Thin domain walls in YBa2Cu3O7−δ and their rocking curves an x-ray diffraction study

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

i

80

1 O0

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

rotation 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
(5)

and

y(x)

=2y(N)

(N
-y(2N-x) ,

2Nand -

2N
(6)

describes two domains for x > 0 and x < 0 , respectively, and domain walls of thickness w at x = 0 and x = _+2N. Because of the strong oscillations, the function FZ(h) was convoluted with a Gaussian resolution function of unit area in order to achieve a smooth intensity curve. The half width of the Gaussian which had to be sufficiently smaller than the frequency of the oscillations was chosen as 0.01. The resulting curves possess two sharp peaks in F 2 at h = _+kC which are correlated to two domains. The excess intensity in between is exclusively generated by the domain walls and is a function of the wall width w. In Fig. 4, F z at h = 0 is plotted as a function o f w illustrating that there exists a linear dependence on larger values of w which can be extrapolated through the origin.

J, Chrosch, E.K.H. Salje / Physica C 225 (1994) 111-116

114 9

140

8

120

9-71

1O0

6

0000

5

~3 2

n

4

.

I

.

6

L

8

,

0 0

20 0

.

0

40

1' i

O

60

BooO00000 2

J

10

.

,

12

.

,

O

80

4 0

O

.

14

L

16

,

,

18

.

t

20

.

,

0

0

olo

22

0

012

014

o18

016

110

Translation (mm)

Wall Width W (A) Fig. 4. Dependence of the wall-related intensity (at h = 0 ) on the wall thickness w (in J~, N = 1000). A third-order polynomial fit f ( w ) =ao+anw+a2w2+a3w 3 yields ao= 1.812 %, a, =0.031%/A, a2 = 0.022%/A 2, a3 = 0.0004%/~ 3.

Fig. 5. Shift of the maximum of the rocking curve vs. the position of the crystal as a consequence of bending. Observed reflection (006) with 46.58 ° < 2 0 < 4 6 . 7 8 ° .

1.0

The intensity ratio ~ W , t o t of wall intensity and total intensity can be calculated as Iwau Iw,tot -- /total

f( w ) 2ds '

(7)

~;~

_= ~

w h e r e f ( w ) is the wall-related intensity function and s = 0.5 o / k C a scaling factor between experiment and calculation. Using this formula w and d can be extracted from the experimental observations.

0.8

f

0.6 0.4

0 o

0.2

•

•

dj

o •

0.0

90.0

I 90.5

i 91.0

91L.5

fresh decomposed ,

92.0

,

92.5

2O

4. Experimental results

Fig. 6. Comparison of integrated intensities of the split peaks (029) and (209) before and after decomposition.

During the investigation we found already by examining the samples with a polarizing microscope that all of them were more or less twinned. Domains were visible in a relatively low magnification and were oriented in 45 ° with respect to the edges of the singlecrystalline specimen, so that it was possible to adjust the samples in the diffractometer. The rocking curves showed that most crystals were slightly bent thus shifting the reflections in 20 when the sample was tilted or rotated. In Fig. 5 we show the results of a measurement where we used a heavily bent crystal. Here we see the dramatic shift of the tilt and 20 angles corresponding to a bending of the order of 0.2 ° / mm. In order to obtain the resolution needed for this investigation we used high counting times so that some of the measurements lasted more than one or two weeks while the crystals had to be left in air. During such a period one sample began to decompose and

obviously lost some of its oxygen content as seen by a shift of the diffraction peaks from the orthorhombic towards the tetragonal positions. Fig. 6 shows the comparison of the two measurements before and after decomposition. The other crystals remained unaffected and it is not clear how the kinetic loss of oxygen was enhanced in the one sample. The diffraction pattern in Fig. 7 shows the split peaks (029) and (209) with excess intensity in between and their respective numerical fit. Here we used the diffraction orientation as depicted in Fig. 3 (a). The intensity can be related to a superposition of diffraction signals from twin walls and from the orthorhombic bulk material which results in a tetragonal signal. The fitted line profile using Eq. (3) and with k = 2 , w= 7 A, and N = 1000 is shown in Fig. 8. In order to determine the order of magnitude of w we proceeded in the following way. The measured values and

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

Using the second orientation we measured rocking curves which yielded split reflections in the directions of the a- and b-axes and confirmed the existence of at least two twin individuals. The numerical analysis lead to the same wall thickness.

10000

8000 (029)

6000

¢3

115

(209)

4000

2000

5. Discussion ~...~(([{[{(((((((((( )

0

L 90.0

i 91.0

90.5

i 92 0

i

91.5

i 92.5

20 Fig. 7. Split reflections (029) and (209) and their numerical fit (Gaussian function G ( x ) = ( A / ( W , J ~ ) ) exp(-2((xcx ) 2 / W 2) ), where A is the peak area, W the full width of half maximum, and xc the peak position). 800

,

.

,

.

,

.

.

.

,

.

,

600

,=

.

,

,

,

,

~(,

i,I

400

200

c~ 01 90.6

90.8

91.0

91.2

91.4

91.6

91.8

92.0

92.2

20 Fig. 8. Calculated peak splitting (parameters: k=2, wall thickness w=7 A, N= 1000) and Gaussian fit. their fitted functions were integrated over the full 20 range in which diffraction occurred and the relative integrated intensity difference /ameas ( W ) = (Imeas --Ifit)/Imeas "~ 3%

(8)

was calculated. Doing the same with the calculated values we obtain

/caalc(W) =

(I¢alc-Int)llc,l¢.

(9)

Using least- squares methods, we determined w ~ 7 /k i.e., in the order of the lengths of the unit cell in the direction perpendicular to the c-axis. Supposing that the whole crystal is twinned we get an average distance between the domains of the order of 230 Jk. HRTEM measurements on the same sample yielded a distance d ~ 200 ~ which is in good agreement with our X-ray data.

Our main experimental findings are, firstly, that twin walls in YBCO are only about one unit cell thick at room temperature and, secondly, that all crystals showed bent and buckled surfaces. Thin twin walls in YBCO were already anticipated from high resolution transmission electron microscopy [ 14 ]. They are in contrast, however, with much thicker domain walls in Co doped YBCO [5]. In this latter case, wall thicknesses of some six unit cells were observed. This raises the question whether thick domain walls in doped YBCO are the result of segregation of the doping atoms in the wall. Alternatively, it might well be that lattice instabilities generated by the doping process couple with the structural order parameter of the tetragonal-orthorhombic phase transition. For symmetry reasons, such coupling is in lowest order biquadratic and Houchmandzadeh et al. [25] have shown that the result of such coupling is the widening of domain walls. In this case, the internal structure of the wall is expected to be different from the crystal structure of tetragonal YBCO and requires further work on well characterized samples of Co (or Fe) doped material. The thickness of the domain wall can also be compared with the prediction of the Landau-Ginzburg theory of the ferroelastic phase transition in YBCO. For a second-order phase transition the wall thickness is [ 5 ] w=

I(T-Tc)/TcI

'

(10)

where g is the Ginzburg coefficient, T~ is the transition temperature and A is the coefficient of the Landau potential of the order parameter Q: G = ½A ( T - Tc) Q 2 "4- ~BQ 4 4- ½g(VQ) 2.

( 11 )

Other transitions such as tricritical ones, lead only to some small modification of the numerical prefac-

116

J. ('hrosch, E.K.H. Sal]e / Physica ('225:1994) 111 I1:~

for for the wall thickness. W i t h 7~.~ 1020 K and 7+=300 K we find g T c / A ~ a 2 where a is the lattice constant p e r p e n d i c u l a r to the wall (i.e. 5.5 .&). Note that this value is identical to the G i n z b u r g conjecture g T J A = a 2. The G i n z b u r g p a r a m e t e r can now be est i m a t e d if we use as entropic prefactor A ~ J / t o o l leading to g ~ 1 × 10-2° J m2/mol K. We finally compare our results with those of computer simulations of microstructures both for YBCO and oxygen-deficient material. Semenovskaya and Khatchaturyan [26] used "realistic" forces in the simulation of organised defect structures and obtain narrow domain walls in agreement with our observations. Molecular dynamics calculations in a 2D model of fully oxygenized material [27-29] also showed rather narrow walls with thicknesses of some three unit cells. These calculations were made at higher temperatures similar to the combined Monte Carlo molecular-dynamics models in 3D by Bratkovsky et al. [ 30,31 ]. It appears that the wall thicknesses used in all these calculations are, indeed, realistic for YBCO.

Acknowledgements The authors are indebted to C.T. Lin (IRC in Superconductivity, Cambridge) for providing the single crystals, to Y. Yang (IRC in Superconductivity, Cambridge) for performing the HRTEM measurements, and to B. Wruck for helpful discussions.

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