Bulk Thermodynamics Research Articles

Phase boundaries near critical end points. III. Corrections to scaling and spherical models.

Thermodynamics in the vicinity of a critical end point is studied. Phenomenological arguments are used to show the presence of further critical nonanalyticities beyond the leading-order singularities found in papers I and II. These contributions are related to the universal correction-to-scaling features of the bulk thermodynamics on the critical \ensuremath{\lambda} line. The predictions are checked on exactly soluble spherical models with short- and long-range interactions.

In-situ X-ray photoelectron spectroscopic study of the reversible phase transition between CoO and Co3O4 in oxygen of 10−3 Pa

The temperature dependence of the Co 2p and O 1s XPS spectra for the cobalt-oxygen system was studied in an oxygen atmosphere of 1 × 10 −3 Pa. The reversible transition between CoO and Co 3 O 4 was observed between 373 and 973 K. Although bulk thermodynamics predicts a transition temperature of 806 K, the transition occurred at about 620 K. This means that surface compositions or phases of the Co-O system are ruled by surface thermodynamics different from that of the bulk.

Structural phase transition in (GaAs)1-xGe2x and (GaP)1-xSi2x alloys: Test of the bulk thermodynamic description.

Nonisovalent (${\mathit{A}}^{\mathrm{III}}$${\mathit{B}}^{\mathrm{V}}$${)}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathit{C}}_{2\mathit{x}}^{\mathrm{IV}}$ semiconductor alloys exhibit a transition as a function of composition between a phase with the zinc-blende symmetry (where the two fcc sublattices of the diamond lattice are unequally occupied by ${\mathit{A}}^{\mathrm{III}}$ and ${\mathit{B}}^{\mathrm{V}}$ atoms) and a phase with the diamond symmetry (where the two sublattices have equal occupations). Previous thermodynamic models of this transition have considered only nearest-neighbor interactions between neutral atoms. This approach ignores the important electrostatic interactions associated with electron transfer between the electron-rich ${\mathit{C}}^{\mathrm{IV}}$-${\mathit{B}}^{\mathrm{V}}$ (``donor'') bonds and the electron-deficient ${\mathit{A}}^{\mathrm{III}}$-${\mathit{C}}^{\mathrm{IV}}$ (``acceptor'') bonds. We have reexamined the validity of a three-dimensional bulk thermodynamic model for (GaAs${)}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ge}}_{2\mathit{x}}$ and (GaP${)}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Si}}_{2\mathit{x}}$ using an energy model that includes such electrostatic interactions and pairwise energies extracted from first-principles local-density total-energy calculations.The associated spin-1 Ising Hamiltonian is solved in the pair approximation of the cluster-variation method. A detailed thermodynamic description is given, including excess enthalpies, phase diagrams, and equilibrium solubilities. Electrostatic interactions stabilize the diamond phase and result in a major increase in the temperature range where both phases are stable. These changes, however, are insufficient to produce a second-order transition at the low (growth) temperatures and intermediate compositions where the transition is observed. While a previous controversy on the validity of thermodynamic models has focused on the question of whether the postulation of ${\mathit{A}}^{\mathrm{III}}$-${\mathit{A}}^{\mathrm{III}}$ and ${\mathit{B}}^{\mathrm{V}}$-${\mathit{B}}^{\mathrm{V}}$ bonds (needed to fit the observed critical compositions in such models) is consistent with independent evidence, we find that, with realistic values for the interaction parameters, the presence or absence of such bonds does not produce any significant change in the phase diagram below melting temperatures. We conclude that bulk thermodynamics is an inappropriate description of the problem. This opens the possibility that surface thermodynamics could be the physical mechanism that determines the final symmetry of the sample.

Phase boundaries near critical end points. I. Thermodynamics and universality.

The vicinity of a critical end point is analyzed in order to reveal singularities arising in the form of the first-order phase boundary to the noncritical phase. Phenomenological arguments are presented and critically assessed that directly relate the nonanalytic behavior of the phase boundary to universal features of the bulk thermodynamics on the associated critical line. Explicit values are given for universal amplitude ratios describing the boundary for various types of criticality.

Superlattice energetics and alloy thermodynamics of GaAs/Ge

We re-examine the validity of the three-dimensional bulk thermodynamic description for the zinc-blende-to-diamond transition observed in ( GaAs) 1− x Ge 2 x alloys. We use interaction parameters extracted from first-principles local-density total-energy calculations for ( GaAs) p /( Ge 2) p superlattices and a cluster-variation solution to the corresponding Ising-like hamiltonian. The resulting phase diagram obtained with such a realistic energy model fails to account for the observed critical composition in the relevant temperature range, suggesting that, contrary to a previous view, the transition is not driven by bulk thermodynamics.

Thermal-expansion, specific-heat, and pressure dependence of T c in YBa 2 (Cu 1−xM x) 3O 7−δ: M=Fe and Zn

High-resolution thermal-expansion and specific-heat measurements of YBa 2(Cu 1− x M x ) 3O 7−δ (M=Fe and Zn; x=0−5%) at the superconducting transition are presented. Thermal expansivity α( T) provides an alternative, to the specific heat, method for examining the bulk thermodynamics of the superconducting phase transition. We show that if, | d T c/d p>0.1 K/kbar, expansivity is a more sensitive probe of the superconducting transition than the specific heat because of a relative smaller background. The expansivity jump δα of the Fe doped samples increases by a factor of 4 with increasing x, in stark contrast to the specific heat jump δ C 0, which decreases and is unobservable for x=5%. For Zn, a jump in α at T c was only observed for the x=1% sample. Calculated d T c/d p values show a large increase (factor of 20) for Fe and little change for Zn doping. These values agree well with actual pressure data, indicating the the jumps in α are electronic in nature and are not due to a structural transition. The large d T c/d p values of the Fe doped samples are discussed in terms of a disturbed oxygen coordination of Fe occupying chain sites. Anomalies in α( T) at 40–90 K and ≈ 250 K, indicative of structural changes, are also discussed.

Thermodynamic instability of ordered (001) AlGaAs2 in bulk form.

Recent tight-binding calculations of bulk electronic total energies by Koiller, Davidovich, and Falicov (KDF) [Phys. Rev. B 41, 3670 (1990)] indicated the tendency for ${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ga}}_{\mathit{x}}$As alloys to form ordered structures. The stablest structure they predicted was the monolayer (AlAs${)}_{1}$(GaAs${)}_{1}$[001] superlattice, which was recently observed in homogeneous vapor-phase growth. In light of these results we have examined the possibility that bulk energetics can explain this ordering. We have subjected KDF's tight-binding total-energy calculations and, separately, our own first-principles pseudopotential total-energy calculations to a statistical-mechanics analysis of order-disorder transitions. We find that bulk thermodynamics is inconsistent with the observed ordering; hence, explanations must be sought elsewhere (e.g., surface thermodynamics or kinetic effects).

Na adsorption on the layered semiconductors SnS 2 and WSe 2

The interaction of Na metal deposits with UHV cleaved van der Waals surfaces (0001) of SnS 2 and WSe 2 was investigated with SXPS and LEED. For SnS 2 an insertion reaction (intercalation) of Na leads to a reduced Sn-species. For WSe 2 “non-reactive” intercalation occurs at room temperature which follows the rigid band model. At 120 K a metallic Na overlayer is formed. The observed reactivity is discussed in terms of bulk thermodynamics and the obtained difference is tentatively related to differences in the electronic structure of the compounds.

Na adsorption on the layered semiconductors SnS 2 and WSe 2

The interaction of Na metal deposits with UHV cleaved van der Waals surfaces (0001) of SnS 2 and WSe 2 was investigated with SXPS and LEED. For SnS 2 an insertion reaction (intercalation) of Na leads to a reduced Sn-species. For WSe 2“non-reactive” intercalation occurs at room temperature which follows the rigid band model. At 120 K a metallic Na overlayer is formed. The observed reactivity is discussed in terms of bulk thermodynamics and the obtained difference is tentatively related to differences in the electronic structure of the compounds.

Bulk and surface thermodynamics of stoichiometric ionic crystals consisting of three ionic species

The bulk and surface thermodynamics of stoichiometric ionic crystals consisting of three ionic species are developed. In contrast with the case of crystals having variable stoichiometry, chemical potentials of two electrically neutral components, λ1 and λ3, cannot be defined in the usual way as derivatives of the Gibbs free energy per ion with respect to composition because the composition is invariant. They may, however, be taken as equal to λ1 and λ3 in the bulk solution at equilibrium with the crystal. If a given crystal separates two bulk solutions for which λ1 and λ3 differ, the system is not at equilibrium with respect to diffusion and the methods of non-equilibrium thermodynamics can be applied. Such an analysis demonstrates the existence of a diffusion potential in the crystal. It also shows that the chemical potentials are functions of T, p and λ1, and that only at constant λ1 does the inner potential conform to the classical Nernst equation. Expressions are derived which enable reduced transport numbers in the crystal phase to be found from suitable e.m.f. measurements. Application of the Gibbs adsorption equation shows that the solution/crystal interfacial tension will exhibit a maximum when the adsorptions of both potential-determining species are zero and also that for a given λ1, σ has its maximum value at the corresponding zero point of charge. When the crystal is an insulator and can support an applied field without any measurable transport effects taking place, it appears that a similar analysis to the case of a conducting crystal can apply only if the adsorptions of all non-potential-determining species are independent of the field strength in the bulk crystal.

Interface Tension in QCD Matter

We have initiated the study of an entirely new class of phenomena in lattice Quantum Chromodynamics: interfaces. After almost ten years of computations on bulk thermodynamics of QCD matter one knows that it can exist in two phases: a low temperature hadron phase and a high temperature quark plasma phase. At critical temperature Tc these two phases can coexist with a stable interface in between. We show how the structure of this interface and its tension α can be determined with lattice Monte Carlo techniques. We have carried out numerical computations on the level of approx 500 h of CPU time in a single processor Cray X-MP. On an Nt = 2 lattice with an 8 × 8 × 40 spatial size the result is α/Tc3 = 0.24 ± 0.06, and the interface extends over more than 2 fm. For the case of Nt = 4 our results are still indecisive.

Wetting of aqueous solutions of organic binder (PVA) on sapphire and fused quartz

Wetting by PVA aqueous solution of sapphire and fused quartz was studied by measuring the contact angle of a sessile drop placed on them. At a given temperature, the contact angle increased with increasing concentration of solution up to 2% and became rather constant for further increase in concentration. The contact angle also increased with increasing temperature. At temperatures over 70° C, the contact angle for sapphire exceeded 90° for PVA aqueous solutions of concentration over 2%. The effects of temperature and concentration on wetting for fused quartz were similar to those found for sapphire. These results are discussed in terms of bulk thermodynamics.

The surface thermodynamics of alkane+ perfluoroalkane and dimethylsiloxane+ perfluoroalkane liquid mixtures

The surface thermodynamics of alkane + perfluorolkane liquid mixtures reflects the bulk thermodynamics of the same class of mixture. In particular, the dominating feature in both is the influence of the as-yet-unexplained anomalous weakness of the unlike interaction energy compared to that predicted by the Berthelot combining rule. The chief outcome in the bulk thermodynamics is the prevalence of large positive deviations from Raoult's law, most characteristically manifest by liquid-liquid immisciblity in almost every mixture and an abundance of positive azeotropy. In the surface thermodynamics the corresponding characteristic feature is the occurrence of large negative deviations from a simple mole-fraction weighted average surface tension which serves in the absence of a superior definition as an operational statement of surface ideality. In a number of mixtures the deviation is sufficiently extreme as to give rise to negative aneotropy or a minimum in the surface tension.The thermodynamics of dimethylsiloxane + perfluoroalkane mixtures bears many similarities to that of alkane + perfluoroalkane mixtures. With a less full set of results we highlight the similarities and differences of the behaviour of the two series of mixtures.We report here the surface tensions as a function of composition of a number of alkane + perfluoroalkane mixtures ranging from methane + tetrafluoromethane at 100 K to octane + octadecafluorooctane at 303 K. In the interpretation of the results we employ with varying degrees of success a variety of theories, chiefly based on the principle of corresponding states.For those mixtures for which appropriate vapour-liquid equilibrium results have been reported we discuss the relative adsorption both in terms of intermolecular forces and the proximity of the consolute point.

Phase diagram for the Bethe lattice spin glass (abstract)

We present the results of rigorous calculations for the ±J Ising spin-glass model on the Bethe lattice. The phase diagram for varying temperature and fraction of ferromagnetic bonds is derived near the paramagnetic phase boundary. In addition to the spin-glass and paramagnetic phases, we find a nontrivial ferromagnetic phase and a magnetized spin-glass phase, characterized by diverging Edwards–Anderson susceptibility. The recursion relation for the distribution of single-site magnetizations is studied as a dynamical system on an appropriate function space, the bulk thermodynamics is described by the attractors of the recursion relation, and the phase transitions correspond to bifurcations in the dynamics. Using bifurcation theory, we establish the existence of a stable distribution of single-site magnetizations near the paramagnetic phase boundary. At least in single-site properties, the existence proof precludes chaos, and infinite hierarchy of transitions, and other conceivable bizarre possibilities. While our phase diagram is very similar to the phase diagram for the Sherrington–Kirkpatrick model, the Bethe lattice provides a useful description of the mean-field behavior of spin glasses because the interactions are short range, the analysis is much more straightforward, and the results have been made completely rigorous.

Thermal transformation of calcium hydroxide: Bulk prereactional effects and thermodynamics

Previous experimental results which give evidence of a series of anomalies in the evolution of some structural parameters of calcium hydroxide with temperature are reviewed. These anomalies are found in the domain of thermodynamic stability of Ca(OH) 2. They are shown to be associated with transitions, of second-order type, which transform the initial solid into a state in which it can undergo the chemical reaction.

Ultrafine Metal Particles in Porous and Dense Silica Gels

The present trend of developing electronic devices with increasingly fine dimensions borders on a number of fundamental scientific questions about the very nature of how materials at ultrafine dimensions behave. This article addresses some of these questions. The fabrication of discrete metallic phases in porous and nonporous glassy matrices presents a number of exciting device possibilities. Methods of fabricating ultrafine metallic phases in silica via the sol-gel route are presented.In attempting to fabricate materials with ultrafine physical dimensions for a wide variety of applications, several fundamental questions arise about the nature of materials behavior. For example, how many metal atoms are necessary to form a cluster exhibiting “metallic“ properties? Moreover, does the number of atoms necessary depend upon which metallic property is examined? This question has been partly addressed by D.C. Johnson and co-workers with regard to magnetism in osmium clusters. Their results show a threefold increase in magnetic susceptibility between clusters containing 3–10 osmium atoms.Another important question, especially when considering device applications, is how the relative contributions of surface and bulk thermodynamics affect such properties as phase transformations. In addition, ultrafine phase dimensions interact with the fundamental unit lengths of a wide range of processes, including the wavelength of visible light, the mean free path lengths of conduction processes, the wavelengths of phonon vibrations, etc. How do these interactions affect optical, thermal, and electronic properties?Fabrication of ultrafine metallic particles in porous and nonporous matrices may lead to many possible device applications including heterogeneous catalysts, nonlinear optic devices, highvoltage switching devices based on interparticle tunneling, and perhaps even new types of charge storage devices (capacitors).

Thermodynamic calculations on sulfide flotation systems, II. Comparisons with electrochemical experiments on the galena-ethyl xanthate system

Extensive thermodynamic calculations have been carried out to study the oxidation of galena and its flotation by potassium ethyl xanthate (KEX). In order to include some kinetic effects, three cases have been considered by assuming that sulfur oxidation can proceed as far as the formation of sulfate, thiosulfate and elemental sulfur. The results of these calculations have been compared with those of linear sweep voltammetry and intermittent galvanostatic polarization experiments conducted on galena at pH 9.2. Analysis of the experimental data indicates that in xanthate-free solutions, galena is oxidized primarily to PbO and S 0 and, to a lesser extent, S 2O 3 2−, rather than to the thermodynamically most favored PbOH + and SO 4 2−. Tests carried out in the presence of collector confirm the previous finding (Woods, 1971) that the interaction of xanthate with the mineral begins with chemisorption by a one-electron reaction. This cannot, of course, be predicted by calculations based on bulk thermodynamics.

Growth, chemical interaction, and Schottky-barrier formation of column-III metal overlayers on InP(110).

We report soft-x-ray valence-band and core-level photoemission studies of the growth and chemical reaction of column-III (Al, Ga, In, and Tl) overlayers on cleaved InP(110). We find that the deposition of submonolayer coverages of these metals leaves the valence-band spectra devoid of any structure other than that characteristic of the clean InP(110) surface. Strong bonding between the Al, Ga, or In adatoms relative to the bond between the adatoms and the substrate leads to cluster formation on the surface. Growth of a uniform overlayer cannot, however, be excluded for Tl. Core-level spectra of substrate atoms and overlayer atoms for Al and Ga interfaces clearly indicate a room-temperature exchange reaction accompanying the islanding of nonreacted metal. No indications of such a reaction are found for In and Tl. The trends of the reaction are in agreement with predictions of bulk thermodynamics. The overall trend in the growth mode agrees with the theoretical predictions of Zunger.

Spherical reference systems for nonspherical hard interactions

Results are presented on three complex systems of hard molecules: linear triatomics, heteronuclear dumbbells, and two-component mixtures of dumbbells. In addition to studying the equation of state generated by the median potential, the Barker-Henderson reference system is also investigated and seen to give results nearly indistinguishable from those obtained from the median system. Both reference systems continue to reproduce the bulk thermodynamics of the true systems moderately well. Both reference potentials are found to be approximately additive when applied to mixtures. These results continue to suggest that either of these two reference systems may form the basis of a successful perturbation theory for fluids of nonspherical molecules. 15 references, 5 figures, 9 tables.

Bulk and surface thermodynamics of polymer alloys

AbstractThis paper presents an overview of the subject of phase separation in polymer blends with an emphasis on the thermodynamic stability criteria for phase stability and the classical thermodynamic and microscopic description of polymer interfaces.