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University of Cambridge, Department of Earth Sciences, Downing Street, Cambridge CB2 3EQ, UK ... The reflections were analysed using a wall profile e = eotanh (r~ w), where w is the effective wall ..... T. Wolf and R. Fltikinger, N. Jhb. Min..\hh.
PHYSICA PhysicaC225 (1994) 111-116

EI~qEVIER

Thin domain walls in YBa2Cu307_~and their rocking curves An X-ray diffraction study J. C h r o s c h

,,b,., E . K . H . S a l j e ,,b

" University of Cambridge, Department of Earth Sciences, Downing Street, Cambridge CB2 3EQ, UK b 1RC in Superconductivity, Madingley Road, Cambridge CB30HE, UK

Received 1 March 1994

Abstract

Twin walls were investigated of single crystals of the high-To superconductor YBa2Cu307_6 (YBCO) using a high-resolution X-ray diffractometer. Rocking curves were recorded for the (029) / (209), (02.10) / (20.10), and (02.11 ) / (20.11 ) pairs of Bragg peaks. The reflections were analysed using a wall profile e = eotanh (r~ w), where w is the effective wall thickness and r the distance from the wall centre. The wall thickness was determined to be 7 A +_2 ,~.

1. In~oducfion

Twinning in YBCO is p r o d u c e d by a ferroelastic phase transition at about 750°C [1,2] or at lower t e m p e r a t u r e s in Co or Fe d o p e d samples [ 3,4 ]. During the structural transition from a tetragonal hight e m p e r a t u r e phase to an o r t h o r h o m b i c low- temperature phase twins spontaneously a p p e a r to compensate the internal strains. The resulting twin planes are d e t e r m i n e d by the lost space group element in the ferroelastic phase i.e., the diagonal m i r r o r planes {I 10} o f space group P 4 / m 2 / m 2 / m , so that two orientations o f twin boundaries, (110) and ( 1 i 0 ) , are observed [5]. The spontaneous strain eso = 2 ( a - b) / ( a + b) generates a spontaneous rotation 0 = 4 5 ° - a r c t a n ( a / b ) between the ferroelastic d o m a i n s [ 6 ]. Using the lattice constants o f the fully oxygenized orthorhombic phase a = 3.8206, b = 3 . 8 8 5 1 , and c = 1 1 . 6 7 5 7 A [7] one obtains the values for the spontaneous strain a n d the rotation: * Corresponding author.

esp ~ 1.67 × 10 -2 and 0 ~ 0.5 ° .

Fig. 1 shows the orientational relationship between the o r t h o r h o m b i c unit cell and the d o m a i n walls in YBCO. The structural nature o f the domains has been investigated previously using electron microscopic techniques [ 8-15 ].

5.49 .~

/

,10,

\ b Fig. 1. Orientational relationship between the orthorhombic phase of YBCO and the domain walls due to twinning.

0921-4534/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSD10921-4534 ( 94 ) 00132-Y

(1)

112

J. Chrosch, E.K.H. Salje / Physica C225 (1994) 111-116

The main motivation for the reinvestigation of the domain structure in YBCO lies in its potential effect on the superconducting transition temperature. On one hand the twins are likely to enhance Tc via the so called twinning-plane superconductivity [ 16-18 ] or via a different kind of interaction [ 19 ]. On the other hand they seem to act as pinning centres for magnetic-flux lines and thus increase the critical current density Jc [20-23]. In order to explore the microstructural features in YBCO from a different perspective we used high-resolution X-ray diffractometry to measure rocking curves on single crystals and determined the twin density and twin-wall thicknesses. 2. Experimental details

2.1. Sample characteristics

Large single crystals of YBCO (2 X 2 X 0.2 m m 3) were chosen from three different crystal-growth experiments. Their oxygen content was characterized by susceptibility measurements. As shown in Fig. 2 they possess a sharp (1 K) transition at Tc=92 K. Further criteria were visible domains in the polarizing microscope and nearly no bending of the crystal surface. The samples were mounted with plasticine or a drop of glycerine on a glass plate for the measurement of the rocking curves.

( 2 = 1.54059 A) was focussed on the surface of the sample with a focal diameter of 0.1 m m 2 and a distance between the monochromator and the sample of 450 m m [24]. Using a 120 ° (20) position-sensitive detector a 120 ° angular range was covered. The intensity changes were automatically registered in dependence of the angle of incidence (rocking angle) of the X-ray beam. For the measurement of the rocking curves the crystals were mounted in different orientations (Figs. 3 (a) and ( b ) ) with two scattering planes in diffraction condition. In the first orientation the (00l) peaks were used to adjust the specimen in its optimal position with respect to the X-ray beam before in a second step suitable Bragg peaks for the measurement of twin walls were chosen. Table 1 shows the list of split reflections used in this study, their diffraction angles

(a)

b

/

~

/

b °

c

2. 2. Diffraction experiments

The rocking curves were measured using the experimental arrangement in which Cu Kctt radiation 140

twin domains

a/b

I

GL~'r "t-rx Ht tff t t ~t x'r't-crx'r'r~-~q-~-(~-c(c~

120 1 O0 .~

80

~

6o

~

40

~'~

2O

twindomains

0 -20

0

210

410

i 60

i

80

rotation

i

1 O0

Temperature Fig. 2. AC susceptibilityvs. temperaturecurve for controlling the samples.

b/a

Fig. 3. Different orientations for X-raymeasurements: (a) (001 ) plane, (b) (100)/(010) planes.

J. Chrosch, E.K.H. Salje / Physica C225 (1994) 111-116 Table 1 Bragg-reflection pairs, diffraction angles 20, angles between (hM) and (001) (gt), and the resulting rocking angles (o9= 20/2-T- ~,)

(hkl)

20( ° )

~,(o)

~o( o)

(017) (107) (018) (108) (019) (109) (028) (208) (01.10) (10.10) (029) (209) (01.11) (10.11) (02.10) (20.10) (01.12) (10.12) (02.11) (20.11)

60.316 60.497 68.607 68.776 77.472 77.633 82.595 83.229 87.038 87.195 91.086 91.716 97.526 97.684 100.615 101.255 109.329 109.496 111.521 112.199

23.245 23.604 20.598 20.924 18.474 18.771 36.932 37.405 16.735 17.001 33.750 34.205 15.288 15.540 31.021 31.457 14.067 14.300 28.665 29.080

6.913 6.645 13.706 13.464 20.263 20.046 4.366 4.210 26.784 26.597 11.793 11.653 33.475 33.302 19.287 19.171 40.598 40.448 27.096 27.020

20, the respective angles between them and (001) (~), and the resulting rocking angles (co) which were used for the measurement. Here we mainly focussed on the ( 0 2 9 ) / ( 2 0 9 ) , (02.10)/(20.10), and (02.11 )/(20.11 ) diffraction signals because of the high diffraction intensity. In the last step these reflections were adjusted again by rotation and translation of the sample in order to achieve the maximum splitting between adjacent diffraction peaks. This optimisation was repeated for each reflection. The rocking curves were measured in steps of 0.01 ° in to with counting times between 30 and 120 s, and for various positions of the samples with respect to the incident beam.

3. Theoretical considerations In order to analyse the wall related diffraction pattern we considered a theoretical wall profile r

e=eo tanh - ,

(2)

w

where w is the effective wall thickness,

r=x/x/~

the

113

spatial coordinate in the [ 110 ] direction, and x parallel to [ 100 ] [ 8 ]. This profile corresponds to a displacement pattern

6y= f edr=Cln(cosh(w-~2)).

(3)

Considering a tetragonal Bragg peak (Okl), 8y splits the reflection in the (h + k) direction into two signals related to two orthorhombic twin orientations. In a 2D projection parallel to the c-axis this means that the diffraction (or rocking) angle of (hlkl) = (02) is no longer equal to the angle of (hzk2)= (20) as it would be in the tetragonal case. The constant factor C is the product of tan ¢ (~ spontaneous rotation) and sin ~ (see Table 1 ). The scattering intensity I is proportional to the square of the structure factor F which is given by

F= ~ cos[2n(hx+ky)

] +i ~

sin[2~(hx+ky) ]. (4)

A linear model with the variable x being an integer in the range of - 2N...2N and y given as

y(x)

= C w l n cosh

x

-----~'

(-N