On the entropy difference between the vitreous and the crystalline state

The paper deals with the entropy difference between frozen-in phases and their equilibrium counterparts. First, the nature of data compiled in thermochemical data collections are briefly reviewed, comprising data for non-equilibrium phases. Then, experimental evidence from earlier literature is compiled showing that the conventional entropy of a frozen-in phase at zero Kelvin assumes a non-zero residual value S(0). Based on calorimetric data from multiple sources, the same evidence is elaborated for diopside glass, yielding S_glass(0) = 24.8 ± 3 J/(mol K), a value reproducing a result publishes earlier. The zero Kelvin enthalpy of this glass is H_glass(0) = 81±8 kJ/mol. For S_glass(0), a structural interpretation in terms of silicate chain mixing is proposed, yielding a lower threshold for S_glass(0). From the point of view of statistical mechanics, non-zero residual entropies of frozen-in phases can be derived from ensemble averages, however, not from time averages.     

Thermodynamic properties of amorphous solids: The electrochemical approach

In the present contribution are critically analyzed and reexamined the possibilities to determine the thermodynamic properties of amorphous solids, of defect crystals and of glasses by means of electrochemical methods. After detailed theoretical considerations performed in the framework of the thermodynamics of irreversible processes it is demonstrated how the most significant thermodynamic parameters of amorphous systems with frozen-in structure—their configurational enthalpy and entropy ΔH_g and ΔS_g—can be electrochemically measured, when the systems under investigation are first order (electron) conductors, capable of forming the electrodes in a glass → crystal Galvanic cell. We refer here to existing classical experimental results with two such systems: vitreous Sb (so-called explosive antimony) and glassy carbon resins both used to demonstrate the applicability of the theoretical considerations developed. Results with several Metglass alloy systems (Ni/P, Fe, Ni/P, B, Co/B and Cu/Ti), obtained via corrosion potentio-dynamic electrochemical measurements are also summarized and used to estimate the thermodynamic properties of variously treated glass-forming systems. The electrochemical evidence analyzed clearly demonstrates in its integrity the particular, frozen-in nature of the basic thermodynamic parameters in the considered glass systems (ΔHg ≈ const > 0, ΔSg ≈ const > 0) as this is expected to be both from classical theory and from known calorimetric measurements. The contribution of direct glass/crystal Voltaic contacts to the thermodynamic properties of electrochemical cells with glassy or vitro-crystalline electrodes is also considered in details. Possible technical applications of Galvanic and Voltaic potentials, determined by glassy or vitro-crystalline electrode materials, including existing conventional battery systems and other horizons, opened to discussion by the present theoretical approach are also outlined.     

Zero-point entropy of glasses as physical reality

This paper presents an analysis of the physical nature of the author’s results obtained since 1995 in the field of thermodynamics of the vitreous state (classic approximation). Excess entropy and free energy at 0 K are considered as the measures of non-equilibrium extent of glass with respect to crystal. Experimental data for melts and glasses of various chemical natures are generalized. A general form of the relations between reversible changes in free energy, enthalpy and entropy and their frozen values at the formation of any glass is shown. The problem of functional dissimilarity of the heat capacity of glass and that of crystal has been solved within the framework of the principle of free energy minimization as a result of self-organization of the vibration spectrum according to the frozen structure. The complete stabilization of glass structure at Kauzmann’s temperature or below it is forbidden by topologic reasons and (or) by thermodynamics. The effects of pressure on the thermodynamic properties of glasses are shown. Possible particular applications of the analysis of self-organization in chaotic systems are exemplified by the modeling of the abilities of neural systems.     

Contribution of floppy modes to configurational and excess entropy in chalcogenide glasses

In this work, following Naumis’ ideas [G.G. Naumis, Phys. Rev. B 61 (2000) R9205], we include the floppy modes as a free energy in order to obtain the configurational and excess entropy as well as the jump of the heat capacity of the chalcogenide glasses as function of the coordination number 〈r〉. Theoretically, we find that S_ex/S_c ranges from 1.5 for strong liquids (〈r〉 = 2) to 2 for fragile ones (〈r〉 = 2.4). These results are consistent with the values reported by Angell and Borick [C.A. Angell, S. Borick, J. Non-Cryst. Solids 307&310 (2002) 393], who find experimentally for selenium, 〈r〉 = 2, S_ex/S_c = 1.47. The proportionality between the configurational and total excess entropies supports the non-existence of the Adam–Gibbs equation paradox. Finally, using S_c in the Adam–Gibbs equation we obtain a VFT-like equation as function of 〈r〉, predicting that when 〈r〉 increases, D decreases as well, as it has been seen in previous work.     

The iso-structural viscosity,configurational entropy and fragility of oxide liquids

This paper describes how the fragility of a liquid is linked to the ratio between the energy barrier (E_eq) for the equilibrium viscous behavior and that (E_iso) for the non-equilibrium iso-structural viscous behavior. Using the concept of iso-structural viscosity, two functions describing the variation of the configurational entropy (S_c) with temperature (T) are obtained from the Avramov-Milchev (AM) and the Vogel-Fulcher-Tammann (VFT) viscosity equations, respectively. The two S_c(T) functions exhibit different relations to the liquid fragility. The AM S_c(T) function is a power function with the exponent of F ? 1, where F is the AM fragility index. In this case, S_c vanishes at T = 0 K. For the VFT function, S_c vanishes as T is lowered to a finite temperature T₀, whereas it reaches the maximum value S_c,max at infinitively high T. S_c,max is proportional to the VFT fragility index. Thus, the VFT equation is not only a dynamical, but also a thermodynamic model. It is proved that for oxide liquids, the VFT equation describes viscosity data better than the AM equation, provided the pre-exponential factor η₀ is fixed to a generally accepted value, e.g., 10^?3.5 Pa s.     

Intermediate Phases,structural variance and network demixing in chalcogenides: The unusual case of group V sulfides

We review intermediate phases (IPs) in chalcogenide glasses and provide a structural interpretation of these phases. In binary group IV selenides, IPs reside in the 2.40 < r < 2.54 range, and in binary group V selenides they shift to a lower r, in the 2.29 < r < 2.40 range. Here, r represents the mean coordination number of glasses. In ternary alloys containing equal proportions of group IV and V selenides, IPs are wider and encompass ranges of respective binary glasses. These data suggest that the local structural variance contributing to IP widths largely derives from four isostatic local structures of varying connectivity r, two include group V based quasi-tetrahedral (r = 2.29) and pyramidal (r = 2.40) units, and the other two are group IV based corner-sharing (r = 2.40) and edge-sharing (r = 2.67) tetrahedral units. Remarkably, binary group V (P, As) sulfides exhibit IPs that are shifted to even a lower r than their selenide counterparts; a result that we trace to excess S_n chains either partially (As–S) or completely (P–S) demixing from network backbone, in contrast to excess Se_n chains forming part of the backbone in corresponding selenide glasses. In ternary chalcogenides of Ge with the group V elements (As, P), IPs of the sulfides are similar to their selenide counterparts, suggesting that presence of Ge serves to reign in the excess S_n chain fragments back in the backbone as in their selenide counterparts.     

Xerographic spectroscopy of gap states in Se-rich amorphous semiconductors review

One of the most important parameters which determine the performance of many modern devices based on amorphous semiconductors is the drift mobility-lifetime product, μτ. There has been much interest in determination of charge-carrier ranges in amorphous semiconductors by various measurement techniques. Although the mobility, μ, can be measured by the conventional time-of-flight transient photoconductivity technique, the determination of the lifetime, τ, is often complicated by both experimental and theoretical limitations. The present article provides an overview of xerographic measurements as a tool for studying the electrical properties of amorphous semiconductors. First, details of the experimental set-up are discussed. Thereafter, the analysis and interpretation of dark discharge, the first cycle residual potential, cycled-up saturated residual potential are considered. It is shown that from such measurements the charge-carrier lifetime, τ, the range of the carriers, μτ, and the integrated concentration of deep traps in the mobility gap can be readily and accurately determined. Xerographic measurements on Se-rich amorphous photoconductors have indicated the presence of relatively narrow distribution of deep hole traps with integrated density of about 10¹³ cm^? 3. These states are located at ~ 0.85 eV from the valence band. A good correlation was observed between residual potential and the hole range, in agreement with the simple Warter expression. The capture radius is estimated to be r_c = 2–3 Å. Since r_c for pure a-Se and a-As_xSe_1 ? x is comparable to the Se–Se interatomic bond length in a-Se, it can be suggested that deep hole trapping centers in these chalcogenide semiconductors are neutral-looking defects, possibly of intimate valence-alternation pair (IVAP) in nature. The absence of any electron spin resonance signal (ESR) at room temperature seemed to be a strong argument in favor of this suggestion. Finally, photoinduced effects on xerographic parameters are discussed. It has been shown that photoexcitation of a-As_xSe_1 ? x amorphous films with band-gap light alters deep hole and electron states. During room-temperature annealing photosensitized states relax to equilibrium. Recovery process becomes slower with increasing As content. Qualitative explanation of the observed behavior may be based on associating the deep states with C₃⁺ and C₁^?intimate-valence-alternation–pair (IVAP) centers.     

Vibrational entropy near glass transition in a chalcogenide glass and supercooled liquid

Raman spectroscopic measurements have been performed on Ge₂₀Se₈₀ glass and supercooled liquid at temperatures ranging between 298 and 500 K. Temperature dependent softening of vibrational mode frequencies has been used in conjunction with the available vibrational density of states data at ambient temperature to estimate the relative contributions of vibrational and configurational entropies across glass transition. Nearly 20% of the additional entropy above glass transition is estimated to be vibrational. Thermal expansion effect on vibrational mode softening is found to be insufficient to account for the anharmonic component of vibrational entropy implying possible coupling between the vibrational and configurational entropies at temperatures above T_g. These results may have important consequences in shaping our understanding of various aspects of glass transition.     

Experimental evidence against the existence of an ideal glass transition

The absolute liquid heat capacity of poly(α-methyl styrene) was determined at temperatures far below T_g and T_K in previous work by use of pentamer/polymer athermal mixtures. Here the data is compared to data compiled by Wunderlich and coworkers from 0 K to above T_g in order to obtain the absolute entropy for the polymer in its equilibrium state at temperatures as much as 180 K below the glass temperature or 130 K below the Kauzmann temperature. The results provide no evidence of a second-order transition or of a smeared transition in the entropy. In addition, we find no evidence that the entropy would become negative at a finite temperature.     

Boroxol rings in SiO2–B2O3 glasses: Influence on low-temperature thermal properties

The heat capacity of a rapidly quenched B₂O₃–SiO₂ glass has been measured by adiabatic calorimetry from 10 to 350 K. The vibrational entropy derived from the measurements, S₂₉₈–S₀ = 54.16 ± 0.10 J/mol K, is close to the linear trend defined by the entropies of pure SiO₂ and B₂O₃ glasses. Owing to the strong sensitivity of S₂₉₈ − S₀ to the oxygen coordination of cations, this result is in agreement with the 3- and 4-fold coordination found for Si and B, respectively, in binary borosilicates. Because additivity of heat capacity extends below 90 K, where the low-frequency modes of boroxol rings dominate the vibrational density of states, the results indicate also that the fraction of boron atoms in these rings is proportional to the B₂O₃ content. According to recent NMR evidence, these conclusions apply to truly homogenous glasses at a microscopic scale.     

Communal entropy and glass transition

Using the partition function formulated by Kirkwood, the glass transition temperature is shown to be the temperature at which the communal entropy vanishes in a liquid system. The non-existence of T₂ is inferred from the theory in accordance with the experimental fact that all the glasses made so far have some residual entropy compared with the crystal state.     

Dielectric study of the segmental relaxation of low and high molecular weight polystyrenes under hydrostatic pressure

In this work we analyze by means of dielectric spectroscopy the dynamics of the α-relaxation process of low and high molecular weight polystyrene over a wide range of pressures and temperatures. The results are interpreted in terms of a recently proposed equation which describes the behavior of the structural relaxation time, τ(T, P), as a function of both pressure and temperature. This equation has been derived from the Adam–Gibbs (AG) theory by writing the configurational entropy, S_c, in terms of the excess thermal heat capacity and of the excess thermal expansion. Consequently, the molecular dynamic of glass-forming liquids can be linked to its thermodynamic properties. The pressure dependence of the segmental dynamics for both polymers is here measured and analyzed in the AG framework for the first time. τ(T, P) was found to be very well described using the extended AG equation. Additionally, the pressure dependence of the fragility and glass transition temperature (T_g) is analyzed and discussed in terms of the role of chain length and end groups.     

Structure of binary neodymium borate glasses by infrared spectroscopy

Using fast roller quenching techniques, a new series of binary rare earth oxide borate glasses were synthesized, with general formula xNd₂O₃ + (1 − x)B₂O₃, where x varies up to 35 mol%. The glasses were investigated by using mid infrared reflectance spectroscopy. The results show that the neodymium acts as a modifier, similar to an alkali metal. As x is increased, the borate glass network is shown to change from a three-coordinated to four-coordinated boron system. The results are further investigated by analyzing the spectra in terms of the location of the bands to show how the borate groups change upon neodymium addition.     

Energetics of Cd-based binary liquid alloys

The thermodynamic properties such as, free energy of mixing (G_M), heat of mixing (H_M), entropy of mixing (S_M) and microscopic properties such as, concentration fluctuation in long wavelength limit (S_CC(0)), Warren–Cowely short range ordering parameter (α₁), ratio of mutual and intrinsic diffusion coefficients (D_M/D_id) of two Cd-based liquid alloys have been studied by using two different models. The properties of Cd–Hg liquid alloy at 600 K have been studied on the basis of regular solution model, and the properties of Cd–Na liquid alloy at 673 K have been studied on the basis of quasi-chemical expression for weakly interacting system.     

On the reality of the residual entropy of glasses and disordered crystals: The entropy of mixing

We have previously shown that the assumption that the configurational entropy of a supercooled liquid vanishes at T_g leads to a non-trivial violation of the second law. Here we consider the example of the entropy of mixing. We use as a model system two similar chemical substances which form an ideal solution in a mixed phase. We apply the reasoning of our earlier paper to show that this vanishing would lead to a dilemma; either it violates the second law of thermodynamics, or else it cannot be demonstrated by any conceivable experiment. We show further that the vanishing of the entropy of mixing on kinetic arrest leads to the counter-intuitive result that the chemical potential of each component in an infinitely dilute kinetically arrested (or glassy) solution can equal or the chemical potential of the pure component. The most parsimonious conclusion from these results is that residual entropies are real.     

Reduction of bulk and interface defects by network self-organizations in gate dielectrics for silicon thin film and field effect transistors (TFTs and FETs,respectively)

Studies of binary chalcogenide alloys have established that the onset of network rigidity is generally delayed by a network self-organization resulting in an intermediate phase with significant deviations from mean-field chemical bonding. In Ge_xSe_1−x, the onset of local chemical bonding rigidity occurs for a mean-field coordination, r_c = 2.4 at x = 0.2, but percolation of stress resulting in network rigidity is delayed until r_c = 2.52. This paper demonstrates that low levels of electrically active defects in gate dielectrics for (i) thin film transistors (TFTs) in liquid crystal displays (LCDs), and (ii) aggressively-scaled metal- oxide-semiconductor field effect transistors (MOSFETs) are derived from similar network self-organizations that occur for a narrow range of dielectric compositions. The dielectrics of this article are non-crystalline (nc-) Si_xN_yH_z alloys in which a chemical self-organization occurs during deposition at 300 °C, and nc-(SiO₂)_x(Si₃N₄)_y(ZrO₂)_z alloys in which it occurs during post-deposition annealing at ∼900 °C. For each of these alloys, the values of x, y and z, are approximately 0.3, 0.4 and 0.3.     

High frequency collective dynamics in liquid potassium

We investigated by inelastic X-ray scattering the dynamical properties of molten potassium in a wide range of momentum transfer, Q, from 1 nm⁻¹ up to the main peak of the structure factor Q ≈ 17 nm⁻¹. The observed increase of sound velocity in the low Q region (1 < Q < 3 nm⁻¹), has been described within a model characterized by two distinct relaxation processes for the collective dynamics. The obtained results are discussed and compared with those from previous neutron scattering experiments. In particular, we associate the speed-up of the sound velocity to the ‘instantaneous’ disorder of the liquid as opposed to the argument, supported by some neutron scattering studies, of a transition from a liquid to solid like response of the system.     

Structure of molten Al–Si alloys

The temperature variation of the structure and microstructure of molten eutectic Al_1−xSi_x alloys (x = 0.122 and 0.20) have been studied by neutron diffraction and small-angle neutron scattering (SANS), as well as measurements performed on pure liquid Al. All measurements have been performed at five temperatures in a heating–cooling loop. The SANS results unambiguously show that for the eutectic alloy (x = 0.122) the microstructure changes with increasing temperature in a partly reversible way while for the hypereutectic (x = 0.20) alloy the change is almost completely irreversible. This change in microstructure also manifests itself in the shape of the static structure factor S(Q).