Phase relations and transformations in the system PbTe-GeTe

Phase relations and transformations in the system PbTe-GeTe

J. Phys. Chem. Solids, 1972,Vol.33, pp. 2053-2062. PergamonPress. Printedin Great Britain PHASE RELATIONS AND TRANSFORMATIONS IN THE SYSTEM PbTe-GeTe...

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J. Phys. Chem. Solids, 1972,Vol.33, pp. 2053-2062. PergamonPress. Printedin Great Britain

PHASE RELATIONS AND TRANSFORMATIONS IN THE SYSTEM PbTe-GeTe D. K. HOHNKE, H. HOLLOWAY and S. KAISER Scientific Research Staff, Ford Motor Company, Dearborn, Mich. 48121, U.S.A. ( R e c e i v e d 2 9 D e c e m b e r 1971)

Abstract--Results of a study of the pseudobinary system P b T e - G e T e are reported and discussed. A new phase diagram, the dependence of the lattice constants on alloy composition, and measurements of a phase transformation in Pb,_~GexTe are presented. Complete solid solubility is found above 570°C. An exsolution dome extends from a maximum at 570°C (near 60 mole % GeTe) to about 5 and 96 mole % G e T e at 300°C. For alloys with compositions near G e T e the unit cell parameters depend markedly on the concentration of cation vacancies. The temperature for the cubic to trigonal phase transformation depends on alloy composition, decreasing from about 670°K for x = l to 0°K for x ~ 0.01. The variation of lattice parameters at the transition temperature is continuous within experimental precision. 1. INTRODUCTION

SOLID solutions of the I V - V I semiconductors have been the subject of much recent attention, generated by the discovery that P b l - : Sn~Te and Pb,_~Sn~Se exhibit a band crossing [1,2]. However, little is known about the phase relationships in the closely related system PbTe-GeTe. Mazelsky e t al.[3] found very limited solubility of GeTe in PbTe at temperatures up to 500°C and Shelimova e t al.[4] reported that mutual solubility increased with increasing temperature, but was limited to the composition ranges PbTe-Pb0.gsGe0.3: Te and Pb0.0sGe0.9~Te-GeTe by the occurrence of a eutectic point at 695°C. Later, work by Woolley and Nikolic[5] showed complete solid solubility between PbTe and GeTe in samples quenched from 600°C. Because of the difference in annealing temperature these last results need not be inconsistent with those of Mazelsky e t al.[3] but they are cIearly incompatible with the phase diagram given by Shelimova e t al.[4]. Phase relationships in the system PbTeGeTe are complicated by the different crystal structures of the binary components. PbTe has a cubic NaCl-type structure, but GeTe attains this structure only above approxi-

mately 400°C (the exact temperature depends on the concentration of native defects). At lower temperatures, GeTe transforms into a slightly distorted NaCl-structure with trigonal symmetry[6-9]. Disagreement exists as to whether this process is discontinuous[8] or continuous [9] and therefore about the possibility that it is of second order. Woolley and Nikolic [5] reported that the room temperature lattice constants of Pb,_xGexTe show a gradual change with composition from the trigonal structure of GeTe to a cubic structure near Pb0.TGe0.3Te. These results suggest the existence of a phase transformation in Pb,_~GexTe. The present paper describes the composition dependence of the lattice constants in Pbx_~Ge~Te, the reinvestigated phase diagram, the composition dependence of the transformation temperature, and the change of the lattice parameters in the region of the phase transformation. 2. EXPERIMENTAL

PbTe and GeTe were synthesized from Pb and Te (nominally 99.9999 per cent pure) and semiconductor grade Ge. For bulk specimens of Pb,_~GexTe, PbTe and GeTe in the correct

2053

2054

D.K.

HOHNKE,

H. H O L L O W A Y and S. K A I S E R

proportions were sealed in evacuated silica tubes at about 10-rtorr, melted, shaken to insure complete mixing, and then quenched in ice water. Subsequently, the resulting ingots were crushed to powder (< 74/zm) and resealed in ampoules for annealing. Vacuum deposited thin films of Pb~_~GexTe were used for equilibration annealing between 300 and 460°C and for phase transformation studies. Layers with thicknesses of 1-4/zm were deposited by evaporation of PbTe and GeTe from two isothermal Knudsen cells in a single rod of spectroscopically pure graphite, This double cell was operated at 700---0.5°C by heating with a coaxial tantalum cylinder. The composition of the flux incident on the substrate was selected by appropriate choice of the orifice sizes. Descriptions of isothermal multiple sources and their application to the vacuum deposition of epitaxial films of I V - V I alloys have been given previously[10, 11]. The substrates were single crystals of BaF~ and KC1 cleaved in air immediately before use. Substrate temperatures were 150-325°C. The large difference between the vapor pressures of PbTe[12] and GeTe[13-15] imposed the need for reduction of temperature gradients during annealing to avoid preferential sublimation of GeTe that would cause a change in alloy composition. With closely controlled furnaces (÷ 0-5°C) and with the specimens inside thick-walled graphite liners, conditions were sufficiently isothermal that no GeTe sublimate was observed. Each anneal was terminated by immersing the sealed tube in ice water, with quench times of about one second. To facilitate rapid quenching the bulk specimens were sealed in small diameter vycor tubes (2-3 mm). Annealing periods ranged from 50 hr for thin film specimens to 500 hr for bulk material. In contrast to previous experiments [5], it was found that annealing periods of approximately 100 hr at 600°C were sufficient to establish equilibrium in bulk material at all compositions. X-ray diffraction was used to determine (i) the variation of lattice parameters with

composition in samples quenched from 600°C, (ii) the number and composition of phases present in samples quenched from temperatures below 600°C, (iii) the temperature for transformation from trigonal to cubic symmetry as a function of alloy composition. Diffraction patterns were obtained with Curadiation (X (CuKai) = 1.54051 ,~) on a Sfemens diffractometer. BaF2 (a z98= 6.2001 .~) or KCI (a298=6.2929.~) were used as internal standards. Annealed powder specimens with grain sizes less than 44/xm gave diffraction peaks that were usually sharp enough to allow the value of 20 to be read to --- 0.02 ° or better. With epitaxial films on BaF2 or KC1, the high intensity and small width of the peaks enables 20 to be read to +_0.002 °. The phase transformation in Pbl-xGexTe was observed by measuring the temperature dependence of its lattice parameters. Lowtemperature trigonal Pb~_~Ge~Te, described with rhombohedral lattice parameters, can be visualized as a slight distortion of the hightemperature cubic phase. The change from trigonal to cubic symmetry was observed by measuring the angular separation of appropriate pairs of reflections, e.g. (hkO) and (hk0), that merge to a single line in the cubic phase. Such pairs were scanned at 4.2 or 77°K and then at 10-20°K intervals. The temperature depencence of the unit cell edge (a) was determined from large-angle reflections. For low-temperature X-ray diffraction experiments a cryostat with a resistance heater was used to control the temperature of the specimen holder to -----l°K in the range 4.2-300°K. Temperatures above 40°K were measured with a copper-constantan thermocouple; a calibrated carbon resistance thermometer was used at low temperatures. 3. LATTICE PARAMETERS

The composition dependence of the roomtemperature lattice constants in Pbl-xGexTe is complicated by the effects of nonstoichio-

THE SYSTEM PbTe-GeTe

metry and also by the varying proximity of the cubic to trigonal phase transformation. It is helpful to discuss these factors in terms of their influence on the lattice constants of the binary components. 1. GeTe. According to Shelimova et al.[7] and Brebrick[15], GeTe has a homogeneity range of 1-1.5at.% which lies entirely,, or almost entirely, o n the Ge-deficient side of the equiatomic composition. This variability of composition is reflected in the change of the lattice parameters across the single-phase field. Table 1 shows the lattice parameters of GeTe that were obtained after equilibration with germanium or tellurium at 420 and at

2055

In contrast to the unit cell edge (a) the literature values of the rhombohedral angle (a) in GeTe(Ge) are widely divergent[5-9, 16-21]. However, scrutiny of the different experimental conditions reveals a pronounced dependence of a on the thermal history of the specimen. Figure 1 shows that a, measured at room temperature, decreases with increasing equilibration temperature from 88° 33' -+ 1' for electrolytically prepared GeTe(Ge)[21] to 88°10.2'--+0.1 ' for GeTe(Ge) annealed at 650°C (this work). This correlation with the thermal history probably arises from the temperature dependence of the stoichiometry at the metal-rich phase boundary. Due to the dominant point defects in GeTe,

Table 1. Lattice parameters for Ge-saturated and Te-saturated G e T e annealed at 420°C and650°C

GeTe(Ge)

a (/~) ot GeTe(Te) ° a(/~) ot

T~ = 650°C

Ta = 420°C

5.984 ± 0"001 88010.2 , ± 0 . 1 ' 5.966+__0.001 88010.0 , ± 0.5'

5.988 ± 0.002 88~20' ±0"5' 5.956±0"002 88o43-5 ' ± 0.5'

650°C. The unit cell edge for GeTe in equilibrium with germanium is in good agreement with most earlier determinations [5-9, 16-20] of a for GeTe synthesized from equiatomic mixtures of Ge and Te. (From the homogeneity range, such specimens would be expected to be at the germanium-rich phase boundary.) The previous results and the present data in Table 1 show that there is little dependence of the unit cell edge of GeTe(Ge)* on annealing temperature between 315°C (5.986 A,[6]) and close to the melting point. Considering the extent of the GeTe phase at 420°C, approximately 1.3at.%[7, 15], and the variation of the unit cell edge across this range (Table 1) we estimate that the composition at the germanium-rich boundary changes less than 0.2 at.% between 315 and 650°C. *GeTe(Ge) and GeTe(Te) denote germanium-saturated G e T e and tellurium-saturated GeTe, respectively.

Ge vacanciest [7], the unit cell of GeTe(Te) is considerably smaller than that of GeTe(Ge). However, while a seems to be directly proportional to the vacancy concentration, the rhombohedral angle is not, in contrast to a previous interpretation[5]. The angles are nearly identical in GeTe(Ge) and GeTe(Te) specimens when quenched from 650°C, despite a difference in their Ge-vacancy concentrations of about an order of magnitude. Since both a and the transition temperature depend on the vacancy concentration[6, 7], (similar t A t 420°C, the compositions G e T e ( G e ) and GeTe(Te) correspond to Gea.497Te0.so3 and Ge0.4asTe0.51z with experimental densities of 6.193 -----0.005gem -a and 6.203 ___0.005 gem -a, respectively [7]. Assuming Ge-vaeancies and using the lattice constants in Table 1, the calculated densities are 6-197±0.01 gem -a and 6.190±0"01gem -a, in good agreement with the experimental values. With a Teinterstitial model the calculated densities are much larger, 6-272 gem -a and 6"493 gem -a, respectively. Thus, the predominant native defects are Ge-vaeancies.

2056

D . K . HOHNKE, H. HOLLOWAY and S. KAISER I

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behavior of SnTe was recently reported [22]) the measured values for a at room temperature depend in a more complex fashion on composition than the unit cell edge. With GeTe(Te), we found no evidence for the more complicated structure mentioned by Schubert and Fricke [6]. 2. PbTe. The lattice parameters for PbT.e(Pb) and PbTe(Te) are the same within experimental precision, 6.460___0.0005 ~, according to Miller et al.[23]. Their results, obtained from specimens equilibrated at 450°C and at 874°C (50°C below the PbTe solidus), have recently been confirmed by Brebrick [24] who found 6.4600 __+0.0002 ~, for PbTe equilibrated with Pb or Te at 400°C. 3. Pb~_=Ge~Te. X-ray analysis of a series of single-phase Pbl_=Ge=Te alloys showed that the unit cell edge varies nearly linearly with composition between cubic PbTe and trigonal G e T e (Table 2). This continuous change in unit cell edge, shown in Fig. 2, is accompanied by a gradual variation of the rhombohedral angle from 90 ° at x = 0.18 to almost 88 ° for x = 1-0, i.e. GeTe. The present data for the lattice parameter a of Pb~_=GeTe at room temperature are in satisfactory agreement with those given by

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Fig. 2. Lattice constants of Pb,_~Ge~Te. Open circles: Metal-saturated alloys; filled circles: Tellurium-saturated alloys. The dashed line shows the dependence of c~ in Sn~_~Ge~Te (Ref. [9]).

Woolley and Nikolic[5]. For compositions 0.7 < x ~< 1.0, the measured rhombohedral angles also agree well, but, at smaller values of x, the present values of o~ diverge considerably from those reported earlier. Instead of following a sigmoid curve, ~ shows a linear dependence on composition which is strikingly similar to that found previously for Snl-xGexTe [9]. In view of the excellent agreement for x > 0.7 it was thought that different preparative conditions might be responsible. As shown above, this accounts for the widely divergent values of a in GeTe(Ge). Figure 3 shows the lattice parameters of Pbl_=Ge=Te obtained from samples annealed at 600°C and lower temperatures. The dashed curve shows the results of Woolley and Nikolic [5], obtained from specimens annealed at 600°(3. By plotting a against a the explicit dependence on mole fraction GeTe, a possible source of discrepancies, is eliminated. As in GeTe(Ge), the rhombohedral angle for alloys near G e T e depends on the annealing temperature. However, with increasing values of a

THE SYSTEM PbTe-GeTe

2057

Table 2. Lattice parameters o f Pbl-xGe~Te. All specimens, except those with x = 0 and 1-0, were annealed at (and rapidly quenched from) 600°C x

J

0.000 0-090_ 0-005 0.185---0-005 0-275 - 0.005 0-375 - 0.005 0.475---0.010 0.700+-0.005 0.800 _+0.005 0.900---0.005 1.000

a(.~)

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6-4600___0-0002 6.422 ± 0.001 6.382___0.002 6.338 - 0.002 6.293 - 0.003 6-245---0.005 6.144___0-002 6-095 +-0-002 [6.040---0-003 [6.018±0.003 ~5-984± 0 . 0 0 1 [5.966___0.001

90 90 90 89'45' ___0-5' 89028' - 1-0' 89011'___3-0 , 88038'___0-5 ' 88027' +-0-5' 88o16' ---0-5' 88013'±2-0 ' 88"10.2'___0.1' 88o10'---0-5 '

(a)

(b) (c) (d) (e)

(a): Ref. [24]. (b), (c): Specimen equilibrated at 600°C with Ge and Te, respectively. (d), (e): Specimen equilibrated at 650°C with Ge and Te, respectively. 90-0

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solve the discrepancies b e t w e e n the p r e s e n t and the p r e v i o u s data for the composition d e p e n d e n c e o f the r h o m b o h e d r a l angle. 4. PHASE RELATIONS IN THE SYSTEM PbTe-GeTe

T h e results o f the present investigation are s h o w n in Fig. 4. X - r a y analyses o f samples Ao o 6_OO*C ./ • 560oc annealed at and q u e n c h e d from 600°C s h o w e d 88-5 single-phase alloys at all compositions bet w e e n P b T e and G e T e , e x c e p t at 60 mole % t I I I i I i I i I G e T e w h e r e the quenching rate was ap88.0 600 6" I0 6"20 6-30 6'40 GeTe parently insufficient. With l o w e r annealing PbTe t e m p e r a t u r e s some samples, depending on Fig. 3. Rhombohedral angle in metal-saturated Pbl-~Gexcomposition and annealing temperature, Te as a function of lattice constant a for several anneals h o w e d two sets o f diffraction peaks with ing temperatures. The dashed line shows the dependence positions intermediate b e t w e e n those o f P b T e for samples annealed at 600°C as given in Ref. [5]. The bar shows the range of values reported for GeTe. and G e T e . This implied the existence o f a miscibility gap. T o d e t e r m i n e the limits o f the (i.e. with larger mole fractions o f P b T e ) this two-phase region samples o f overall composid e p e n d e n c e b e c o m e s less p r o n o u n c e d , prob- tions indicated by crosses in Fig. 4 w e r e ably as a result o f a decreasing h o m o g e n e i t y annealed at the indicated t e m p e r a t u r e s and range. B e y o n d a = 6.14 A (corresponding to then rapidly quenched. T h e equilibrium comP b l - x G e ~ T e with x <~ 0.7) variations o f o~ positions o f the two phases p r e s e n t w e r e then with annealing t e m p e r a t u r e w e r e not detected. d e t e r m i n e d from the k n o w n relationship beT h u s , different thermal histories do not re- t w e e n unit cell edge and composition.

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JPCS Vc~.33, No. 1! -- E

2058

D.K.

H O H N K E , H. H O L L O W A Y and S. K A I S E R

those specimens is attributed to inadequate quenching although the quench times were about one second. Despite several attempts, the composition at 60 mole % GeTe was not 800 quenched fast enough to retain a single phase. Rapid dissociation of Pbo.4Geo.6Te was confirmed when two samples were quenched at 700 slightly different rates because of different wall thicknesses of their vycor ampoules. 2 Exsolution had progressed appreciably further 600 in the thick walled ampoule as indicated by the E extent of the splitting of the difflaction peaks into two sets that corresponded to slightly 500 different compositions. However, from the shape of the two-phase region, it seems evident that it closes smoothly between Pb0.5400 Ge0.sTe and Pb0.3Ge0.TTe to give complete solid solubility above 570°C. The existence of a miscibility gap in the 300 ! ! system PbTe-GeTe and the rapid dissociation u, , i i i i , ~ , " reconcile or explain-the observations of 0-10-20-3 040.50-60-7 0.8 0-9 Mole fracl"ion GeTe earlier workers. The limited solid solubility at 500°C [3] as well as the complete solubility Fig. 4. Phase diagram for the system PbTe-GeTe. at 600°C[5] are consistent with the phase Quenched to one solid: @. Quenched to two solids: +. Two-phase boundary: ©. Single phase solids, Ref. [3]: diagram in Fig. 4. Diffuse X-ray diffraction • (quenched from 500°C), • (heated from room temperawas previously observed [5] for alloys near the ture). Liquidus and solidus, Ref. [4]; n . center of the composition range, but attributed to insufficient annealing rather than to Data for 460°C and below were obtained by phase separation, although annealing periods annealing vacuum deposited thin films. In of up to four weeks were used. In the present contrast to the PbTe-rich phase, which was study 100-200 hr were found to be adequate highly oriented (< 100> on KC1, <111 ) on BaF2) and even the 18-24hr periods, used by and gave intense diffraction peaks, the GeTe- Mazelsky e t al.[3] were apparently enough rich phase was randomly oriented, with dif- considering our agreement with their data. fraction peaks that were too weak to serve for Shelimova e t al.[4] quenched a series of accurate lattice parameter determinations. samples of Pbl_=Ge=Te from 650°C. Their Data for the GeTe-rich side of the miscibility observation of limited solubility at this temgap are, therefore, limited to temperatures perature appears to be a consequence of phase above 460°C. separation due to insufficient quenching rates. The present results show a broad asym- This interpretation is supported by inspection metric exsolution dome with a maximum at of their table which gives the results of annealabout 570°C for Pb0.~sGeo.35Te. X-ray diffrac- ing specimens with overall compositions tion patterns from specimens quenched from between PbTe and Pb0.sGe0.sTe. The componear the dome maximum were considerably sitions Pb0.sGe0.2Te and Pb0.TGe0.3Te were more diffuse than patterns obtained from reported to be single phase alloys. However, samples quenched from above the steeper their values of a are considerably larger than slopes at the sides. The poor crystallinity of those reported here. Such results would be I

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THE SYSTEM PbTe-GeTe

expected for a phase separation where the second phase, the alloy with the larger GeTe mole fraction, remained unobserved. Using their lattice parameters togethe~ with the data in Figs. 2 and 4, we calculate that the GeTerich phase would have given about one tenth the diffracted intensity due to the PbTe-rich phase. From this, it seems likely that there was an undetected, GeTe-rich, phase in some of these specimens. Apparently limited solid solubility at 650°C and the shape of the liquidus and solidus lines, measured by thermal analysis, led Shelimova et al. to propose a simple eutectic phase diagram with a eutectic point at Pb0.2Ge0.sTe. However, with complete miscibility at temperatures above 570°C established by the present investigation and by Woolley and Nikolic [5], it is evident that the liquidus and solidus have a common minimum at that composition rather than a eutectic point. As shown in Fig. 4, the thermal analysis data of Shelimova e t al. a r e consistent with this reinterpretation. Similar behavior of the liquidus and solidus has been found with several other I V - V I alloys[25] (for example in the system PbS-PbTe, which also shows an exsolution dome [26]. 5. PHASE TRANSFORMATIONS

With increasing temperature the rhombohedral angle in GeTe gradually increases, reaching 90° at about 400°C [6-9]. Above this temperature GeTe is cubic. Studies of Snl-~Ge~Te have shown a reduction of the transformation temperature with increasing SnTe content [9] and the possibility of an analogous dependence in Pbl_~Ge=Te has been suggested [25]. The present study shows that a similar phase transformation does exist in Pbl-=Ge~Te. The transformation occurs at room temperature when x = 0 - 1 8 (Fig. 2). Figure 5 shows the temperature dependence of o~ and the extrapolated transition temperatures for several other values of x. The rhombohedral angles at different temperatures were calcul-

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ated from the separation of the (420) and (420) diffraction peaks, except for x = 0.02 where the (642)-(642) separation was used. The precision of the transformation temperatures is limited to ___5-10°K by the gradual approach to the cubic structure. This is shown in more detail for Pb0.asGe0.02Te in Fig. 6. For this composition the (420)-(420) separation is too small, even at 4.2°K, to give useful information. Although the (642)-(642) separation was not resolved either, it was possible to follow the gradual merger of the two peaks with increasing temperature by measuring the decreasing width of the peak that results from I

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2060

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H O H N K E , H. H O L L O W A Y and S. K A I S E R

their partial overlap. Points for x = 0.02 in Fig. 5 were obtained by adjusting the superposition of two identical peaks (with profiles that had been measured at 156°1{) to fit the observed peak widths.* Above 60--+5°K the width remained essentially constant, indicating that the alloy is cubic in this region. The trigonal to cubic transition temperatures for two other alloys, with compositions Pbo.ss3Geo.04rTe and Pbo.s25Geo.o~sTe,were obtained by measuring the temperature dependence of the unit cell edge. Figure 7 shows the results for these alloys as well as the data for Pbo.ssGeo.o2Te and PbTe/r "n-r 6-430

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Lattice constants for PbTe and Pb0.ss3Ge0.o4~Te were obtained from the (800) diffraction angle of epitaxial layers on KCI substrates and that for Pbo.92sGe0.o75Te from the (600) diffraction angle of a layer with a (100) fiber orientation on BaF~. All measurements were corrected by using the substrates as internal standards. (Coefficients of thermal expansion for BaF~[27] and KC1128] were used to calculate the temperature dependence of their lattice constants.) The estimated relative precision of the alloy lattice constants from these measurements is _ 0-0002 .~. The data for Pb0.asGeo.o2Te are from a powder specimen; no internal standard was used. The unit cell edge, like the rhombohedral angle, shows no discontinuity at the transition temperature, only a change of the coefficient of thermal expansion. This is indicated by the changing slopes of curves III and IV in Fig. 7. The change becomes particularly evident when the difference of the lattice constants of Pb0.925Geo.o75Te and its BaFz substrate (Aa) is plotted as a function of temperature (Fig. 8). In this case the thermal expansion coefficients of the high and low temperature modifications of the alloy are, respectively, slightly larger and smaller than those for BaF2, as indicated by the sudden reversal of the slope at the transition temperature of 190+10°K. The magnitude of this change, 7 × 10-6deg -1, is

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Fig. 7. Lattice constants of Pbl_~GexTe as a function of temperature. Arrows indicate the trigonal to cubic transformation. Internal standards: BaF2 (I and IV), KCI (III), none (I 1).

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*The cubic (642) reflection splits into four rhombohedral reflections. In the peak width analysis only the widely separated (642) and (642) peaks were considered. T h e error in neglecting the contribution of the two other peaks is small. ?The lattice constant of PbTe at 298"K in Fig. 7, measured on a single crystal film on BaF~, is 6.462 A and thus considerably larger than the value of 6.4600 [24] for bulk specimens. Repeated measurements on other films, careful alignment of the diffractometer, use of BaF2 and KCI as internal standards and extrapolation to 20 = 180° gave 6-4622 ± 0.0005 A.

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THE SYSTEM PbTe-GeTe

comparable to that of 8 × 10-6 deg -1 observed at the transformation point of GeTe[7]. A transition temperature of 130+-10°K was obtained for Pb0.a~aGe0.047Te on a KCI substrate (III in Fig. 7). Figure 9 shows the dependence of the transition temperature on composition. The fact that the transition temperatures of Pb~_~GexTe are higher than those of Sn~_~Ge~Te[9, 29, 30] over most of the range o f x studied may be, in part, a consequence of the smaller cation vacancy concentration. In G e T e this effect causes the transition temperature to change from 365°C for GeTe(Te) to 430°C for GeTe(Ge)[7]. (A similar result has been obtained with SnTe [22].) The curves in Fig. 9 are for alloys with stoichiometries that correspond to the metal-saturated phase boundaries, at 500-600°C for Pba_~Ge~Te, I

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Snr_,,Ge x Te

2061

the trend toward such a transformation may be inferred from the observation of paraelectric behavior with a Curie temperature of --79_+ 4°K[31]. Previous work on the cubic to trigonal phase transformation in I V - V I compounds has drawn attention to the possibilities of a second-order transformation and of ferroelectric behavior in the trigonal phase[6, 9, 32-37]. The existence of a second-order transformation has been inferred [33, 34] from the temperature dependence of the lattice parameters [6, 9]. However, the temperature dependence of a had not been studied in the range 89o30'-90 °. Subsequently a discontinuous jump from 89o44 ' to 90 °, as well as a discontinuous change of a, was reported[8], implying a first-order transformation. In view of the disagreement about the order of the phase transformation in G e T e , the temperature dependence of the lattice parameters of Pbl_xGe~Teacross the phase transition was studied in detail. As illustrated by Figs. 5-7, no discontinuities were found within the relatively high precision of the present experiments. The present data are, therefore, consistent with a second-order phase transformation in Pbl_=GexTe with x < 0-1.

/"

~.~,.i / I

PbTe TM Sn Te

Trigonol I 0-2

I 0"3

I 0"4

I 0"5

I 06

I 0.7

I 0"8

I 0"9

Mole frocfion GeTe

Fig. 9. Temperature for transformation from trigonal to cubic Pb,_=Ge~Te. The dashed line for Sn,_~Ge=Te is from data given in Refs. [9, 29, 30]. Data for GeTe(Ge): A, Ref. [6]; &, Ref. [7]; O, Ref. [9]. Data for GeTe(Te): I--I. Ref. [6]; i , Ref. [9].

and at somewhat below the melting point for Snl_~Ge~Te. In contrast to the almost linear dependence of the transition temperature upon x in Snl_xGe~Te, the transition temperature of Pb~_~Ge~Te decreases more rapidly with x when x < 0.1, reaching 0°K at x 0.01. The cubic to trigonal phase transformation appears not to occur in PbTe. However,

6. CONCLUSIONS 1. The phase diagram for the P b T e - G e T e system has been established. Complete solid solubility is found above 570°C. Below this temperature the solid solubilities are limited and temperature dependent. Reevaluation of previous liquidus and solidus data indicates the existence of a common minimum at about 695°(2, with a composition near Pb0.zGe0.aTe. 2. Lattice parameters of Pbl _xGexTe, in samples quenched from 6000(2, vary continuously between PbTe and G e T e despite a transition from cubic to trigonal symmetry of the crystal structure (near x = 0.18 at 300°K). There is a nearly linear dependence of the unit cell edge on composition. F o r large values o f x the unit cell parameters

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D . K . HOHNKE, H. HOLLOWAY and S. KAISER

depend significantly on vacancy concentration. The large range of the values that has been reported for the rhombohedral angle in Ge-saturated GeTe is correlated with the thermal histories of the specimens and probably arises from the temperature-dependence of the stoichiometry at the phase boundary. 3. On cooling, the crystal structure of Pbl-xGexTe transforms from cubic to trigonal symmetry. This transformation is continuous within experimental uncertainty. The transition temperature depends on alloy composition and reaches 0°K near x = 0-01. The present data are consistent with a second order phase transformation, although a first order transition cannot be definitely excluded. REFERENCES 1. D I M M O C K J. O., MELNGAILIS I. and STRAUSS A. J., Phys. Rev. Lett. 16, 1193 (1966). 2. STRAUSS A. J., Phys. Rev. 157, 608 (1967). 3. MAZELSKY R., LUBELL M. S. and KRAMER W. E.,J. chem. Phys. 37, 45 (1962). 4. SHELIMOVA L. E., ABRIKOSOV N. Kh. and BESSONOV V. L, lzv. akad. nauk. SSSR, Metal. i. Gornoe Delo 1, 180 (1964). 5. WOOLLEY J. C. and NIKOLIC P., J. electrochem. Soc. 112, 82 (1965) and 112, 906 (1965). 6. SCHUBERT K. and FRICKE H., Z. Metallkunde 44, 457 (1953). 7. SHELIMOVA L. E., ABRIKOSOV N. Kh. and ZHDANOVA V. V., Russ. J. lnorg. Chem. 10, 650 (1965). 8. ZHUKOVA T. B. and ZASLAVSKII A. I., Soviet Phys. Crystallogr. 12, 28 (1967). 9. BIERLY J. N., MULDAWER L. and BECKMAN O.,Acta Metall. 11, 447 (1963). 10. HOLLOWAY H., HOHNKE D. K., CRAWLEY R. L. and WILKES E., J. Vae. Sci. Technol. 7, 586 (1970). 11. HOLLOWAY H., LOGOTHETIS E. M. and WILKES E., J. appl. Phys. 41, 3543 (1970). 12. BREBRICK R. F. and STRAUSS A. J., J. chem. Phys. 40, 3230 (1964).

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