L G AKSELRUD, I A IVASHCHENKO, O F ZMIY  Description of concentration polytypism in cdcuinse by commensurately modulated structures  страница 1
Chemistry of Metals and Alloys
Chem. Met. Alloys 2 (2009) 108114 Ivan Franko National University of Lviv www. chemetalj ournal. org
Description of concentration polytypism in Cdi_xCuxIn2Se4 by commensurately modulated structures
L.G. AKSELRUD1*, I.A. IVASHCHENKO2, O.F. ZMIY2, I.D. OLEKSEYUK2, J. STEPIENDAMM3
1 Ivan Franko National University of Lviv, Kyryla i Mefodiya St. 6, 79005 Lviv, Ukraine
2 Lesya Ukrainka Volyn National University, Voli Ave. 13, 43009 Lutsk, Ukraine
3 W. Trzebiatowski Institute of Low Temperatures and Structure Research, Polish Academy of Sciences,
P.O.Box 1410, 50950 Wroclaw 2, Poland * Corresponding author. Tel.: +380322600388; email: lev@is.lviv.ua
Received May 19, 2009; accepted June 30, 2009; available online November 16, 2009
The description of polytypes as commensurately modulated structures with different modulation vectors is presented for the concentration polytypism appearing in the solid solution of the CdIn2Se4 compound in the multinary system CdCuInSe. The crystal structure of the 4QCd1xCuxIn2Se4 polytype was determined.
Chalcogenide / Polytype / Commensurate modulated structure
Introduction
The compound CdIn2Se4 is characterized by a pseudocubic lattice (tetragonal space group P42m, а ~ b ~ c ~ 5.82 A, Z = 1) [1,2]. The Cd atoms occupy Wyckoff position 1а (0 0 0), the In atoms position 2f (// 0 /4), and the Se atoms position 4n (x x z) with x ~ Уд. The coordination polyhedra of the Cd and In atoms are Se4 tetrahedra. Position 1 d (/ / 0), which is vacant in the ideal structure, has tetrahedral surrounding too and may be partly occupied by Cd cations. Consequently, position 1а will be defective as required by the charge balance and the structure will be partly disordered (Fig. 1). In the case of complete statistical occupation of positions 1 a and 1 d and an ideal value of the parameter x = lA for position 4n, the structure contains the Bravais translation /4 /4 0 and can be transformed into a smaller tetragonal cell with a = a0/V2, corresponding to space group P4m2.
However, the vacancies may alternate regularly. For instance, in the ZnIn2Se4 structure (space group I42m, а ~ b ~ 5.71, c ~ 11.45 A, Z = 2) Zn and In atoms occupy randomly positions 2a (0 0 0) and 4d (0 У), and Se atoms occupy position 8i (x x z) with x ~ У [3,4]. This structure can also be described in space group I4, with the Se atoms occupying Wyckoff position 8g (x y z) with x ~ y ~ У [5]. The main difference between the two descriptions of this structure consists in the displacements of the Se atoms, which are in the case of space group I42m related by the symmetry plane and the 2fold axis (Fig. 2). Literature data also contain information about the existence of a tetragonal structure for CdIn2Se4 with unitcell parameter ratio с/a ~ 4 [6,7].
The subject of this paper was to study the crystal structure of phases formed by partial substitution of Cd and In atoms by Cu atoms in the system Cu2Se
CdSeIn2Se3.
Experimental
Samples of the system Cu2SeCdSeIn2Se3 were synthesized by the direct singletemperature method. The maximal temperature of synthesis for samples in the range 90100 mol.% CdIn2Se4 was 1223 K. The synthesis was followed by annealing at 823 K for 300 hours. The phase analysis was based on Xray powder diffraction patterns obtained in the stepscan mode using a DRON413 diffractometer (Cu Ka radiation, Ni filter). Structure refinements were performed by the Rietveld method [8]. Single crystals were investigated using Laue and rotation techniques at the first stage. Intensities for the structure refinement were recorded on an automatic diffractometer CAD4 (graphite monochromator, Mo Ka1 radiation). An absorption correction was applied based on azimuth scans. All calculations for the determination and refinement of the structure were performed using the WinCSD program package [8].
Results and discussion
During the investigation of the phase equlibria in the system Cu2SeCdSeIn2Se3 a compound with composition close to the ternary phase CdIn2Se4, but with different lattice parameters, was discovered. For
Fig. 2 Projection of the structure of ZnIn2Se4 (space group I42m) onto the YZ plane.
a bodycentered tetragonal cell (a = 5.806(2), c = 23.252(6) A), the noncentrosymmetric space groups I422, I42m, I4m2, and I4mm and are allowed in Laue class 4/mmm. The experimental set of hkl reflections was characterized by nonstandard extinctions. Only reflections with l = 4n and l = 4n±1 were present, which was the evidence for a special pseudosymmetry of the structure. For instance, lines hk2 and hk6 were not observed. The structure was solved by the analysis of a 3D distribution of interatomic functions in space group I42m and refined by the leastsquares method (Table 1). The refinement showed strong correlations between the variations of the displacement parameters due to the
Table i Parameters from the refinements of three models for the structure of Cd0.95Cu0.05In2Se4.
Model
3D superstructure
modulated model (1)
modulated model (2)
Space group
I42m
P4m2 (4 4 у)
P4m2 (4 4 у)
a (A)
5.806(2)
5.806(2)
5.806(2)
c (A)
23.252(6)
11.626(3)
5.813(2)
Modulation vector

0 0 4
0 0 У
Z
4
2
1
tsection (t0)

У
0
No. of collected reflections
418
418
418
No. of independent
249
249
249
reflections
2#max (°)
65.0
65.0
65.0
Weighting scheme
1/er2(F)+0.008F2
1/er2(F)+0.002F2
1/o2(F)+0.0015F2
R, wR (all reflections)
0.0530, 0.0549
0.0431, 0.0442
0.0443, 0.0461
R, wR (main reflections

0.0406, 0.0415
0.0424, 0.0426
HKL0)
R, wR (satellite reflections

0.0477, 0.0485
0.0478, 0.0486
HKLM)
Goodness of fit
1.00
1.00
1.05
No. of refined parameters
12 (isotropic approximation)
25
13
Atomic coordinates,
Cd 4e (0 0 z)
Cd 4e (0 0 z)
Cd 2d (0 4 4),
equivalent isotropic
z=0.1250(1), B=1.38(5)
z=0.2556(2),
p = 0.5, B=1.18(1)
displacement
In1 4d (0 4 У),
p = 0.5, B=0.93(2)
U1=[cosx4]zx0.0012(4)
parameters (A2), population
B=1.2(2)
U1=[cosx4]zx0.0035(3)
U2=[sinx4]px0.667(5)
and modulation parameters
In2 4c (0 4 0), B=1.2(2)
U2=[sinx4]zx0.0123(4)
In 2a (0 0 0), B=1.15(2)
Se1 8 i ( x x z)
U3=[sinx4]px0.275(3)
Se 4g (У У z)
x=0.2262(3)
U4=[cosx4]px0.389(3)
z=0.7267(2), B=1.10(1)
z=0.3181(1), B=1.27(7)
In1 2d (0 4 4),
U1={[cosx4]x+[cosx4]y}x
Se2 8 i ( x x z)
B=0.94(2)
0.0289(6)
x=0.2725(3)
In2 2c (0 4 0),
U2={[sinx4]x+[sinx4]y}x
z=0.0686(2), B=1.37(7)
B=0.94(2)
Se1 4g (У У z) z=0.6370(2), B=1.08(3) U1={[cosx4]x[cosx4]y}x
0.0082(3)
U2={[sinx4]x[sinx4]y}x
0.0710(7)
Se2 4g (У У z) z=0.1364(2), B=0.88(2) U1={[cosx4]x+[cosx4]y} x
0.0120(3)
0.0404(6) U2=
{[sinx4]x+[sinx4]y}x 0.0067(3)_
pseudosymmetry of the structure. A projection of the structure of Cd0.95Cu0.05In2Se4 onto the YZ plane is shown in Fig. 3.
The structure of Cd0.95Cu0.05In2Se4 contains the double number of structural slabs in the translation periodicity along the 4fold axis compared to the ZnIn2Se4 structure, and four times more than the simplest prototype, CdIn2Se4. Following the generally accepted nomenclature of heteropolytypical structures, one should use the following designations: 1Q for the CdIn2Se4 structure (Q  tetragonal symmetry), 2Q for the ZnIn2Se4 structure, and 4Q for the Cd0 95Cu005In2Se4 structure.
The special symmetry revealed by the peculiar extinctions in the diffraction pattern indicated an alternative way to describe the symmetry of the structure. It was possible to introduce a fourth index, M, in two models: (1) M = mod(L,2), (2) M = mod(L,4). For both models the reflection set was transformed to HKLM with regular extinctions H+K+M Ф 2n. This gave a possibility to describe the structure of the 4QCd0.95Cu0.05In2Se4 compound as a
Fig. 3 Projection of the structure of Cd095Cu005In2Se4 (space group I42m) onto the YZ plane.
і і і і і і і і і і і її
20 30 40 50 є0 70 80 90
Fig. 4 Experimental (dotted line), calculated (solid line), and difference diffraction patterns of CdIn2Se4 (Cu Ka radiation).
Table 2 Parameters from the refinements of two models for the structure of Cd0.982Cu0.018In2Se4.
Model
3D superstructure
modulated model
Space group
a (A) c (A)
Modulation vector Z
tsection (t0)
No. of collected reflections No. of independent reflections
2^max ( )
Weighting scheme
R, wR (all reflections)
R, wR (main reflections HKL0)
R, wR (satellite reflections HKLM)
Goodness of fit
No. of refined parameters
I42m
5.8043(2)
11.6380(5)
2
1599
276
58.2
1/er2(F)+0.004F2 0.0456, 0.0572
1.02 11
P4m2 (4 4 у)
5.8043(2)
5.8190(3)
0 0 4 1
У
1599
276
58.2
1/er2(F)+0.002F2
0.0466, 0.0506 0.0402, 0.0435
0.0612, 0.0648
1.00
8
Atomic coordinates, equivalent isotropic displacement parameters (A2) and modulation parameters
Cd 2a (0 0 0), B=1.09(5)
In 4d (0 4 У), B=1.08(4)
Se 8i (x x z) x=0.2719(3) z=0.1142(1), B=0.72(3)
Cd 2a (0 0 0), p = 0.5, B=0.92(4)
U1=[cosx4]px0.490(5)
In 2d (0 4 4), B=1.01(2)
Se 4g (У У z) z=0.7710(2), B=0.58(2)
U1={[cosx4]x+[cosx4]y}x0.0159(6)
U2={[sinx4]x+[sinx4]y}x0.0148(7)
Table 3 Parameters from the refinements of two models for the structure of CdIn2Se4.
Model
3D superstructure
modulated model
Space group
a (A)
c (A)
Modulation vector
Z
tsection (t0)
No. of independent reflections
2^max ( )
Rb
Rp
No. of refined parameters
P42m
5.8289(4)
5.8186(8)
1
82
100.0 0.0686 0.0803 6
P4m2 (4 4 у)
5.8281(3)
5.8202(5)
0 0 0
1
0.125 46
100.0 0.0699 0.0812 8
Atomic coordinates, equivalent isotropic displacement parameters (A2) and modulation parameters
Cd 1a (0 0 0), B=0.7(2)
In 2f (4 0 4), B=0.79(9)
Se 4n (x x z) x=0.2690(5) z=0.2285(9), B=0.55(4)
Cd 2a (0 0 0), p = 0.5, B=0.92(4) U1=[sinx4]zx0.0091(1) U2=[cosx4]px0.2217(9) In 2d (0 4 4), B=0.75(6)
Se 4g (У У z) z=0.7845(1), B=0.43(5)
U1={[cosx4]x+[cosx4]y}x0.0115(1)
U2={[sinx4]x+[sinx4]y}x0.0114(1)
4D modulated structure, with a fourth Bravais vector [4 4 0 4] and the following commensurate modulation vectors: q = {0 0 4} for (1) and q = {0 0 У} for (2) [911]. The unitcell parameters are consequently a = 5.806(2) A and
c = 23.252/2 = 11.626 A for (1), c = 23.252/4 = 5.813 A for (2) . Model (2) corresponds to the 1Q structure with average symmetry described in the 3Dspace group P4m2. Systematic extinctions of the satellite reflections corresponding to centering indicated the superspace group P4m2 (4 4 у) (or WP4m2(1 1 1) in agreement with [11]), which was confirmed by leastsquares refinements for both models. Calculations of the structure factors led to values of the fourth coordinate ti = ti + t0, where ti is equal to 0 and 4 with the initial value t0 = У for the model (1), and 0, У, 4, and % with the initial value t0 = 0 for the model (2), determined in the process of the structure refinement. A special feature of these structure models is the modulation of the occupancy of the position of the Cd(Cu) atoms, which has both sine and cosine components of the modulation wave with different amplitudes, resulting in both different substitution and defects with respect to the fourth coordinate (coinciding with the Z axis). The application of a leastsquares refinement to the commensurately modulated structure made it possible to avoid correlations in the refinement of the anisotropic displacement parameters and to decrease the number of variables. Results of the refinements of the different models are presented in Table 1.