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Time dependence of electrical resistance at high pressure in some tellurium based amorphous alloys
Journal of Non-Crystalline Solids 46 (1981) 33-43 North-Holland Publishing Company
33
TIME DEPENDENCE OF ELECTRICAL RESISTANCE AT HIGH P R E S S U R E IN S O M E T E L L U R I U M B A S E D A M O R P H O U S A L L O Y S S.T. L A K S H M I K U M A R , V.C. P A D A K I , R.M. M A L L Y A * and E.S.R. G O P A L Department of Ph.vsics, Indian Institute of Science, Bangalore, 560 012. India
Received 14 January 1981 Revised manuscript received 19 May 1981
Electrical resistance measurements are reported for amorphous In2oTes0 and Cu25AusTeTo alloys up to a pressure of 80 Kbar using a Bridgman anvil apparatus and a four lead arrangement to measure resistances. The amorphous samples are produced by liquisol quenching. The resistance shows time dependent changes which are analysed in detail. The contention that there is a pressure-induced transformation from the amorphous to the crystalline phase is confirmed by X-ray diffraction of samples recovered after they were pressurised to 35 Kbar in a hydrostatic environment.
1. Introduction The theory of electrical conduction in a m o r p h o u s semiconductors has interesting features [1]. F r o m the work of Mott and A n d e r s o n it is now k n o w n that in an a m o r p h o u s semiconductor there is still a b a n d g a p but that the states at the end of the b a n d gap are localised. W h e n a semiconductor is subjected to high pressure it is normally found that the resistance of the sample decreases. This is due to the decrease in the b a n d gap. This p h e n o m e n o n is found in m a n y a m o r p h o u s semiconductors, for example in As4oSexTer0_ X [2]. In some cases a transition from the semiconducting a m o r p h o u s phase to a crystalline metallic phase is observed. Examples of this type of behaviour can be found in InSb [3] and arsenic [4]. This is reflected in the resistance measurements as a sharp change in the resistivity by about 3 orders of magnitude. In some cases, however, some time dependent changes have been noticed. This has been reported in InSb [3], arsenic [4] and other systems [5]. In the case of arsenic it is mentioned that the resistance keeps drifting for more than 10 to 20 rain. However, the plot given in ref. 4 indicates that while the changes are smaller after about 30 rain, the changes are not completely zero. In the same work it was mentioned that the cause of these time dependent changes is not * Department of Metallurgy, Indian Institute of Science, Bangalore, 560 012, India 0 0 2 2 - 3 0 9 3 / 8 1 / 0 0 0 0 - 0 0 0 0 / $ 0 2 . 7 5 © 1981 N o r t h - H o l l a n d
34
S.T. Lakshmikumar et al. / Time dependence of electrical resistance
known. The authors suggest that a non-hydrostatic nature of the pressure could be responsible for these time dependent changes. Since glasses are metastable systems, glass relaxation and crystallization are both possible. It is known that any relaxation near the glass transition can cause continuous time dependent changes in various physical properties [6]. Thus, a detailed analysis of these time dependent changes in the high pressure measurement is of extreme importance, particularly if the times involved can be accurately measured along with the other parameters. This could hopefully help in the identification of the physical processes which cause the time dependent changes in the resistance at high pressures.
2. Experimental The details of sample production are published elsewhere [7]. The alloys were produced by melting together the constituents in sealed quartz ampoules. They were roller quenched on an assembly developed at our laboratory. They were confirmed to be amorphous by X-ray diffractometry and DSC. In the present work, measurements were performed using a Bridgman-type opposed anvil system. This system consists of two tungsten carbide anvils each with 4 mm diameter faces. This was fabricated and calibrated at our laboratory. The procedure used for sample mounting and measurements is the same as in the previous work [8]. In this system steatite is used as the pressure transmitting medium. As with all other solid pressure transmitting media, this does not generate a truly hydrostatic pressure environment. But this setup has shown very sharp transitions when it has been calibrated with bismuth and ytterbium [8]. This shows that the non-hydrostatic nature is very small and that the pressure variations across the sample are less than about 1 kbar at approximately 50 kbar. The pressure calibration of the system and the experiments are done during the loading cycle. The gaskets are made of heat treated pyrophyllite. For the resistance measurements a Keithley model-225 constant current source and a Datel PD-10 data logger are used. The data logger has a 4½ digit display and print facility. This enables us to measure the resistance with an accuracy of 0.01%. The data logger measures the voltage every 60 s, and prints the value. This gives the resistance, since a constant current is always used. The use of the data logger has allowed us to measure the time dependence reasonably accurately since the data logger has an accuracy of about 0.1 s.
3. Experimental results Even in the initial measurements on the samples, it was noticed that there are time dependent changes in resistance. Hence the pressure was increased from one value to another only when the time dependent changes had died
S.T. Lakshmikumar et a L / Time dependence of electrical resistance
35
down. (SR less than 0.2% min-I). The increment in pressure was usually 2-3 kbar, corresponding to a change in oil pressure of 10 to 15 psi. It would have been better to wait for very long periods of time but this caused some problems in the present system. The pressurisation of the oil pump is done by hand with a valve along the oil line. Because of the inevitable small leakage past the Valve, the pressure was not very stable over long periods of time. In our system, the pressure is stable only for about 100 min. This gives us 50 to 75 points for the plot of the variation of resistance with time at
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Fig. 1. Variation of the resistance of the InzoTe80 sample with pressure.
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S. 7". Lakshmikumar et al. / Time dependence of electrical resistance
36
constant pressure. Another limiting factor is the possible drift in resistance with temperature. All measurements reported here were performed at (300 ± 1) K. Here again improvements are possible in future measurements. The results obtained on the In20Tes0 and Cu25-AusTeT0 samples are presented in figs. 1-4. In figs. 1 and 2, logR is plotted against pressure. There are two points indicated at each pressure. These indicate the higher value of the resistance at the start and the lower value of the resistance at the end of the time dependent changes. These are referred to as R s and R E. The time dependent changes in R occur between R s and R E at each pressure. The typical change in the resistance between R s and R E is shown in fig. 3. Here R is plotted against time. The lack of scatter in the plot clearly shows that the
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Fig. 3. Typicalvariation of resistance with time. changes are not because of any problems in the measuring system. In fig. 4, the variation of (R s -- R E ) / R s has been plotted. This plot is further discussed in section 5.
4. X-ray investigations at high pressure Since some interesting results are obtained from the resistance measurements, an X-ray investigation becomes very significant. There are, however, some serious problems in any X-ray measurement. Since there are obviously changes with time, X-ray exposure for long durations will be ambiguous if there are changes in the sample during exposure. Hence an X-ray investigation of the samples recovered after pressurisation was attempted. As already mentioned, in the present study, an opposed anvil setup with solid pressure transmitting medium is used. After pressurisation, it was found that the sample, the pressure transmitting medium (steatite) and the gaskets became very solidly bonded together and the recovery of the sample was very difficult. Also, the size of the sample used is very small and X-ray work on such samples has been very difficult.
S.T. Lakshmikumar et aL / Time dependence of electrical resistance
38
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Fig. 4. Variation of (R s -- R E ) / R s with pressure for TeToCU25Au5 and TesoIn2o samples.
Hence X-ray identification has been attempted of samples pressurized to about 35 kbar in a piston-cylinder apparatus. A calibrated system developed at the National Aeronautical Laboratory, Bangalore, with the kind assistance of Dr. T.G. Ramesh, was used. Here a mixture of 20% ethanol and 80% methanol is used as the liquid pressure transmitting medium. Hence pressures are truly hydrostatic. Also since the cell is large, larger samples can be used. The recovery of the sample from the liquid medium is also easy.
S.T. Lakshmikumar et al. / Time dependence of electrical resistance
39
Laue photographs of the foils before and after pressurisation show that samples are crystallised at high pressures.
5. Discussion of the results
The results of electrical resistance measurement show the usual trend shown in any semiconductor, if the time dependent changes in resistance are not considered. The resistance continuously decreases. The value of d R / d P decreases at higher pressures. This increase in conduction could be explained as a decrease in band gap Eg. If we write, R ( P ) = R o exp[--Eg(P)/KT]. Then BEg(P, -- Pz) = K T [ I ° g R ( P2) - logR(P, )]. Physically the band gap decreases due to the compression of the sample and the resultant reduction in lattice parameters. As P is increased, further reductions of Eg are difficult. Hence the resistance changes slowly at very high pressures. Such results are known in various amorphous semiconductors, for example, in the As-Te-Se systems [2], Eg varies from 0.5 eV to 0.1 eV. No calculations of Eg were performed on the present systems because of large time dependent changes. The more important results are those of time dependent changes. As already mentioned, time dependent changes were noticed previously but their origin was not dearly known [4]. Our results indicate that these changes in resistance, are not any experimental artifacts but indicate genuine changes in the sample. The slow changes in resistance of the present samples at single pressures arise from a pressure induced amorphous-to-crystalline phase transformation, while nothing conclusive can be said about the results of earlier workers. This contention is supported by the following facts. If the non-hydrostatic nature etc. were responsible for the time dependent changes, this type of time dependence should be noticed in every sample. The present experimental setup has been extensively used to make measurements on metallic samples Bi, Pb and Yb. Also a number of measurements were made on semiconducting organic charge transfer complexes and quasi-one-dimensional systems [9]. No time dependent change was noticed in all these measurements when resistance values from 0.1 to 10 9 ~ were measured. Furthermore the calibration curves show very sharp transitions indicating the high degree of the hydrostatic nature of the pressure. Secondly in the In 20Tea0 system, time dependent changes are noticed in the complete pressure range. But the changes are very small in the Te70Cu25Au 5 system at pressures of 45 kbar and above. However, any non-hydrostatic nature of the pressure should worsen at higher pressures and one should expect the time dependent changes to be highest at the highest pressure. The present
40
S.T. Lakshmikumar et al. / Time dependence of electrical resistance
results thus show that the time dependent changes are genuine manifestations of changes in the samples. In an attempt to qualify these changes to some extent, the values of (R s - R E ) / R s have been plotted against pressure in fig. 4. This value represents the total percentage change of resistance at any particular pressure. This can, in a very approximate sense, be taken as a representation of the total transformation within the sample that occurs at any particular pressure. As shown in fig. 3, the variation of resistance with time does not completely stop. While d R / d t becomes small, a careful look at the figure shows that it is never zero. We consider that the resistance has completely stabilised if the change in R is not above 0.02 or 0.03% min-i. Hence the possible error in absolute values of (R s -- R E ) / R E may be as high as 10%. Even with this limitation, some qualitative observations can be made. One is that in the range of pressures where the time dependent changes are noticed, the changes of R with time are larger than the changes .in R caused by a step increment in pressure. Also, fig. 4 shows that there are changes in the time dependent behaviours of the two samples. The plot of (R s - R E ) / R s has a broad maximum for the In20Tes0 system. Also (R s - R E ) / R s is large even at 80 kbar. This shows that the transformations in this system are not complete in this pressure range. But in the case of the TeToCu25Au5 system the plot has two peaks and also (R s - - R E ) / R s is essentially zero beyond about 50 kbar. This indicates that transformations are complete in this system. It has now been shown that time dependent changes are the manifestations of transformations within the sample. In amorphous materials, glass relaxation and crystallisation are the phenomena which can show such time dependent changes. It is known that a relaxation of the glassy structure can cause time dependent changes in the resistance of some metallic alloys at temperatures near Tg [10]. A similar effect is noticed in the thermal expansivity of Se [11]. In amorphous ferromagnets, it is known that at temperatures well below the crystallisation temperature (in most amorphous ferromagnets, no Tg is detected and it is generally accepted that this is because T~ = Tg), there are manifestations of structural relaxation on physical properties. It is also found that in amorphous ferromagnets, the degree of topological short range order can increase as logt, where t is the time [12]. Thus the glass relaxation is a possible mechanism for these changes, since relaxation of glasses due to pressure is possible. Since crystallisation of a glass is possible when a glass is heated, we can argue that a pressure induced crystalfisation is another possible mechanism. As already mentioned, the X-ray work has been performed to resolve this dilemma and the data very clearly indicate that the mechanism is crystallisation. A direct in situ high pressure X-ray diffraction experiment would have been very useful in identifying the total amounts of transformation at various stages and also the exact identity of the crystalline phases. However, this could not be done here at present. The X-ray work on the pressurised samples however clearly indicates that the crystallisation of the samples is the mechanism involved.
S.T. Lakshmikumar et al. / Time dependence of electrical resistance
41
The next question is whether high pressure can really cause crystallisation. The information available is quite limited. In amorphous semiconductors there is evidence of a sharp transition at high pressures from an amorphous semiconducting phase to a crystalline metallic phase [3,4]. In metallic glasses some workers report that high pressure has increased the temperature of spontaneous crystallisation [13,14]. It is possible that the directional nature of the covalent bond causes crystallisation at high pressures, while in the metallic glasses, the bonding is non-directional and hence high pressures may not lead to crystallisation. If we indicate the high pressure crystallisation as the cause of these changes, it is of interest to see if any process can be identified in more detail. In our measurements, the final phase is also semiconducting. This is seen from the fact that the R value increases as the pressure is released. Since the setup is not calibrated while unloading the cell, it is not possible to get any quantitative information. The equilibrium phases are eutectics of tellurium and a compound of tellurium with a metal [15]. Unfortunately, the ternary phase diagram of the C u - A u - T e system is not known and only the binary phase diagram for the C u - T e system is known. Te is a large component in the compound and so it is probable that the compound is also a semiconductor. Since both phases of the eutectic are semiconductors, the final phase can be semiconducting as can be seen from our experiment. It is however, not necessary that the final phase after pressurisation be the equilibrium phase. The qualitative nature of the curves in fig. 4 can now be explained. In general the structures of glasses based on selenum and tellurium are known to be due to the formation of chains of trigonal symmetry. Both the elements form a trigonal crystal. In selenium a monoclinic structure is also known. Here rings of Se (8 atoms) form a monoclinic lattice. Raman and vibrational spectroscopy of amorphous Se and Te has shown that chains do form. In Se some contribution of the rings has also been identified [16]. This is not found in Te glass. It is also known that in G e - T e glasses, the Te retains the twofold co-ordination [17]. The detailed structure of glasses involving tellurium and a metallic constituent element is not known but the general features could be interacting chains of tellurium and copper or indium in the voids. Indium is more covalent and forms a number of covalently bonded glasses like In-Sb. Thus the interaction of In into the chains of Te could be more than that of copper. Also in sulphur which also forms chains, a temperature dependence of the chain length is known [18]. Sulphur forms chains in glasses and even in molten sulphur. The variation of chain length is also possible under the influence of pressure. A slow segregation of the metal compound phase from Te might be the process of crystallisation in these systems. Since In is more covalent, it seems possible that the range of pressure required to complete the transformations should be more than it is in a system containing copper. This explains the complete transformation of the T e - C u - A u sample and the incomplete transformation of the I n - T e sample. The double peak in the case
42
S.T. Lakshmikumar et al. / Time dependence of electrical resistance
of T e - C u - A u is more difficult to explain. It is known that the chain length in selenium is 10 4 atoms near the melting point [18]. The value for tellurium is not known but must be smaller since it is more difficult to form tellurium as a glass. It could be that the chain length variation is in two steps leading to two peaks. Another possibility is that there is some intermediate metastable phase. The transformation into this is first completed and then there is a further change in another phase. In a number of metallic and other glasses it is known that the crystallisation at high temperatures proceeds through a number of partially or completely crystalline intermediate metastable phases, for example the F e - N i - B system [19], the M g - Z n system [20], and the T e - G e - P b system [21] show such behaviour as is evident from DSC data. The DSC plots for our two samples are shown in fig. 5. At high temperatures it is the I n - T e system which crystallises through a series of metastable phases. But it is possible that this may occur in the T e - C u - A u system under high pressure. A more
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S. 1". Lakshmikumar et al. / Time dependence of electrical resistance
43
quantitative calculation of the total amount of transformation at each pressure cannot be obtained with any reasonable accuracy since the plot shown in fig. 4 has a large source of error as discussed already. In conclusion, we can summarize the results as follows: (1) there are time dependent changes; (2) these are not caused by experimental deficiencies like non-hydrostatic stresses and so on; (3) the changes are due to crystallisation and not due to relaxation at least in these systems; (4) the transformations in the sample can be qualitatively accounted for on the basis of some ideas of the structures of the In-Te and C u - A u - T e glasses. We wish to thank Dr. S.V. Subramanyam for many useful suggestions and encouragement during the work, A.K. Bandyopadhyay for allowing us to use the anvil setup developed by him, Dr. T.G. Ramesh of NAL for help in preparing the samples for X-ray work. Financial assistance from PL-480 funds is also gratefully acknowledged.
References [I] [2] [3] [4] [5] [6] [7] [8] [9] [10] [1 I] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]
N.F. Mott, J. Non-Crystalline Solids 28 (1978) 147. G. Ramani, A. Giridhar, A.K. Singh and K.J. Rao, Phil. Mag. 39 (1979) 385. O. Shimomura, K. Asoumi, N. Sakai and S. Minomura, Phil. Mag. 34 (1976) 839. G.N. Greaves, S.R. Elliott and E.A. Davis, Adv. Phys. 28 (1979) 49. R.T. Johnson and R.K. Quinn, J. Non-Crystalline Solids 28 (1978) 273. E. Kittinger J. Non-Crystalline Solids 27 (1978) 421. S.T. Lakshmikumar, R.M. Mallya and ES.R. Gopal, Bull. Mat. Sci. 3 (1981) 233. A.K. Bandyopadhyay, A.V. Nalini, E.S.R. Gopal and S.V. Subramanyam, Rev. Sci. Instr. 51 (1980) 136. A.K. Bandyopadhyay and S.V. Subramanyam, J. Appl. Phys. to be published. M.A. Marcus, Acta Met. 29 (1979) 879. E. Kittinger, Phys. Stat. Sol. 44A (1977) K35. C.D. Graham Jr and T. Egami, Ann. Rev. Mat. Sci. 8 (1978) 423. W.C. Emmens, J. Vrijen and S. Radelaar, J. Non-Crystalline Solids 18 (1975) 299. W. Iwasaki and T. Masumoto, J. Mat. Sci. 13 (1978) 2171. M. Hansen, Constitution of binary alloys (McGraw-Hill, New York, 1958). M.H. Brodsky and M. Gardona J. Non-Crystalline Solids 31 (1978) 81. G.A.N. Connell and G. Lucovsky, J. Non-Crystalline Solids 31 (1978) 122. R.H. Doremus, Ann. Rev. Mat. Sci. 2 (1972) 93. B.G. Lewis, H.A, Davies and K.D. Ward, Script. Met. 13 (1979) 313. A. Calka, M. Madhava, D.E. Polk, B.G. Geissen, H. Matyja and J. Vander Sande, Scrip. Met. 11 (1977) 65. M. Lasocka, J. Mat. Sci. 13 (1978) 2055.
33
TIME DEPENDENCE OF ELECTRICAL RESISTANCE AT HIGH P R E S S U R E IN S O M E T E L L U R I U M B A S E D A M O R P H O U S A L L O Y S S.T. L A K S H M I K U M A R , V.C. P A D A K I , R.M. M A L L Y A * and E.S.R. G O P A L Department of Ph.vsics, Indian Institute of Science, Bangalore, 560 012. India
Received 14 January 1981 Revised manuscript received 19 May 1981
Electrical resistance measurements are reported for amorphous In2oTes0 and Cu25AusTeTo alloys up to a pressure of 80 Kbar using a Bridgman anvil apparatus and a four lead arrangement to measure resistances. The amorphous samples are produced by liquisol quenching. The resistance shows time dependent changes which are analysed in detail. The contention that there is a pressure-induced transformation from the amorphous to the crystalline phase is confirmed by X-ray diffraction of samples recovered after they were pressurised to 35 Kbar in a hydrostatic environment.
1. Introduction The theory of electrical conduction in a m o r p h o u s semiconductors has interesting features [1]. F r o m the work of Mott and A n d e r s o n it is now k n o w n that in an a m o r p h o u s semiconductor there is still a b a n d g a p but that the states at the end of the b a n d gap are localised. W h e n a semiconductor is subjected to high pressure it is normally found that the resistance of the sample decreases. This is due to the decrease in the b a n d gap. This p h e n o m e n o n is found in m a n y a m o r p h o u s semiconductors, for example in As4oSexTer0_ X [2]. In some cases a transition from the semiconducting a m o r p h o u s phase to a crystalline metallic phase is observed. Examples of this type of behaviour can be found in InSb [3] and arsenic [4]. This is reflected in the resistance measurements as a sharp change in the resistivity by about 3 orders of magnitude. In some cases, however, some time dependent changes have been noticed. This has been reported in InSb [3], arsenic [4] and other systems [5]. In the case of arsenic it is mentioned that the resistance keeps drifting for more than 10 to 20 rain. However, the plot given in ref. 4 indicates that while the changes are smaller after about 30 rain, the changes are not completely zero. In the same work it was mentioned that the cause of these time dependent changes is not * Department of Metallurgy, Indian Institute of Science, Bangalore, 560 012, India 0 0 2 2 - 3 0 9 3 / 8 1 / 0 0 0 0 - 0 0 0 0 / $ 0 2 . 7 5 © 1981 N o r t h - H o l l a n d
34
S.T. Lakshmikumar et al. / Time dependence of electrical resistance
known. The authors suggest that a non-hydrostatic nature of the pressure could be responsible for these time dependent changes. Since glasses are metastable systems, glass relaxation and crystallization are both possible. It is known that any relaxation near the glass transition can cause continuous time dependent changes in various physical properties [6]. Thus, a detailed analysis of these time dependent changes in the high pressure measurement is of extreme importance, particularly if the times involved can be accurately measured along with the other parameters. This could hopefully help in the identification of the physical processes which cause the time dependent changes in the resistance at high pressures.
2. Experimental The details of sample production are published elsewhere [7]. The alloys were produced by melting together the constituents in sealed quartz ampoules. They were roller quenched on an assembly developed at our laboratory. They were confirmed to be amorphous by X-ray diffractometry and DSC. In the present work, measurements were performed using a Bridgman-type opposed anvil system. This system consists of two tungsten carbide anvils each with 4 mm diameter faces. This was fabricated and calibrated at our laboratory. The procedure used for sample mounting and measurements is the same as in the previous work [8]. In this system steatite is used as the pressure transmitting medium. As with all other solid pressure transmitting media, this does not generate a truly hydrostatic pressure environment. But this setup has shown very sharp transitions when it has been calibrated with bismuth and ytterbium [8]. This shows that the non-hydrostatic nature is very small and that the pressure variations across the sample are less than about 1 kbar at approximately 50 kbar. The pressure calibration of the system and the experiments are done during the loading cycle. The gaskets are made of heat treated pyrophyllite. For the resistance measurements a Keithley model-225 constant current source and a Datel PD-10 data logger are used. The data logger has a 4½ digit display and print facility. This enables us to measure the resistance with an accuracy of 0.01%. The data logger measures the voltage every 60 s, and prints the value. This gives the resistance, since a constant current is always used. The use of the data logger has allowed us to measure the time dependence reasonably accurately since the data logger has an accuracy of about 0.1 s.
3. Experimental results Even in the initial measurements on the samples, it was noticed that there are time dependent changes in resistance. Hence the pressure was increased from one value to another only when the time dependent changes had died
S.T. Lakshmikumar et a L / Time dependence of electrical resistance
35
down. (SR less than 0.2% min-I). The increment in pressure was usually 2-3 kbar, corresponding to a change in oil pressure of 10 to 15 psi. It would have been better to wait for very long periods of time but this caused some problems in the present system. The pressurisation of the oil pump is done by hand with a valve along the oil line. Because of the inevitable small leakage past the Valve, the pressure was not very stable over long periods of time. In our system, the pressure is stable only for about 100 min. This gives us 50 to 75 points for the plot of the variation of resistance with time at
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Fig. 1. Variation of the resistance of the InzoTe80 sample with pressure.
8O
S. 7". Lakshmikumar et al. / Time dependence of electrical resistance
36
constant pressure. Another limiting factor is the possible drift in resistance with temperature. All measurements reported here were performed at (300 ± 1) K. Here again improvements are possible in future measurements. The results obtained on the In20Tes0 and Cu25-AusTeT0 samples are presented in figs. 1-4. In figs. 1 and 2, logR is plotted against pressure. There are two points indicated at each pressure. These indicate the higher value of the resistance at the start and the lower value of the resistance at the end of the time dependent changes. These are referred to as R s and R E. The time dependent changes in R occur between R s and R E at each pressure. The typical change in the resistance between R s and R E is shown in fig. 3. Here R is plotted against time. The lack of scatter in the plot clearly shows that the
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Fig. 3. Typicalvariation of resistance with time. changes are not because of any problems in the measuring system. In fig. 4, the variation of (R s -- R E ) / R s has been plotted. This plot is further discussed in section 5.
4. X-ray investigations at high pressure Since some interesting results are obtained from the resistance measurements, an X-ray investigation becomes very significant. There are, however, some serious problems in any X-ray measurement. Since there are obviously changes with time, X-ray exposure for long durations will be ambiguous if there are changes in the sample during exposure. Hence an X-ray investigation of the samples recovered after pressurisation was attempted. As already mentioned, in the present study, an opposed anvil setup with solid pressure transmitting medium is used. After pressurisation, it was found that the sample, the pressure transmitting medium (steatite) and the gaskets became very solidly bonded together and the recovery of the sample was very difficult. Also, the size of the sample used is very small and X-ray work on such samples has been very difficult.
S.T. Lakshmikumar et aL / Time dependence of electrical resistance
38
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\
®
Lt ®
0.~
\
I
20
40 PRESSURE IN Kbor - ~
60
80
Fig. 4. Variation of (R s -- R E ) / R s with pressure for TeToCU25Au5 and TesoIn2o samples.
Hence X-ray identification has been attempted of samples pressurized to about 35 kbar in a piston-cylinder apparatus. A calibrated system developed at the National Aeronautical Laboratory, Bangalore, with the kind assistance of Dr. T.G. Ramesh, was used. Here a mixture of 20% ethanol and 80% methanol is used as the liquid pressure transmitting medium. Hence pressures are truly hydrostatic. Also since the cell is large, larger samples can be used. The recovery of the sample from the liquid medium is also easy.
S.T. Lakshmikumar et al. / Time dependence of electrical resistance
39
Laue photographs of the foils before and after pressurisation show that samples are crystallised at high pressures.
5. Discussion of the results
The results of electrical resistance measurement show the usual trend shown in any semiconductor, if the time dependent changes in resistance are not considered. The resistance continuously decreases. The value of d R / d P decreases at higher pressures. This increase in conduction could be explained as a decrease in band gap Eg. If we write, R ( P ) = R o exp[--Eg(P)/KT]. Then BEg(P, -- Pz) = K T [ I ° g R ( P2) - logR(P, )]. Physically the band gap decreases due to the compression of the sample and the resultant reduction in lattice parameters. As P is increased, further reductions of Eg are difficult. Hence the resistance changes slowly at very high pressures. Such results are known in various amorphous semiconductors, for example, in the As-Te-Se systems [2], Eg varies from 0.5 eV to 0.1 eV. No calculations of Eg were performed on the present systems because of large time dependent changes. The more important results are those of time dependent changes. As already mentioned, time dependent changes were noticed previously but their origin was not dearly known [4]. Our results indicate that these changes in resistance, are not any experimental artifacts but indicate genuine changes in the sample. The slow changes in resistance of the present samples at single pressures arise from a pressure induced amorphous-to-crystalline phase transformation, while nothing conclusive can be said about the results of earlier workers. This contention is supported by the following facts. If the non-hydrostatic nature etc. were responsible for the time dependent changes, this type of time dependence should be noticed in every sample. The present experimental setup has been extensively used to make measurements on metallic samples Bi, Pb and Yb. Also a number of measurements were made on semiconducting organic charge transfer complexes and quasi-one-dimensional systems [9]. No time dependent change was noticed in all these measurements when resistance values from 0.1 to 10 9 ~ were measured. Furthermore the calibration curves show very sharp transitions indicating the high degree of the hydrostatic nature of the pressure. Secondly in the In 20Tea0 system, time dependent changes are noticed in the complete pressure range. But the changes are very small in the Te70Cu25Au 5 system at pressures of 45 kbar and above. However, any non-hydrostatic nature of the pressure should worsen at higher pressures and one should expect the time dependent changes to be highest at the highest pressure. The present
40
S.T. Lakshmikumar et al. / Time dependence of electrical resistance
results thus show that the time dependent changes are genuine manifestations of changes in the samples. In an attempt to qualify these changes to some extent, the values of (R s - R E ) / R s have been plotted against pressure in fig. 4. This value represents the total percentage change of resistance at any particular pressure. This can, in a very approximate sense, be taken as a representation of the total transformation within the sample that occurs at any particular pressure. As shown in fig. 3, the variation of resistance with time does not completely stop. While d R / d t becomes small, a careful look at the figure shows that it is never zero. We consider that the resistance has completely stabilised if the change in R is not above 0.02 or 0.03% min-i. Hence the possible error in absolute values of (R s -- R E ) / R E may be as high as 10%. Even with this limitation, some qualitative observations can be made. One is that in the range of pressures where the time dependent changes are noticed, the changes of R with time are larger than the changes .in R caused by a step increment in pressure. Also, fig. 4 shows that there are changes in the time dependent behaviours of the two samples. The plot of (R s - R E ) / R s has a broad maximum for the In20Tes0 system. Also (R s - R E ) / R s is large even at 80 kbar. This shows that the transformations in this system are not complete in this pressure range. But in the case of the TeToCu25Au5 system the plot has two peaks and also (R s - - R E ) / R s is essentially zero beyond about 50 kbar. This indicates that transformations are complete in this system. It has now been shown that time dependent changes are the manifestations of transformations within the sample. In amorphous materials, glass relaxation and crystallisation are the phenomena which can show such time dependent changes. It is known that a relaxation of the glassy structure can cause time dependent changes in the resistance of some metallic alloys at temperatures near Tg [10]. A similar effect is noticed in the thermal expansivity of Se [11]. In amorphous ferromagnets, it is known that at temperatures well below the crystallisation temperature (in most amorphous ferromagnets, no Tg is detected and it is generally accepted that this is because T~ = Tg), there are manifestations of structural relaxation on physical properties. It is also found that in amorphous ferromagnets, the degree of topological short range order can increase as logt, where t is the time [12]. Thus the glass relaxation is a possible mechanism for these changes, since relaxation of glasses due to pressure is possible. Since crystallisation of a glass is possible when a glass is heated, we can argue that a pressure induced crystalfisation is another possible mechanism. As already mentioned, the X-ray work has been performed to resolve this dilemma and the data very clearly indicate that the mechanism is crystallisation. A direct in situ high pressure X-ray diffraction experiment would have been very useful in identifying the total amounts of transformation at various stages and also the exact identity of the crystalline phases. However, this could not be done here at present. The X-ray work on the pressurised samples however clearly indicates that the crystallisation of the samples is the mechanism involved.
S.T. Lakshmikumar et al. / Time dependence of electrical resistance
41
The next question is whether high pressure can really cause crystallisation. The information available is quite limited. In amorphous semiconductors there is evidence of a sharp transition at high pressures from an amorphous semiconducting phase to a crystalline metallic phase [3,4]. In metallic glasses some workers report that high pressure has increased the temperature of spontaneous crystallisation [13,14]. It is possible that the directional nature of the covalent bond causes crystallisation at high pressures, while in the metallic glasses, the bonding is non-directional and hence high pressures may not lead to crystallisation. If we indicate the high pressure crystallisation as the cause of these changes, it is of interest to see if any process can be identified in more detail. In our measurements, the final phase is also semiconducting. This is seen from the fact that the R value increases as the pressure is released. Since the setup is not calibrated while unloading the cell, it is not possible to get any quantitative information. The equilibrium phases are eutectics of tellurium and a compound of tellurium with a metal [15]. Unfortunately, the ternary phase diagram of the C u - A u - T e system is not known and only the binary phase diagram for the C u - T e system is known. Te is a large component in the compound and so it is probable that the compound is also a semiconductor. Since both phases of the eutectic are semiconductors, the final phase can be semiconducting as can be seen from our experiment. It is however, not necessary that the final phase after pressurisation be the equilibrium phase. The qualitative nature of the curves in fig. 4 can now be explained. In general the structures of glasses based on selenum and tellurium are known to be due to the formation of chains of trigonal symmetry. Both the elements form a trigonal crystal. In selenium a monoclinic structure is also known. Here rings of Se (8 atoms) form a monoclinic lattice. Raman and vibrational spectroscopy of amorphous Se and Te has shown that chains do form. In Se some contribution of the rings has also been identified [16]. This is not found in Te glass. It is also known that in G e - T e glasses, the Te retains the twofold co-ordination [17]. The detailed structure of glasses involving tellurium and a metallic constituent element is not known but the general features could be interacting chains of tellurium and copper or indium in the voids. Indium is more covalent and forms a number of covalently bonded glasses like In-Sb. Thus the interaction of In into the chains of Te could be more than that of copper. Also in sulphur which also forms chains, a temperature dependence of the chain length is known [18]. Sulphur forms chains in glasses and even in molten sulphur. The variation of chain length is also possible under the influence of pressure. A slow segregation of the metal compound phase from Te might be the process of crystallisation in these systems. Since In is more covalent, it seems possible that the range of pressure required to complete the transformations should be more than it is in a system containing copper. This explains the complete transformation of the T e - C u - A u sample and the incomplete transformation of the I n - T e sample. The double peak in the case
42
S.T. Lakshmikumar et al. / Time dependence of electrical resistance
of T e - C u - A u is more difficult to explain. It is known that the chain length in selenium is 10 4 atoms near the melting point [18]. The value for tellurium is not known but must be smaller since it is more difficult to form tellurium as a glass. It could be that the chain length variation is in two steps leading to two peaks. Another possibility is that there is some intermediate metastable phase. The transformation into this is first completed and then there is a further change in another phase. In a number of metallic and other glasses it is known that the crystallisation at high temperatures proceeds through a number of partially or completely crystalline intermediate metastable phases, for example the F e - N i - B system [19], the M g - Z n system [20], and the T e - G e - P b system [21] show such behaviour as is evident from DSC data. The DSC plots for our two samples are shown in fig. 5. At high temperatures it is the I n - T e system which crystallises through a series of metastable phases. But it is possible that this may occur in the T e - C u - A u system under high pressure. A more
ENOO
In2oTeBo EXO
I
350
400
I
450 500 TEMPERATURE IN K
l
l
I
550 >
600
650
ENDO
EXO
Cu25AusTeT0
330
360
390 420 TEMPERATURE IN K
Fig. 5. DSC plots of In2oTe80 and Cu25AusTeT0 samples.
I
I
450
480.
S. 1". Lakshmikumar et al. / Time dependence of electrical resistance
43
quantitative calculation of the total amount of transformation at each pressure cannot be obtained with any reasonable accuracy since the plot shown in fig. 4 has a large source of error as discussed already. In conclusion, we can summarize the results as follows: (1) there are time dependent changes; (2) these are not caused by experimental deficiencies like non-hydrostatic stresses and so on; (3) the changes are due to crystallisation and not due to relaxation at least in these systems; (4) the transformations in the sample can be qualitatively accounted for on the basis of some ideas of the structures of the In-Te and C u - A u - T e glasses. We wish to thank Dr. S.V. Subramanyam for many useful suggestions and encouragement during the work, A.K. Bandyopadhyay for allowing us to use the anvil setup developed by him, Dr. T.G. Ramesh of NAL for help in preparing the samples for X-ray work. Financial assistance from PL-480 funds is also gratefully acknowledged.
References [I] [2] [3] [4] [5] [6] [7] [8] [9] [10] [1 I] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]
N.F. Mott, J. Non-Crystalline Solids 28 (1978) 147. G. Ramani, A. Giridhar, A.K. Singh and K.J. Rao, Phil. Mag. 39 (1979) 385. O. Shimomura, K. Asoumi, N. Sakai and S. Minomura, Phil. Mag. 34 (1976) 839. G.N. Greaves, S.R. Elliott and E.A. Davis, Adv. Phys. 28 (1979) 49. R.T. Johnson and R.K. Quinn, J. Non-Crystalline Solids 28 (1978) 273. E. Kittinger J. Non-Crystalline Solids 27 (1978) 421. S.T. Lakshmikumar, R.M. Mallya and ES.R. Gopal, Bull. Mat. Sci. 3 (1981) 233. A.K. Bandyopadhyay, A.V. Nalini, E.S.R. Gopal and S.V. Subramanyam, Rev. Sci. Instr. 51 (1980) 136. A.K. Bandyopadhyay and S.V. Subramanyam, J. Appl. Phys. to be published. M.A. Marcus, Acta Met. 29 (1979) 879. E. Kittinger, Phys. Stat. Sol. 44A (1977) K35. C.D. Graham Jr and T. Egami, Ann. Rev. Mat. Sci. 8 (1978) 423. W.C. Emmens, J. Vrijen and S. Radelaar, J. Non-Crystalline Solids 18 (1975) 299. W. Iwasaki and T. Masumoto, J. Mat. Sci. 13 (1978) 2171. M. Hansen, Constitution of binary alloys (McGraw-Hill, New York, 1958). M.H. Brodsky and M. Gardona J. Non-Crystalline Solids 31 (1978) 81. G.A.N. Connell and G. Lucovsky, J. Non-Crystalline Solids 31 (1978) 122. R.H. Doremus, Ann. Rev. Mat. Sci. 2 (1972) 93. B.G. Lewis, H.A, Davies and K.D. Ward, Script. Met. 13 (1979) 313. A. Calka, M. Madhava, D.E. Polk, B.G. Geissen, H. Matyja and J. Vander Sande, Scrip. Met. 11 (1977) 65. M. Lasocka, J. Mat. Sci. 13 (1978) 2055.