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Order disorder elements in antiferrodistortive phase transitions
ELSEVIER
Physica B 208&209 (1995) 325-326
Order disorder elements in antiferrodistortive phase transitions B. Rechav a'*, Y. Yacoby a, E.A. Stern b, J.J. Rehr b, M.
Newville b
aRacah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel b Physics Department, FM-15, University of Washington, Seattle, WA 98195, USA
Abstract Detailed analysis of XAFS spectra of the antiferrodistortive crystals K 1- xNaxTaO3 show that the local rotation angles of the oxygen octahedra in crystals with x > 0.6 are non-zero and large, hundreds of degrees above the transition temperatures to the cubic phase.
Antiferrodistortive phase transitions (APTs), involving the rotation of X octahedra in ABX3 perovskite crystals, have been the subject of intense experimental and theoretical investigations [1,2]. ESR measurements of the order parameter - the octahedra rotation angle - in SrTiO3 and LaAIO3, and the detection of a Brillouin zone boundary soft phonon mode that tends to condense at To, have suggested that the transition is displacive. This means that the X atoms vibrate around center of symmetry points above T¢ and displace to new equilibrium points below it, where the atomic displacements correspond to the eigenvector of the soft phonon mode [3]. We examined six K~_xNaxTaO3 crystals - the two pure crystals and four mixed crystals with 82%, 70%, 63% and 40% Na. Pure NaTaO3 (NTO) undergoes three successive APTs, the highest being at 900 K [4,1; at RT its octahedra are rotated around [1 1 1] type axes. In the mixed crystal of 82% Na the transition temperature to the cubic phase is 490 K [5, 6]. The crystals below 70% Na are cubic at RT, and undergo ferroelectric transitions below 60 K [5,1. Pure KTaO3 is cubic at all temperatures. We measured the Ta Lm edge XAFS spectrum in these crystals. The measurements were done on powder sam-
* Corresponding author.
pies in transmission mode. The experimental details are described in Ref. [6,1. Octahedra rotations around [1 1 1] type axes have two major effects on the XAFS spectrum of the Ta probe: (1) The rotation of the octahedron around the probe moves the O atoms from the line connecting the probe and the third shell Ta atoms, thus changing the collinear scattering from that shell. This change is proportional to the second moment of the rotation angle distribution function. (2) The rotation of the adjacent octahedra splits the fourth O shell into two sub-shells with unequal distances to the probe. The two effects were measured independently, thus introducing a self consistency check of the analysis. The analysis of the data was done by fitting theoretical XAFS calculations based on F E F F 5 [7-1, to the experimental spectra, in the range 1-4.2 A. Each fit consisted of less than 16 parameters, including 7 correction parameters which were held fixed in all fits, while each experimental spectrum consisted of over 27 independent points [6]. The RT fits of the 40%, 63% and 70% crystals are shown in Fig. 1 as examples illustrating the fit quality. Fig. 2 shows the rotation angles found in the different crystals as a function of temperature. The angle at each temperature is the average of the two independent measurements described above; The two are given explicitly for the 82% crystal. The discrepancy between the
0921-4526,/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 4 ) 0 0 8 5 0 - 7
326
B. Rechav et al. / Physica B 208&209 (1995) 325-326 . . . .
,
. . . .
,
. . . .
r . . . .
,
. . . .
Experiment
If ~
.
.
.
.
T h e o r e t i c a l fit
.
/L/~,%//j,/~ [/ z~..)y ~-~
~
,.
/-'/,
".
(a) .
0
i
1
2
3 r [A]
4
5
Fig. 1. XAFS Fourier transforms absolute values of 40%, 63% and 70% Na concentration crystals at room temperature. Fits
between theory and experiment are between 1 and 4.2/~.
12 mlO _m
•
NaTaO 3
•
70% Na
x
63% Na
•
8 2 % N a (1)
•
82%Na(2)
xx x x
0
>£xT
4TT jI
12
[ Tci
; n
200
8
-::•. A
6
"
x
3 components of the rotation axis of an adjacent octahedron (see Fig. 3). Thus, a system of semi-rigid octahedra, all of which rotated along [1 1 1] type axes, can be arranged in ~ 23"/~ configurations, where n is the number of octahedra. This could have explained the disorder we see. However, if we assume any finite short range interaction between the octahedra, the model resembles a threefold, one dimensional system with nearest neighbor interaction that scales like the cross-section of the antiferrodistortive model. Thus as n ~ oo the interaction also tends to infinity resulting in an ordered state at any temperature. Our conclusion, therefore, is that a rigid model of the octahedra cannot account for our experimental results.
4 k
0
10 I
r
~ 8 g ;':.*
(b)
Fig. 3. Two possible rotations of the left octahedron are consistent with the rotation of the right one: (a) [1 :[I] and (b) [1 1 1].
J
400 600 Temperature [K]
i
800
This work was supported in part by D O E Grant No. DE-FG06-90ER45425 and BSF Grant No. 92-00348. Beamline X l l - A is supported by D O E Grant No. DEFG05-89ER45384.
Fig. 2. Rotation angles in four crystals as a function of temperature. For the 82% Na crystal, the two independent measurements of the rotation angle are shown. The transition temperatures to the cubic phases are indicated for each crystal.
References
two measurements does not exceed 1.5 ° in any of the crystals and is smaller than the error bars. N o rotations were found in the 40% crystal. The results we find indicate the existence of substantial disorder in the cubic phases of the high N a concentration ( ~> 60%) crystals, as well as some disorder in their distorted phases. To discuss the nature of this disorder, one starts from the semi-rigid octahedron model. In this model, a small angle rotation about an arbitrary axis can be described as a vector sum of the rotations around the three x, y and z axes [8]. It follows that a rotation of a given octahedron around a [1 1 1] type axis, determines only 2 of the
[1] K.A. Miiller, in: Local Properties at Phase Transitions, eds. K.A. Miiller and A. Rigamonti (North-Holland, Amsterdam, 1976) ch. 2. [2] S.R. Andrews, J. Phys. C 19 (1986) 3721. [3] J. Feder and E. Pytte, Phys. Rev. B 1 (1970) 4803. [4] M. Ahtee and C.N.W. Darlington, Acta Crystallogr. B 36 (1980) 1007. I-5] T.G. Davis, Phys. Rev. B 5 (1972) 2530. 1-6] B. Rechav, Y. Yacoby, E.A. Stern, J.J. Rehr and M. Newville, Phys. Rev. Lett. 72 (1994) 1352. I-7] J.J.Rehr, S.I. Zabinsky and R.C. Albers, Phys. Rev. B 41 (1990) 8139. 1-8] A.M. Glazer, Acta Crystallogr. B 28 (1972) 3384.
Physica B 208&209 (1995) 325-326
Order disorder elements in antiferrodistortive phase transitions B. Rechav a'*, Y. Yacoby a, E.A. Stern b, J.J. Rehr b, M.
Newville b
aRacah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel b Physics Department, FM-15, University of Washington, Seattle, WA 98195, USA
Abstract Detailed analysis of XAFS spectra of the antiferrodistortive crystals K 1- xNaxTaO3 show that the local rotation angles of the oxygen octahedra in crystals with x > 0.6 are non-zero and large, hundreds of degrees above the transition temperatures to the cubic phase.
Antiferrodistortive phase transitions (APTs), involving the rotation of X octahedra in ABX3 perovskite crystals, have been the subject of intense experimental and theoretical investigations [1,2]. ESR measurements of the order parameter - the octahedra rotation angle - in SrTiO3 and LaAIO3, and the detection of a Brillouin zone boundary soft phonon mode that tends to condense at To, have suggested that the transition is displacive. This means that the X atoms vibrate around center of symmetry points above T¢ and displace to new equilibrium points below it, where the atomic displacements correspond to the eigenvector of the soft phonon mode [3]. We examined six K~_xNaxTaO3 crystals - the two pure crystals and four mixed crystals with 82%, 70%, 63% and 40% Na. Pure NaTaO3 (NTO) undergoes three successive APTs, the highest being at 900 K [4,1; at RT its octahedra are rotated around [1 1 1] type axes. In the mixed crystal of 82% Na the transition temperature to the cubic phase is 490 K [5, 6]. The crystals below 70% Na are cubic at RT, and undergo ferroelectric transitions below 60 K [5,1. Pure KTaO3 is cubic at all temperatures. We measured the Ta Lm edge XAFS spectrum in these crystals. The measurements were done on powder sam-
* Corresponding author.
pies in transmission mode. The experimental details are described in Ref. [6,1. Octahedra rotations around [1 1 1] type axes have two major effects on the XAFS spectrum of the Ta probe: (1) The rotation of the octahedron around the probe moves the O atoms from the line connecting the probe and the third shell Ta atoms, thus changing the collinear scattering from that shell. This change is proportional to the second moment of the rotation angle distribution function. (2) The rotation of the adjacent octahedra splits the fourth O shell into two sub-shells with unequal distances to the probe. The two effects were measured independently, thus introducing a self consistency check of the analysis. The analysis of the data was done by fitting theoretical XAFS calculations based on F E F F 5 [7-1, to the experimental spectra, in the range 1-4.2 A. Each fit consisted of less than 16 parameters, including 7 correction parameters which were held fixed in all fits, while each experimental spectrum consisted of over 27 independent points [6]. The RT fits of the 40%, 63% and 70% crystals are shown in Fig. 1 as examples illustrating the fit quality. Fig. 2 shows the rotation angles found in the different crystals as a function of temperature. The angle at each temperature is the average of the two independent measurements described above; The two are given explicitly for the 82% crystal. The discrepancy between the
0921-4526,/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 4 ) 0 0 8 5 0 - 7
326
B. Rechav et al. / Physica B 208&209 (1995) 325-326 . . . .
,
. . . .
,
. . . .
r . . . .
,
. . . .
Experiment
If ~
.
.
.
.
T h e o r e t i c a l fit
.
/L/~,%//j,/~ [/ z~..)y ~-~
~
,.
/-'/,
".
(a) .
0
i
1
2
3 r [A]
4
5
Fig. 1. XAFS Fourier transforms absolute values of 40%, 63% and 70% Na concentration crystals at room temperature. Fits
between theory and experiment are between 1 and 4.2/~.
12 mlO _m
•
NaTaO 3
•
70% Na
x
63% Na
•
8 2 % N a (1)
•
82%Na(2)
xx x x
0
>£xT
4TT jI
12
[ Tci
; n
200
8
-::•. A
6
"
x
3 components of the rotation axis of an adjacent octahedron (see Fig. 3). Thus, a system of semi-rigid octahedra, all of which rotated along [1 1 1] type axes, can be arranged in ~ 23"/~ configurations, where n is the number of octahedra. This could have explained the disorder we see. However, if we assume any finite short range interaction between the octahedra, the model resembles a threefold, one dimensional system with nearest neighbor interaction that scales like the cross-section of the antiferrodistortive model. Thus as n ~ oo the interaction also tends to infinity resulting in an ordered state at any temperature. Our conclusion, therefore, is that a rigid model of the octahedra cannot account for our experimental results.
4 k
0
10 I
r
~ 8 g ;':.*
(b)
Fig. 3. Two possible rotations of the left octahedron are consistent with the rotation of the right one: (a) [1 :[I] and (b) [1 1 1].
J
400 600 Temperature [K]
i
800
This work was supported in part by D O E Grant No. DE-FG06-90ER45425 and BSF Grant No. 92-00348. Beamline X l l - A is supported by D O E Grant No. DEFG05-89ER45384.
Fig. 2. Rotation angles in four crystals as a function of temperature. For the 82% Na crystal, the two independent measurements of the rotation angle are shown. The transition temperatures to the cubic phases are indicated for each crystal.
References
two measurements does not exceed 1.5 ° in any of the crystals and is smaller than the error bars. N o rotations were found in the 40% crystal. The results we find indicate the existence of substantial disorder in the cubic phases of the high N a concentration ( ~> 60%) crystals, as well as some disorder in their distorted phases. To discuss the nature of this disorder, one starts from the semi-rigid octahedron model. In this model, a small angle rotation about an arbitrary axis can be described as a vector sum of the rotations around the three x, y and z axes [8]. It follows that a rotation of a given octahedron around a [1 1 1] type axis, determines only 2 of the
[1] K.A. Miiller, in: Local Properties at Phase Transitions, eds. K.A. Miiller and A. Rigamonti (North-Holland, Amsterdam, 1976) ch. 2. [2] S.R. Andrews, J. Phys. C 19 (1986) 3721. [3] J. Feder and E. Pytte, Phys. Rev. B 1 (1970) 4803. [4] M. Ahtee and C.N.W. Darlington, Acta Crystallogr. B 36 (1980) 1007. I-5] T.G. Davis, Phys. Rev. B 5 (1972) 2530. 1-6] B. Rechav, Y. Yacoby, E.A. Stern, J.J. Rehr and M. Newville, Phys. Rev. Lett. 72 (1994) 1352. I-7] J.J.Rehr, S.I. Zabinsky and R.C. Albers, Phys. Rev. B 41 (1990) 8139. 1-8] A.M. Glazer, Acta Crystallogr. B 28 (1972) 3384.