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Crystal structure and cation distribution in the solid solution series 2(ZnX)–CuInX2 (X=S, Se, Te)
Journal of Physics and Chemistry of Solids 66 (2005) 1961–1965 www.elsevier.com/locate/jpcs
Crystal structure and cation distribution in the solid solution series 2(ZnX)–CuInX2 (XZS, Se, Te) S. Schorr a,*, M. Tovar b, D. Sheptyakov c, L. Keller c, G. Geandier d a
Institute of Mineralogy, Crystallography and Materials Science, University of Leipzig, Scharnhorststr. 20, D-04275 Leipzig, Germany b Hahn-Meitner-Institute, Berlin, Germany c Laboratory for Neutron Scattering, ETH Zu¨rich and PSI Villigen, Switzerland d European Synchrotron Radiation Facility (ESRF), Grenoble, France
Abstract The solid solution series (2ZnX)x (CuInX2)1Kx (XZS, Se, Te) were studied by the combination of laboratory and synchrotron X-ray and by neutron powder diffraction. Within the homologous series the tetragonal distortion 1⁄4 -u increases in the sequence S/Se/Te whereas the tetragonal deformation hZc/2a decreases. Besides that, with increasing 2ZnX content in CuInX2 the anion position parameter u increases as expected. The cation site occupancy in the chalcopyrite type phase of single phase tetragonal samples was obtained by Rietveld analysis of the neutron diffraction data. A non-statistic Zn distribution could be deduced for all three systems. The high temperature in situ diffraction experiments with synchrotron radiation on CuInX2 powder samples revealed the Cu–In anti-site occupation as the driving force of the temperature dependent phase transition from the chalcopyrite to the zinc-blende type structure. q 2005 Elsevier Ltd. All rights reserved. Keywords: A. Alloys; A. Semiconductors; C. X-ray diffraction; C. Neutron Scattering; D. Phase transition
1. Introduction Solid solution series of I–III–VI2 ternary chalcopyrites with their isoelectronic analogs of the II–VI binaries allow a systematic variation of structural and physical properties with composition. The semiconducting systems Zn2x(CuIn)1KxX2 (XZS, Se, Te) are formed by alloying the binary semiconductor ZnX in the ternary semiconductor CuInX2 and thereby substituting 2Zn4(Cu,In). These alloys were studied over many years with respect to their structure and phase relations [1,2], structure and superstructures [3–5], the structural phase transition [6,7] and relations between structure and electronic band gap [8,9]. ZnX are II–VI binary compound semiconductors crystallizing at room temperature in the cubic zinc-blende structure (Sp. Gr. F 43m). CuInX2 belongs to the ternary AI BIII CVI 2 chalcopyrite compound family (isoelectric analogs of the II–VI binaries), a large group of semiconducting materials with diverse optical, electrical and structural properties [10]. The crystal structure of ternary chalcopyrites (Sp. Gr. I 42d) is * Corresponding author. E-mail address: [email protected] (S. Schorr).
0022-3697/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2005.09.035
closely related to the that of the zinc-blende analogs, but with a tetragonal deformation parameter hZc/2a and an anion displacement parameter us1⁄4 (deviation of the anion x coordinate from 1⁄4 ) [11,12]. This both independent parameters, determining the chalcopyrite structure, reflect the unequal bond-lengths RAC and RBC, rising from the coordination of the anions by two A cations and two B cations [13]. Depending on chemical composition as well as temperature Zn2x(CuIn)1KxX2 undergoes a structural phase transition from the tetragonal chalcopyrite structure to the cubic zincblende structure. The complete x-T-phase diagram for XZS is reported in [14], where the existence of a miscibility gap (2-phase field) between 0.1!x!0.42 is shown (for room temperature data see also [15]). The coexistence of both a tetragonal and cubic phase was also found for XZSe between 0.1!x!0.35 [16,17] and for XZTe between 0.1! x!0.31 [18]. The distribution of the cations Zn, Cu and In over the both cation sites (Me1 site refers to Cu, Me2 site refers to In) of the chalcopyrite structure, especially important for the anion displacement parameter, is not discussed in literature, where some authors [6,7] suggest a statistic Zn distribution. Because conventional X-ray and synchrotron radiation methods fail in Zn/Cu differentiation due to the electronic similarity of Zn and Cu (only one electron difference) and because of the chalcopyrite space group parities [19] neutron powder
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S. Schorr et al. / Journal of Physics and Chemistry of Solids 66 (2005) 1961–1965
diffraction was used to reveal the cation site occupancies for XZS [20]. The results indicate a non-statistic Zn distribution on the both cation sites of the chalcopyrite structure and moreover that Zn prefers the Me2 site (In site) causing a Cu–In anti-site occupation. Although (2ZnX)x(CuInX2)1Kx alloys are studied since long time, open questions, especially concerning the cation distribution, still remain and a detailed study of the solid solution series using especially the neutron powder diffraction technique is necessary, which will be presented in this work. Besides that a distinct study of the temperature dependent phase transition in CuInX2 is given. 2. Experiment Zn2x(CuIn)1KxX2 powder samples were synthesised by solid state reaction of the elements (purityO99.999%) in sealed evacuated silica tubes at TZ950 8C for XZS, TZ 850 8C for XZSe and TZ700 8C for XZTe (0%x%0.1) and homogenised at room temperature. This procedure was repeated three times homogenising the samples in between by grinding in an agate mortar. Finally the samples were cooled down to room temperature with 10 K/h. Zn2x(CuIn)1KxTe2 powder samples with 0.4!x!1 were prepared by the directional freezing method as described in [21]. The chemical composition and homogeneity of the samples was determined by 2 MeV HC-PIXE (protron induced X-ray emission). XRDdata were collected on a XRD3000-diffractometer using Cu Ka radiation (lZ1.54) and a secondary graphite monochromator. Neutron powder diffraction experiments were carried out for XZSe at the Hahn-Meitner-Institute Berlin, Germany, at the high resolution powder diffractometer E9 with a wavelength ˚ and for XZTe at the Swiss Spallation Source SINQ lZ1.79 A at Paul Scherrer Institute (Villigen), using the high resolution powder diffractometer for thermal neutrons (HRPT) with ˚ and the diffractometer DMC with a wavelength of lZ1.1545 A ˚ . The data treatment was done by a wavelength of lZ2.568 A Rietveld analysis using the FullProf program [22]. Thus the lattice parameter acubic, atetragonal and c, the anion x coordinate and the cation site occupancies were determined. To study the temperature dependent phase transition, in situ powder diffraction experiments using synchrotron radiation were carried out at the European Synchrotron Radiation ˚ ). The experFacility (ESRF), beamline 15B (lZ0.141068 A imental setup consisted of a heigh energy (w87 keV) monochromatic primary beam, a ceramic oven with two small holes at the beam hight and an on-line 2D detector, MAR 345 image plate. The samples, placed in small evacuated silica ampoules (diameter 4 mm) were heated with w38 K/h which allowed collecting diffraction patterns with 1 K steps.
Fig. 1. Lattice parameter in dependence of chemical composition for (2ZnS)x(CuInS2)1Kx single phase samples and within the 2-phase field (at room temperature). The solid line corresponds to a linear fit, the dotted lines to the 2-phase field. The dashed line within the 2-phase field should guide the eye.
domains in the cubic matrix of the crystalline particles. The other samples are single phased and crystallize in the tetragonal chalcopyrite-type structure (x%0.1) or cubic sphalerite-type structure (xR0.4, 0.35 and 0.31 for XZS, Se and Te correspondingly). The results concerning the lattice parameter acubic, atetragonal and ctetragonal for all three solid solution series are represented in Fig. 1 (XZS, data taken from [18]), Fig. 2 (XZSe) and Fig. 3 (XZTe). It was found, that within the single phase regions of the solid solution series the lattice parameter follow Vegards rule. For (2ZnS)x(CuInS2)1Kx alloys also the lattice parameter of tetragonal domains and cubic matrix within the 2-phase field is shown (Fig. 1). It should be noticed that an elongation of the linear fit of the tetragonal lattice parameter atetragonal pointed to the value of the fit of the cubic lattice
3. Results and discussion In agreement with literature [14–18], the systems 2(ZnX)– CuInX2 were found to form a solid solution series with a miscibility gap. Powder samples within the miscibility gap consist of two coexisting phases occurring as tetragonal
Fig. 2. Lattice parameter in dependence of chemical composition for (2ZnSe)x(CuInSe2)1Kx single phase samples (at room temperature). The solid line corresponds to a linear fit, the dotted lines to the 2-phase field.
S. Schorr et al. / Journal of Physics and Chemistry of Solids 66 (2005) 1961–1965
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Table 1 Experimentally determined and calculated average neutron scattering length [fm] of the both cation sites in the chalcopyrite type structure of (2ZnX)x (CuInX2)1Kx tetragonal single phase samples X
x
bMe1 (exp)
bMe2 (exp)
bMe1 (calc)
bMe2 (calc)
S [20] S [20] Se Se Te Te Te
0.055 0.09 0.042 0.070 0.056 0.060 0.080
7.594 (100) 7.363 (100) 7.648 (90) 7.448 (90) 7.471 (80) 7.533 (80) 7.656 (80)
4.134 (60) 4.301 (60) 4.349 (75) 4.484 (75) 4.228 (60) 4.309 (60) 4.423 (60)
7.616 7.555 7.643 7.522 7.571 7.533 7.435
4.162 4.226 4.147 4.136 4.130 4.108 4.098
For the calculation a statistic Zn distribution was assumed.
Fig. 3. Lattice parameter in dependence of chemical composition for (2ZnTe)x(CuInTe2)1Kx single phase samples (at room temperature). The solid line corresponds to a linear fit, the dotted lines to the 2-phase field.
parameter acubic at xZ0.42, which corresponds to the cubic end member of the 2-phase field. For tetragonal single phase samples crystallizing in the chalcopyrite type structure, the anion position parameter u was determined by Rietveld analysis of the neutron diffraction data (see Fig. 4), showing an increasing value with increasing ZnX content within Cu0.5In0.5X. This indicates, that the tetragonal distortion 1⁄4 -u is decreasing as expected because the heterovalent exchange of CuCCIn3C by 2Zn2C decreases the deformation around the anions raising from the similar radii of Cu- and Zn-ions against the In-ions (rZn2C Z 0:64; rCuC Z 0:635; rIn3C Z 0:765 for XZS [23]). In X-ray and neutron diffraction experiments the measured intensities are proportional to the structurePfactor Fhkl, which is in the case of neutrons defined as Fhkl Z Nj bj exp½2piðhxjC kyj C lzj Þ. Here b is the neutron scattering length of the atom j,
describing the strength of the interaction between the neutron and the nucleus of the atom j. The atomic coordinates are x, y and z, and N is the site occupancy multiplier. The latter can be refined in the Rietveld analysis of the neutron powder diffraction data setting bMe1ZbCuZ7.718 fm and bMe2Z bInZ4.456 fm [24] and reflects directly the cation site occupancy. Thus an average neutron scattering length b Me1 (exp)ZNMe1$bCu and b Me2 (exp)ZNMe2$bIn can be calculated from the experimental data (see Table 1). These values were compared with average scattering lengths calculated assuming a certain distribution (i.e. a statistic Zn distribution and no Cu–In anti-site occupation) by bMe1 ðcalcÞZ ZnCu $bZn C CuCu $bCu C InCu $bIn and b Me2 ðcalcÞZ ZnIn $bZn C CuIn $bCu C InIn $bIn with bZnZ5.67 fm [25] (see Table 1). Here ZnCu, CuCu and InCu are the mole fraction of the cation on the Me1 site, ZnIn, CuIn and InIn are the cation mole fractions on the Me2 site, which gives in sum the total amount of Zn-, Cu- and Inatoms in the (2ZnX)x(CuInX2)1Kx samples (i.e. ZnCuCZnInZ 2x). Because of the disagreement between the experimental and the calculated average neutron scattering lengths of the Me1 and Me2 site in the chalcopyrite type structure it can be concluded, that in the tetragonal single phase region Zn is distributed non-statistically on this both sites for all three (2ZnX)x(CuInX2)1Kx systems. Rietveld analysis of the diffraction data using synchrotron radiation, taken in situ at high temperatures, made a detailed study of the temperature dependent phase transition from the chalcopyrite type to the zinc-blende type structure in CuInX2 possible. In Table 2, the determined transition temperatures are given, in the case of CuInS2 a second transition from the zincblende type structure to the wurtzite type structure was observed. Of special interest were the temperature dependent behaviour of the anion position and the tetragonal deformation h, which is shown in Fig. 5. It can be seen, that within the homologous series, the tetragonal distortion 1⁄4 -u increases Table 2 Transition temperatures of structural phase transitions in CuInX2
Fig. 4. Experimentally determined tetragonal deformation h (left) and anion position (right) for (2ZnX)x(CuInX2)1Kx tetragonal single phase samples (at room temperature). Solid lines are guided by the eye; dotted lines correspond to the 2-phase field. The open circles refer to single crystal samples [24].
CuInX2
Chalcopyrite–zinc-blende (8C)
Zinc-blende–wurtzite
XZS XZSe XZTe
967.6 806.8 662.4
1027.3 8C – –
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S. Schorr et al. / Journal of Physics and Chemistry of Solids 66 (2005) 1961–1965
Fig. 5. Tetragonal deformation h (left) and anion position (right) for CuInX2 in dependence of TcKT (Tc is the phase transition temperature).
from S/Se/Te, whereas the tetragonal deformation h decreases. These both independent parameters of the chalcopyrite type structure change dramatically just before the phase transition point Tc, indicating a critical region of the phase transition of w10–15 K. Within this temperature range also the cation site occupancy changes, i.e. the value for the Me1 site increases whereas the value for the Me2 site decreases (see Fig. 6), indicating an Cu–In anti site occupation. Thus it can be concluded, that the structural phase transition is driven by the site change of the cations. 4. Conclusions For the first time (2ZnX)x(CuInX2)(1Kx) alloys with XZS, Se and Te have been studied by the combination of X-ray and neutron powder diffraction, diffraction using synchrotron radiation and high resolution electron transmission microscopy
equipped with an EDX-analysis. The results concerning structure and phase relations at room temperature showed that the systems form solid solution series with a miscibility gap. Here two phases coexist as tetragonal domains with chalcopyrite type structure and a cubic matrix with sphaleritetype structure, causing the region named 2-phase field. In the single phase region the lattice parameter show a linear dependence of chemical composition, whereas within the 2-phase field the both phases try to match in the a–b-plane (note that atetr–acub), which gives rise to an increase of the tetragonal lattice constant c and herewith a strong increase of the tetragonal deformation h. From the neutron powder diffraction experiments at room temperature a non-statistical Zn distribution on the both cation sites of the chalcopyrite type structure could be deduced for (2ZnX)x(CuInX2)1Kx alloys with XZS, Se, Te, which is in disagreement to the assumptions in literature. The high temperature in situ diffraction experiments with synchrotron radiation revealed the Cu–In anti-site occupation as the driving force of the phase transition in a way that the structural parameters (lattice constant, anion position) changes dramatically as far as the anti-site occupation starts. Acknowledgements
Fig. 6. Cation site occupancy in dependence of temperature for CuInSe2. The phase transition occurs at TcZ806.8 8C, the dramatically change of the site occupancy values start w10 K before the transition temperature.
The author thank especially D. Spemann (Institute of Experimental Physics II, University Leipzig) for the PIXE measurements and Dr V. Gremenok (Institute of Physics of Solids and Semiconductors, National Academy of Sciences, Minsk, Belarus) for the preparation of the cubic Zn2x(CuIn)1Kx Te2 samples. Moreover thanks are due to Dr Honkimaki (ESRF Grenoble) for providing his self-made software packages for the synchrotron data pre-processing. This work is partly based on experiments performed at the Swiss spallation neutron source SINQ, Paul Scherrer Institute, Villigen, Switzerland and has been supported by the European Commission under the 6th Framework Programme through the Key Action: Strengthening the European Research Area, Research Infrastructures. Contract n8: RII3-CT-2003-505925.
S. Schorr et al. / Journal of Physics and Chemistry of Solids 66 (2005) 1961–1965
References [1] M. Robbins, M.A. Mikskovsky, Journal of Solid State Chemistry 5 (1972) 462–466. [2] C. Sombuthawee, S.B. Bonsall, F.A. Hummel, Journal of Solid State Chemistry 25 (1978) 391–399. [3] K. Bente, T. Do¨ring, Chemie der Erde - Geochemistry 51 (1991) 291–295. [4] G. Wagner, D. Oppermann, K. Bente, J. Lenzner, M. Lorenz, Thin Solid Films 376 (2000) 82–88. [5] M. Heuer, K. Bente, Z. Kristallogr, NCS 217 (2002) 13–14. [6] O.V. Parasyuk, S.V. Voronyuk, L.D. Gulay, G. Ye Davidyuk, V.O. Halko, Journal of Alloys and Compounds 348 (2003) 57–64. [7] P.G. Gallardo, Physica Status Solidi (a) 134 (1992) 119–125. [8] I. Luck, R. Scheer, H.-J. Lewerenz, Crystal Research and Technology 31 (1996) 841. [9] I. Luck, R. Scheer, H.-J. Lewerenz, Proceedings of 14th European Photovoltaic and Solar Energy Conference 1997. [10] J.L. Shay, J.H. Wernick, Ternary Chalcopyrite Semiconductors: Growth Electric Properties and Applications, Pergamon Press, Oxford, 1974. [11] J.E. Jaffe, A. Zunger, Physical Review B28 (1983) 5822.
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[12] S.C. Abrahams, J.L. Bernstein, Journal of Chemical Physics 59 (1973) 5415–5422. [13] J.E. Jaffe, A. Zunger, Physical Review B27 (1983) 5176. [14] Wagner G., Fleischer F., Schorr S., Bente K., submitted for publication. [15] Schorr S., Wagner G., J. Alloys Comp 396 (2005) 202–207 [16] Lehmann S., Diploma Thesis, University Leipzig (2003) [17] Wagner G., Lehmann S., Schorr S., Bente K., J. Cryst. Growth in press. [18] Roussak L., PhD Thesis, University Leipzig (2005) [19] Wendschuh-Jostis T.M., PhD Thesis, University Go¨ttingen, Germany (1990) [20] S. Schorr, M. Tovar, N. Stu¨ßer, K. Bente, Physica B 350 (2004) e411– e414. [21] I.V. Bodnar, A. Eiffler, Th. Do¨ring, W. Schmitz, K. Bente, V.F. Gremenok, I.A. Victorov, V. Riede, Crystal Research and Technology 35 (2000) 1135–1140. [22] Rodriguez-Carjaval J., FullProf: A Rietveld analysis program for X-ray and neutron diffraction data, LLB, www-llb.cea.fr/fullweb [23] R.D. Shannon, in: M. O’Keeffe, A. (Eds.), Structure and bonding in crystals (1981). [24] Heuer M., Private communication. [25] V.F. Sears, Neutron News 3 (1992) 26.
Crystal structure and cation distribution in the solid solution series 2(ZnX)–CuInX2 (XZS, Se, Te) S. Schorr a,*, M. Tovar b, D. Sheptyakov c, L. Keller c, G. Geandier d a
Institute of Mineralogy, Crystallography and Materials Science, University of Leipzig, Scharnhorststr. 20, D-04275 Leipzig, Germany b Hahn-Meitner-Institute, Berlin, Germany c Laboratory for Neutron Scattering, ETH Zu¨rich and PSI Villigen, Switzerland d European Synchrotron Radiation Facility (ESRF), Grenoble, France
Abstract The solid solution series (2ZnX)x (CuInX2)1Kx (XZS, Se, Te) were studied by the combination of laboratory and synchrotron X-ray and by neutron powder diffraction. Within the homologous series the tetragonal distortion 1⁄4 -u increases in the sequence S/Se/Te whereas the tetragonal deformation hZc/2a decreases. Besides that, with increasing 2ZnX content in CuInX2 the anion position parameter u increases as expected. The cation site occupancy in the chalcopyrite type phase of single phase tetragonal samples was obtained by Rietveld analysis of the neutron diffraction data. A non-statistic Zn distribution could be deduced for all three systems. The high temperature in situ diffraction experiments with synchrotron radiation on CuInX2 powder samples revealed the Cu–In anti-site occupation as the driving force of the temperature dependent phase transition from the chalcopyrite to the zinc-blende type structure. q 2005 Elsevier Ltd. All rights reserved. Keywords: A. Alloys; A. Semiconductors; C. X-ray diffraction; C. Neutron Scattering; D. Phase transition
1. Introduction Solid solution series of I–III–VI2 ternary chalcopyrites with their isoelectronic analogs of the II–VI binaries allow a systematic variation of structural and physical properties with composition. The semiconducting systems Zn2x(CuIn)1KxX2 (XZS, Se, Te) are formed by alloying the binary semiconductor ZnX in the ternary semiconductor CuInX2 and thereby substituting 2Zn4(Cu,In). These alloys were studied over many years with respect to their structure and phase relations [1,2], structure and superstructures [3–5], the structural phase transition [6,7] and relations between structure and electronic band gap [8,9]. ZnX are II–VI binary compound semiconductors crystallizing at room temperature in the cubic zinc-blende structure (Sp. Gr. F 43m). CuInX2 belongs to the ternary AI BIII CVI 2 chalcopyrite compound family (isoelectric analogs of the II–VI binaries), a large group of semiconducting materials with diverse optical, electrical and structural properties [10]. The crystal structure of ternary chalcopyrites (Sp. Gr. I 42d) is * Corresponding author. E-mail address: [email protected] (S. Schorr).
0022-3697/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2005.09.035
closely related to the that of the zinc-blende analogs, but with a tetragonal deformation parameter hZc/2a and an anion displacement parameter us1⁄4 (deviation of the anion x coordinate from 1⁄4 ) [11,12]. This both independent parameters, determining the chalcopyrite structure, reflect the unequal bond-lengths RAC and RBC, rising from the coordination of the anions by two A cations and two B cations [13]. Depending on chemical composition as well as temperature Zn2x(CuIn)1KxX2 undergoes a structural phase transition from the tetragonal chalcopyrite structure to the cubic zincblende structure. The complete x-T-phase diagram for XZS is reported in [14], where the existence of a miscibility gap (2-phase field) between 0.1!x!0.42 is shown (for room temperature data see also [15]). The coexistence of both a tetragonal and cubic phase was also found for XZSe between 0.1!x!0.35 [16,17] and for XZTe between 0.1! x!0.31 [18]. The distribution of the cations Zn, Cu and In over the both cation sites (Me1 site refers to Cu, Me2 site refers to In) of the chalcopyrite structure, especially important for the anion displacement parameter, is not discussed in literature, where some authors [6,7] suggest a statistic Zn distribution. Because conventional X-ray and synchrotron radiation methods fail in Zn/Cu differentiation due to the electronic similarity of Zn and Cu (only one electron difference) and because of the chalcopyrite space group parities [19] neutron powder
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S. Schorr et al. / Journal of Physics and Chemistry of Solids 66 (2005) 1961–1965
diffraction was used to reveal the cation site occupancies for XZS [20]. The results indicate a non-statistic Zn distribution on the both cation sites of the chalcopyrite structure and moreover that Zn prefers the Me2 site (In site) causing a Cu–In anti-site occupation. Although (2ZnX)x(CuInX2)1Kx alloys are studied since long time, open questions, especially concerning the cation distribution, still remain and a detailed study of the solid solution series using especially the neutron powder diffraction technique is necessary, which will be presented in this work. Besides that a distinct study of the temperature dependent phase transition in CuInX2 is given. 2. Experiment Zn2x(CuIn)1KxX2 powder samples were synthesised by solid state reaction of the elements (purityO99.999%) in sealed evacuated silica tubes at TZ950 8C for XZS, TZ 850 8C for XZSe and TZ700 8C for XZTe (0%x%0.1) and homogenised at room temperature. This procedure was repeated three times homogenising the samples in between by grinding in an agate mortar. Finally the samples were cooled down to room temperature with 10 K/h. Zn2x(CuIn)1KxTe2 powder samples with 0.4!x!1 were prepared by the directional freezing method as described in [21]. The chemical composition and homogeneity of the samples was determined by 2 MeV HC-PIXE (protron induced X-ray emission). XRDdata were collected on a XRD3000-diffractometer using Cu Ka radiation (lZ1.54) and a secondary graphite monochromator. Neutron powder diffraction experiments were carried out for XZSe at the Hahn-Meitner-Institute Berlin, Germany, at the high resolution powder diffractometer E9 with a wavelength ˚ and for XZTe at the Swiss Spallation Source SINQ lZ1.79 A at Paul Scherrer Institute (Villigen), using the high resolution powder diffractometer for thermal neutrons (HRPT) with ˚ and the diffractometer DMC with a wavelength of lZ1.1545 A ˚ . The data treatment was done by a wavelength of lZ2.568 A Rietveld analysis using the FullProf program [22]. Thus the lattice parameter acubic, atetragonal and c, the anion x coordinate and the cation site occupancies were determined. To study the temperature dependent phase transition, in situ powder diffraction experiments using synchrotron radiation were carried out at the European Synchrotron Radiation ˚ ). The experFacility (ESRF), beamline 15B (lZ0.141068 A imental setup consisted of a heigh energy (w87 keV) monochromatic primary beam, a ceramic oven with two small holes at the beam hight and an on-line 2D detector, MAR 345 image plate. The samples, placed in small evacuated silica ampoules (diameter 4 mm) were heated with w38 K/h which allowed collecting diffraction patterns with 1 K steps.
Fig. 1. Lattice parameter in dependence of chemical composition for (2ZnS)x(CuInS2)1Kx single phase samples and within the 2-phase field (at room temperature). The solid line corresponds to a linear fit, the dotted lines to the 2-phase field. The dashed line within the 2-phase field should guide the eye.
domains in the cubic matrix of the crystalline particles. The other samples are single phased and crystallize in the tetragonal chalcopyrite-type structure (x%0.1) or cubic sphalerite-type structure (xR0.4, 0.35 and 0.31 for XZS, Se and Te correspondingly). The results concerning the lattice parameter acubic, atetragonal and ctetragonal for all three solid solution series are represented in Fig. 1 (XZS, data taken from [18]), Fig. 2 (XZSe) and Fig. 3 (XZTe). It was found, that within the single phase regions of the solid solution series the lattice parameter follow Vegards rule. For (2ZnS)x(CuInS2)1Kx alloys also the lattice parameter of tetragonal domains and cubic matrix within the 2-phase field is shown (Fig. 1). It should be noticed that an elongation of the linear fit of the tetragonal lattice parameter atetragonal pointed to the value of the fit of the cubic lattice
3. Results and discussion In agreement with literature [14–18], the systems 2(ZnX)– CuInX2 were found to form a solid solution series with a miscibility gap. Powder samples within the miscibility gap consist of two coexisting phases occurring as tetragonal
Fig. 2. Lattice parameter in dependence of chemical composition for (2ZnSe)x(CuInSe2)1Kx single phase samples (at room temperature). The solid line corresponds to a linear fit, the dotted lines to the 2-phase field.
S. Schorr et al. / Journal of Physics and Chemistry of Solids 66 (2005) 1961–1965
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Table 1 Experimentally determined and calculated average neutron scattering length [fm] of the both cation sites in the chalcopyrite type structure of (2ZnX)x (CuInX2)1Kx tetragonal single phase samples X
x
bMe1 (exp)
bMe2 (exp)
bMe1 (calc)
bMe2 (calc)
S [20] S [20] Se Se Te Te Te
0.055 0.09 0.042 0.070 0.056 0.060 0.080
7.594 (100) 7.363 (100) 7.648 (90) 7.448 (90) 7.471 (80) 7.533 (80) 7.656 (80)
4.134 (60) 4.301 (60) 4.349 (75) 4.484 (75) 4.228 (60) 4.309 (60) 4.423 (60)
7.616 7.555 7.643 7.522 7.571 7.533 7.435
4.162 4.226 4.147 4.136 4.130 4.108 4.098
For the calculation a statistic Zn distribution was assumed.
Fig. 3. Lattice parameter in dependence of chemical composition for (2ZnTe)x(CuInTe2)1Kx single phase samples (at room temperature). The solid line corresponds to a linear fit, the dotted lines to the 2-phase field.
parameter acubic at xZ0.42, which corresponds to the cubic end member of the 2-phase field. For tetragonal single phase samples crystallizing in the chalcopyrite type structure, the anion position parameter u was determined by Rietveld analysis of the neutron diffraction data (see Fig. 4), showing an increasing value with increasing ZnX content within Cu0.5In0.5X. This indicates, that the tetragonal distortion 1⁄4 -u is decreasing as expected because the heterovalent exchange of CuCCIn3C by 2Zn2C decreases the deformation around the anions raising from the similar radii of Cu- and Zn-ions against the In-ions (rZn2C Z 0:64; rCuC Z 0:635; rIn3C Z 0:765 for XZS [23]). In X-ray and neutron diffraction experiments the measured intensities are proportional to the structurePfactor Fhkl, which is in the case of neutrons defined as Fhkl Z Nj bj exp½2piðhxjC kyj C lzj Þ. Here b is the neutron scattering length of the atom j,
describing the strength of the interaction between the neutron and the nucleus of the atom j. The atomic coordinates are x, y and z, and N is the site occupancy multiplier. The latter can be refined in the Rietveld analysis of the neutron powder diffraction data setting bMe1ZbCuZ7.718 fm and bMe2Z bInZ4.456 fm [24] and reflects directly the cation site occupancy. Thus an average neutron scattering length b Me1 (exp)ZNMe1$bCu and b Me2 (exp)ZNMe2$bIn can be calculated from the experimental data (see Table 1). These values were compared with average scattering lengths calculated assuming a certain distribution (i.e. a statistic Zn distribution and no Cu–In anti-site occupation) by bMe1 ðcalcÞZ ZnCu $bZn C CuCu $bCu C InCu $bIn and b Me2 ðcalcÞZ ZnIn $bZn C CuIn $bCu C InIn $bIn with bZnZ5.67 fm [25] (see Table 1). Here ZnCu, CuCu and InCu are the mole fraction of the cation on the Me1 site, ZnIn, CuIn and InIn are the cation mole fractions on the Me2 site, which gives in sum the total amount of Zn-, Cu- and Inatoms in the (2ZnX)x(CuInX2)1Kx samples (i.e. ZnCuCZnInZ 2x). Because of the disagreement between the experimental and the calculated average neutron scattering lengths of the Me1 and Me2 site in the chalcopyrite type structure it can be concluded, that in the tetragonal single phase region Zn is distributed non-statistically on this both sites for all three (2ZnX)x(CuInX2)1Kx systems. Rietveld analysis of the diffraction data using synchrotron radiation, taken in situ at high temperatures, made a detailed study of the temperature dependent phase transition from the chalcopyrite type to the zinc-blende type structure in CuInX2 possible. In Table 2, the determined transition temperatures are given, in the case of CuInS2 a second transition from the zincblende type structure to the wurtzite type structure was observed. Of special interest were the temperature dependent behaviour of the anion position and the tetragonal deformation h, which is shown in Fig. 5. It can be seen, that within the homologous series, the tetragonal distortion 1⁄4 -u increases Table 2 Transition temperatures of structural phase transitions in CuInX2
Fig. 4. Experimentally determined tetragonal deformation h (left) and anion position (right) for (2ZnX)x(CuInX2)1Kx tetragonal single phase samples (at room temperature). Solid lines are guided by the eye; dotted lines correspond to the 2-phase field. The open circles refer to single crystal samples [24].
CuInX2
Chalcopyrite–zinc-blende (8C)
Zinc-blende–wurtzite
XZS XZSe XZTe
967.6 806.8 662.4
1027.3 8C – –
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Fig. 5. Tetragonal deformation h (left) and anion position (right) for CuInX2 in dependence of TcKT (Tc is the phase transition temperature).
from S/Se/Te, whereas the tetragonal deformation h decreases. These both independent parameters of the chalcopyrite type structure change dramatically just before the phase transition point Tc, indicating a critical region of the phase transition of w10–15 K. Within this temperature range also the cation site occupancy changes, i.e. the value for the Me1 site increases whereas the value for the Me2 site decreases (see Fig. 6), indicating an Cu–In anti site occupation. Thus it can be concluded, that the structural phase transition is driven by the site change of the cations. 4. Conclusions For the first time (2ZnX)x(CuInX2)(1Kx) alloys with XZS, Se and Te have been studied by the combination of X-ray and neutron powder diffraction, diffraction using synchrotron radiation and high resolution electron transmission microscopy
equipped with an EDX-analysis. The results concerning structure and phase relations at room temperature showed that the systems form solid solution series with a miscibility gap. Here two phases coexist as tetragonal domains with chalcopyrite type structure and a cubic matrix with sphaleritetype structure, causing the region named 2-phase field. In the single phase region the lattice parameter show a linear dependence of chemical composition, whereas within the 2-phase field the both phases try to match in the a–b-plane (note that atetr–acub), which gives rise to an increase of the tetragonal lattice constant c and herewith a strong increase of the tetragonal deformation h. From the neutron powder diffraction experiments at room temperature a non-statistical Zn distribution on the both cation sites of the chalcopyrite type structure could be deduced for (2ZnX)x(CuInX2)1Kx alloys with XZS, Se, Te, which is in disagreement to the assumptions in literature. The high temperature in situ diffraction experiments with synchrotron radiation revealed the Cu–In anti-site occupation as the driving force of the phase transition in a way that the structural parameters (lattice constant, anion position) changes dramatically as far as the anti-site occupation starts. Acknowledgements
Fig. 6. Cation site occupancy in dependence of temperature for CuInSe2. The phase transition occurs at TcZ806.8 8C, the dramatically change of the site occupancy values start w10 K before the transition temperature.
The author thank especially D. Spemann (Institute of Experimental Physics II, University Leipzig) for the PIXE measurements and Dr V. Gremenok (Institute of Physics of Solids and Semiconductors, National Academy of Sciences, Minsk, Belarus) for the preparation of the cubic Zn2x(CuIn)1Kx Te2 samples. Moreover thanks are due to Dr Honkimaki (ESRF Grenoble) for providing his self-made software packages for the synchrotron data pre-processing. This work is partly based on experiments performed at the Swiss spallation neutron source SINQ, Paul Scherrer Institute, Villigen, Switzerland and has been supported by the European Commission under the 6th Framework Programme through the Key Action: Strengthening the European Research Area, Research Infrastructures. Contract n8: RII3-CT-2003-505925.
S. Schorr et al. / Journal of Physics and Chemistry of Solids 66 (2005) 1961–1965
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