Crystal structure redetermination of ε-Ni3Si2

Journal of Alloys and Compounds 672 (2016) 505e509

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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom

Crystal structure redetermination of ε-Ni3Si2 from a single nanowire by dynamical refinement of precession electron diffraction data â a, b, *, Mariana Klementova a, Vladislav Drínek c, Jaromír Kope Cinthia Antunes Corre cek d, s Palatinus a, ** Luka 112, Prague, 162 00, Czech Republic Institute of Physics of the Academy of Sciences of the Czech Republic, Cukrovarnicka Department of Physics of Materials, Charles University in Prague, Ke Karlovu 5, Prague, 121 16, Czech Republic c 1, Prague, 165 Department of Analytical and Material Chemistry, Institute of Chemical Process Fundamentals of the Czech Academy of Sciences, Rozvojova 02, Czech Republic d Institute of Physics of the Academy of Sciences of the Czech Republic, Na Slovance 2, Prague, 182 21, Czech Republic a

b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 6 October 2015 Received in revised form 19 February 2016 Accepted 21 February 2016 Available online 24 February 2016

Accurate crystal structure of single nanocrystals as small as tens of nanometers can be obtained by the recently published full dynamical structure refinement of precession electron diffraction tomography (PEDT) data. Here we apply the method to the structure redetermination of the nickel silicide ε-Ni3Si2 from a nanowire with the diameter of 35 nm. The structure was determined as centrosymmetric Cmcm, in disagreement with the published structure, which was determined by single crystal X-ray diffraction in 1961 in the noncentrosymmetric space group Cmc21. The structure was also determined by single crystal X-ray diffraction (SCXRD), giving the same results as PEDT. The average difference of the atomic positions between the models obtained by PEDT and SCXRD was smaller than 0.007 Å. © 2016 Elsevier B.V. All rights reserved.

Keywords: Precession electron diffraction tomography Structure determination Nanowire Dynamical refinement

1. Introduction Given the wide scope of application of nanomaterials, their accelerated development, and the correlation between structure and properties, accurate crystal structure determination of single nanocrystals becomes increasingly important. Structure information of single crystals as small as tens of nanometers can be obtained by electron diffraction (ED), which went through fast development in the last decade [1e6] with the introduction of electron diffraction tomography (EDT) [7,8]. EDT allows collecting three-dimensional diffraction data from single nanocrystals following a methodology comparable to the single crystal X-ray diffraction (SCXRD). However, the interaction between the electron beam and the sample is much stronger than for X-ray (about a thousand times) and the beam suffers multiple scattering while passing through the sample. This complicates the

* Corresponding author. ** Corresponding author. â), [email protected] E-mail addresses: [email protected] (C.A. Corre (M. Klementov a), [email protected] (V. Drínek), [email protected] (J. Kope cek), [email protected] (L. Palatinus). http://dx.doi.org/10.1016/j.jallcom.2016.02.190 0925-8388/© 2016 Elsevier B.V. All rights reserved.

interpretation of the diffracted intensities, because a proper description of the electron diffraction requires the use of dynamical diffraction theory. Thereby, the kinematical approximation (where IgfjFgj2), widely used for the refinement of structure parameters of X-ray diffraction data, is not completely appropriate for structure refinement against electron diffraction data. Precession electron diffraction (PED) [9,10] is a procedure used for suppressing the dynamical character of the ED [11e14] and to reduce the sensitivity of the intensities to the thickness and orientation of the sample [15]. In PED, the incident beam is precessed along a cone whose vertex is at the sample surface and the intensities are integrated over all the positions of the beam. Data sets collected using precession electron diffraction tomography (PEDT) provide intensities closer to the kinematical limit, and allow reliable ab initio structure solution. However, least squares refinement against such data still provides structure parameters with low accuracy and high residue factors. In order to improve the accuracy of the structure parameters, dynamical diffraction effects must be considered for electron diffraction data sets. Until very recently the lack of a general routine to analyze the structures considering the dynamical theory for non-oriented diffraction patterns of EDT data (either combined or not with precession) prevented the wide use of the technique and the

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kinematical approximation was used for the structure refinement. Full dynamical refinement against (P)EDT data [16,17] enables the remarkable possibility of structure analysis of single nanocrystals with few tens of nanometers in size, giving accurate structure parameters with small deviation from what can be obtained by the widely used single crystal X-ray diffraction. To our knowledge, the only routine that allows the full dynamical refinement for (P)EDT data sets is implemented within the crystallographic software Jana2006 [18]. The objective of this work is to use the full dynamical refinement against PEDT data to accurately determine the structure of ε-Ni3Si2 on a nanowire with the diameter of 35 nm, and to demonstrate the accuracy of the result by comparing it with a model obtained from single crystal X-ray diffraction data. Silicide nanowires (NWs) are of great interest for diverse application in nanoscale electronics, photonic, sensor and photovoltaic devices. Therefore, synthesis and properties of silicide NWs have been increasingly studied [19e24]. Within the transition metal silicides, nickel silicides are used as contacts to CMOS devices in the source, drain and gate, due to the low Si consumption, low electrical resistivity, adequate work function and formation controlled by Ni diffusion [25,26]. Nickel silicide has six stable phases at room temperature [27]. The ε-Ni3Si2 phase is obtained during the reaction of d-Ni2Si and NiSi [28e30] and it has potential application in micro and nano-sized electronic devices [31], such as Li-ion batteries [32] and photovoltaic devices [24,33,34]. The only structure determination of ε-Ni3Si2 available in the literature dates to 1961 [35], when the space group was identified to be Cmc21. In this work we demonstrate that the assignment of the noncentrosymmetric space group Cmc21 is incorrect and that the correct space group is Cmcm. 2. Material and methods 2.1. Sample preparation Nanowires grown by chemical vapor deposition (CVD) using the precursor SiH4 over Ni substrate at 500 C and 110 Pa (Fig. 1) were suspended in ethanol and dropped on a Cu grid covered with carbon foil. PEDT measurement was performed in a transmission electron microscope (TEM) Philips CM120, with a LaB6 cathode at acceleration voltage of 120 kV. The TEM is equipped with the precession device NanoMegas DigiStar, a CCD camera Olympus SIS Veleta, 2048 2048 pixels 14-bits dynamic range and an energydispersive analyzer Octane silicon drift detector (SDD) EDAX. Automated electron diffraction tomography was performed using the in-house module RATS, which reduces the exposure time of the sample under the beam and optimizes the total measurement

Fig. 1. Left: SEM image of the Ni substrate covered with the Ni3Si2 nanowires grown by CVD. Right: A TEM image of the nanowire used for the data collection. The diameter of the nanowire is 35 nm. The inset shows an image of the illuminated part of the nanowire, which was recorded during the data acquisition.

time. The tilt series was collected with a step of 1, from 56 to 55 , giving a total of 112 frames. The data collection time was 30 min. The selected crystal had the diameter of 35 nm, total length of 1 mm. The length of the illuminated part of the nanowire was 150 nm (Fig. 1). Parameters of the PEDT measurement are shown in Table 1. The bulk sample for single crystal X-ray diffraction was prepared from pure elements by arc melting under the argon atmosphere. The melting was repeated 5 times for homogenization. The sample has rough casting microstructure with grains elongated in the direction of the thermal gradient and few voids are present between grains. Border parts of the sample contain eutectic mixture of ε-Ni3Si2 with the admixture of d-Ni2Si. The characterization was done using Tescan FERA 3 microscope with EDAX Octane 80 mm2 EDS detector. The SCXRD data was collected on a single crystal with dimensions 0.101 0.065 0.044 mm3, in an Agilent Xcalibur Gemini Ultra diffractometer with an Atlas detector. Details of the X-ray single crystal measurement are shown in Table 2. 2.2. Data processing and structure solution Intensities obtained by EDT must be extracted from ED patterns to be used in the structure solution, which was done using PETS [36]. The unit cell was determined in the graphic interface of Jana2006 and the orientation matrix was used in PETS to integrate the intensities. PETS creates a file containing a list of reflection indices and intensities, suitable for further processing by standard crystallographic software. The structure could be easily solved from both datasets (SCXRD and PEDT) using the program Superflip [37] interfaced from Jana2006. Symmetry analysis of the solution [38] suggested in both cases the space group Cmcm. Since SCRXD is a well established technique and because of the low residue values obtained during the refinement, the model obtained by SCXRD was considered suitable to be used as the reference during the comparison to the model from PEDT data. The agreement between the PEDT and SCXRD models was evaluated using the average distance from the reference atomic position (ADRA) and on the maximum distance from the reference atomic position (MDRA). 2.3. Structure refinement 2.3.1. PEDT For the kinematical refinement, the intensities are integrated across the diffraction patterns, giving the total intensity of each reflection. The kinematical approximation is used for the calculated intensities during the refinement of the structure parameters. In dynamical refinement each diffraction pattern has its intensities integrated individually. The reflections considered during the refinement are selected according to their distance to Bragg condition. For this, several parameters are used, which influence the dynamical refinement as explained in detail in Refs. [15e17]. Within these parameters, the thickness and orientation of the crystal play important role and are optimized prior to the refinement of the structure. In Ref. [17] a set of test refinements was used to establish the recommended values of the parameters of the dynamical refinement. We shortly review the main aspects here, because it is important for understanding the procedure of the dynamical refinement. The selection of the intensities used during the refinement is max done with the maximal excitation error Sg (data) and the ratio RSg ¼ S0g =jgfj. The selection for the calculated intensities which will be considered in the structure matrix A uses the diffraction


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Table 1 Experimental details of the PEDT data collection. *Unit cell parameters from EDT are known to have distortions and lower accuracy [8,40]. Crystal data Chemical formula Crystal system, space group a, b, c (Å) Vuc (Å3) Z l (Å) Diameter length (nm2) Length illuminated by the beam (nm) Density (g.cm3)

Ni3Si2 Orthorhombic, Cmcm 12.35, 10.92, 6.98* 940.998 16 0.0335 35 1000 150 6.5572

Data collection Temperature (K) hmin hmax, kmin kmax, lmin lmax Resolution (Å) No of recorded frames Precession angle 4 ( ) Completeness (%), qfull ( ) No. of measured, independent and observed reflections [I > 3s(I)]

293 15 14, 15 15, 9 9 0.7163 112 2.0 82.00, 0.95 25248, 8250, 4681

Dynamical Refinement (anisotropic atomic displacement parameters) R1[F2 > 3s(F2)], wR(F), GOF (obs/all) (%) No. of refined parameters

8.23/13.48, 8.04/9.70, 2.37/2.16 170

vector g, and the maximal excitation error Smax (matrix). g A number of test cases [17] allowed identifying the optimal settings for most of the parameters of the method. It was shown that the refinement is largely insensitive to most parameters, max (data) except for Smax (data) and Rmax g Sg . It was shown that Sg should be set effectively to infinity, and the parameter Rmax to Sg 0.4. Here, Rmax was tested in the range from 0.2 to 2.0. The lowest Sg ADRA was found for Rmax Sg ¼ 0.4 (Supplementary Material Fig. S1), in agreement with [17]. The parameters used for the dynamical refinement were, therefore, used at the recommended values: Nsteps ¼ 128, g ¼ 2 Å1, Smax (matrix) ¼ 0.01 Å1, g 1 max max Sg (data) ¼ 0.1 Å and RSg ¼ 0.4. With these parameters, 8250 reflections were obtained for the refinement of the structure parameters. There were 139 parameters to be refined for the refinement with isotropic atomic displacement parameters (ADP), and 170 parameters for the refinement with anisotropic displacement parameters. For both cases the ratio of observed reflections per

parameter was larger than 25. Since the crystal was a nanowire lying roughly along the tilt axis, the thickness of the crystal was constrained to be constant for all frames and there was no correction of the thickness due to crystal tilt during the refinement. One frame with deviation of orientation higher than 0.5 was removed from the refinement. The high misorientation of this frame might have been caused by one stronger reflection, which may have hampered the procedure of orientation optimization. This behavior was also observed for other samples in Ref. [17]. 2.3.2. X-ray The least-squares refinement was performed in Jana2006 based on the structure factors F and weight w ¼ 1/ (s2(F) þ 0.0001F2). There were 676 independent reflections, from which 609 had I > 3s(I), for the refinement of 59 parameters (considering anisotropic ADPs). Details of the refinement are shown in Table 2.

Table 2 Experimental details of the single crystal X-ray data collection. Crystal data Chemical formula Crystal system, space group a, b, c (Å) Vuc (Å3) Z l (Å) (Mo Ka) Specimen size (mm3) Density (g.cm3) m (mm1)

Ni3Si2 Orthorhombic, Cmcm 12.2174(9), 10.8014(7), 6.9222(4) 913.49(10) 16 0.71073 0.101 0.065 0.044 6.7547 25.099

Data collection Temperature (K) hmax kmax lmax Resolution (Å) Absorption correction Tmax, Tmin Rint(obs/all) (%) Completeness (%), qfull ( ) No. of measured, independent and observed reflections [I > 3s(I)]

300.00(10) 15 14 9 0.7280 Analytical [CrysAlis Pro [41], based on crystal shape]. 0.489 0.212 3.81/3.87 98.00, 28.88 7705, 676, 609

Refinement R1[F2 > 3s(F2)], wR(F), GOF (obs/all) (%) Drmax, Drmin (e Å3) No. of refined parameters

1.65/2.21, 1.98/2.14, 1.19/1.21 0.52 0.58 59


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3. Results and discussion 3.1. PEDT The dynamical refinement against PEDT data gave structure parameters with the precision approaching that of the refinement against the SCXR data. The standard deviation of the parameters obtained by the dynamical refinement were 2e5 times the standard deviation of the parameters from SCXR, in average sPEDT ¼ 3sSCXRD. The average and maximum distances comparing to the X-ray structure were ADRA ¼ 0.00647 Å and MDRA ¼ 0.01402 Å. Within the 17 pairs of atomic coordinates compared, 5 had differences in relation to their standard uncertainties over 3s and the maximum was 7.5s (Supplementary Material Table S1). The refinement of the anisotropic atomic displacements slightly improved the R1 value (R1iso ¼ 8.45% and R1aniso ¼ 8.23%), and maintained ADRA without considerable changes (ADRAiso ¼ 0.00647 Å and ADRAaniso ¼ 0.00666 Å) (Table 3). The superposition of the PEDT model and the SCXRD model presented in Fig. S2 (Image generated with Diamond [39]) from the Supplementary material clearly shows the good agreement between the atomic positions (Supplementary Material Table S1) and the atomic displacement parameters (Supplementary Material Table S2). It is also important to note the improvement of the structure accuracy by the dynamical refinement over the kinematical, which can be directly seen from ADRA, MDRA and from the residue values. Note that the kinematical refinement already gave a good result, most probably due to the small dimensions of the nanowire. Nevertheless, the dynamical refinement still improved the results. ADRA decreased from ADRAkin ¼ 0.01634 Å to ADRAdyn ¼ 0.00647 Å and R1 decreased from 17.95% to 8.45% (Table 3). Kinematical refinement against PEDT data resulted in 1 atom with negative definite isotropic ADP and 6 atoms with negative definite anisotropic ADPs, while the dynamical refinement had all positive definite ADPs. In general, dynamical refinement gave ADPs closer to those obtained by SCXRD than the ones from kinematical refinement (Supplementary Material Table S2). The kinematical

refinement resulted in 3 pairs with differences higher than 3s and maximum difference 4.0s (7.5s for the dynamical refinement) (Supplementary Material Table S3). However, the uncertainties from the parameters refined by the kinematical refinement were about 5 times larger than those from the dynamical refinement. The largest difference in fractional coordinates was 0.0044 for kinematical refinement and 0.0010 for the dynamical refinement. In order to compare with the structure from the literature, the model from the dynamical refinement (with isotropic ADPs) was transformed to Cmc21. Three out of the 10 independent atoms of the structure lost equivalence due to lack of the center of symmetry. The difference can be seen in the Supplementary Material Fig. S3. The refinement of this Cmc21 model resulted in 9 atomic parameters with correlation larger than 0.7, and R1 and wR were almost iso the same (R1iso Cmcm (obs) ¼ 8.45% to R1Cmc21 (obs) ¼ 8.44%, and iso iso wRCmcm (all) ¼ 9.98% to wRCmc21 (all) ¼ 9.97%). Hence, the transformation does not bring any improvement to the fit and Cmcm is indeed the best space group for the description of this structure. 3.2. X-ray The correctness of the structure was also verified through the transformation of the model obtained by SCXRD from Cmcm to Cmc21. The refinement of the model in the noncentrosymmetric space group increased the R1 value (R1Cmcm(obs) ¼ 1.65%, R1Cmc21 (obs) ¼ 1.77%). Also, more than 20 atomic correlations were higher than 0.9 for atomic parameters of the atoms which should be related by the center of symmetry in the model Cmcm. 4. Conclusions The recently developed full dynamical refinement against PEDT data allowed accurate structure redetermination of the transition metal silicide ε-Ni3Si2 from a single nanowire with the diameter of 35 nm and the length under the beam of about 150 nm. The structure had a good match with the model obtained by single crystal X-ray diffraction, giving an average distance to the atomic positions of the X-ray model of 0.00647 Å. The structure was shown to be centrosymmetric Cmcm, in disagreement with the published

Table 3 Residue values and atomic distances and ADRA compared to the X-ray model, for kinematical and full dynamical PEDT refinements (isotropic and anisotropic atomic displacements). Parameter

Kinematical

Kinematical(aniso)

Dynamical

Dynamical(aniso)

R1(obs) (%)a wR(all) (%)b GOF(all) (%)c Nrefl(obs) Nrefl(all) Nparameters

17.95 21.34 12.82 549 571 28

17.12 20.03 12.39 549 571 59

8.45 9.98 2.22 4681 8250 139

8.23 9.70 2.16 4681 8250 170

Distance to the atomic position from the X-ray model (Å) Ni2eNi2 Ni3eNi3 Ni4eNi4 Ni5eNi5 Ni6eNi6 Ni8eNi8 Si1eSi1 Si2eSi2 Si4eSi4 Si5eSi5

0.01088 0.00933 0.01324 0 0.02121 0.00106 0.03367 0.01058 0.04820 0.01523

0.00735 0.00452 0.00947 0 0.01817 0.00185 0.02742 0.01481 0.04901 0.01493

0.00353 0.00612 0.01402 0 0.01298 0.00559 0.00288 0.01386 0.00222 0.00352

0.00310 0.00598 0.01538 0 0.01321 0.00639 0.00410 0.01225 0.00294 0.00328

0.01634 P P R1 ¼ jjFo j jFc jj= jFo j. P P wR ¼ ½ wðFo2 Fc2 Þ2 = wðFo2 Þ2 1=2 . P GOF ¼ ½ wðFo2 Fc2 Þ2 =Nref Npar 1=2 .

0.01475

0.00647

0.00666

ADRA a b c


structure determined in 1961 as Cmc21. In this way, dynamical refinement against PEDT data opens the remarkable possibility of routine structure analysis of nanocrystals, giving accurate structure parameters with lower residue factors and much higher accuracy compared to the ones obtained by the kinematical refinement, with the advantage of using single crystals with dimension well below 1 mm.

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Acknowledgments

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This project is financially supported by the Czech Science Foundation, project number 13-25747S. Appendix A. Supplementary data

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Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.jallcom.2016.02.190.

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