L G AKSELRUD, I A IVASHCHENKO, O F ZMIY - Description of concentration polytypism in cdcuinse by commensurately modulated structures - страница 1

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Chemistry of Metals and Alloys

Chem. Met. Alloys 2 (2009) 108-114 Ivan Franko National University of Lviv www. chemetal-j 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. STEPIEN-DAMM3

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, 50-950 Wroclaw 2, Poland * Corresponding author. Tel.: +38-032-2600388; e-mail: lev@is.lviv.ua

Received May 19, 2009; accepted June 30, 2009; available on-line 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 Cd-Cu-In-Se. The crystal structure of the 4Q-Cd1-xCuxIn2Se4 polytype was determined.

Chalcogenide / Polytype / Commensurate modulated structure

Introduction

The compound CdIn2Se4 is characterized by a pseudo-cubic 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 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 2-fold axis (Fig. 2). Literature data also contain information about the existence of a tetragonal structure for CdIn2Se4 with unit-cell 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-

CdSe-In2Se3.

Experimental

Samples of the system Cu2Se-CdSe-In2Se3 were synthesized by the direct single-temperature method. The maximal temperature of synthesis for samples in the range 90-100 mol.% CdIn2Se4 was 1223 K. The synthesis was followed by annealing at 823 K for 300 hours. The phase analysis was based on X-ray powder diffraction patterns obtained in the step-scan mode using a DRON-4-13 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 CAD-4 (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 Cu2Se-CdSe-In2Se3 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 body-centered tetragonal cell (a = 5.806(2), c = 23.252(6) A), the non-centrosymmetric space groups I422, I42m, I4m2, and I4mm and are allowed in Laue class 4/mmm. The experimental set of hkl reflections was characterized by non-standard extinctions. Only reflections with l = 4n and l = 4n±1 were present, which was the evidence for a special pseudo-symmetry 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 least-squares 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

t-section (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)_

pseudo-symmetry 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 4-fold 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 4Q-Cd0.95Cu0.05In2Se4 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

t-section (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

t-section (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) [9-11]. The unit-cell 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 3D-space 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 least-squares 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 least-squares 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.

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