). The unit cell

FIG. 17 Side view (left) and projection on the (001) plane (right) of the DyB2C2 type of structure. Large gray, small black, and small gray spheres represent Dy, B, and C atoms, respectively.

TABLE 4 Atomic Parameters for SmB2C2 Atom

Site

x

y

z

Sm

2a

0

0

0

B

4h

0.3600

0.8600

1/2

C

4h

0.1594

0.6594

1/2

˚ , c ¼ 3.690 A ˚ [58]. SG P4/mbm, a ¼ 5.366 A

302 181


volume is four times larger than the original small cell, i.e., √ 2a √ 2a 2c. The B/C ordering within a layer is identical to that observed in DyB2C2, but successive layers are rotated by 90°, leading to doubling of the c-axis. The fourth member of this family is a hypothetical “MB2C2,” not observed so far, with the particularity of containing four-membered rings formed by either only carbon or only boron atoms generating eight-membered rings similar to those in LaB2C2 with BBCC atomic distribution. The question of the B vs C distribution in the boron–carbon layers encountered in these RB2C2 compounds deals with the so-called coloring problem. More than 30 years ago, Burdett et al. introduced it with the following question: “Given a molecular or extended network and two different types of atoms, we may wonder what is the best way to distribute them in the network for a fixed stoichiometry” [124,125]. Indeed, the way the atoms are distributed can influence the nature of the electronic structure and therefore the physical and chemical properties. Initially addressed by Burdett et al. [126,127] on the basis of theoretical EH and EH-TB calculations, the coloring problem was definitely solved a few years later combining 11B solid-state NMR experiments [128] and DFT calculations [129]. Indeed, the BCBC coloring encountered in DyB2C2 (Fig. 17) is computed to be the most stable arrangement regardless of the metal. In other words, all RB2C2 compounds crystallize in the P4/mbm space group. Another structural arrangement is observed for ScB2C2 [19]. The compound crystallizes in the orthorhombic space group Pbam with lattice constants and atomic parameters given in Table 5. Sc is too small to sit above and below the eight-membered rings. Consequently, the B/C nets are rather composed of fused five- and seven-membered rings with the scandium atoms situated above and below the seven-membered rings (Fig. 18). There is no RB4 example with five- and seven-membered rings, but numerous ternary MM0 B4 with the YCrB4 type of structure show this arrangement [9,130,131]. The distribution of boron and carbon is ordered in the nets. Each seven-membered ring contains three C and four B atoms, whereas each five-membered ring contains three

TABLE 5 Atomic Parameters for ScB2C2 Atom

Site

x

y

z

Sc

4g

0.1375

0.1488

0

B1

4h

0.3608

0.4667

0.5

B2

4h

0.4835

0.1900

0.5

C1

4h

0.3904

0.446

0.5

C2

4h

0.2948

0.3122

0.5

SG Pbam, a ¼ 5.175 A˚, b ¼ 10.075 A˚, c ¼ 3.440 A˚ [19].


FIG. 18 Projection on the (001) plane of ScB2C2. Large gray, small black, and small gray spheres represent Sc, B, and C atoms, respectively.

C and two B atoms. As pointed out by Smith et al. [19], since these are oddmembered rings, at least one homopolar B–B or C–C bond in each is unavoidable. Recent DFT calculations have confirmed the thermodynamical stability of such a distribution over other possible ones which minimizes the number of B–B and C–C contacts and maximizes the number of boron atoms in the heptagons [132]. 4.1.1.2 Physical Properties of RB2C2 Electrical property measurements carried out on some RB2C2 compounds by Sakai et al. [108] indicate a metallic-type conductivity, which is confirmed by DFT calculations [129]. Superconducting transition is observed for YB2C2 and LuB2C2 at 3.6 and 2.4 K, respectively, whereas LaB2C2 remains in the normal metallic state down to 1.8 K. The electrical resistivity of CeB2C2 shows an antiferromagnetic transition temperature at 7 K and another anomaly below 110 K, which can likely be ascribed to spin disorder scattering due to crystal field splitting effects of the Ce3+ ions. For PrB2C2 the crystal field splitting of the Pr3+ ions is detected at 20 K. All other borocarbides RB2C2 (R ¼ Nd, Sm, Gd, Tb, Dy, Ho, Er, and Tm) show a rapid decrease of resistivity at low temperatures starting at 9, 53, 48, 23, 16, 7, 15, and 16.5 K, respectively. The results of electronic transport measurements are in good agreement with the magnetic ordering temperatures determined earlier by the same authors [107,108] which showed that most of the diboride dicarbides RB2C2 (R ¼ Ce, Nd, Sm, Gd, Tb, Er, and Tm) are antiferromagnetic. PrB2C2 becomes a Van Vleck paramagnet at low temperature. The main magnetic interactions in RB2C2 according to Sakai et al. [107] are f–f indirect exchange via conduction electrons (RKKY interaction). Recently, Michor et al. [110] reinvestigated the superconductivity of YB2C2. The measurements of specific heat


302 183

and magnetic susceptibility reveal bulk superconductivity with weak coupling BCS features below the transition temperature Tc ¼ 1 K. Earlier signatures of superconductivity reported by Sakai et al. [108] have been identified as spurious anomalies, and the samples which were measured then may have contained superconducting (Tc ¼ 3.9 K) YC2 impurities. Watanuki et al. [133] investigated the topology of the Fermi surfaces of LaB2C2 by measuring the de Haas–van Alphen oscillations. Results obtained indicate the presence of multiple 3D Fermi surfaces formed by the La 5d orbitals strongly hybridized with the 2p orbitals of the boron and carbon atoms of the nonmetal sheets. The magnetic phase diagram was determined for CeB2C2 by means of specific heat, magnetization, and magnetic susceptibility measurements [134,135]. CeB2C2 is an antiferromagnet with TN ¼ 7.3 K with moment direction in the tetragonal (001) plane and shows an order–order transition at 6.5 K. The crystal field excitations for CeB2C2 were studied by Hillier et al. [136]. A strong hybridization between the localized 4f electrons and the conduction electrons was observed using an inelastic neutron scattering technique. Metamagnetic transitions at low fields were observed. The boride carbides TbB2C2. DyB2C2 and HoB2C2 are ferromagnets with complex magnetic structures. The magnetic phase diagram was studied for NdB2C2 by Ohoyama et al. [137]. The compound is a uniaxial anisotropic antiferromagnet with TN ¼ 8.8 K. The coupling between the nearest neighbor magnetic moments is antiferromagnetic in the ab-plane and ferromagnetic along the [001] direction. Spontaneous magnetization of DyB2C2 appears along the [110] direction below Tc ¼ 15.3 K. The compound exhibits a large magnetic anisotropy [121,138] with a high antiferroquadrupolar ordering at TQ ¼ 24.7 K. The antiferroquadropular order in DyB2C2 was confirmed both by Tanaka et al. [139] and by Hirota et al. [140], who reported a direct observation of the 4f orbital order in the antiferroquadropular phase by means of resonant X-ray scattering. Onodera et al. [141] investigated the magnetic phase diagrams of HoB2C2. An antiferromagnetic transition occurs at 5.8 K and a spin reorientation is observed at 5.0 K. Below 5.0 K both the ferromagnetic and antiferroquadrupular ordered states coexist. The magnetic structure of CeB2C2 was also investigated by using neutron powder diffraction [142] and inelastic scattering experiments [143] and compared to those of other RB2C2. Except CeB2C2, RB2C2 generally exhibits AFM structures with propagation vectors k ¼ (1, 0, 0) or (1, 0, 1/2). The fundamental magnetic coupling in the ab-plane is antiferromagnetic. CeB2C2 undergoes a magnetic ordering at TN ¼ 7.3 K and, below the first order–order transition temperature Tt ¼ 6.5 K, shows a modulated long periodic magnetic structure with a propagation vector k ¼ (0.167, 0.167, 0.114). Ce substitution by Lu in Ce1xLuxB2C2 (0 x 0.31) changes the nature of the magnetic transition change from a first to a second order. The substitution breaks the


competition between AFM and FM interactions and introduces randomness in the exchange interactions between the Ce moments. A spin-glass phase appears at Lu concentration x ¼ 0.31 [144]. A neutron diffraction study of the magnetic structure of GdB2C2 performed by Yamaguchi et al. [145] reveals antiferromagnetism in the ab-plane and ferromagnetism along the c-axis. The ordered magnetic structures of the compounds TbB2C2, DyB2C2, HoB2C2, and ErB2C2 were also determined from powder neutron diffraction measurements [122]. TbB2C2, HoB2C2, and ErB2C2 exhibit long-period magnetically ordered states with periodicity in the ab-plane characterized by a propagation vector k ¼ (0, 0, 1/2). For ErB2C2 the magnetic moments alternate between [001] and [00 1] orientations and their magnitudes are sinusoidally ˚ in the [110] direction [122]. DyB2C2 and modulated with periodicity of 67.5 A HoB2C2 have net ferromagnetic moments, whereas TbB2C2 exhibits anomalous antiferromagnetism. These properties were reinvestigated by Kaneko et al. [146]. A new transition temperature at TN ¼ 21.7 K was then found. The magnetic structures and properties of ErB2C2 were investigated in detail again some years later by Ohoyama et al. [147,148] and Onodera et al. [149]. The compound exhibits a short-range ordering below 16 K, as well as an order–order transition at 13.0 K. The magnetic structure of TmB2C2 below TN ¼ 16.5 K is k ¼ (1, 0, 1/2)-type one with a magnetic moment of 6.5 mB parallel to the c-axis, which is different from the fundamental magnetic structure with k ¼ (1, 0, 0) in other RB2C2 compounds [150]. Indeed, although they display the same structural arrangement, the magnetic structures of the RB2C2 compounds depend on the lanthanoid contraction, indicating that the distance between the rare-earth atoms must be an important factor to determine their magnetic properties. The magnetic B–T phase diagrams of Y-diluted Tb1xYxB2C2 (0.2 x 0.5) compounds were examined by Haino et al. [151]. The Y dilution results in a scaling down of the ordered phase regions in the B–T space. The scale down of the ordered phase is different between two magnetic field directions along the tetragonal [100]- and [110]-axes, so the anisotropy of phase stability is increased by Y dilution. Princep et al. [152] studied holmium 4f multipoles in HoB2C2 using soft resonant X-ray Bragg diffraction. They concluded that the quadrupolar interaction in this compound is strong and that quadrupolar order only occurs when the magnetic order gives rise to a quasidoublet ground state, which results in a lock-in of the orbitals at TQ. The transition temperature TN in HoB2C2 increases monotonically upon increasing pressure up to 9.8 GPa, whereas TQ decreases and vanishes at approximately 4 GPa, indicating that applying pressure enhances the AFM interactions and simultaneously the AFQ order [153]. Finally, the thermoelectric power was measured in the temperature range 120–300 K for nearly all the RB2C2 compounds [108]. The negative sign of the Seebeck coefficients indicates that they are electron-type conductors.


302 185

4.1.2 The RB2C Phases 4.1.2.1 Structural Properties of RB2C and Ac2RB6C3 Three different structure types have been reported so far with the RB2C stoichiometry, namely LuB2C [27], ThB2C [81], and aUB2C [85]. Closely related quaternary compounds, i.e., Th2ScB6C3 and U2ScB6C3, have also been reported [84,89]. The first structure of this family—YB2C—was reported by Bauer and Nowotny in 1971 [1], soon after followed by DyB2C [71]. Terbium, holmium, erbium, thulium, and ytterbium diboride monocarbides were found to be isostructural by Bauer and Debuigne [100], and finally, Bauer [20] showed that LuB2C and ScB2C are also members of this series. No single-crystal analysis was available at the time and the structure model was proposed on the basis of striking similarities of the X-ray powder patterns of the tetraborides and the diboride monocarbides. Indeed, the proposed model of the crystal structure of these phases was related to that of the rare-earth metal tetraborides discussed earlier, in the same manner as the structure of the diboride dicarbides is related to that of the rare-earth metal hexaborides. The geometry of the B/C network, made of four- and seven-membered rings, can easily be derived from the tetragonal RB4 arrangement [154]. In the latter, the 3D boron network consists of B-interconnected 2D sheets made of fused four- and seven-membered rings (B4 squares and B7 heptagons, respectively). By eliminating the connecting interplanar boron atoms, i.e., those, which convert the B4 squares into B6 octahedra, one obtains a stratified (hypothetical) RB3 structure of tetragonal symmetry. Substitution in an alternating fashion of two boron positions in the four-membered rings by two carbon atoms then gives the planar B2C network characteristic for RB2C. The metal lattice remains the same as in RB4 with the R atoms located above and below the heptagons. Among different possible ways of stacking the B2C sheets, the one with the ABAB stacking, i.e., where the B atoms from one sheet are placed above the C atoms of the next sheet, was retained, leading a doubling of the c-axis. Some years later, the crystal structure of HoB2C obtained on the basis of powder X-ray and neutron powder diffraction data was found to be different from the earlier proposed tetragonal YB2C-type structure [72]. Indeed, orthorhombic or monoclinic symmetry was assumed within the B2C layers stacked directly above each other. In order to solve this discrepancy, single-crystal X-ray data of DyB2C and LuB2C were analyzed some years ago by Babizhetskyy et al. [27,69]. No doubling of the c-axis, proposed earlier for YB2C, could be detected. RB2C phases indeed crystallize in the orthorhombic space group Pbam (for LuB2C, see Tables 1 and 6). The boron and carbon atoms form infinite, planar 2D nets, which alternate with sheets of rare-earth metal atoms (Fig. 19). Inside the nonmetal atom nets, a coloring with fused B2C2 rhombi and B5C2 heptagons was proposed, which was confirmed later by 11B solidstate NMR experiments performed on YB2C crystalline powder samples combined with DFT calculations [27,155]. The four-membered B2C2 rings have a


TABLE 6 Atomic Parameters for LuB2C Atom

Site

x

y

z

Lu

4h

0.30878

0.30880

1/2

C

4g

0.037

0.332

0

B1

4g

0.094

0.0.095

0

B2

4g

0.333

0.037

0

SG Pbam, a ¼ 6.7429 A˚, b ¼ 6.7321 A˚, c ¼ 3.5890 A˚ [27].

FIG. 19 Top view (left) and side view (right) of the structural arrangement of RB2C (R¼ Y, Tb–Lu). Large gray, small black, and small gray spheres represent R, B, and C atoms, respectively.

twofold symmetry with internal angles of 89.7° and 90.3°. B–C distances of ˚ were established. The seven-membered B5C2 rings have internal ca. 1.63 A angles varying between 116.8° and 135.9°, relatively close to the ideal value of 128.6° expected for an ideal heptagon. Investigations of the Ce–B–C ternary system have shown that the compound CeB2C [36] (Table 7) crystallizes in the ThB2C type of structure (Fig. 20). This is the only compound in the lanthanide series exhibiting this particular structure type, which is adopted by some actinoids (Th, U (hightemperature modification), Np, and Pu). This is likely be due to the fact that Ce4+ valency is needed to balance the negative charges of the 2D B/C networks, also see later [106]. In this crystal structure, slightly puckered 63-layers of cerium atoms alternate with planar sheets composed of regular hexagons of boron atoms linked via linear carbon atoms leading to the formation of 2D layers made of fused nine-membered B6C3 rings and regular B6 hexagons. Each Ce atom sits between a B6 hexagon and a nine-membered B6C3 ring due to the ABAB stacking of the nonmetal sheets along the c-axis.


302 187

TABLE 7 Atomic Parameters for CeB2C Atom

Site

x

y

z

Ce1

3a

0

0

0

Ce2

6c

0

0

0.3156

C

9d

1/2

0

1/2

B

18g

0.2762

0

1/2

˚ , c ¼ 11.259 A ˚ [36]. SG R-3 m, a ¼ 6.613 A

FIG. 20 Crystal structures of ThB2C (A), U2ScB6C3 (B), and aUB2C (C).

The quaternary structures Ac2ScB6C3 (Ac ¼ Th, U) [84] (see Table 8 for the atomic parameters of U2ScB6C3) are closely related to that of CeB2C (Fig. 20B). The nonmetal sheets correspond to those encountered in ThB2C but with the …AA… stacking. Metal atoms intercalated between the B/C layers form a planar hexagonal net of thorium atoms centered by smaller scandium atoms. Finally, the aUB2C phase (low-temperature modification) (Table 9), only observed with U so far, is made of fused eight-membered rings of boron and carbon atoms, alternating with planar nonregular hexagonal layers of uranium


TABLE 8 Atomic Parameters for U2ScB6C3 Atom

Site

x

y

z

M1a

1a

0

0

0

U2

2c

1/3

2/3

0

B

6k

0.272

0

1/2

C

3g

1/2

0

1/2

SG P6/mmm, a ¼ 6.5096 A˚, c ¼ 3.4265 A˚ [89]. a M1 ¼ 0.95 Sc + 0.05 U.

TABLE 9 Atomic Parameters for aUB2C Atom

Site

x

y

z

U

2e

0.25

0

0.2981

B

4j

0.9018

0.5

0.1602

C

2d

0

0.5

0.5

˚ , b ¼ 3.5177 A˚, c ¼ 4.1067 A˚ [85]. SG Pmma, a ¼ 6.0338 A

˚ , respecatoms (Fig. 20C) [85]. B–B and B–C distances of 1.80 and 1.50 A tively, were reported. In fact, ThB2C and aUB2C are strongly related to each other from the structural viewpoint since the 2D arrangement of the nonmetallic networks in both compounds is made of the same linear B(sp2)–C(sp)–B (sp2) building blocks. It turns out that a formal charge of 4 per B2C unit accounts for the structure of the B/C net in ThB2C and aUB2C, whereas a formal charge of 3 must be attributed to the one in the LuB2C type [106]. 4.1.2.2

Physical Properties of RB2C

The magnetic properties of CeB2C studied by Hirotra and Ishikawa [134] show a low TN of 1.5 K. Here, the magnetic ordering temperature is decreased and the electronic specific heat is enhanced compared to CeB2C2. Other RB2C (R ¼ Dy, Ho, and Er) compounds were studied by powder neutron diffraction at 2–30 K by van Duijn et al. [156,157]. ErB2C exhibits a two-sublattice antiferromagnetic order below TN ¼ 16.3 K. On the other hand, DyB2C and HoB2C show a coexistence of a conventional canted k ¼ (0 0 0) ferromagnetic structure and unconventional magnetic correlations. The k ¼ (0 0 0) phase orders at TC ¼ 8.5 and 7.1 K for DyB2C and HoB2C, respectively. The latter


302 189

shows low-Q diffraction peaks from the unconventional correlations that appear above TC with different critical temperatures for different peaks at 8, 10.5, and 15.7 K. This scattering is due to diffraction from a Warren-type random magnetic layer lattice and may result from quadrupolar interactions between R3+ ions. The magnetic properties of these borocarbides were also studied by magnetization and specific heat measurements at 1.8–300 K in a magnetic field up to 5 T [158]. The two-sublattice antiferromagnetic order below TN ¼ 16.3 K is confirmed for ErB2C. As observed before, HoB2C and DyB2C show a 3D magnetic order below TC ¼ 7.0 and 8.5 K, respectively. However, they still show large magnetic fluctuations below TCs. The magnetic ordering temperatures of these two compounds do not follow the de Gennes relation, since their ordering temperatures are suppressed. The suppression of the ordering temperatures and the unconventional fluctuating ground states of HoB2C and DyB2C originate from spin frustration effects. The instability of the unconventional magnetic phase associated with the frustration is significant in this series. The fluctuating ground state results from the complex spin–spin interactions or spin–quadrupole interactions. The muon (mSR) measurements of DyB2C and HoB2C performed by van Duijn et al. [157] confirm the presence of two independent magnetic processes in these two compounds. The onset of correlations corresponding to the magnetic random layer phase occurs at higher critical temperatures than expected from neutron diffraction experiments. This discrepancy between the muon and neutron diffraction measurements can be a result of different time windows probed by the two techniques. The electrical resistivity and magnetic properties of TmB2C were studied by Babizhetskyy et al. [76]. The inverse magnetic susceptibility vs temperature reveals Curie–Weiss behavior above 150 K (see Fig. 21 for two different applied magnetic fields). The derived values of effective magnetic moments, meff, are in good agreement with the theoretical tripositive R3+ moment values of localized 4f electrons, which are listed together with yps for several RB2C (R ¼ Dy, Ho, Er, Tm) in Table 10. The isothermal magnetization was measured at T ¼ 2 K and is given in Fig. 22. At low magnetic field the magnetization increases linearly due to an antiferromagnetic ground state. However, at higher fields (B > 2 T), the values of M dramatically rise and saturate above B > 5 T originating from a metamagnetic transition. The magnetization curve is fully reversible. TmB2C also consists of a basic two-sublattice antiferromagnetic structure. Sheets of ferromagnetically coupled rare-earth atoms (the positive paramagnetic Weiss temperature, yp, supports this assumption) separated by the planar networks of the boron/carbon atoms are coupled antiferromagnetically. These negative exchange interactions are, however, much weaker than the positive in-plane interactions, which gives rise to a spin flip at elevated fields leading to the establishment of field-induced 3D ferromagnetism. The saturation moments of 7.4 mB/Er and 5.5 mB/Tm are smaller than the free R3+ ion values gJ ¼ 9 and 7 mB, respectively. Such moment reduction


FIG. 21 Reciprocal susceptibility vs temperature for TmB2C in fields B ¼ 0.1 T (open circles) and B ¼ 7 T (filled circles). Lines show the linear least-squares fit to the Curie–Weiss law.

TABLE 10 Magnetic Data for the Boride Carbides RB2C Compound

8.5

a

7.0

DyB2C

HoB2C

ErB2C

TC (K)

a

a

TmB2C

b

TN (K)

up (K)

meff (mB)

mS (mB)

0.1

10.63

5.1

0.58

10.64

4.4

4.75

10.05

16.3

38.6

9.28

7.4

12.0

56.6

7.41

5.5

a

Ref. [154]. Ref. [76].

b

is commonly observed in measurements of bulk samples. Usually, only 1/2 of the full moment is found experimentally for compounds exhibiting easy-axis anisotropy. The moments of TmB2C are aligned in the ab-plane. Neutron diffraction analyses of the related compounds DyB2C and HoB2C reveal canted spin structures with pronounced ferromagnetic spin components in the abplane [156]. On the other hand, the moments are found aligned parallel to the c-axis for ErB2C. bUB2C, the high-temperature modification of UB2C which adopts the ThB2C structure type, orders ferromagnetically below 74.5 K [159]. The uranium moments are close to the ab-plane (Ф ¼ 47° and Y ¼ 84°, where Ф and


302 191

FIG. 22 Isothermal magnetization vs applied field for TmB2C at T ¼ 2 K. Open symbols represent increasing fields, and filled symbols represent decreasing fields.

Y are the spherical angles relative to the x and z crystal axes, respectively) forming ferromagnetic chains parallel to the hexagonal c-axis. In addition to the ferromagnetic transition, a characteristic temperature T* ¼ 37 K was found, at which both the electrical resistivity and specific heat show anomalies. The thermoelectric power is positive and displays a maximum at 12 K [159]. A highpressure electrical resistivity study of bUB2C shows that both Tc and T* decrease with increasing pressure, and the critical pressure, where the longrange ferromagnetic order becomes completely quenched, is estimated as large as Pcr 18 kbar. The metallic character of the r(T) curves of the compound is changed into the Kondo-like one around 12 kbar [160]. The measured spin–lattice relaxation rate in the magnetically ordered state of bUB2C suggests that the 5f electrons exist in two different substates, exhibiting both localized and itinerant nature [161]. Contrary to bUB2C, both ThB2C and aUB2C are temperature-independent paramagnets [88]. Magnetic ordering was found for all members U1xRxB2C (R ¼ Th, Sc, Lu), which adopt the ThB2C structure type. The general result of the dilution of the uranium moments by nonmagnetic elements is successive reduction of the ferromagnetic ordering temperature: 74.5 K for bUB2C, 60 K for U0.85Th0.15B2C, 59 K for U0.85 Sc0.15B2C, and 14 K for U0.85Lu0.15B2C [88]. The transuranium metal boron carbides AcB2C (Ac ¼ Np, Pu), which adopt the ThB2C structure type, show magnetic behaviors consistent with the Hill criterion [91]. Magnetic susceptibility and heat capacity data indicate the occurrence of antiferromagnetic ordering for NpB2C with Neel temperature of 68 K. The magnetic ordering of the Np sublattice in NpB2C is


FIG. 23 Electrical resistivity (r) vs temperature for TmB2C. Inset: Low-temperature details with the solid line representing r ¼ ro + AT4.5.

confirmed by 237Np M€ ossbauer measurements and indicates a formal 3 + oxidation state for Np [162]. PuB2C is a Pauli paramagnet [91]. Finally, magnetization, specific heat, and resistivity of Th2ScB6C3 indicate metallic characteristics [84]. For the isostructural compound U2ScB6C3 a ferromagnetic transition is observed at TC ¼ 61 K, followed by presumably a spin orientation below 45 K [89]. The thermoelectric power of U2ScB6C3 is positive over the temperature range 5–300 K and reaches a relatively large value of 29 mV/K at room temperature [163]. Electrical resistivity (r) vs temperature for TmB2C (Fig. 23) reveals a typical shape of a magnetic metal. The values of the measured resistivities decrease with falling temperature down to T 50 K, resulting from a reduction of the electron–phonon scattering, and pass a shallow minimum at T ¼ 30 K before a relative maximum is reached at 12 K due to the onset of AFM ordering. The inset of Fig. 23 shows the fit r ¼ ro + ATa with a ¼ 4.5, a typical value for AFM. Such a behavior is commonly attributed to “super zone” scattering. The electronic and mechanical properties of YB2C were theoretically explored by DFT methods [164]. Interestingly, the estimated hardness of the P42/mbc-YB2C phase—this symmetry group has been debated for YB2C—is around 23 GPa, comparable with the well-known ultra-incompressible oP6OsB2 diboride [165]. Additionally, the analysis of the ideal shear and tensile strengths of YB2C reveals the importance of covalent bonding between Y and B/C layers, which might help to enhance the resistance under deformation.


302 193

4.1.3 The R2B4C Phases A few representatives with the R2B4C stoichiometry were reported with R ¼ Tb, Dy, Ho, and Er [65]. Their crystal structures were solved from X-ray single-crystal data (see Table 11 for Dy2B4C, for instance). In this structure, planar 63 nets formed by dysprosium atoms alternate with planar nonmetal atom layers. In the latter, boron atoms form infinite chains of fused B6 rings in the [100]-direction joined with linear carbon atoms along the [010] direction to form planar, 2D networks (Fig. 24). There are no direct C–C contacts in the structure. Each B1 atom is bonded to three other boron atoms with ˚ and B1–B1 ¼ 1.75 A ˚ , while the B2 atoms are distances of B1–B2 ¼ 1.87 A ˚ ) (see Fig. 24 for the atom bonded to two B1 and one C atom (B2–C ¼ 1.51 A numbering). The VEC per nonmetal atom in these phases such as Dy2B4C is 4.4, which is comparable to that of other compounds containing 2D B/C nets, e.g., YB2C2, ScB2C2 (VEC ¼ 4.25), LuB2C, ThB2C, and UB2C (VEC ¼ 4.33) (see Table 3). The electron partitioning (Dy3+)2(B4C)6, which corresponds to a closed-shell configuration, accounts for a quinoid form with alternating single B1–B2 and double B1–B1 and B2–C bonds (Fig. 24). This was confirmed by theoretical EH-TB calculations, which indicate a Fermi level in a hole in the DOS [65]. 4.1.4 The R2B3C2 and R2B2C3 Phases 4.1.4.1 Structural Properties of R2B3C2 and R2B2C3 Gd2B3C2 (orthorhombic, space group Cmmm) is another borocarbide compound containing 2D sheets of nonmetal atoms [60] (Table 12). The same arrangement was found later for Y2B3C2 [28]. Indeed, Gd2B3C2 was labeled “Gd30B40C30” when it was first discovered by Smith and Gilles [97]. It was later wrongly described as “GdBC” with the YBC structure type by Bauer and Debuigne [71] (see Section 4.2.1). In the structure, boron atoms in

TABLE 11 Atomic Parameters for Dy2B4C Atom

Site

x

y

z

Dy

4i

0

0

0.2343

C

2b

1/2

0

0

B1

4g

1/2

0.133

1/2

B2

4h

1/2

0.770

0

SG Immm, a ¼ 3.2772 A˚, b ¼ 6.567 A˚, c ¼ 7.542 A˚ [65].


FIG. 24 Crystal structure of R2B4C.

TABLE 12 Atomic Parameters for Gd2B3C2 Atom

Site

x

y

z

Gd

4i

0

0.1343

0

B1

4j

0

0.719

1/2

B2

2c

0

1/2

1/2

C

4j

0

0.603

1/2

˚ , b ¼ 13.733 A˚, c ¼ 3.710 A˚ [60]. SG Cmmm, a ¼ 3.445 A

triangular prismatic metal coordination form infinite zigzag chains branched with carbon atoms. The boron/carbon chains are linked to a planar 2D network by additional linear boron atoms forming rather tight bonds with the branched carbon atoms (Fig. 25). Theoretical EH-TB calculations suggest a formal charge of 5 per B3C2 unit to account for this boron/carbon structural arrangement. With not fully oxidized Gd (formally Gd2.5+) atoms, a metallic behavior is expected [60]. Interestingly, the compound Tb2B2C3 [66] adopts a structure very similar to that of Gd2B3C2 with the same arrangement of the metal atoms, but a different distribution and ratio of boron and carbon atoms (Table 13; Fig. 26).


302 195

FIG. 25 The ab (A) and bc (B) projections of the Gd2B3C2 crystal structure. Large gray, small black, and small gray spheres represent Tb, B, and C atoms, respectively.

TABLE 13 Atomic Parameters for Tb2B2C3 Atom

Site

x

y

z

Tb

4i

0

0.13492

0

B

4j

0

0.717

1/2

C1

4j

0

0.605

1/2

C2

2c

0

1/2

1/2

˚ , c ¼ 3.669 A ˚ [66]. SG Cmmm, a ¼ 3.412 A˚, b ¼ 13.699 A

FIG. 26 The ab (A) and bc (B) projections of the Tb2B2C3 crystal structure. Large gray, small black, and small gray spheres represent Tb, B, and C atoms, respectively.


The central B atom in the linear C–B–C bridge in Gd2B3C2 is replaced by a C–C–C moiety in Tb2B3C2. It was argued that it is difficult to distinguish between B and C by X-ray investigations, but EPMA analyses as well as a thorough bond distance analysis support this assignment. 4.1.4.2

Physical Properties of R2B3C2

Magnetizations of single-crystal “GdBC” samples (indeed Gd2B3C2) using pulsed magnetic fields up to 30 T were performed by Matsumoto et al. [166]. The magnetization for the b-axis at 4.2 K shows three steps at 1, 5, and 15 T, saturating above 23 T. The saturation moment is almost 7 mB/Gd. Temperature dependence of the step fields is obtained for all crystallographic directions. This finding implies that Gd2B3C2 exhibits successive antiferromagnetic transitions with the complex magnetic structures in spite of the simple spin system of Gd3+ ions. The antiferromagnetic-like transition temperature, TN ¼ 45 K, is inferred from the magnetic susceptibility, electrical resistance, and heat capacity measurements. Another magnetic transition may occur around Tm ¼ 25 K where the magnetic susceptibility shows a broad peak and the heat capacity shows a small anomaly. It has recently been proposed on the basis of DFT calculations that Y2B3C2 could be a promising candidate for applications in thermal sealing at ultra-high temperatures [167]. Indeed, a strain-stiffening behavior is predicted under (010) [001] and (010) [100] shear deformations. Calculations indicate that the moduli against these two shears are extremely low at small strain, but gradually increase to considerably large values of 62 and 101 GPa. This strain-stiffening effect might originate from the deformable planar B–C network, where the linear CBC chain connecting the zigzag boron infinite chains can tilt easily.

4.1.5 The R2BC3 Phase Only one representative with the approximate R2BC3 stoichiometry was discovered in 1999 with R ¼ Sc [15,21]. X-ray single-crystal and HRTEM analyses of this scandium boron carbide revealed the composition Sc2B1.1C3.2 and a trigonal crystal structure (SG P-3m1; Table 14). The crystal structure is composed of alternating [B1/3C2/3]∞ ScCSc[B1/3C2/3]∞ laminar layers (Fig. 27). Boron and carbon atoms form a significantly puckered graphite-like ˚ . The ScCSc units appear to be rather layer with a mean bond length of 1.533 A loosely accommodated between the graphite-like [B1/3C2/3]∞ layers. The ˚ reflects rather close mean Sc–Sc distance inside the ScCSc layers of 3.161 A metal–metal contacts. Scandium atoms in the layers form slightly distorted octahedra that accommodate isolated C atoms. Transport and NMR properties were investigated [168]. The temperature dependence of the resistivity shows a large anisotropy. The in-plane resistivity shows a metallic quadratic dependence, whereas the resistivity along the

TABLE 14 Atomic Parameters for Sc2B1.1C3.2 Atom

Site

x

y

z

Atom

Site

x

y

z

Sc1

2d

1/3

2/3

0.3648

C8

6h

0

0.7141

1/2

Sc2

12j

0.0993

0.7656

0.6430

M1

6i

0.1861

0.8139

0.0868

Sc3

12j

0.1946

0.9599

0.2992

M2

6i

0.2566

0.6283

0.0701

Sc4

12j

0.0433

0.6650

0.3088

M3

12j

0.0359

0.6278

0.0191

Sc5

12j

0.1963

0.6664

0.3268

M4

12j

0.1851

0.9277

0.9373

Sc6

12j

0.0967

0.6243

0.6699

M5

6i

0.1478

0.8522

0.9231

Sc7

6i

0.0987

0.9013

0.6553

M6

12j

0.1476

0.9633

0.9737

Sc8

6i

0.2349

0.7651

0.6695

M7

6i

0.1838

0.5919

0.0407

Sc9

6i

0.0494

0.5247

0.3305

M8

12j

0.1487

0.7403

0.9470

Sc10

6i

0.0479

0.9521

0.3248

M9

12j

0.0729

0.7014

0.9550

Sc11

6i

0.2342

0.6171

0.7103

M10

6i

0.2950

0.5900

0.0584

Sc12

6i

0.1930

0.8070

0.2781

M11

6i

0.0367

0.7402

0.9719

C1

1b

0

0

1/2

M12

6i

0.1480

0.6289

0.0025

C2

6h

0

0.5717

1/2

M13

6i

0.0728

0.9272

0.9776

C3

6i

0.1431

0.8569

0.4414

M14

6i

0.0368

0.9632

0.9839

C4

6i

0.1436

0.5718

0.5114

M15

12j

0.1847

0.7031

0.0145

C5

6h

0.1442

0

1/2

M16

6i

0.2583

0.7417

0.0196

C6

12j

0.1435

0.7153

0.4670

M17

12j

0.0730

0.5918

0.0060

C7

6i

0.2857

0.7143

0.5330

M18

6i

0.0362

0.5181

0.9878

SG P-3m1, a ¼ 23.710 A˚, c ¼ 6.703 A˚ [21]. a M—statistically distributed (В, С) atoms in the [B1/3C2/3]∞ layer.

a


FIG. 27 (001) (A) and (110) (B) projections of the Sc2B1.1C3.2 crystal structure. Large gray, small black, and small gray spheres represent Sc, B, and C atoms, respectively.

c-axis increases with decreasing temperature. NMR results indicate a large distribution of the chemical shifts of the boron nuclei, which is consistent with the existence of disorder within the graphitic [B1/3C2/3]∞ layers.

4.2 Infinite Boron–Carbon Chains 4.2.1 The RBC and R2B2C3 Phases 4.2.1.1 Structural Properties of RBC and R2B2C3 Three different structure types corresponding to the RBC stoichiometry were initially proposed, namely YBC [1], UBC [87,88], and ThBC [83]. Later, it was demonstrated that the so-called YBC arrangement probably does not exist, in fact representing a different borocarbide—Y2B3C2 [28]. In ThBC and UBC, the metal atoms form trigonal prisms, which condense along one direction through square faces, making infinite channels. The boron atoms occupy the middle of the metallic prisms and form 1D zigzag chains, to which the carbon atoms are connected. The assembly of these infinite zigzag chains along a second dimension by sharing metallic triangular faces makes 2D RBC slabs. These slabs can be stacked in several ways, leading to different structure types: UBC (Table 15; Fig. 28A) and ThBC (Table 16; Fig. 28B) [169].


302 199

TABLE 15 Atomic Parameters for UBC Atom

Site

x

y

z

U

4c

0

0.1386

0.25

B

4c

0

0.4624

0.25

C

4c

0

0.3357

0.25

˚ , b ¼ 11.978 A˚, c ¼ 3.3473 A˚ [88]. SG Cmcm a ¼ 3.5899 A

FIG. 28 Crystal structures of UBC (A), ThBC (B), and Th2B2C3 (C).

TABLE 16 Atomic Parameters for ThBC Atom

Site

x

y

z

Th

8d

0.2025

0.3017

0.1795

B

8d

0.197

0.298

0.019

C

8d

0.204

0.311

0.080

SG P4122, a ¼ 3.762 A˚, c ¼ 25.246 A˚ [83].


The existence of orthorhombic UBC was first described by Matterson et al. [170]. Somewhat later it was shown by Toth et al. [87] from X-ray powder diffraction data that it can be derived from either of the two closely related structure types—CrB or ZrSi2. Investigation of the uranium–boron–carbon system by Rogl et al. [86] confirmed the existence of the stoichiometric UBC composition with an extended solid solution UB1xC1+x with x up to 0.22, i.e., from UBC to UB0.78C1.22. Some years later, Rogl et al. [88] determined the crystal structures of stoichiometric UBC and the carbon-rich solid solution. X-ray single-crystal analysis revealed in both cases the orthorhombic space group Cmcm (Fig. 28A; Table 15). UBC shows a fully ordered nonmetal arrangement, i.e., C-branched boron zigzag chains, whereas random occupation by boron and carbon atoms is observed on the boron site in UB0.78C1.22. A powder neutron diffraction study of UB0.78C1.22 performed at 9 K [88] confirmed the full occupation of the nonmetal atom sites as well as a statistical distribution of B and C atoms on the B sites. Importantly, this study indicated the monoclinic space group C2/m, in which the boron atom chains exhibit alternating short and long B–B bond distances (1.706 and ˚ ). Unfortunately, no neutron diffraction study was performed for the 2.043 A stoichiometric UBC. These UB1xCx alloys reveal a temperature-independent paramagnetism with typical intermediate valence fluctuation behavior and TSF 350 K [88,90]. We also note that the UBC arrangement is also adopted by plutonium and neptunium and that the solubility of carbon in these phases is much smaller than in UB1xC1+x [90]. The second structure type ThBC can be deduced from UBC by a diagonal translation (1/2 a + 1/2 c) [83]. Such a double shift does not change the environment of the carbon atoms and the nature of the interslab contacts, which remain of the same type as in UBC. The major difference concerns the boron zigzag chains, which show greater differences in the alternating B–B bonds ˚ ) (Fig. 28B). (1.77 vs 2.47 A The structure of Th3B2C3 [82] is closely related to ThBC. Condensation of the boron-centered trigonal prisms composed of thorium atoms via common square faces leads to distorted 1D zigzag chains of nonmetal atoms with ˚ , similar to ThBC. AddiB–B distances alternating between 1.77 and 2.20 A tional carbon atoms are located in the centers of Th6 octahedra (Fig. 28C; Table 17). A simple ionic picture between the metallic framework and the boron– carbon chains can easily explain the arrangement, regular or distorted, in these compounds. Thus, a formal charge of 3 per BC unit accounts for the regular chains encountered in UBC. This renders the chain isoelectronic to polyketone, which is unstable with respect to carbon monoxide. With a formal charge greater than 3 per BC unit, distorted chains due to a Peierls instability are expected as observed in UB0.78C1.22, ThBC, and Th3B2C3. EH-TB calculations indicate that a metallic behavior is expected for all of these compounds [169].


302 201

TABLE 17 Atomic Parameters for Th3B2C3 Atom

Site

x

y

z

Th1

1a

0

0

0

Th2

2n

0.6329

0.359

0.5

B

2m

0.191

0.454

0

C1

1e

0.5

0

0.5

C2

2m

0.128

0.281

0

˚ , b ¼ 9.146 A˚, c ¼ 3.773 A˚, b ¼ 100.06° [82]. SG P2/m, a ¼ 3.703 A

4.2.1.2

Physical Properties of RBC

The UB1xCx alloys reveal a temperature-independent paramagnetism with typical intermediate valence fluctuation behavior (TSF 350 K). No superconductivity was observed down to 1.5 K [88]. NpBC and PuBC, isotypic to UBC, show long-range FM and AFM orderings, respectively. From the temperature-dependent magnetic susceptibility data, an antiferromagnetic ordering below TN ¼ 44 K was established for PuBC. A ferromagnetic ordering below TC ¼ 61 K was found for NpBC. Heat capacity measurements prove the bulk character of the observed magnetic transitions in both compounds. In contrast to NpBC, both the transition temperature and the shape of the temperature dependence of the specific heat curve for PuBC do not depend on the applied magnetic field [92].

4.2.2 The R10B9C10 Phases 4.2.2.1 Structural Properties of R10B9C10 The existence of a compound with the composition near Tb10B9C10 was suggested by the systematic study of the isothermal section of the ternary phase diagram Tb–B–C [67]. This was verified by chemical and structural analyses. Later, the ternary rare-earth metal boride carbides with compositions close to R10B9C10 were prepared for R ¼ Gd and Tb. The composition Tb10B9+xC10x (x 0.2) was suggested on the basis of single-crystal X-ray diffraction data for the Tb compound, which crystallizes in the monoclinic space group P21/ c (Table 18) [62]. The crystal structure shown in Fig. 29 contains slabs composed of nonmetal and rare-earth metal atoms, which are stacked along the b-axis. In each slab, infinite zigzag boron chains made of B10 entities sepa˚ that run in channels formed by slightly corrugated square rated by 2.42 A metal nets. Eight BC2 units and two single carbon atoms are attached to every zigzag B10 chain forming branched B18C18 units. In addition, isolated carbon atoms occupy the centers of elongated metal octahedra. B–B distances in the


TABLE 18 Atomic Parametersa for Tb10B9C10 Atom

x

y

z

Tb1

0.34099

0.06168

0.35615

Tb2

0.46560

0.19843

0.13892

Tb3

0.05221

0.19932

0.05935

Tb4

0.04498

0.06097

0.05507

Tb5

0.23992

0.19935

0.55688

Tb6

0.23896

0.06097

0.25391

Tb7

0.65819

0.29886

0.25174

Tb8

0.84839

0.07638

0.14792

0.46395

0.06385

0.44607

b

0.1452

0.18009

0.3471

b

0.1466

0.1966

0.3482

Tb9 Tb10 Tb11 C1

0.645

0.0851

0.1535

C2

0.744

0.1991

0.0434

C3

0.5607

0.0852

0.0449

C4

0.656

0.1979

0.2460

C5

0.052

0.2001

0.5520

C6

0.544

0.2018

0.3524

C7

0.058

0.0890

0.4533

C8

0.145

0.0793

0.6528

C9

0.737

0.0894

0.2540

C10

0.854

0.1962

0.1528

B1

0.054

0.0244

0.436

B2

0.150

0.0135

0.6525

B3

0.751

0.0230

0.2510

B4

0.647

0.0199

0.1445

B5

0.548

0.0184

0.0491

B6

0.038

0.1406

0.5120

B7

0.604

0.1417

0.327

B8

0.667

0.1387

0.205

B9

0.681

0.1383

SG P21/c, a ¼ 7.937, b ¼ 23.786, c ¼ 11.172 A˚, b ¼ 133.74° [62]. a All atoms occupy the Wyckoff position 4(e). b Occupation: Tb10 ¼ 0.80, Tb11 ¼ 0.20.

0.0185


302 203

FIG. 29 Crystal structure of Tb10B9C10 projected on the bc-plane. Dashed lines between B–B ˚ ) between B18C18 units. Large gray, small black, atoms represent the long B–B distances (2.42 A and small gray spheres represent Tb, B, and C atoms, respectively.

˚ are not significantly different zigzag chains ranging between 1.84 and 2.12 A from those observed in Tb2B2C3 mentioned earlier [66]. In the chains, all boron atoms are three (sp2)- or two (sp)-connected, whereas the carbon atoms are only two (sp)-connected. The electron partition (Tb3+)20(B18C18)40(C4)2 12e can be assigned, accounting for a closed-shell configuration of the nonmetal network. With formally 12 metal electrons left in the conduction band, this compound is expected to be metallic in character [62]. 4.2.2.2 Physical Properties of R10B9C10 Magnetic properties of R10B9C10 compounds were studied only for Tb10 B9+xC10x (x 0.2) in external fields, B, up to 7 T in the temperature interval 2–330 K [62]. As seen in Fig. 30, the inverse magnetic susceptibility measured at B ¼ 7 T decreases linearly down to 150 K. This observation is also true for the applied fields B ¼ 0.01, 0.1, and 1 T (not shown). The paramagnetic Weiss temperature Yp ¼ 50 K and an effective moment meff of 10.2 mB were calculated. The latter is in agreement with the theoretical moment meff of 9.7 mB expected for a trivalent terbium (Tb3+). Plots of the magnetization, M(T), shown in Figs. 31 and 32, indicate distinct features. In moderate fields with zfc samples the magnetization increases with rising temperatures, passes two peaks at 12 and 25 K, and subsequently falls off. The magnetization of the fc samples passes the maximum at 25 K again, but levels off at Mmax at the lowest temperatures after passing through a shallow minimum at 20 K (Fig. 31). Hence the following conclusion can be drawn: The observed maximum of the magnetization at 12 K probably originates from the impurity phase Tb2B2C3. The occurrence of the maximum at 25 K, however, is an intrinsic property due to the presence of narrow domain walls in ferromagnets as frequently observed in related rare-earth


FIG. 30 Reciprocal magnetic susceptibility vs temperature of Tb10B9+xC10x (x 0.2) measured in an external field B ¼ 7 T. Solid and dashed lines represent the fit to a modified Curie–Weiss law. Inset: Magnetization vs applied field at T ¼ 1.85 K. Adapted from V. Babizhetskyy, K. Hiebl, Hj. Mattausch, A. Simon, New ternary boride carbides RE10B9+ xC10-x (RE ¼ Gd, Tb; x 0.2): infinite boron carbon branched chains, Z. Anorg. Allg. Chem. 636 (2010) 1229–1235. Copyright (2010) John Wiley and Sons.

FIG. 31 Magnetization vs temperature of Tb10B9+xC10x (x 0.2) measured in weak applied magnetic fields. Open symbols for increasing, and filled symbols for decreasing temperature. Adapted from V. Babizhetskyy, K. Hiebl, Hj. Mattausch, A. Simon, New ternary boride carbides RE10B9+ xC10-x (RE ¼ Gd, Tb; x 0.2): infinite boron carbon branched chains, Z. Anorg. Allg. Chem. 636 (2010) 1229–1235. Copyright (2010) John Wiley and Sons.


302 205

FIG. 32 Magnetization vs temperature of Tb10B9+xC10x (x 0.2) measured in 1 and 7 T applied magnetic fields. Open symbols for increasing, and filled symbols for decreasing temperature. Adapted from V. Babizhetskyy, K. Hiebl, Hj. Mattausch, A. Simon, New ternary boride carbides RE10B9+ xC10-x (RE ¼ Gd, Tb; x 0.2): infinite boron carbon branched chains, Z. Anorg. Allg. Chem. 636 (2010) 1229–1235. Copyright (2010) John Wiley and Sons.

boride carbides. The increase of the magnetization of the zfc sample is caused by the thermal activation of the Bloch wall movement with rising temperature. At elevated fields, B > 1 T, the magnetization plots M(T) for zfc and fc samples are identical and show the typical shape of simple ferromagnetic behavior (Fig. 32). The Curie temperature TC was estimated at 45 K. From the saturation value Mmax ¼ 224 Am2/kg of the M(T) plot in the 7 T magnetic field, a saturation moment mS ¼ 7.2 mB was calculated, which amounts for 80% of the expected value gJ ¼ 9 mB for Tb3+ ions. The isothermal magnetization M(B) vs applied field at T ¼ 1.85 K is shown in the inset of Fig. 30. The initial magnetization (zfc) plot reveals that the critical field where the Bloch wall movement sets in at this temperature is Bcrit 1 T. The hysteresis loop is rather narrow when compared with the closely related compound Tb15B4C14 (see below), suggesting a smaller magnetocrystalline anisotropy due to larger domain walls. Rather moderate values for the remnant magnetization MR ¼ 21 Am2/kg and the coercive field Bcoerc ¼ 0.3 T were derived.

4.3 Coexisting Infinite and Finite Boron–Carbon Chains 4.3.1 The R4B3C4 Phases The X-ray crystal and electronic structure of Gd4B3C4 were reported by Jardin et al. [63]. The compound crystallizes in the triclinic space group P1 (Z ¼ 1, Table 19). In this structure, depicted in Fig. 33, the boron and carbon atoms


TABLE 19 Atomic Parameters for Gd4B3C4 Atom

Site

x

y

z

Gd1

2i

0.1980

0.9717

0.34983

Gd2

2i

0.6124

0.4354

0.13729

C1

2i

0.123

0.927

0.1202

C2

2i

0.697

0.464

0.3317

B1

1a

0

0

0

B2

2i

0.740

0.477

0.455

SG P-1, a ¼ 3.637 A˚, b ¼ 3.674 A˚, c ¼ 11.859 A˚, a ¼ 93.34°, b ¼ 96.77°, g ¼ 90.24° [63].

FIG. 33 Crystal structure of Gd4B3C4.

form two different types of nonmetal arrangements: infinite carbon-branched boron zigzag chains, (BC)∞ (1D) and finite (0D) linear CBC “molecular” units. Before the discovery of Gd4B3C4, no rare-earth metal borocarbides containing nonmetal atom subsystems of different dimensionality (2D, 1D, or 0D) were characterized, with the exception of the actinide compound Th3B2C3 in which 1D (BC)∞ chains and isolated C atoms are present. Gd4B3C4 was the first example of what later became a series of compounds


302 207

such as Tb10B7C10 or Tb10B9C10 (see below) discovered later. Although the structure of Gd4B3C4 is triclinic, the environments of the boron–carbon substructures have rather high local symmetry. The (BC)∞ ribbons are almost perfectly planar. Their zigzag boron chain exhibits only a slight bond alternation with two crystallographically different B2–B2 distances of 2.06 and ˚ (see Fig. 33 for atom numbering). Owing to the associated standard 2.15 A deviations, these distances are not significantly different and the zigzag chains can then be considered regular as observed in UBC where the B–B distances ˚ . This is in contrast to ThBC where much stronger differentiation are 1.90 A ˚ ). Similar regular between the B–B bonds is observed (1.77 and 2.47 A (BC)∞ chains are encountered in the quaternary compounds Ce3Br3BC [10] ˚, and Gd4Br3BC2 [171] with comparable B–B distances of 2.18 and 2.08 A respectively. The carbon atoms attached to the boron chains are at a distance ˚ from boron indicative of a double-bond character. These carbon of 1.45 A atoms are found in square pyramids, which cap distorted trigonal prisms fused via the triangular and the two uncapped rectangular faces to form 2D layers. These layers alternate with layers of distorted cubes centered by the boron ˚ in these atoms of the linear CBC units. The B1–C1 separation of 1.48 A anionic units again indicates a double-bond character. The C1 atoms are situated in square pyramids of the same size as those hosting the C2 atoms belonging to the infinite zigzag chains. From a structural and theoretical analysis, the following formal charge distribution can be proposed within the ionic limit: (Gd3+)4([BC2]5)(BC3) 2e. Gd2BC2 as a pure phase has not been reported yet, and even the existence of GdBC without additional stabilizing B atoms is questioned. Nevertheless, in the case of this solid we may chose the following topochemical definition 2 GdBC (or better Gd2B2C2) + Gd2BC2 ¼ Gd4B3C4. Some years after the work of Jardin et al. [63], Babizhestkyy et al. [30] reported the existence of this structural arrangement with the rare-earth metals Tb, Dy, Ho, Er, Tm, Yb, and Lu and found all of them to be isotypic to Gd4B3C4. Lattice parameters of R4B3C4 are presented in Table 1. The larger light lanthanide metals do not form this phase as they do not form diborides either (at least at normal pressures). The actinoids would fit with respect to their sizes, but here their valence as well as the thermodynamic stability of the neighboring phases must be preventing their formation. 4.3.1.1 Physical Properties of R4B3C4 Physical properties of the compound Tm4B3C4 were studied by Babizhetskyy et al. [76]. The plot of reciprocal susceptibility vs temperature for Tm4B3C4 in an external field of B ¼ 7 T (see Fig. 34) shows a linear dependence above 150 K. The paramagnetic data were derived from a least-squares refinement according to the Curie–Weiss law and resulted in an effective moment meff ¼ 7.8 mB together with a paramagnetic Weiss temperature yp ¼ 11.2 K. In the low field, B ¼ 0.01 T, a maximum in the M(T) plot is revealed at the Neel


FIG. 34 Reciprocal susceptibility vs temperature for Tm4B3C4 measured in a magnetic field B ¼ 7 T.

FIG. 35 Magnetization vs temperature for Tm4B3C4 measured in a magnetic field B ¼ 0.01 T.

temperature, TN ¼ 3 K (see Fig. 35), which is attributed to an antiferromagnetic ordering of the thulium atoms. However, in elevated fields (B > 0.1 T) a saturation of the magnetization is observed below T < 10 K. This is due to a metamagnetic transition, which is the result of a nearly parallel spin alignment of the Tm moments. The isothermal magnetization curve vs external field (see Fig. 36) corroborates the ferromagnetic behavior. The inset of


302 209

FIG. 36 Isothermal magnetization vs applied fields for Tm4B3C4 measured at various temperatures. Inset: M(B) plots for B < 0.1 T (same symbols as above).

Fig. 35 represents the magnetization data measured in low external fields (B < 0.1 T). The linear behavior of M(B) in the vicinity of the ordering temperature proves the antiferromagnetism as well as the metamagnetic behaviors. No hysteresis was observed in decreasing fields for Tm4B3C4. The calculated saturation moment mS ¼ 4.5 mB is smaller than the expected theoretical value mS ¼ gJ ¼ 7 mB, indicating an imperfectly collinear spin structure. The result of the resistivity data [76] of Tm4B3C4 vs temperature reveals the typical shape of a “bad” metal. A rough estimate of the room temperature resistivity leads to a rather large value of r300Κ 1–10 mO cm, compared to 100 mO cm for Tm metal or 1.5 mO cm for Cu metal. The values of the measured resistivities decrease only slightly with falling temperatures down to T 7 K, originating from a weak reduction of the electron–phonon scattering. Furthermore, a tendency of an increase of the resistivity below 50 K is observed.

4.3.2 The R10B7C10 Phases The first X-ray crystal structure of R10B7C10 stoichiometry was Tb10B7C10 reported by Babizhetskyy et al. [30]. It crystallizes in the monoclinic space group C2/c (Z ¼ 8) (see Fig. 37; Table 20). It was also shown that all of the other ternary compounds R10B7C10 (R ¼ Gd, Tb, Dy Ho, Er) crystallize in the same Tb10B7C10 structure type. The existence of a phase with the composition Y10xB7C10+x closely related to Tb10B7C10 was also proposed by Tanaka et al. [29]. These phases belong to the family of boride carbides containing both 0D and 1D boron–carbon chains. Indeed, the crystal structure of Tb10B7C10 contains two types of slabs. One slab is formed of finite nearly


FIG. 37 Crystal structure of Tb10B7C10. Large gray, small black, and small gray spheres represent Tb, B, and C atoms, respectively.

linear CBC units and isolated carbon atoms, whereas the other is made of 1D planar ribbons (BC)∞. Similar finite CBC units are observed in R4B3C4 discussed earlier. Carbon atoms of the CBC units in Tb10B7C10 are located in a slightly distorted square pyramidal environment of metal atoms (average ˚ ). The boron atoms of the CBC units lie in the middle of C–Tb distance 2.55 A ˚ ). Interelongated cubes made of metal atoms (average B–Tb distance 3.0 A ˚ and atomic boron–carbon distances in the CBC unit range from 1.46 to 1.50 A C–B–C angles vary from 172.7° to 179.3°. With bond distances indicating a double-bond character and angles close to linearity, the formal charge 5 of the CBC unit can be assigned, rendering them isoelectronic to CO2 [5,22]. The isolated (C1) atoms in Tb10B7C10 occupy the centers of elongated square bipyramids with distances to apical Tb atoms, which can vary from 2.59 to ˚ and almost identical distances to equatorial Tb atoms (2.47 A ˚ on 2.89 A average). The CBC units as well as (BC)∞ chains in the Tb10B7C10 crystal structure are oriented differently with respect to one another. The CBC units themselves that belong to the same slab exhibit different with respect to the c-axis. On the other hand, the (BC)∞ chains are all parallel within the same slab (Fig. 37). The metal atom environment for the (BC)∞ chains is almost


302 211


Site

x

y

z

Tb1

8f

0.19693

0.97495

0.42734

Tb2

8f

0.63312

0.27886

0.31875

Tb3

8f

0.32537

0.17100

0.31905

Tb4

8f

0.49825

0.07593

0.42477

Tb5

8f

0.42586

0.87923

0.31903

Tb6

8f

0.29811

0.67412

0.42404

Tb7

8f

0.23224

0.47516

0.30792

Tb8

8f

0.53321

0.57135

0.31831

Tb9

8f

0.59749

0.77597

0.42417

Tb10

8f

0.39686

0.37467

0.42408

C1

8f

0.2304

0.9729

0.3160

C2

8f

0.5006

0.5726

0.4160

C3

8f

0.8349

0.1757

0.3098

C4

8f

0.2014

0.474

0.4111

C5

8f

0.3992

0.8754

0.4164

C6

8f

0.3006

0.1728

0.4160

C7

8f

0.4323

0.3714

0.3076

C8

8f

0.5320

0.0727

0.3096

C9

8f

0.6000

0.2744

0.4155

C10

8f

0.1284

0.2759

0.3065

B1

8f

0.683

0.980

0.4763

B2

8f

0.020

0.077

0.4798

B3

8f

0.278

0.178

0.4808

B4

8f

0.387

0.867

0.4795

B5

8f

0.080

0.778

0.4799

B6

4e

1/2

0.073

1/4

B7

4e

1/2

0.380

1/4

B8

8f

0.349

0.726

0.251

˚ , b ¼ 11.276 A˚, c ¼ 23.583 A˚, b ¼ 98.28° [30]. SG C2/c, a ¼ 11.310 A


identical to that in R4B3C4 described earlier. The zigzag boron chains exhibit ˚ . Interslightly different bonds with B–B distances ranging from 1.92 to 2.13 A atomic boron–carbon distances in the (BC)∞ chains are similar to those in the ˚. CBC units and range from 1.49 to 1.52 A EH-TB calculations performed for this kind of infinite zigzag chain also present in RBC (see above) have shown that the formal charge of 3 per BC repeat unit has to be assigned to this type of regular arrangement [5,167]. So, the structural units found in Tb10B7C10 can be discussed within the Zintl–Klemm concept as (Tb3+)10([BC]3)5 ([BC2]5)2(C4) e. The compound should be metallic in character with some metal electrons in the conduction band. The magnetic susceptibility of Y10B7C10 was measured by Tanaka et al. [29]. A superconducting transition was noted at 7.5 K. However, the observed magnetic susceptibility is on the order of 106 emu/g, which is too small for bulk superconductivity. Indeed, this superconductivity was attributed to an unidentified impurity phase and the authors concluded that Y10B7C10 does not exhibit superconductivity above 2 K.

4.4 Finite Linear Chains 4.4.1 The R15B14C19 Phase Crystal structure of La15B14C19 has been determined from single-crystal X-ray diffraction data by Gougeon et al. [37,172]. It crystallizes in the monoclinic space group P21/c (Table 21). La15B14C19 is one member of a large class of ternary compounds in which the metallic sublattice results from an irregular stacking of slightly corrugated 2D square nets, yielding a 3D framework (Fig. 38A). This leads to the formation of small channels of different sizes in which two kinds of roughly linear 11-membered units, B4C7 and B5C6, are inserted (Fig. 38B and C). The boron atoms are generally tightly bound to two carbon atoms and often located in a distorted cube of metals, whereas the carbon atoms generally are accommodated in [R4B2] or [R5B] octahedra. The B–B, B–C, and C–C bond distances suggest some multiple bond character. EH molecular orbital calculations and ab initio calculations on these various BxCy units confirm the boron/carbon distribution—boron and carbon are difficult to differentiate by X-ray—and indicate a cumulene-like character (formal double bonds) along the chains for the formal charges (B5C6)9 and (B4C7)8. This leads to metal atoms partially oxidized (1.73 +) [172,173]. 4.4.2 The RBC Phases The crystal structure of LaBC [39], which crystallizes in the space group P212121, consists of a 3D framework of La atoms resulting from the stacking of slightly corrugated 2D square nets, leading to voids filled with B5C5 finite units (Fig. 39; Table 22). The atom arrangement in the LaBC-type structure strongly differs from that found for the same stoichiometry with actinides


302 213

TABLE 21 Atomic Parameters for La15B14C19 Atom

Site

x

y

z

La1

4e

0.3030

0.4001

0.00441

La2

4e

0.8856

0.2056

0.97336

La3

4e

0.9695

0.8997

0.84540

La4

4e

0.1652

0.2884

0.83282

La5

4e

0.4352

0.9068

0.17779

La6

4e

0.6306

0.2019

0.63878

La7

4e

0.2364

0.9880

0.69320

La8

2b

1/2

0

0

C1

2c

0

1/2

0

C2

4e

0.061

0.588

0.865

C3

4e

0.122

0.671

0.726

C4

4e

0.133

0.700

0.660

C5

4e

0.263

0.507

0.323

C6

4e

0.192

0.418

0.455

C7

4e

0.305

0.360

0.593

C8

4e

0.386

0.297

0.731

C9

4e

0.487

0.386

0.8691

C10

4e

0.602

0.305

0.0042

B1

4e

0.022

0.528

0.929

B2

4e

0.076

0.604

0.792

B3

4e

0.256

0.489

0.394

B4

4e

0.206

0.397

0.530

B5

4e

0.328

0.300

0.658

B6

4e

0.452

0.391

0.795

B7

4e

0.559

0.326

0.934

˚ , c ¼ 19.953 A ˚ , b ¼ 104.45° [37]. SG P21/c, a ¼ 8.671 A˚, b ¼ 8.656 A

Th and U (see above). Other ternary compounds CeBC, PrBC, and NdBC crystallize in this LaBC type of structure [45], which is closely related to the crystal structures of other ternary compounds containing finite boron– carbon chains of different lengths (see Table 1). The specific stacking gives


FIG. 38 Projection of the structure of La15B14C19 along [010] (A). Lanthanum atom environment of B4C7 (B) and B5C6 (C).

FIG. 39 Structural arrangement of LaBC (left) and rare-earth metal environments and B/C sequence of the B5C5 units (right).


302 215

TABLE 22 Atomic Parameters for LaBC Atom

Site

x

y

z

La1

4a

0.6588

0.9094

0.5981

La2

4a

0.8363

0.4964

0.5799

La3

4a

0.9484

0.5995

0.8578

La4

4a

0.0598

0.6956

0.1287

La5

4a

0.7527

0.7878

0.3280

C1

4a

0.856

0.497

0.372

C2

4a

0.055

0.892

0.339

C3

4a

0.356

0.605

0.095

C4

4a

0.752

0.796

0.115

C5

4a

0.028

0.307

0.937

B1

4a

0.063

0.305

0.817

B2

4a

0.519

0.614

0.543

B3

4a

0.885

0.893

0.787

B4

4a

0.101

0.970

0.240

B5

4a

0.686

0.191

0.507

SG P212121, a ¼ 8.646 A˚, b ¼ 8.691 A˚, c ¼ 12.479 A˚ [39].

rise to the formation of tubular voids in which finite C5B5 units are encapsulated (Fig. 39). Every void formed from 22 metal atoms results from four fused distorted square antiprisms capped at both ends by single R atoms. Bond lengths measured within the chain suggest a C–B–C–B–C–B–B–C–B– C distribution, which is confirmed by theoretical calculations. The B–C bond ˚ on average fall in the range of distances observed in related lengths of 1.46 A ˚ . The B5C5 chains contained in compounds. The B–B bond length is 1.55 A LaBC deviate from linearity with angles varying from 147.7° to 159.8°. According to the distances measured, the boron–carbon chain B5C5 may be considered as a cumulene-like molecule with formal double bonds along the chain complexed by metal atoms. EH molecular calculations on an isolated B5C5 chain suggest a formal charge of 9. This is rather in agreement with DFT calculations on the whole solid which suggest a formulation as (La5)8.3(B5C5)8.3. The compound is expected to be metallic in character with rather a high density of states at the Fermi level [39].


4.4.2.1 Physical Properties of RBC Physical properties of the compounds RBC (R ¼ Ce, Pr, Nd) were studied by Babizhetskyy et al. [45]. In the paramagnetic regime (for T > 50 K) the reciprocal susceptibilities of the compounds follow the Curie–Weiss law with the exception of CeBC as shown in Fig. 40. The values of the effective magnetic moments and the paramagnetic Curie temperatures are listed in Table 23. A strongly reduced effective moment meff ¼ 1.77 mB < 2.54 mB (Ce3+) and a negative value of yp (19 K) are found for the Ce compound. It is inferred that this behavior is the result of a hybridization of the 4f electrons of at least some of the five different cerium atoms in the unit cell with the p-states of the boron and/or carbon atoms. This assumption corroborates the unit cell volume vs the lanthanide atomic number for the RBC (R ¼ La–Sm) phases and reveals a pronounced negative deflection from the “linear” lanthanide contraction. In the low-temperature regime (T < 20 K) PrBC and NdBC are characterized by an onset of ferromagnetic order. The ordering temperatures (TC) are listed in Table 23. It is conspicuous that the magnetization (M(T)) of the

FIG. 40 Reciprocal susceptibility vs temperature for CeBC. Applied field B ¼ 1 T.

TABLE 23 Magnetic Data for Boride Carbides RBC Compound

TC (K)

up (K)

meff (mB)

m(R3+) (mB)

mS (mB)

CeBC

6

19

1.77

2.54

0.3

PrBC

10

21

3.79

3.58

1.7

NdBC

8

18

3.66

3.62

2.0


302 217

FIG. 41 Magnetic susceptibility vs temperature of NdBC measured at various magnetic fields (● 1 mT, 0.1 T, □ 1 T, . 5 T). Inset: Isothermal magnetization vs magnetic field at T ¼ 2 K.

zfc samples rises in low external fields (B < 0.1 T) at increasing temperatures (see Fig. 41), passes through a maximum, and decreases rapidly to low values near the ordering temperatures. Upon cooling the sample in applied field (fc) a higher net magnetization below TC is frozen in. Such a magnetic behavior was attributed to the presence of narrow domain walls. The critical magnetic fields where wall movements set in are around B 0.1 T at T ¼ 2 K. The values for the saturation moments were derived from isothermal magnetization plots vs field at T ¼ 2 K (see the inset of Fig. 41). The reduced moments mS 2 mB < gJ ¼ 3.2 mB for PrBC and NdBC are typical values for bulk samples of axial symmetry (in our case the lattice parameters are a b) where the rare-earth moments reside in the ab-plane (easy plane anisotropy). The strongly reduced saturation moment of the compound CeBC is not easy to understand. Either only one or two of the five cerium atoms order ferromagnetically or the cerium atoms order in a ferrimagnetic manner with the two sublattices A (two Ce atoms) and B (three Ce atoms) leading to a net moment of 0.4 mB as observed. The curvilinear-shaped 1/w vs T plot together with the negative yp value supports the latter assumption. The temperature dependence of the relative electrical resistance for NdBC presented in Fig. 42 proves generally the metallic character of these compounds and shows a slight effect near 10 K possibly related to the onset of ferromagnetism.

4.4.3 The R10B9C12 Phases Four compounds with stoichiometry R10B9C12 (R ¼ La, Ce, Pr, Nd) have been reported so far (Table 1) [38,44,48,172]. The atomic parameters of Pr10B9C12 are given in Table 24. Their structure (space group P41212) consists of


FIG. 42 Normalized electrical resistivity vs temperature for NdBC.

TABLE 24 Atomic Parameters for Pr10B9C12 Atom

Site

x

y

z

Pr1

8b

0.48112

0.40237

0.31159

Pr2

8b

0.67857

0.00648

0.33185

Pr3

8b

0.39785

0.09850

0.20933

Pr4

8b

0.19835

0.08694

0.69603

Pr5

8b

0.28619

0.79720

0.32036

C1

8b

0.3837

0.1059

0.3118

C2

8b

0.2945

0.1841

0.4182

C3

8b

0.6835

0.0072

0.4326

C4

8b

0.0973

0.0111

0.2005

C5

8b

0.9184

0.2115

0.9630

C6

8b

0.2095

0.4748

0.2621

B1

8b

0.3057

0.4137

0.1549

B2

8b

0.7775

0.2938

0.2757

B3

8b

0.8556

0.3652

0.3839

B4

8b

0.368

0.5106

0.1068

B5

4a

0.420

x

0

SG P4121/2, a ¼ 8.4365 A˚, c ¼ 25.468 A˚ [48].


302 219

FIG. 43 Crystal structure of R10B9C12 projected along [010] (A), B4C4 (B), and B5C8 (C) units with R coordination polyhedra.

slightly corrugated 2D metal atom square nets forming two types of polyhedra wherein B4C4 and B5C8 finite units are located (Fig. 43). The B5C8 unit represents the longest oligomer found to date in ternary rare-earth boride carbides. The B4C4 and B5C8 chains are not strictly linear (Fig. 43). Indeed, theoretical calculations on finite BxCy chains have shown that a small bending of cumulenic chains is not costly in energy and is enhanced as they become longer [172,173]. Interestingly, accurate structure refinements result in the sequence C–C–B–C–B–C–B–C–B–C–B–C–C for Ce10B9C12 [44] and C–C–C–B–B–C– B–C–B–B–C–C–C for the La10B9C12 [38], Pr10B9C12 and Nd10B9C12 [48] for the 13-membered B5C8 chain. B–B and B–C distances indicate some double-bond character and, regardless of the boron/carbon distribution in the B5C8 chains, a formal ionic formula (R1.7+)10(B4C4)8(B5C8)9 can be proposed for these R10B9C12 compounds with cumulene-like BxCy anionic units interacting with not fully oxidized metallic cations [172,173]. 4.4.3.1 Physical Properties of R10B9C12 The compound La10B9C12 is a temperature-independent Pauli paramagnet down to T ¼ 6 K. Due to the partially filled 4f shells, the other compounds


R10B9C12 (R ¼ Ce, Pr, Nd) show complex magnetic behaviors with anomalies in the magnetic susceptibility, and magnetic contributions to the heat capacity are shown [48]. A detailed analysis of the magnetic ground state is particularly complicated because of the presence of five different crystallographically metal sites with different CEF split ground states for the individual ions. The formation of a long-range ordered state at low temperatures depends essentially on the arrangement of the rare-earth ions. Due to the complex topology involving coupling within the rare-earth metal triangles, geometrical frustration effects will also be of importance. The reciprocal susceptibilities vs temperature of R10B9C12 (R ¼ Pr, Nd) follow a Curie–Weiss law above 50 K (e.g., see Fig. 44). From the isothermal magnetization curves (see the inset of Fig. 44) saturation moments at 2 K were derived. Both moment values are 1/2 gJ only. All magnetic data are summarized in Table 25. The heat capacity (B ¼ 0 T) experiments performed down to 1.8 K (Fig. 45) showed a sharp anomaly, indicating a long-range magnetic order only for Nd10B9C12. The magnetic entropy removed in this anomaly amounts to about 1/2 ln 2 per Nd atom. For Ce10B9C12, the reciprocal susceptibility does not follow the Curie–Weiss behavior in the whole temperature range up to 900 K (Fig. 46). At very low temperatures, no clear indication of long-range magnetic ordering is found, which was also missing from the heat capacity measurements down to 2 K (Fig. 47). For a quantitative analysis of the magnetic contributions to the heat capacity of Ce10B9C12, the lattice contribution was subtracted which is rather well represented by the heat capacity of La10B9C12. Fig. 47 displays the magnetic contribution at various magnetic fields up to 9 T. The temperature dependence of the

FIG. 44 Reciprocal magnetic susceptibility vs temperature of Nd10B9C12 measured in an external field B ¼ 7 T. Solid and dashed lines represent the Curie–Weiss fit. Inset: Magnetization vs applied field at T ¼ 2 K with open symbols for increasing, and filled symbols in decreasing field.


302 221

TABLE 25 Magnetic Data for Boride Carbides R10B9C12 [48] Compound

TC (K)

up (K)

meff (mB)

mS (mB)

Ce10B9C12

5

26

2.23

0.4

Pr10B9C12

12

4

3.79

1.2

Nd10B9C12

13

7

3.76

1.7

FIG. 45 Heat capacity Cp vs temperature for R10B9C12. The inset displays Cp/T. The magnetic contributions to the heat capacity of the compounds containing magnetic rare-earth ions are clearly visible from a comparison with the heat capacity of La10B9C12, which represents the phonon contributions.

magnetic entropy gained is indicated in the inset. Above 25 K, Cp follows a power law ∞T1/2, and below 20 K it becomes higher. The field-induced maximum and the shift, possibly due to the onset of magnetic ordering, to higher temperatures are clearly visible. The measured temperature dependence of the resistivity, r(T), confirms the metallic character of Ce10B9C12. The anomalies seen at low temperatures ( 50 K) deviates from the Curie–Weiss law


TABLE 26 Atomic Parametersa for Nd5B4C5 Atom

Occ.

x

y

z

Nd1

1

0.80355

0.43376

0.0006

Nd2

1

0.80227

0.0385

0.7932

Nd3

1

0.79887

0.23736

0.4065

Nd4

1

0.82152

0.83156

0.2000

Nd5

1

0.80293

0.6347

0.5985

Nd6

1

0.56197

0.44800

0.4049

Nd7

1

0.55809

0.0464

0.5951

Nd8

1

0.57996

0.84010

0.1987

Nd9

1

0.55029

0.2464

0.9892

Nd10

1

0.56612

0.64282

0.7874

C1

1

0.4064

0.464

0.592

C2

1

0.4100

0.052

0.387

C3

1

0.2018

0.465

0.803

C4

0.8

0.3032

0.369

0.102

C5

1

0.0866

0.352

0.303

C6

0.8

0.4067

0.259

0.992

C7

1

0.2022

0.066

0.994

C8

1

0.1970

0.264

0.397

C9

1

0.0758

0.160

0.695

C10

1

0.3073

0.166

0.693

B1

1

0.5279

0.934

0.893

B2

1

0.1445

0.041

0.013

B3

1

0.9680

0.056

0.598

B4

1

0.0249

0.371

0.295

B5

1

0.1447

0.487

0.826

B6

1

0.3580

0.333

0.057

B7

1

0.1398

0.302

0.372

B8

1

0.5150

0.362

0.692

SG Pna21, a ¼ 24.301 A˚, b ¼ 8.3126 A˚, c ¼ 8.3545 A˚ [49]. a All atoms in Wyckoff position 4a.


302 225

FIG. 49 Structural arrangement of Ce5B4C5 along [001] (A) and rare-earth metal atom environments of B3C3 (B), B4C4 (C), BC2 (D), and C (E).

(Fig. 50). On the other hand, both Pr5B4C5 and Nd5B4C5 compounds follow the Curie–Weiss behavior (Fig. 51). The values of the effective magnetic moments and the paramagnetic Weiss temperatures were calculated and are given in Table 27. The values of the magnetic moments agree with the theoretical tripositive rare-earth moment values except for Ce5B4C5. In the lowtemperature regime (T < 20 K) all three compounds are characterized by the onset of magnetic order. In low fields for Ce5B4C5 (B < 1 T) the M(T) curves reversibly pass through a maximum at 5 K (Fig. 52). Hence the magnetic ground state of this compound is antiferromagnetic. At elevated fields the maximum vanishes, and the magnetization seems to saturize at the lowest temperatures. Furthermore, the isothermal magnetization vs field at 2 K reveals the typical s-shaped plot of a metamagnetic transition (Bcrit 1.5 T). However from the reduced saturation moment, mS ¼ 0.5 mB at B ¼ 7 T, it is inferred that the spin structure is not collinear, likely reminiscent of canted ferromagnetism. For Pr5B4C5 and Nd5B4C5, the susceptibility (M/H (T)) of the zfc samples rises


FIG. 50 Reciprocal susceptibility vs temperature for Ce5B4C5 measured in applied field B ¼ 5 T. Solid line represents a fit to a modified Curie–Weiss law. Inset: Isothermal magnetization vs applied field for Ce5B4C5 measured at T ¼ 2 K. Open symbols in rising fields, and filled symbols in decreasing fields.

FIG. 51 Reciprocal magnetic susceptibility vs temperature for Nd5B4C5 measured in applied field B ¼ 5 T. Solid line represents a fit to the Curie–Weiss law. Inset: Isothermal magnetization vs applied field for Nd5B4C5 measured at T ¼ 2 K. Open symbols in rising fields, and filled symbols in decreasing fields.

in low external fields (B < 0.1 T) at increasing temperatures, passes through a maximum, and decreases rapidly to low values near the ordering temperatures. Upon cooling the sample in applied field (fc) a higher net magnetization below TC is frozen in. The critical magnetic fields where wall movements set in are


302 227

TABLE 27 Magnetic Data for Boride Carbides R5B4C5 (R 5 Ce, Pr, Nd) Compound

TC (K)

Ce5B4C5

TN (K)

up (K)

meff (mB)

m(R3+) (mB)

5

8.5

2.17

2.54

0.5

mS (mB)

Pr5B4C5

12

5.5

3.73

3.58

1.3

Nd5B4C5

15

14.5

3.67

3.62

1.7

FIG. 52 Magnetization vs temperature for Ce5B4C5 measured at various magnetic fields. Open symbols are for rising temperature, and filled symbols for decreasing temperatures.

around B 0.1 T at T ¼ 2 K. From isothermal magnetization plots vs field at T ¼ 2 K (see the inset of Fig. 51), the values for the saturation moments were derived. The reduced moments mS < 2 mB ¼ 1/2 gJ ¼ 1.6 mB for Pr5B4C5 and Nd5B4C5 are typical values for bulk samples of axial symmetry. For both compounds hysteresis is observed and the remnant magnetization is approximately 10 Am2/kg. The coercive forces were determined by reversing the direction of the magnetic fields and were found to be 0.06 and 0.15 T, respectively. The temperature dependence of the electrical resistance of Ce5B4C5 in a temperature range of 1.8–290 K proves overall the metallic character of this rare-earth metal boride carbide system [49].

4.4.5 The R25B14C26 and R25B12C28 Phases The ternary rare-earth metal boride carbides R25B14C26 (R ¼ Pr, Nd) and R25B12C28 (R ¼ Nd) were synthesized by co-melting the elements. R25B14C26 phases exist above 1270 K and Nd25B12C28 is stable up to 1440 K. The crystal


structures of these compounds were investigated by Babizhetskyy et al. [51] by means of single-crystal X-ray diffraction. Atomic parameters of Nd25B14C26 (space group P21/c, Z ¼ 2) and Nd25B12C28 (space group P1, Z ¼ 2) are given in Tables 28 and 29, respectively. The rare-earth metal atom sublattice of these phases (Fig. 53) consists of a 3D framework resulting from the stacking of slightly corrugated and distorted square nets along the [001] direction and rotated with respect to each other by about 45°. Such a stacking leads to the formation of four different types of octahedral, distorted bicapped square-antiprismatic, distorted monocapped square-antiprismatic, and distorted bicapped double antiprismatic cavities encapsulating isolated carbon atoms, BC2 chains, and B2C4 and B3C3 (already encountered in R5B4C5) oligomers (see Fig. 54A–E). The nonmetal atom part of the structure of R25B14C26 (Fig. 53A) contains two types of slabs. One slab is made of nearly linear and finite CBC units and isolated carbon atoms. The other slab contains B2C4, B3C3, bent CBC chains (C–B–C ¼ 148.7° in Nd25B14C26 for instance), and isolated carbon atoms. The triclinic structure Nd25B12C28 (Fig. 53B) also contains two types of slabs. One slab is similar to that in R25B14C26 with nearly linear CBC units and isolated carbon atoms. The second slab differs from that in R25B14C26 and is made of B2C4 chains, bent CBC entities (C–B–C ¼ 146.3°), and isolated carbon atoms. Note that strongly bent CBC units are also present in quaternary phases, such as La9Br5B3C6 [174], La4I5B2C, and La3Br2BC2 [10].

4.4.6 The R5B2C6 Phases 4.4.6.1 Structural Properties of R5B2C6 Gd5B2C6 was first discovered by Smith and Gilles [97], but described as “Gd2BC2.” Some years later, the crystal structure of Ce5B2C6 [175] and La5B2C6 [176] was proposed with P4 symmetry. A homogeneous sample of La5B2C6 annealed at 1270 K investigated later [41] by X-ray powder and single-crystal analysis as well as electron diffraction [102] indicates that La5B2C6 crystallizes in the space group P4/ncc (Z ¼ 4). Atomic parameters are given in Table 30. Indeed, these phases known today with nearly all R elements (Y, La–Sm, Gd–Tm) exhibit large homogeneity regions, which can lead to a significant variation of the unit cell c-parameter (see Table 1). The borocarbides (La1xGdx)5B2C6 with 0 x 1 form a continuous solid solution and are found to be isostructural to La2B2C6. The unit cell volume ˚ 3 after in the (La1xGdx)5B2C6 solid solution decreases from 934.1 to 783.6 A annealing of the samples at 1270 K [177]. The structure consists of a 3D framework of rare-earth metal atoms resulting from the stacking of slightly corrugated 2D square lattice, which contains octahedral voids and distorted bicapped square-antiprismatic cavities which are filled with isolated carbon atoms or C2 units and twofold disordered CBCC units, respectively [178, 179] (Fig. 55). The CBCC units are somewhat


302 229

TABLE 28 Atomic Parameters for Nd25B14C26 Atom

Site

Occ

x

y

z

Nd1

4e

1

0.00799

0.00590

0.197143

Nd2

4e

1

0.20358

0.11639

0.304667

Nd3

4e

1

0.59991

0.30508

0.303628

Nd4

4e

1

0.19164

0.30590

0.112180

Nd5

4e

1

0.20424

0.40939

0.20497

Nd6

4e

1

0.39724

0.08954

0.10522

Nd7

4e

1

0.21293

0.11258

0.112051

Nd8

4e

1

0.18983

0.40433

0.00066

Nd9

4e

1

0.41388

0.50035

0.111309

Nd10

4e

1

0.58676

0.20484

0.01887

Nd11

4e

1

0.59208

0.19943

0.19209

Nd12

4e

0.774

0.01366

0.20750

0.39084

Nd13

4e

0.226

0.0031

0.2103

0.4029

Nd14

2a

1

0

0

0

C1

4e

1

0.2825

0.6109

0.1147

C2

4e

1

0.135

0.312

0.0334

C3

4e

1

0.3196

0.1897

0.1161

C4

4e

1

0.1061

0.7079

0.2053

C5

4e

1

0.1001

0.3080

0.2036

C6

4e

1

0.5070

0.5039

0.2029

C7

4e

1

0.1212

0.4104

0.1216

C8

4e

1

0.3057

0.4082

0.3044

C9

4e

1

0.3185

0.1054

0.0242

C10

4e

1

0.5120

0.2061

0.1122

C11

4e

1

0.0862

0.0076

0.1179

C12

4e

1

0.6923

0.6078

0.2935

C13

4e

1

0.4678

0.5131

0.0250

B1

4e

1

0.5925

0.5576

0.2485

B2

4e

1

0.1439

0.0210

0.0690

B3

4e

1

0.1013

0.7529

0.2512 Continued


TABLE 28 Atomic Parameters for Nd25B14C26—Cont’d Atom

Site

Occ

x

y

z

B4

4e

1

0.3456

0.5836

0.0663

B5

4e

1

0.2745

0.1666

0.0664

B6

4e

1

0.094

0.396

0.0726

B7

4e

1

0.2717

0.0830

0.0260

˚ , b ¼ 8.3096 A˚, c ¼ 30.599 A˚, b ¼ 106.065° [51]. SG P21/c, a ¼ 8.3404 A

TABLE 29 Atomic Parameters for Nd25B12C28 Atom

Site

Occ.

x

y

z

Nd1

2i

1

0.24237

0.04386

0.61105

Nd2

2i

1

0.08340

0.12530

0.19711

Nd3

2i

1

0.15120

0.15091

0.38789

Nd4

2i

1

0.44511

0.34368

0.61175

Nd5

2i

1

0.47224

0.31849

0.19577

Nd6

2i

1

0.66817

0.07418

0.19756

Nd7

2i

1

0.27577

0.26760

0.19539

Nd8

2i

1

0.11313

0.71191

0.48162

Nd9

2i

1

0.40401

0.80776

0.00080

Nd10

2i

0.546

0.1214

0.5232

0.2013

Nd11

2i

1

0.04478

0.45047

0.39541

Nd12

2i

1

0.54519

0.65338

0.11187

Nd13

1a

1

0

0

0

Nd14

2i

1

0.17827

Nd15

2i

1

0.74519

Nd16

2i

0.80

0.3596

0.7506

0.3916

Nd17

2i

1

0.0650

0.14315

0.11250

Nd18

2i

1

0.30944

0.09501

0.49931

Nd19

2i

1

0.21593

0.41750

0.30303

0.22509

0.30812

0.26393

0.11297

302 231



Site

Occ.

x

y

z

Nd20

2i

1

0.41564

0.01157

Nd21

2i

0.45

0.195

Nd22

2i

1

0.02249

0.80891

0.30504

Nd23

2i

1

0.13670

0.46259

0.10871

Nd24

2i

1

0.33403

0.06109

0.10276

Nd25

2i

1

0.37609

0.61883

0.30471

Nd26

1h

1

1/2

1/2

Nd27

2i

0.454

0.1198

0.5212

Nd28

2i

0.55

0.199

0.394

Nd29

2i

0.20

0.3610

0.7505

0.4043

C1

2i

1

0.143

0.251

0.3877

C2

2i

1

0.043

0.158

0.1181

C3

2i

1

0.021

0.823

0.2048

C4

2i

1

0.577

0.382

0.2028

C5

2i

1

0.238

0.245

0.1152

C6

2i

1

0.221

0.221

0.2055

C7

2i

1

0.441

0.353

0.1158

C8

2i

1

0.344

0.643

0.3846

C9

2i

1

0.278

0.914

0.2957

C10

2i

1

0.479

0.311

0.2938

C11

2i

1

0.113

0.111

0.2958

C12

2i

1

0.249

0.446

0.3823

C13

2i

1

0.055

0.844

0.3847

C14

2i

1

0.179

0.429

0.2028

C15

2i

1

0.450

0.041

0.3781

C16

2i

1

0.084

0.514

0.3017

C17

2i

1

0.638

0.042

0.1173

C18

2i

1

0.375

0.023

0.1968

C19

2i

1

0.840

0.554

0.1177

C20

2i

1

0.320

0.712(2)

0.2934

0.403

0.29563 0.0192

1/2 0.2141 0.0092

Continued



Site

Occ.

x

y

z

C21

2i

1

0.500

0.517(1)

0.0248

C22

2i

1

0.783

0.401(1)

0.4766

C23

2i

1

0.118

0.696(1)

0.0241

C24

2i

1

0.808

0.406(1)

0.5273

C25

2i

1

0.077

0.715(1)

0.0266

C26

2i

1

0.004

0.024(1)

0.5249

C27

2i

1

0.590

0.174(2)

0.4650

C28

2i

1

0.294

0.117(2)

0.0331

B1

2i

1

0.061

0.108(1)

0.5666

B2

2i

1

0.318

0.640(2)

0.4334

B3

2i

1

0.258

0.451(2)

0.4304

B4

2i

1

0.008

0.191(2)

0.0682

B5

2i

1

0.046

0.150(2)

0.2508

B6

2i

1

0.491

0.075(2)

0.4274

B7

2i

1

0.194

0.235(2)

0.0657

B8

2i

1

0.445

0.387(2)

0.0659

B9

2i

1

0.555

0.343(2)

0.2492

B10

2i

1

0.254

0.159(1)

0.2501

B11

2i

1

0.637

0.051(2)

0.0693

B12

2i

1

0.240

0.355(2)

0.2492

˚ , c ¼ 29.888 A ˚ , a ¼ 83.730°, b ¼ 83.294°, g ¼ 89.764° [51]. SG P1, a ¼ 8.3209 A˚, b ¼ 8.3231 A

bent (C–C/B–C/B ¼ 158.1° in La5B2C6 for instance) but the C/B–C and C/B– ˚ in La5B2C6 for instance) reflect some cumuleC/B distances (1.32 and 1.65 A nic character. 4.4.6.2


The physical properties of these R5B2C6 compounds have been studied. They reveal a remarkably distinct magnetic behavior depending on the lanthanoid element [31]. The magnetic data are summarized in Table 31. Gd5B2C6 is an antiferromagnet with a Neel temperature TN ¼ 26 K. Within the solid


302 233

FIG. 53 Crystal structures of Nd25B14C26 (A) and Nd25B12C28 (B) viewed along [010]. Boron– carbon chains are bonded. Large gray, small black, and small gray spheres represent Nd, B, and C atoms, respectively.

solution (La1xGdx)5B2C6 with 0 x 1, the ordering temperature increases gradually from 7 to 26 K with x increasing from just over 0.4 to 1. For x 0.4 all samples remain paramagnetic above T > 4.2 K [31]. Y5B2C6 and La5B2C6 are Pauli-type paramagnets below room temperature. The latter was believed to become superconducting at a critical temperature of 6.8 K [179]. However, this finding was later proved as an artifact due to lanthanum segregation at grain boundaries [178]. The magnetic susceptibility variation upon temperature for Ce5B2C6 measured up to 900 K is shown in Fig. 56. No magnetic ordering was observed down to 4.2 K. The reduced value of meff ¼ 2.3 mB < 2.54 mB and the rather high negative value yp ¼ 93 K together with the shallow maximum in the w(T) curve around 50 K are reminiscent of an intermediate valence (Ce3+/Ce4+) system (see the inset of Fig. 56). However, at the lowest temperatures, the susceptibility rises with temperature decreasing instead of approaching a constant value as expected for Ce4+ compounds. The measured w(T) dependences were corrected for impurities subtracting the term n ¼ Cimp/T from the experimental data in the entire temperature range, which was studied, where C is the Curie constant of free Ce3+ ions. The so-corrected 1/w(T) curves are displayed in Fig. 56 (filled symbols). In the paramagnon model of intermediate valence materials developed


FIG. 54 Arrangements of the quasimolecular boron–carbon entities in R25B14C26 and their rareearth metal atom environments: isolated carbon atoms (A), nearly linear (B), and bent (C) BC2 units, B2C4 (D), and B3C3 (E) chains.

by Beal-Monod and Lawrence, the susceptibility varies with (T/TSF)2, where TSF denotes a characteristic temperature related to spin fluctuations which is given by TSF ¼ C/2w(0) ¼ 98 K. This value is consistent with the prediction offered by Lawrence et al. [180], where TSF ¼ 3/2 T(wmax) ¼ 75 K. The interconfiguration fluctuation model describes quite well the magnetic behavior of Ce5B2C6 observed in the entire temperature range. The least-squares fit of the experimental w(T) data are shown in Fig. 56 by a medium-dashed line, and the fitting parameters are as follows: Eex/kB ¼ 183 K, TSF ¼ 83 K, and wo ¼ 2.5 104 emu/mol for the Ce atoms. The temperature dependence of the effective cerium atom valence shows a strong decrease from 3.60 + at 5 K to 3.16+ at 900 K.


302 235

TABLE 30 Atomic Parameters for La5B2C6 Atom

Site

Occ.

x

y

z

La1

16g

1

0.65022

0.05076

0.10695

La2

4c

1

1/4

1/4

0.13684

C1

16g

1

0.6537

0.0451

0.9110

C2/B2

16g

1

0.6324

0.0610

0.8065

C3

4c

0.32

1/4

1/4

0.382

SG P4/ncc, a ¼ 8.590 A˚, c ¼ 12.398 A˚ [41].

FIG. 55 Crystal structure of La5B2C6 along [010]. Boron–carbon chains are bonded. Large gray, small black, and small gray spheres represent La, B/C, and C atoms, respectively.

TABLE 31 Magnetic Data of R5B2C6 Compound

TC (K)

TN (K)

up (K)

meff (mB)

mS (mB)

Remanence (%)

BC (T)

La5B2C6

7 K < T < 300 K Pauli paramagnet

Ce5B2C6

—

—

93.4

2.3

—

—

—

Pr5B2C6

6.5

—

17.3

3.7

1.2

15

0.10

Nd5B2C6

7.9

—

10.6

3.7

1.4

6

0.05

Sm5B2C6

17.8

—

No CW

—

—

—

—

Gd5B2C6

—

26.9

48.7

7.8

3.6

—

—

Tb5B2C6

35.6

—

51.4

10.0

4.92

12

0.16

Dy5B2C6

20.8

—

39.3

10.9

5.0

4

0.05

Ho5B2C6

17.8

—

23.7

10.6

5.7

6

0.10

Er5B2C6

5.9

—

15.3

9.6

4.9

4

0.05

Tm5B2C6

0.5 T as shown in Fig. 58. The measured ordering temperatures TC for the light lanthanides increase with atomic number, whereas they decrease for the heavy lanthanides. The values for TC and yp thereby scale approximately with the de Gennes factor, (g 1)2J(J + 1), which is a strong argument that the R–R spin coupling is dominated by the indirect exchange interaction via the conduction electrons (RKKY mechanism). The temperature


302 239

dependence of the magnetization curves of the Pr, Nd, Tb–Tm borocarbides in the ordered state depends on sample history prior to the measurements, i.e., zfc, fc, or magnetizing in maximum field (fm) as it is particularly shown for the Ho borocarbide in Fig. 59. This is reminiscent of the behavior of typical narrow domain wall ferromagnets, where the wall movement is thermally activated in applied fields. The critical field where wall movement sets in is close to the coercive field and was estimated from isothermal magnetization curves at 5 K (Figs. 58 and 59). These data for BC Bcoerc together with the values for the remnant magnetization as percentage of the “saturation” magnetization at B ¼ 3 T and T ¼ 5 K are presented in Table 31. The presence of narrow domain walls can be understood as the result of a high anisotropy energy caused by the crystal field interactions of the moments containing an orbital contribution. Hence, in the case of gadolinium with L ¼ 0, where no such effects are expected, the metamagnetic behavior can be explained as the consequence of a formation of ferromagnetically coupled sheets of Gd atoms, where adjacent sheets are coupled antiparallel. The observed positive value for yp supports this assumption.

4.4.7 The R15B6C20 Phases 4.4.7.1 Structural Properties of R15B6C20 The ternary rare-earth metal boride carbides R15B6C20 (R ¼ Pr, Nd) were synthesized by Babizhetskyy et al. [50] by melting from the elements. They exist above 1270 K. Their crystal structures were determined from singlecrystal X-ray diffraction data. Both crystallize in SG P1 (Z ¼ 1). The atomic parameters for Pr15B6C20 are given in Table 32. These compounds are closely related structurally to other ternary rare-earth boride carbides containing discrete boron–carbon chains of different lengths. The rare-earth metal sublattice consists of a 3D framework resulting from the stacking of slightly corrugated and distorted square nets along the [001] direction and rotated with respect to each other by about 45° (Fig. 60). Such a stacking along the c-direction leads to the formation of three different types of cavities: octahedral, distorted bicapped square-antiprismatic, and distorted bicapped double antiprismatic cavities stuffed by isolated carbon atoms, disordered C3 chains, and finite B2C4 oligomers, respectively (Fig. 60A). Interestingly, each disordered C3 unit sits in a distorted bicapped square antiprism (Fig. 60B). Such a metal atom cage frequently encountered in rare-earth metal boride carbides generally contains three-membered chains such as BC2 in R5B2C5 (see below), or four-membered chains such as BC3 in R5B2C6 (see above) and B2C2 in Nd2BC (see below). In the C3 moiety, the C atoms which are external to the cage have fractional (0.5) occupancies (Table 32). This suggests (a) two disordered C3 groups in the ratio 1:1 or (b) three disordered C2 (1:1:1). Note that C3 chains are also found in Sc3C4, Ho4C7, and Y4C7 [96,181, 182]. No carbon chains longer than three atoms have been reported in borocarbide compounds to date. Three B2C4 units



Site

Occ.

x

y

z

Pr1

1a

1.00

0

0

0

Pr2

2i

1.00

0.40225

0.00535

0.19205

Pr3

2i

1.00

0.26458

0.36103

0.26966

Pr4

2i

1.00

0.19781

0.05256

0.59936

Pr5

2i

1.00

0.06709

0.36024

0.86299

Pr6

2i

1.00

0.45901

0.35982

0.66373

Pr7

2i

1.00

0.12862

0.65200

0.53278

Pr8

2i

0.55

0.6783

0.2944

0.0741

Pr9

2i

0.45

0.6652

0.346

0.0625

C1

2i

1.00

0.5697

0.3718

0.3615

C2

2i

1.00

0.2366

0.6312

0.2371

C3

2i

1.00

0.0378

0.6233

0.8365

C4

2i

1.00

0.1638

0.3612

0.5604

C5

2i

1.00

0.1126

0.9228

0.3016

C6

2i

1.00

0.5037

0.0802

0.4857

C7

2i

1.00

0.074

0.0843

0.288

C8

2i

1.00

0.314

0.128

0.896

C9

2i

1.00

0.621

0.759

0.036

C10

2i

0.5

0.705

0.011

0.103

C11

2i

0.5

0.623

0.624

0.025

B1

2i

1.00

0.9983

0.2228

0.197

B2

2i

1.00

0.558

0.2151

0.399

B3

2i

1.00

0.188

0.7864

0.237

˚ , b ¼ 9.249 A˚, c ¼ 8.358 A˚, a ¼ 84.7°, b ¼ 89.6°, g ¼ 84.2° [50]. SG P1, Z ¼ 1, a ¼ 8.343 A

are located in the unit cell, one symmetrical and two asymmetrical with the proposed C–B–C–C–B–C atom distribution. B–C distances range from 1.43 to ˚ and C–C distances are 1.49 A ˚ in Pr15B6C20. Structural and theoretical 1.50 A analyses suggest the ionic formulation (R3+)15([B2C4]6)3([C3]4)2(C4)2.11e for these compounds. Accordingly, DFT calculations indicate that the


302 241

FIG. 60 Crystal structure of R15B6C20 along [84] (left) and rare-earth metal atom environments of the B2C4 chain (A), (disordered) C3 units (B), and isolated carbon atoms (C).

compounds are metallic. Both structural arguments and energy calculations on different boron vs carbon distributions in the B2C4 chains support the presence of a CBCCBC unit [50]. 4.4.7.2


The measurements of physical properties of R15B6C20 (R ¼ Pr, Nd) were performed by Babizhetskyy et al. [50]. The data follow an almost linear Curie– Weiss law above 50 K and were least squares fitted (Fig. 61). The derived values of the effective moments, meff ¼ 3.60 mB/Pr and meff ¼ 3.64 mB/Nd, agree well with the theoretical moments of the respective R3+ ions. The paramagnetic Weiss temperatures, yp, are 13.8 and 14.2 K for the Pr and Nd compounds, respectively, indicating ferromagnetic coupling. Upon lowering the temperature both samples undergo magnetic transitions. The w(T) plot (Fig. 62) of Pr15B6C18 reveals a pronounced maximum at a Neel temperature TN ¼ 8 K for measurements of zfc as well as fc samples, i.e., in increasing or decreasing temperatures, in an external field B ¼ 0.01 T. This behavior is attributed to an antiparallel spin alignment of the praseodymium sublattice. Above a critical field B > 0.03 T a meta-magnetic transition toward parallel spin alignment is observed. The magnetic susceptibility in external fields B ¼ 0.1 and 1 T shows saturation below T ¼ 5 K characteristic for ferromagnets (Fig. 62). From isothermal magnetization curves vs applied magnetic fields at T ¼ 2 K, a saturation moment mS ¼ 1.52 mB at B ¼ 7 T is derived as can be seen in the inset of Fig. 61. The results of the magnetic measurements of the compound Nd15B6C20 are somewhat different when compared with those of Pr15B6C20. The w(T) plots in low external field, B ¼ 0.1 T, reveal a pronounced difference depending on the sample history prior to the measurements and is commonly attributed to the presence of narrow domain walls. The net


FIG. 61 Reciprocal magnetic susceptibility vs temperature for Pr15B6C20 at B ¼ 7 T. Solid line represents the Curie–Weiss fit. Inset: Isothermal magnetization vs magnetic field at T ¼ 2 K.

FIG. 62 Magnetic susceptibility vs temperature for Pr15B6C20 at various magnetic fields.

magnetization of zfc samples increases at rising temperature due to thermal activation of the domain wall movement, reaches a maximum, and falls off to small values at the ordering temperature TC ¼ 40 K, whereas a high net magnetization is frozen in when the sample is fc in decreasing temperature. From isothermal magnetization curves vs applied magnetic fields at T ¼ 5 K for Nd15B6C20, a saturation moment mS ¼ 1.60 mB at B ¼ 7 T is observed. The


302 243

FIG. 63 Electrical resistivity vs temperature for Nd15B6C20.

reduced values of the saturation moments mS ¼ 1/2 gJ are possibly due to a noncollinear spin alignment of the ordered moments in these compounds crystallizing in a low-symmetry space group. The overall shape of the r(T) curve of Nd15B6C20 is reminiscent of the behavior of a magnetic metal (Fig. 63). Starting at room temperature the resistivity decreases upon lowering the temperature due to the temperature-dependent electron–phonon interaction. Below the ferromagnetic ordering temperature of approximately 40 K, in good agreement with the magnetic data, a characteristic change of the slope of the r(T) curve owing to the additional contribution of the spin wave scattering of the conduction electrons in the ordered state is encountered. The resistivity data fitted at low temperatures according to the general formula r(T) ¼ r0 + AT2 ¼ 0.8 + 3.06 * 105 T2 (dashed line in Fig. 63) indicate a metallic behavior.

4.4.8 The R2BC2 Phases The existence and some structural details of Sc2BC2 were first mentioned by Bauer et al. [183]. A congruent melting behavior of this compound was observed by the same authors. A graphical outline of the unit cell and a prediction of possible anisotropic transport properties were reported later by Halet et al. [22]. A structural model was refined later by Shi et al. in 1999 [15] with I4/mmm symmetry (Z ¼ 2) (Table 33). The crystal structure of Sc2BC2 is unique and is related to that of CaC2 ˚ ) and C2 dumbbells subwith Ca atoms replaced by Sc2 pairs (Sc–Sc ¼ 3.144 A stituted by symmetrical and linear C–B–C units (Fig. 64). These BC2 moieties are encapsulated in bicapped cubic cavities formed by the metal atoms. The ˚ indicate a double-bond character. short interatomic B–C distances of 1.484 A


TABLE 33 Atomic Parameters for Sc2BC2 Atom

Site

Occ.

x

y

z

Sc

4e

1

0

0

0.34759

C

4e

1

0

0

0.13816

B

2a

1

0

0

0

SG I 4/mmm, a ¼ 3.325 A˚, c ¼ 10.674 A˚ [22].

FIG. 64 The crystal structure of Sc2BC2. [Sc10] bicapped square prismatic polyhedron is emphasized.

Theoretical calculations have shown that this compound can be described in the first approximation as being built of (BC2)5 anionic units isoelectronic to CO2 surrounded by not fully oxidized Sc2.5+ cations [22,173].

4.4.9 The R5B2C5 Phases 4.4.9.1 Structural Properties of R5B2C5 The crystal structures of R5B2C5 were first determined for R ¼ Sm, Gd using single-crystal X-ray diffraction data [47]. A few years later, the crystal structures with R ¼ Y, Dy, Ho, Tm [32] and R ¼ Pr [53] were reported. These R5B2C5 borocarbides, known now for nearly all rare-earth elements (Y, Ce– Yb) (Table 1), can be prepared by arc melting from the pure rare-earth metals,


302 245


Site

x

y

z

Pr1

16g

0.65508

0.04201

0.10285

Pr2

4c

1/4

1/4

0.14280

C1

16g

0.6477

0.0515

0.1264

B1

8f

0.5930

x

1/4

C2

4c

1/4

1/4

0.402

SG P4/ncc, a ¼ 8.448 A˚, c ¼ 10.970 A˚ [53].

FIG. 65 Crystal structure of Pr5B2C5 (A) and a projection along [001] (B). The chains of edgesharing Pr6C octahedra are emphasized. The distorted square-antiprismatic coordination of the BC2 unit is shown (C).

boron and carbon. In contrast to the heavy lanthanide metal (Gd–Tm)containing compounds, which melt congruently, those with the early lanthanide elements (Ce–Sm) are formed peritectically [47]. It was shown by means of HRTEM that the domains of compounds with the R5B2C5 and R3C4 structure types may intergrow coherently [103]. The structural arrangement of these compounds, which crystallize in the tetragonal space group P4/ncc (see Table 34 for the atomic parameters of Pr5B2C5), consists of a 3D framework of rare-earth atoms resulting from the stacking of slightly corrugated 2D squares (Fig. 65B), which leads to the


formation of octahedral holes and distorted bicapped square-antiprismatic cavities filled with isolated carbon atoms and CBC chains, respectively (Fig. 65C). The BC2 chains are nearly linear (C–B–C ¼ 173.9° in Pr5B2C5) and show short ˚ in Pr5B2C5), indicative of double bonds, similar to B–C distances (1.475 A those observed in Sc2BC2 just mentioned earlier. DFT calculations indicate that these compounds should be metallic in character and that a rather strong covalency occurs between the metallic matrix and the BC2 groups and the isolated carbon atoms, respectively [47]. 4.4.9.2 Physical Properties of R5B2C5 The magnetic behavior of the ternary compounds R5B2C5 (R ¼ Ce–Sm, Gd– Tm) is generally characterized by the onset of ferromagnetic order of the rare-earth sublattice [47]. The results are summarized in Table 35. In the paramagnetic regime, TC < T 500 K, the magnetic susceptibility data of the Gd– Tm-containing samples follow the Curie–Weiss law. The magnetic constants, the effective moment meff, and the paramagnetic Weiss temperature yp were calculated and the values for the effective moments are in good agreement with the theoretical moments of the tripositive rare-earth ions (see Table 35). All samples (including the light lanthanide borocarbides) exhibit ferromagnetic ordering, (confirmed by the temperature dependence of the imaginary part of the susceptibility wAC) upon lowering the temperature, which is in agreement

TABLE 35 Magnetic Data for Boride Carbides R5B2C5 Compound

TC (K)

up (K)

meff (mB)

mS (mB)

Remanence (%)

BC (T)

Ce5B2C5

7

—

—

—

—

—

Pr5B2C5

20

—

—

—

—

—

Nd5B2C5

45

—

—

—

—

—

Sm5B2C5

22

No CW

—

—

—

—

Gd5B2C5

130

219.5

7.6

6.8

—

—

Tb5B2C5

42

87.5

9.8

5.4

36

0.2

Dy5B2C5

30

72.2

11.0

5.7

18

0.1

Ho5B2C5

21

43.8

10.6

6.3

12

0.1

Er5B2C5

22

13.5

9.6

5.3

6

0.05

29.5

7.7

6.3

Tm5B2C5 Y5B2C5

4.5

0 5

Paramagnetic, T < 300 K, wg 1.8 * 10

0 3

cm /g


302 247

with the observed positive values of yp. The measured ordering temperatures, TC, increase in case of the Ce–Sm-containing samples, whereas they decrease for the heavy lanthanide metal borocarbides upon increasing of the R atomic number. TC as well as yp values scale approximately with the de Gennes factor indicate that the coupling of the R–R moments is due to indirect exchange interaction via conduction electrons (RKKY interaction). The compound Gd5B2C5 shows a rather peculiar magnetic behavior. The magnetization of a zfc sample increases in a moderate external field, passes through a broad maximum, and then decreases sharply at the Curie temperature. When the sample is measured under the same conditions but after being fully magnetized (fm, B ¼ 3 T), the higher “frozen-in” net magnetization first decreases as the temperature increases, passes a minimum, and merges into the zfc curve above ca. 50 K (Fig. 66). The isothermal magnetization vs field at T ¼ 5 K reveals a remarkable hysteresis loop between increasing and decreasing fields. The magnetic ground state of Gd5B2C5 resembles a “spin glass‘-like (asperomagnetism) or’ cluster glass”-like (mictomagnetism) state. In an external field higher than 0.5 T a spin reorientation takes place leading to an almost collinear spin arrangement above 1 T. The derived saturation moment mS ¼ 6 mB gJ is in good agreement with this assumption. The difference of the M(T) curves measured in increasing temperature and in moderate fields strongly depends on the experimental history (zfc or fm sample) and is attributed to the spin-glass freezing below TSG 55 K associated with thermal blocking of cluster moments. The temperature dependence of the magnetization curves of the Tb–Tm borocarbides in the ordered state is reminiscent of the typical behavior of narrow domain wall ferromagnets, where wall movement is

FIG. 66 Magnetization vs temperature for Gd5B2C5 measured in external field 0.1 T. Filled symbols, zfc sample; open symbols, fm sample. Inset: Magnetization vs field measured at 5 K.


FIG. 67 Magnetization vs temperature for Tb5B2C5 measured in external field 0.1 T. Open symbols, zfc sample; filled symbols, fm sample. Upper inset: Magnetization vs field measured at 5 K. Lower inset: Dynamic magnetic susceptibilities vs temperature.

thermally activated in applied fields (see the inset of Fig. 67). The critical field where wall propagation sets in is close to the coercive field and was estimated from isothermal magnetization plots at T ¼ 5 K (see the inset of Figs. 66 and 67). These data (Bcrit Bcoerc) are listed in Table 35 together with the values for the remanent magnetization MR ¼ 36% of the saturation magnetization at B ¼ 3 T and T ¼ 5 K, which are maximum in the case of Tb5B2C5 and decrease as the atomic number of the rare-earth metals increases. The presence of narrow domain walls can be understood as the result of a high magnetocrystalline anisotropy energy caused by the crystal field interaction of the moments having an orbital contribution.

4.4.10 The R3BC3 Phases Sc3B0.75C3 is the first example of the phases with approximate composition R3BC3 characterized by Shi et al. [23]. The compound crystallizes in the space group P4/mmm (Z ¼ 1; Table 36). It can be described as being built from chains of bicapped cubic Sc10 polyhedra, which as in Sc2BC2 (see above) contain linear CBC units running parallel to the c-axis (Fig. 68). Every Sc10(BC2) unit is face-linked with four other Sc10(BC2) polyhedra along the a and b directions and corner-linked with two other similar polyhedra along the c-direction. Such a polyhedral arrangement forms slightly distorted octahedra to accommodate isolated C atoms. Linear CBC units exhibit a short B–C bond length of ˚ of double-bond character. This short contact, quite shorter than the 1.417 A corresponding B–C distance in Sc2BC2 for instance, can be attributed to the partial occupancy of the B atom in the CBC units. Close Sc–Sc contacts, from ˚ , are measured, comparable to those in Sc2BC2. 3.194 to 3.331 A


302 249

TABLE 36 Atomic Parameters for Sc3B0.75C3 Atom

Site

x

y

z

Sc1

2h

1/2

1/2

0.2812

Sc2

1a

0

0

0

C1

1c

1/2

1/2

0

C2

2g

0

0

0.315

a

1b

0

0

1/2

B

˚ , c ¼ 6.6737 A ˚ [23]. P4/mmm, a ¼ 3.331 A a Occ. ¼ 0.75.

FIG. 68 Crystal structure of Sc3B0.75C3. [Sc10] bicapped square prismatic polyhedron and [Sc6] octahedron are emphasized.

A second example of R3BC3 phase is Lu3BC3, which crystallizes in the space group Cmcm (Table 37) [80]. Its crystal structure contains discrete carbon atoms and linear CBC entities in slightly distorted octahedral and bicapped cubes of metal atoms, respectively, which form a 3D array resulting from distorted square nets packed in the [001] direction (Fig. 69). The average ˚ , compared to that of elemental Lu, indiLu–Lu distance is rather long, 3.44 A ˚ in cating some weak bonding interactions. Short B–C separations of 1.446 A


TABLE 37 Atomic Parameters for Lu3BC3 Atom

Site

x

y

z

Lu1

4c

0

0.09165

1/4

Lu2

8f

0

0.58557

0.39605

C1

4c

0

0.5950

0.2500

B1

4a

0

0

1/2

C2

8f

0

0.0959

0.4129

˚ , b ¼ 5.0109 A˚, c ¼ 15.669 A˚ [80]. SG Cmcm, a ¼ 4.9788 A

FIG. 69 Crystal structure of Lu3BC3.

the BC2 chains are indicative of double bonds. Similar linear BC2 entities with comparable B–C distances exist in many other metal boride carbide compounds such as for instance Sc3B0.75C3, R4B3C4, R25B14C26, Sc2BC2, and R5B2C5 described earlier. An ionic bonding picture suggests the formal


302 251

charge distribution (Lu3+)3([BC2]5)(C4), i.e., with a fully oxidized metal. This is in agreement with theoretical DFT calculations, which show a hole in the DOS at the Fermi level and with resistivity measurements, which indicate that Lu3BC3 is a poor metal [80]. The electronic structure of Lu3BC3 was compared to that of the other ternary metal borocarbide compounds Sc2BC2 and Al3BC3 which all contain linear BC2 units using DFT calculations. Results reveal covalent bonding between the metallic matrix and the formally (BC2)5 nonmetal anions, which is stronger for the aluminum compound than for the two others [184].

4.4.11 The R15B4C14 and Related Phases 4.4.11.1 Structural Properties of R15B4C14 Bauer and Nowotny [1] obtained the phase “Y15C19” by adding only 5–10 at.% of boron. Later, the compounds Y3C4xBx [96], Gd3C4xBx [185], and Ho3 C4 xBx [186] were found to be closely related to the binary carbide Sc3C4 [96], although crystal structure investigations were not performed. Strongly related ternary compounds are Er15B4C16 [75] and R15B4C14 (R ¼ Y, Gd–Lu) [33]. Atomic parameters for Tb15B4C14 are given in Table 38. A ternary compound of this family Er15B4C16, which belongs to the Sc3C4structure type, was found [75]. In the structure of Er15B4C16 the chains of octahedra along [001] are filled alternatively with isolated C atoms and C2 dumbbells. The CBC units are located inside distorted bicapped square antiprisms. The crystal structure of the ternary compounds R15B4C14 (Table 1; Fig. 70) was investigated by Babizhetskyy et al. [33] and is closely related to the Sc3C4 type. Atomic parameters for Tb15B4C14 are presented in Table 38.


Site

Occ.

x

y

z

Tb1

2a

1.00

0

0

0

Tb2

4e

0.906

0

0

0.3138

Tb3

8h

1.00

0.39895

0.19203

0

Tb4

16i

1.00

0.10162

0.29591

0.14938

Tb5

4e

0.094

0

0

0.3434

C1

4e

1.00

0

0

0.162

C2

8h

1.00

0.696

0.103

0

C3

16i

1.00

0.401

0.199

0.1671

B1

8g

1.00

0.345

0.155

1/4

SG P4/mnc, a ¼ 8.1251 A˚, c ¼ 15.861 A˚ [33].


FIG. 70 Crystal structure of R15B4C14.

The crystal structure of R15B4C14, such as Tb15B4C14, is composed from two kinds of slabs formed from bilayers of metal atoms with nonmetal atoms in between (Fig. 70). This leads to the formation of distorted octahedral and bicapped square-antiprismatic cavities where isolated carbon atoms and nearly linear CBC chains (C–B–C ¼ 174.9°) are encapsulated. B–C distances ˚ are characteristic of B–C double bonds. Note that the presence of of 1.438 A both single carbon atoms and CBC units is a common structural feature of a few ternary rare-earth metal boride carbides rich in carbon (Gd5B2C5 [47], Tb10B7C10 [30], etc.). The main difference between Tb15B4C14 and related Sc3C4-type structure lies in the fact that there are empty octahedral voids in the former, which are occupied by C2 dumbbells in the latter. In the related ternary compound Er15B4C16, chains of octahedra are filled alternatively with isolated C atoms and C2 units, and distorted bicapped square antiprisms accommodate nearly linear CBC chains. The electronic structure of R15B4C14 corresponds to the electron partitioning (R3+)15([BC2]5)4(C4)6.e, giving rise to a single metallic electron which, according to EH-TB calculations performed on Tb15B4C14, occupies the bottom of the conduction band [33]. 4.4.11.2 Physical Properties of R15B4C14 and Related “R3BxC42x” Compounds The yttrium compound Y3B0.2C3.8, which can be stabilized by adding 5 at.% boron, is a Pauli-type paramagnet [184]. Magnetic properties of other

302 253


“R3BxC4x” (R ¼ Gd, Ho) phases were investigated by Bidaud et al. [185]. Partial replacement of carbon by boron in the pseudobinary system Ho3BxC4x has a strong impact on the magnetic behavior of this compound (see Table 39): (i) the magnetic order at low temperature is ferromagnetic, (ii) the Curie temperature is strongly increased with increasing boron concentration, and (iii) the magnetic anisotropy is enhanced with increasing x. For the Gd3BxC4x phases, at the composition Gd3B0.56C3.44 the reciprocal magnetic susceptibility vs temperature obeys the Curie–Weiss law. The effective moments together with yp are listed in Table 39. Below TC ¼ 159 K the compound orders ferromagnetically. The magnetic ground state of Gd3B0.56C3.44 resembles a spin-glass-like or a cluster-glass-like structure in very low external fields, whereas in increasing fields a reorientation of the spin system toward a collinear spin arrangement is easily induced [185]. The results of the magnetic measurements of the compounds with idealized formulae R15B4C14 (R ¼ Tb, Dy, Er) are summarized in Table 40 and Figs. 71–73 [33]. For the paramagnetic regime (T > 200 K) the magnetic susceptibility data, measured in a 7 T external field, were fitted according to a simple linear Curie–Weiss law shown as solid and dashed lines in Figs. 71–73. The derived values of the effective moments, meff, agree well with the theoretical moments of the R3+ ions and are listed together with the asymptotic paramagnetic Weiss temperatures, yp, in Table 40.

TABLE 39 Magnetic Data of R3BxC42x (R 5 Gd, Ho; 0 ≤ x < 1) [185] Composition

TC (K)

up (K)

meff (mB)

mS (mB)

Gd3B0.56C3.44

159

219.8

7.8

7.1

Ho3B0.35C3.65

24

19.0

10.0

5.6

Ho3B0.8C3.2

35

38.7

10.5

6.4

“Ho3BC3”

33

TABLE 40 Magnetic Data of R15B4C14 (R 5 Tb, Dy, Er) [33] meff (mB)

up (K)

TC (K)

mS (mB)

MS (Am2/kg)

MR (Am2/kg)

BC (T)

Tb15B4C14

9.8

140.9

145

6.4

207

172

1.95

Dy15B4C14

10.6

121.4

120

6.5

206

189

3.15

Er15B4C14

9.3

41.8

50

6.4

197

93

0.48

Compound


FIG. 71 Reciprocal magnetic susceptibility vs temperature for Tb15B4C14. Solid and dashed line represents the Curie–Weiss fit. Inset: Isothermal magnetization vs applied field at T ¼ 2 K.

FIG. 72 Reciprocal susceptibility vs temperature for Dy15B4C14. Solid and dashed line represents the Curie–Weiss fit. Inset: Isothermal magnetization vs applied field at T ¼ 2 K.

At temperatures lower than 150 K, all three compounds order ferromagnetically (Table 40). The temperature dependencies of the magnetization M(T) for R15B4C14 (R ¼ Tb, Dy, Er) reveal pronounced differences in the zfc data measured with rising temperatures and the fc data. The origin of such a behavior is due to the presence of narrow domain walls. At the lowest temperature


302 255

FIG. 73 Reciprocal susceptibility vs temperature for Er15B4C14. Solid and dashed line represents the Curie–Weiss fit. Inset: Isothermal magnetization vs applied field at T ¼ 2 K.

the net magnetization of the zfc samples is small due to the fact that the thermal energy is not sufficient to move the narrow walls. M(T) strongly rises with increasing temperatures, passes a maximum, and falls off near the Curie temperature, TC. The isothermal magnetization plots at T ¼ 2 K presented in the insets of Figs. 71–73 prove the presence of narrow walls by practically field independence of the first part of the initial magnetization curve. The values of the saturation moments, mS, are listed together with the values of the coercive fields BC and the remnant magnetization MR in Table 40. The reduced values for mS 2/3 gJ are attributed to the magnetic anisotropy (easy plane or easy axis) in bulk samples. The magnetic hardness is due to the presence of narrow domain walls. Hence, it has to be assumed that the boron atoms act as pinning centers for the walls.

4.4.12 The R2BC Phases 4.4.12.1 Structural Properties of R2BC The crystal structures of R2BC (R ¼ Pr, Nd) were determined from singlecrystal X-ray diffraction data [52,56,57]. They crystallize in the monoclinic space group C2/m. The cell parameters and the atomic parameters are given in Table 41 for Nd2BC. In this crystal structure the metal atoms form a 3D framework resulting from the stacking of slightly corrugated 2D square nets (Fig. 74). This stacking creates pairs of capped trigonal prisms sharing square faces where puckered CBBC chains (C–B–B ¼ 134°) are embedded. The boron atoms center the trigonal prisms, whereas the carbon atoms are located in ˚ , respectively) tetragonal pyramids. C–B and B–B distances (1.51 and 1.65 A


TABLE 41 Atomic Parameters for Pr2BC Atom

Site

x

y

z

Nd1

4i

0.79726

0

0.38291

Nd2

4i

0.43498

0

0.14037

C

4i

0.874

0

0.697

B

4i

0.576

1/2

0.106

˚ , c ¼ 9.398 A˚, b ¼ 130.43° [56]. SG C2/m, a ¼ 12.732 A˚, b ¼ 3.684 A

FIG. 74 Projection of the structure of Nd2BC along [010]. The unit cell is outlined.

suggest B–C double-bond and B–B single-bond characters. Using the Zintl– Klemm approach, Nd2BC can be described as (Nd3+)4(B2C2)8.4e, i.e., with extra electrons located in the conduction band formed by the 5d orbitals of Nd mixed with B2C2 antibonding p* orbitals. DFT calculations support this statement and suggest metallic behavior [56]. Interestingly, the (B2C2)8 chains are isoelectronic to trans-butadiene. This kind of puckered B2C2 chain is encountered only in R2BC compounds. 4.4.12.2

Physical Properties of R2BC

Extrapolation of the magnetic moment obtained from the measured magnetic susceptibility at high temperatures [56] leads to 3.65 mB per Nd atom in Nd2BC, in good agreement with the expected value of 3.62 mB for Nd with 4f3 configuration (see Fig. 75). This curve also shows that an extrapolation according to the Curie–Weiss law gives a positive yp value of around 18 K corresponding to dominantly ferromagnetic interaction, and Nd2BC orders ferromagnetically around 40 K.


302 257

FIG. 75 Temperature dependence of the inverse molar magnetic susceptibility of Nd2BC € measured at 1 T. Adapted from V. Babizhetskyy, J. Kohler, Hj. Mattausch, A. Simon, Synthesis, structure and properties of Nd2BC containing the trans-dibora-(1,3)-butadiene [C ¼B-B¼C]8-unit, Z. Kristallogr. 226 (2011) 93–98. Copyright (2011) De Gruyter.

5 COVALENT METAL-TO-NONMETAL BONDING IN RXBYCZ COMPOUNDS We have seen above that a simple Zintl–Klemm ionic bonding scheme between metal cations and nonmetal anions is sufficient to rationalize rather easily the structure and bonding within the B/C framework encountered in the rare-earth metal boride carbide compounds. Indeed, the B/C network can often be described with the help of simple Lewis formulae in which the atoms generally satisfy the octet rule [5,7,8]. In the case of compounds containing extended 2D or 1D nonmetallic networks, the metal atoms are generally fully or almost fully oxidized. This is different in the case of compounds containing finite B/C chains, where the metal atoms are often in an oxidation state close to 2+ rather 3+. Must we conclude that metal–nonmetal covalency is absent in these compounds? Not at all. Indeed, these compounds show a significant degree of metal–nonmetal covalent bonding character, in which the outer electron clouds of the boron–carbon anions are polarized toward the metal cations. As a consequence, the existence of various B/C arrangements, which are encountered, is due to the presence of the metal atoms, which act as stabilizing agents through metal–nonmetal bonding interactions. Theoretical calculations performed on a fairly large number of RxByCz compounds all indicate a significant back electron transfer from the nonmetal anionic framework to that of the metal cations. The highest occupied levels of the boron–carbon moieties, which are nonbonding and/or p-bonding, are stabilized by metal– metal bonding levels of the bottom of the d band of the metal matrix, which is empty or weakly occupied. This is illustrated in Fig. 76. Through-bond interactions explain the presence of metal–metal bonding in these compounds even when the metal atoms are formally fully oxidized. In the cases where the metal


FIG. 76 Simplified electronic band structure diagram of RxByCz compounds resulting from the interaction between the d band of the metal sublattice and the bands of the anionic B/C sublattice.

atoms are not fully oxidized, the occupation of the bottom of the d band also contributes to metal–metal bonding as well as to the electron transport properties in these compounds—nearly all are metallic in character.

6 CONCLUSIONS More than 140 rare-earth and actinoid metal boride carbides have been reported and at least partially characterized to date. They crystallize with 38 different structure types and display a large range of stoichiometries. They show a surprising variety of stable B/C arrangements ranging from 2D to 1D to 0D networks embedded in the metal atom sublattice, which are not observed among carbides, silicides, germanides, borides, aluminides, or gallides. Apart from a few boron-rich compounds such as RB17C0.25 and related structures, the rare-earth metal boride carbides, which were characterized, have been reported with a maximum of 50 at.% rare-earth metal content. Some ternary systems exhibit extended solid solutions such as La5(BC)x (5.6 x 8.8). Phase analytical investigations at different annealing temperatures should certainly give access further to new rare-earth metal-rich phases. Compared to large numbers of ternary rare earth–transition metal carbides and borides, which are known (more than 400 and 850, respectively), ternary boron–carbon rare-earth metal systems certainly have a great potential for many more phases to be discovered. Unambiguous location of C vs B in the boron–carbon units is often difficult from X-ray measurements. A few studies have shown that HRTEM and neutron and electron diffraction investigations can give supplementary information about the formation and the crystal structure of rare-earth metal boride carbides.


302 259

An electronic and structural analysis has shown that the attractive architectures formed by the boron–carbon sublattice are dominated by three families which can be systematized on the basis of the VEC per main group atom considering an ionic Zintl–Klemm approach. A peculiar interplay between metals and nonmetals results in varied properties, which can be “tuned” by stoichiometry. However, they have been mostly studied as crystallographic oddities so far. Despite the efforts made in the area over the past 50 years, the applications of rare-earth metal boride carbides have been extremely limited. In addition to structural and magnetic properties, which have been well investigated, it remains to be seen if other properties such as mechanical, thermoelectric, or catalytic, for instance, would be worthy of attention for possible applications. It is why the chemistry of rare-earth metal boride carbides should continue to be considered as a vivid area of research in the future.

ABBREVIATIONS 1D 2D 3D a, b, c, a, b, g AFM AFQ at.% B BSC C CEF Dt DFT DOS E EH EH-TB EPMA fc HRTEM ICF kB LT M N

one-dimensional two-dimensional three-dimensional unit cell parameters antiferromagnetic antiferroquadrupolar ordering atomic percent magnetic field vector Bardeen–Cooper–Schrieffer superconducting theory specific heat crystal electric field thermal diffusivity constant density functional theory density of states electric field vector extended H€ uckel extended H€ uckel tight binding electron probe microanalysis field cooling high-resolution transmission electron microscopy inertial confinement fusion Boltzmann constant low temperature magnetization number of spins


NA NMR R RKKY SG ST T T0 TC Tc Tf TN TQ V VEC WDX zfc x «F g mB meff mSR r

Avogadro number nuclear magnetic resonance rare earth Ruderman–Kittel–Kasuya–Yoshida space group structure type temperature characteristic temperature of variable range hopping Curie temperature critical temperature peak temperature of the zero field-cooled susceptibility in spin glasses Neel temperature characteristic temperature of antiferroquadrupolar ordering unit cell volume valence electron concentration wavelength-dispersive X-ray spectroscopy zero field cooling magnetic susceptibility Fermi energy electronic specific heat coefficient Bohr magneton effective paramagnetic moment muon spin relaxation electrical resistivity

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