Pressure Dependence of Glass Transition in As - American

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Pressure Dependence of Glass Transition in As2Te3 Glass K. Ramesh* Department of Physics, Indian Institute of Science, Bangalore 560012, India ABSTRACT: Amorphous solids prepared from their melt state exhibit glass transition phenomenon upon heating. Viscosity, specific heat, and thermal expansion coefficient of the amorphous solids show rapid changes at the glass transition temperature (Tg). Generally, application of high pressure increases the Tg and this increase (a positive dTg/ dP) has been understood adequately with free volume and entropy models which are purely thermodynamic in origin. In this study, the electrical resistivity of semiconducting As2Te3 glass at high pressures as a function of temperature has been measured in a Bridgman anvil apparatus. Electrical resistivity showed a pronounced change at Tg. The Tg estimated from the slope change in the resistivity−temperature plot shows a decreasing trend (negative dTg/dP). The dTg/dP was found to be −2.36 °C/kbar for a linear fit and −2.99 °C/kbar for a polynomial fit in the pressure range 1 bar to 9 kbar. Chalcogenide glasses like Se, As2Se3, and As30Se30Te40 show a positive dTg/dP which is very well understood in terms of the thermodynamic models. The negative dTg/dP (which is generally uncommon in liquids) observed for As2Te3 glass is against the predictions of the thermodynamic models. The Adam−Gibbs model of viscosity suggests a direct relationship between the isothermal pressure derivative of viscosity and the relaxational expansion coefficient. When the sign of the thermal expansion coefficient is negative, dTg/dP = Δk/Δα will be less than zero, which can result in a negative dTg/dP. In general, chalcogenides rich in tellurium show a negative thermal expansion coefficient (NTE) in the supercooled and stable liquid states. Hence, the negative dTg/dP observed in this study can be understood on the basis of the Adams−Gibbs model. An electronic model proposed by deNeufville and Rockstad finds a linear relation between Tg and the optical band gap (Eg) for covalent semiconducting glasses when they are grouped according to their average coordination number. The electrical band gap (ΔE) of As2Te3 glass decreases with pressure. The optical and electrical band gaps are related as Eg = 2ΔE; thus, a negative dTg/dP is expected when As2Te3 glass is subjected to high pressures. In this sense, As2Te3 is a unique glass where its variation of Tg with pressure can be understood by both electronic and thermodynamic models.

1. INTRODUCTION Generally, glasses are prepared by quenching their corresponding melt. Upon heating, the viscosity, specific heat, and thermal expansion coefficient of a melt quenched glass undergo rapid change.1−3 The point at which these changes take place is called the glass transition temperature (Tg), and it occurs over a limited temperature range. Properties of glass depend on thermal and pressure history. Tg values can be different for the same glass prepared with different cooling rates.4 Similarly, the melt quenched glass when heated at different rates shows a variation in Tg. Cooling rates of about 1012 K/s can be achieved by computer simulations with which even liquid argon can be formed into glass.5 Hence, it is important to mention the cooling/heating rates when a value of Tg for a glass is recorded.6 Glass transition has frequently been studied in relation to the composition changes in multicomponent systems. Experimental studies on pressure dependence of glass transition have been very scarce.7,8 High pressure experiments are relatively difficult and time-consuming which might be the reason for the lack of insufficient experimental data on the pressure dependence of glass transition. Among various models available in the literature to explain the glass transition phenomena, free volume 9−11 and entropy12,13 models have attracted much attention. In the © 2014 American Chemical Society

free volume model, particles are assumed to be oscillating in their own cages. When the temperature increases, the cage volume also increases. This promotes the oscillatory motions of the particles into diffusive motion by which the transport takes place. When the glass is heated, the temperature at which the free motion of the particles or molecules occurs is called the glass transition temperature. In the entropy model, it is assumed that the liquid consists of regions that rearrange as units. The size of the units is a function of temperature and is determined by the configurational entropy of the liquid. As the temperature of the liquid decreases, a larger number of particles in the system is involved in cooperatively achieving configurational changes. Thus, the size of the units increases and the rearrangement becomes difficult. At sufficiently low temperature, the configurational entropy may become zero, leading to a second order transition to an ideal glass.14 However, in real situations, the intervention of kinetic solidification leads to glass transition much before the configurational entropy becomes zero and the glass retains frozen entropy. According to these models, Tg will increase with an increase in pressure (dTg/dP is Received: May 1, 2014 Revised: June 18, 2014 Published: June 24, 2014 8848

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Figure 1. (A) DSC thermogram of As40Te60 glass recorded at 2 °C/min. (B) The Y-axis is magnified to show the glass transition clearly.

furnace. The ampoule is heated to 600 °C and kept for 6 h, and then, the temperature is slowly raised to 800 °C and kept for 48 h. The melt was continuously rotated to ensure homogenization and then quenched in ice water + NaOH mixture. The cooling rate achieved is approximately 300 K/s. The melt quenched sample was confirmed to be amorphous in nature by X-ray diffraction (XRD). A modulated differential scanning calorimeter (TA Instruments: MDSC 2920 system) in normal DSC mode has been used to measure the Tg of the prepared glass at a heating rate of 2 °C/min. The DSC system was calibrated with indium and zinc at a heating rate of 2 °C/min. Throughout the experiment, the DSC cell was purged with nitrogen gas. Bulk As2Te3 glass that weighed about 18 mg was loaded into aluminum crimped pans and then sealed. An empty Al pan was taken as a reference. Figure 1A shows the DSC thermogram of the As2Te3 glass. The Tg of the As2Te3 glass was measured to be 89 °C. The Y-axis is magnified in Figure 1B to show the glass transition clearly. High temperature electrical resistivity measurements at high pressures were carried out in a Bridgman anvil high pressure apparatus.27,28 Anvils of 12 mm size were used with pyrophyllite as the gasket material and steatite as the quasihydrostatic pressure transmitting medium. The pressure calibration was done at 300 K using the fixed points of bismuth (Bi) transitions at 25.4, 27, and 77 kbar and ytterbium (Yb) transition at 40 kbar. It has been shown that the pressure calibration at room temperature holds good at both low temperatures and high temperatures.29,30 A two-probe technique is used to measure the resistance of the samples placed in between the anvils. A copper guide ring has been used to align the anvils. The entire anvil assembly is heated externally by an insulated heater enclosed in a cylindrical steel housing and tightly fitted around the copper guide ring. Radial heat losses from the anvil assembly were avoided using a ceramic tube placed around the heater coil. Asbestos insulation was also provided between the flanges and the anvils both at the top and the bottom. A dimmerstat (maximum load 20 A) was used to supply the necessary power to the heater. A maximum of 400 °C was achieved with this heater system. Suitable windows were provided both in copper guide ring and heater to take out the electrical and thermocouple leads. A thin K-type (chromel−alumel) thermocouple of diameter 12.7 μm was placed near the sample to sense the temperature. For Ktype thermocouples, the temperature corrections up to 700 °C

positive). For example, application of hydrostatic pressure to amorphous selenium shifts the Tg to higher values.15 Joiner and Thompsun16 measured the pressure dependence of Tg for As2Se3, Ge2Te15As3, and Cd6Ge3As11 glasses using changes in the transit time of an ultrasonic pulse. Tg for As2Se3 and Ge2Te15As3 glasses increases initially and levels off at higher pressures. For Ca(NO3)2 mixtures and As40Se30Te30, the application of high pressure shifts the glass transition to higher side.17,18 These results are adequately explained by the free volume model. However, in some cases, glass transition behaves differently with pressure. For example, in alkali acetate + water systems, Tg is found to be independent of pressure.17 A decrease in Tg with pressure (dTg/dP is negative) has been observed when the water content in the alkali acetate (LiOAc· 10H2O) increases. Electrical resistivity shows a pronounced change at the glass transition temperature. Temperature dependent of electrical resistivity measured at atmospheric pressure for many glasses showed distinct changes at Tg.19−21 In the present work, electrical resistivity of As2Te3 (As40Te60) glass as a function of temperature has been measured at different pressures. Tg identified as a slope change in the resistivity vs temperature plot at different pressures. A decrease in Tg has been observed with the increase of pressure (negative dTg/dP), which is uncommon for the undercooled liquids. The electrical band gap in chalcogenide glasses usually decreases with the increase of pressure.22 deNeufville and Rockstad23 measured Tg and Eg for many covalent semiconducting glasses and found a linear relation between them when these glasses are grouped according to their average coordination number. It has also been suggested that the sign of dTg/dP can be negative for liquids which show a negative thermal expansion (NTE).24 Liquid chalcogenides rich in tellurium are found to show NTE.25 Inelastic neutron diffraction studies on As2Te3 in the liquid state show NTE.26 In the present work, an attempt has been made to correlate the decrease of electrical band gap with pressure and the NTE to the observed negative dTg/dP in As2Te3 glass.

2. EXPERIMENTAL SECTION Bulk As40Te60 glass was prepared by the conventional melt quenching method. Appropriate amounts of high purity elements (99.999%) were sealed in a quartz ampoule under a vacuum of better than 10−5 Torr and heated in a resistive 8849

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and pressures up to 35 kbar were found to be extremely small.31 Hence, temperature correction has not been applied in the present studies. For each pressure run, the sample was initially pressurized to 2 kbar and then released to atmospheric pressure. This was done to have a better electrical contact between the electrical leads and the sample. Then, to measure the temperature dependence of the electrical resistivity at different pressures, the pressure is slowly increased at room temperature and locked at a desired pressure with a control valve. The pressure was controlled within ±0.15 kbar. Then, the high pressure cell is heated at a heating rate of 2 °C/min and the temperature and the resistance of the sample were recorded at a time interval of 30 s using an SC-7501 Multilogger (Iwatsu, Japan).

3. RESULTS AND DISCUSSION Figure 2 shows the electrical resistivity of bulk As40Te60 glass as a function of temperature at different pressures. Glass transition

Figure 3. Pressure dependence of glass transition temperature showing negative dTg/dP.

not in harmony with these models. There are few systems34 which behave differently and show negative dTg/dP. For alkali acetate + water systems, Tg was found to be independent of pressure.17 When the water content increases, Tg decreases and exhibits a negative dTg/dP. According to Gupta,24 LiOAc· 10H2O may have a negative thermal expansion coefficient, which results in the decrease of Tg with the increase of pressure. The glass transition of poly(bisphenol A-co-epichlorohydrin), glycidyl end-capped sample (PBGD) increases nonlinearly with the increase of pressure.7 These observations show that the pressure dependence of glass transition is a complex problem and not fully understood or explained with the free volume and entropy models.8,34 Usually the band gap (Eg) increases with pressure for tetrahedral semiconductors (both crystalline and amorphous) and decreases for chalcogenide glasses. The valence band in chalcogenide glasses is formed by the lone pair electrons due to which they are called lone-pair semiconductors.1 For the tetrahedrally bonded germanium family of semiconductors, dEg/dP is found to be >0, while for chalcogenide semiconductors dEg/dP < 0. This contrast in band gap variation with pressure is attributed to the distinct bonding mechanism between these two classes of semiconductors. Chalcogenide glasses are layered structures; the bonding between the layers is van der Waals, and that between the atoms is covalent. The applied pressure directly compresses the covalent bonds in the tetrahedral semiconductors, whereas in chalcogenides pressure majorly affects the van der Waals bonding and the covalent bonds are less influenced. When the covalent bonds are influenced by the external parameters like pressure and temperature, the band gap is altered to a larger extent. Hence, Tg has a strong dependence on Eg for tetrahedral semiconductors and a weak dependence for chalcogenide glasses. deNeufville and Rockstad23 proposed a model which finds a linear relation between Tg and Eg when grouped according to their average coordination number. For example, in Se, As2Se3, and GeAsSe systems, Tg values vary from 35 to 420 °C, but their optical band gap remains approximately the same.23 Thus, the Tg and Eg relation is valid only when the semiconducting glasses are grouped according to their average coordination number. Hence, this (Tg−Eg−Zav) model has been used to understand the present results. In this model, Tg has been taken as the index of atomic mobility and Eg as the index of covalent bond strength. The

Figure 2. Electrical resistivity of As40Te60 glass at various pressures showing the glass transition and crystallization.

is seen as a change in slope in the resistivity plots. To make sure that the observed changes in resistivity are associated with the Tg, differential scanning calorimetric (DSC) measurements were carried out at a heating rate of 2 °C/min (the heating rate used in the resistivity measurement). The Tg value (89 °C) obtained from the DSC measurement as shown in Figure 1B is closely matching with the Tg value (88 °C) estimated from the electrical resistivity measurement at atmospheric pressure. In addition, the crystallization of the As2Te3 glass can be seen at 140 °C. When a semiconducting glass undergoes a glass to crystal transition, the resistivity drops rapidly.32,33 In the present studies, also Tc can be located where a sudden drop in resistivity occurs after Tg. The variation of Tg with pressure is shown in Figure 3. Interestingly, Tg decreased with the increase of pressure. It is seen from Figure 3 that the Tg data fits a second order polynomial better than a linear relation. The coefficient of the second order term is of the order 0.07 °C/kbar2, while the linear term is around −2.99 °C/kbar. If only a linear relation is fitted to the data, the dTg/dP value is found to be −2.36 °C/ kbar. As discussed in the previous section, a positive dTg/dP is expected for glasses at high pressures that can be adequately explained with the free volume and entropy models. In the present study, the observed negative dTg/dP for As2Te3 glass is 8850

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atoms is covalent, and that between the chains is van der Waals. For these materials, Tg is independent of Eg, because Tg in these materials represents the breaking of the van der Waals bond between the chains and the rings, whereas Eg is related to the covalent bond strength. Hence, the dependence of Tg on Eg for the glasses with Zav = 2 is not valid. Also, this model cannot be applied to understand the pressure dependence of Tg in conductors (like metallic glasses) and insulators, as the main parameter is the optical band gap which is zero in conducting glasses and very high in insulating glasses. It is well-known that chalcogenide glasses are insensitive to doping and the valence requirements of surrounding atoms are always satisfied by obeying the 8 − n rule.38 These glasses are intrinsic-like, so the optical band gap and the electrical conductivity activation energy (ΔE) can be related by

average coordination number (Zav) indicates the average number of bonds per atom which must be broken to obtain fluidity. In a sufficiently cross-linked network, the bonding between the atoms is three-dimensional. Cross-linking increases the connectivity of the network which in turn increases the glass transition.35,36 deNeufville and Rockstad measured Tg and Eg for many amorphous semiconducting glasses and plotted them according to their average coordination number. In the plot of Eg vs Tg, materials having the same average coordination number lie essentially on the same line. In general, the viscosity (η) of glasses can be given by the Vogel−Tammann−Fulcher (VTF) equation6 ⎡ B ⎤ η = η0 exp⎢ ⎥ ⎣ T − T0 ⎦

(1)

where T is the temperature and η0, B, and T0 are constants. In the free volume treatment, viscosity can be written as

⎡ B0 ⎤ η = η0 exp⎢ ⎥ ⎣ V − V0 ⎦

Eg = 2ΔE

The activation energy for electrical conductivity of As−Te glasses calculated from the temperature dependence of resistivity decreases with the increase of pressure.39 In solids, the valence and conduction bands are constituted by bonding and antibonding bands.40 Application of pressure decreases the interatomic distance. In semiconductors, the separation between bonding and antibonding bands gets smaller as the interatomic distance decreases.41 In addition, the bands will widen upon the application of high pressure. The decrease of ΔE with pressure implies the decrease of optical band gap. A relation between density and the electrical band gap is established by Nunoshita and Arai.42 The activation energy for electrical conduction decreases with the increase of density. Application of high pressure increases the density of the glasses. Hence, the increase in density and the reduction in band gap shifts the glass transition to lower values under high pressure. In the present studies, the Tg value determined from DSC at a heating rate of 2 °C/min is 89 °C (see Figure 1). The band gap values reported for As2Te3 glass are 0.87 and 0.62 eV.43 From a figure (Tg vs Eg) in Rockstad’s paper,23 one can roughly estimate a Tg value of about 100 °C for Eg = 0.87 eV and 90 °C for Eg = 0.62 eV. The band gap value of 0.62 eV is matching with the Tg value of 89 °C for a heating rate of 2 °C/min in the present studies. As mentioned earlier, in some cases, a decrease in Tg with pressure has been observed. In the tetrahedrally coordinated Ge3Cd6As11, Tg first increases with pressure up to 1.5 kbar. For pressures >1.5 kbar, Tg begins to decrease.23 The initial increase in Tg can be attributed to the widening of the band gap of germanium at lower pressures.44 However, at high pressures, the band gap of germanium decreases, which results in the overall reduction in the band gap of Ge3Cd6As11 which in turn causes the reduction in Tg. Generally, when a material is heated, it expands. There are some exceptions to this rule in solids and even in liquids. It is known that diamond and other zinc-blend semiconductors exhibit negative thermal expansion.45 The well-known example in liquids is water, which undergoes NTE in a 4 K range above its melting point.46 It is found that chalcogenide glasses rich with Te exhibit negative thermal expansion (NTE) in the stable liquid state and in the supercooled liquid state.25 For example, HgTe,47 In2Te3,48 and Ga2Te348 systems show NTE. The pressure dependence of Tg can be represented by the Ehrenfest equation6

(2)

Here, V is the specific volume of the liquid and V0 is its closepacked specific volume. V − V0 is proportional to T − T0. At some temperature T0, the molecules are packed together with the specific volume V0 and in this condition no molecular motion is possible. As the temperature increases, some excess or free volume V − V0 develops in the liquid, providing space for molecular motion and ultimately for flow. The application of high pressure decreases the volume, which means the free volume is squeezed under pressure and the movement of the atoms is restricted. To excite the free volume, more energy is needed. Hence, the glass transition is expected to shift to higher side with the increase in pressure. Using the viscosity equation, deNeufville and Rockstad obtained a relationship between Tg and Eg. The constant B in eq 1 was related to the covalent bond strength by B=

αEg k

(3)

where α is a suitable constant which is determined in terms of Zav for each material. Accordingly, a relation between α and Zav has been arrived as

α = δ(Zav − 2)

(4)

δ is an independent parameter which varies between 0.47 and 0.65. In this way, deNeufville and Rockstad related the fluidity, Zav, Tg, and Eg as ⎡ δ(Zav − 2)Eg ⎤ ⎥ ϕ = ϕ0 exp⎢ ⎢⎣ k(T − T0) ⎥⎦

(6)

(5)

For Zav > 2, the value of δ is about 0.55. For Zav = 2.4 and 2.67, T0 is 325 K, and for Zav = 3, T0 is about 355 K. Fluidity is the inverse of viscosity and is directly proportional to its free volume.37 The fluidity of a liquid increases with temperature and decreases the pressure. The average coordination number indicates the average number of bonds per atom must be broken to obtain fluidity. In eq 5, Zav − 2 indicates that the model is valid only for the covalent semiconductors with Zav > 2. For example, the structure of the glasses with Zav = 2 (like glassy Se, Se−Te, and S−Se) consists of chains and rings. The bonding between the 8851

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dTg dP

=

Article

TgVg Δα ΔCp

glasses. Application of high pressure decreases the interatomic distance which in turn decreases the separation between the valence and conduction bands (optical band gap). This reduction in optical band gap in As40Te60 glass under high pressure shifts the glass transition to lower values. It is also suggested that the sign of the pressure derivative of Tg can be negative (negative dTg/dP) if the thermal expansion coefficient is negative. Inelastic neutron diffraction studies show a negative thermal expansion coefficient for As2Te3 glass. This leads to dTg/dP = Δk/Δα < 0 and a negative dTg/dP. It should also be mentioned that the Tg−Eg−Zav model is formulated on the basis of the Tg and Eg values measured at atmospheric pressure. This linear relation between Tg and Eg may change at high pressures. However, still, the decrease of electrical conductivity activation energy ((1/2)Eg) occurs upon the application of high pressure. From this study, we can conclude that the negative dTg/dP observed is very much unique to As2Te3 glass, as it obeys both thermodynamic and electronic Tg−Eg−Zav models.

(7)

where Vg is the molar volume at Tg and Δα and ΔCp are changes in volume and expansion coefficient and constant pressure heat capacity which occur at Tg. Similar to this, using discontinuities in the compression and thermal expansion, the following equation can be derived

dTg dP

=

Δk T Δα

(8)

where Δk is the isothermal compressibility at Tg and Δα is the thermal expansion coefficient at Tg. The terms involved in these two equations are experimental quantities. If the two theories are equal, then Δk TΔCp TgVg Δα 2

=1

■

(9) 49

which is the well-known Prigogine−Defay ratio. It is observed that only eq 7 is valid in the majority of the materials investigated.50,51 Experimental observations imply that the ratio (eq 9) is greater than unity and has a value in between 2 and 5.52,53 It should be noted that the values of dTg/dP strongly depend on whether the sample is pressurized in the glassy state or in the liquid state.50,51,54,55 For example, dTg/dP for polystyrene is 74.2 °C/kbar when pressure is applied to the glass formed at atmospheric pressure and 31.6 °C/kbar for the glass formed from the liquid at high pressures. When the pressure is applied in the liquid state, and then cooled to room temperature, the density of the resultant glass is higher than the glass formed at normal pressure. In the glassy state, the configurational changes are arrested and the changes in the structure to the applied pressure are less, whereas in the liquid state configurational changes can occur and the response of the structure to the applied pressure is large. Therefore, a glass heated above its glass transition temperature is pressurized and then cooled to room temperature and can form into a new glass because of the increase in density and higher response to the applied pressure. For different pressures, one will end up forming different glasses. Hence, a comparison of properties among these glasses may not be correct. For a better comparison, the pressure can be applied at room temperature and locked at a desired pressure and then the properties can be monitored across Tg upon heating. In this procedure, the state of the starting material is the same for the different locked pressures. Inelastic neutron scattering studies on As2Te3 in the liquid state show a negative thermal expansion.26 Since the thermal expansion shows a negative value, the sign of dTg/dP can be negative (dTg/dP = Δk/Δα < 0). In the light of the above discussions, As2Te3 is a unique system in which the observed negative dTg/dP follows the thermodynamic as well as electronic (Tg−Eg−Zav) models.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 91-8022932716. Fax: 91-80-23602602. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The author would like to thank Prof. Chandan Dasgupta and Prof. E. S. R. Gopal for many helpful discussions. The reviewers are thanked for their valuable time and thorough review of the manuscript. The author also highly appreciates the comments and suggestions of the reviewer, which significantly contributed to improving the quality of this paper to a large extent.

■

REFERENCES

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4. CONCLUSIONS The pressure induced changes in the glass transition of As40Te60 glass have been studied in light of the thermodynamic and Tg−Eg−Zav models. Tg was found to decrease with the increase of pressure (negative dTg/dP). The Tg−Eg−Zav model proposed by deNeufville and Rockstad finds a linear relation between Tg and Eg according to the network connectivity of the 8852

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