Nucleation of the D1a type ordered phase in the near-surface of A4B alloy: II. Nucleation at surface

Nucleation in the D1_a type A₄B ordering alloy was investigated by means of an atomistic calculation based on a phenomenological nucleation theory and the Bragg-Williams approximation. The nucleation rate at the Ni₄Mo surface is presented as a function of temperature, surface orientation, and type of the plane to which the surface is parallel (fundamental plane or superlattice plane). The radius, degree of order and activation free energy of the critical nucleus are also given as a function of temperature. The value of the nucleation rate at the surface is compared with that in the bulk. The results are as follows: (i) at temperatures near T_c. the nucleation rate is higher at the surfaces than in the bulk and the {200}_FCC surfaces are the highest in nucleation rate; (ii) however, at temperatures near the instability temperature t₀, the nucleation rate is lower at the surface than in the bulk; (iii) the present calculated results give reasonable explanations to our experimental results on the Ni₄ Mo alloy: (a) preferential surface ordering at high temperatures near T_c; (b) surface disordering at intermediate temperatures near the nose temperature.     

Nucleation of the D1a type ordered phase in the near-surface of A4 B alloy: I. Nucleation in bulk

Nucleation in the D1_a type A₄B ordering alloy was studied by means of an atomistic calculation based on the Bragg-Williams approximation, as a first step in the understanding of ordering phenomena in the near-surface. A detailed investigation was made for bulk Ni₄ Mo on the free energy (ΔF) surface of the system containing a nucleus as a function of the size and the degree of order of the nucleus. The nucleation rate, and the degree of order and the size of the nucleus at temperatures above the instability temperature T₀ were given as a function of temperature by employing a phenomenological nucleation theory. Above T₀ (= 0.844 T_c) the Δ F surface is dam-shaped and has a saddle point, while it has neither dam shape nor saddle point below T₀. The nature of nucleation is different at higher and lower temperatures: at temperatures higher than T₀ a critical nucleus must have a high degree of order although the value is not so large as the equilibrium degree of order, while the nature of nucleation has a continuous mode at lower temperatures. By examining the calculated results, it was concluded that the use of this nucleation theory was valid at least qualitatively.     

Surface free energies of solid metals: Estimation from liquid surface tension measurements

An equation is derived on semi-theoretical grounds which expresses the solid-vapour surface free energy as a function of the liquid surface tension and the solid-liquid interfacial free energy. A means of calculating reliable values for the solid-liquid energy is presented, which then allows an accurate estimate of solid surface energy at the melting temperature, T_m, to be made for the large number of elements for which dependable liquid surface tension data exist. A method of estimating surface entropy is presented, and has been used to calculate the energies typical of “average”, high-index surfaces at temperatures ranging from 0 K to T_m. It is felt that this paper describes the most accurate method presently available for the calculation of the surface energy of solids in the absence of direct experimental measurement.     

The instability point H s of the Meissner state for large-κ superconductors

The critical field H _s corresponding to the emergence of vortices in a superconductor without a threshold is found near the transition temperature and in the limit as T→0 for an arbitrary value of the depairing factor Γ. In superconductors of the second kind, this field value coincides with the absolute instability point of the Meissner state. In large-κ superconductors, the order parameter tends to zero on the surface of the super-conductor if the external magnetic field reaches the value H _s. We obtain that H _s=H _cm (where H _cm is the thermodynamic critical field) for an arbitrary value of the depairing factor Γin the temperature region near T _c and at T=0.     

Studies of vibrational surface modes in ionic crystals: III. Vibrational contributions to the surface thermodynamic functions for the (001) face of LiF,MgO, NaF,NaCl, Nal,RbF, and RbCl

The temperature dependence of the vibrational contributions to surface specific heat, surface entropy, surface energy, and surface Helmholtz free energy have been calculated for the (001) face of seven crystals having the rocksalt structure. The calculations assume a perfect, unrelaxed surface and make use of shell models fitted to bulk phonon spectra determined from inelastic neutron scattering. In terms of the bulk zero-temperature Debye temperature θ₀, the surface specific heat C_v^s exhibits an effective power law behavior, T^α, from at least T = 0.02 θ₀ up to 0.05 θ₀ in most cases (and up to 0.07 θ₀ for NaF), with α ≈ 2.5 in most cases — in contrast with the result of α = 2 in a Debye-like model. (Below 0.02 θ₀, results derived for our 15-layer films depart significantly from intrinsic surface effects because of the finite thickness.) C_v^s attains a maximum at a temperature T(C_max^s) ranging from 0.14 θ₀ to 0.20 θ₀, in contrast with the result T(C_max^s) = 0.21 θ₀ for the Debye-like model. The peak value C_max^s ranges from 0.34 k_BA_SUC to 0.41 k_BA_SUC, where A_SUC is the area of the surface unit cell. The shap the peak in C_v^s differs characteristically between that class of crystals in which there is some overlap of the acoustical and optical bulk bands and that class in which there is an appreciable absolute gap between the acoustical and optical bulk bands; in the latter class the peak is flattened on the low side of the maximum, with the maximum pushed to somewhat higher temperature. On those points of comparison with the rather sparse existing data for surface-excess heat capacity in which the value of specific surface area is not required (e.g., the value of T(C^s_max)), the agreement ranges from encouraging to equivocal. On those comparisons which require the surface area of the experimental samples (e.g., the magnitude of C^s_max) the agreement ranges from only fair to bad. Further experimental work is needed, and great care in surface area determinations is necessary.     

A possible role of the surface free enthalpy excess of solid chemical elements in their melting and critical temperature

A 5–20% increase in the average number of neighbors of an atom (n_avrg) in the surface phase between 0 K and melting temperature T_m makes the solid surface “geometrically impossible” to exist at some temperature called the melting temperature. The latter results in the collapse of crystal structure, beginning with the formation of surface layers of liquid a few atoms thick, in agreement with recently published studies. The critical temperature of solid chemical elements is also discussed. The derivation yields expressions for the heat of melting (ΔH_m), entropy of melting (ΔS_m), melting temperature (T_m) and critical temperature (T_c) in case of pure metals.     

Surface anchoring and temperature variations of the pitch in thin cholesteric layers

The temperature variations of the cholesteric pitch in thin planar layers of cholesterics and their dependence on the surface anchoring force are investigated theoretically. It is shown that the temperature variations of the pitch in a layer are of a universal character. This is manifested in the fact that they depend not separately on the parameters of the sample but only on one dimensionless parameter S _d =K ²²/dW, where K ₂₂ is the torsional modulus in the Frank elastic energy, W is the height of the surface-anchoring potential, and d is the thickness of the layer. The investigation is performed the parameter S _d in a range where the change per unit number of cholesteric half-turns within the thickness of the layer accompanying a change in the temperature is due to the slipping of the director on the surface of the layer through the potential barrier for surface anchoring. The critical values of the parameter S _d (which are most easily attained experimentally by varying the thickness of the layer), determining the region of applicability of the approach employed, are presented. The temperature variations of the free energy of the layer and the pitch of the cholesteric helix in the layer as well as the temperature hysteresis in the variations of the pitch with increasing and decreasing temperature are investigated for the corresponding values of S _d . Numerical calculations of the quantities mentioned above are performed using the Rapini anchoring potential.     

Two-dimensional superconductive state near the intermediate plane

The superconductive layer near a plane surface arises due to the electronic states (Tamm levels) localized on the surface at temperature T₀, higher than the bulk critical temperature.     

Physical mechanism of the (tri)critical point generation

We discuss some ideas resulting from a phenomenological relation recently declared between the tension of string connecting the static quark-antiquark pair and surface tension of corresponding cylindrical bag. This relation analysis leads to the temperature of vanishing surface tension coefficient of the QGP bags at zero baryonic charge density as T _?? = 152.9 ± 4.5 MeV. We develop the view point that this temperature value is not a fortuitous coincidence with the temperature of (partial) chiral symmetry restoration as seen in the lattice QCD simulations. Besides, we argue that T _?? defines the QCD (tri)critical endpoint temperature and claim that a negative value of surface tension coefficient recently discovered is not a sole result but is quite familiar for ordinary liquids at the supercritical temperatures.     

Phase transition in a linear chain of classical spins with a logarithmic nearest neighbour pair potential

We present the complete calculation of the partition function and correlation functions of a linear array of classical spins coupled by a nearest neighbour logarithmic pair potential. In the case of a ferromagnetic coupling there occurs a phase transition at T_c > 0. The critical exponents of the specific heat C and the magnetic susceptibility χ (in the absence of an external field) are shown to have the non-classical value α = 2 and classical value γ = 1 respectively. The underlying mathematical mechanism of the phase transition is the complete degeneracy of all the eigenvalues of the corresponding integral equation (Kac's mechanism). Below T_c the partition function becomes complex. For antiferromagnetic coupling the free energy is analytic in the whole temperature range and so no phase transition occurs in this case.     

Energy relaxation of electrons in the (100) n-channel of a Si-MOSFET: II. Surface phonon treatment

The electron energy relaxation is investigated as a function of the “electron temperature” T_e in the n-channel of a (100) surface silicon MOSFET device by inspecting the phenomenological energy relaxation time τ_ε(T_e). τ_ε is determined theoretically and compared to experimental results in order to identify the energy relaxation mechanism(s) present at the interface. Two dimensional electron transport is assumed. Single activation temperature (θ) Rayleigh wave scattering and acoustic Rayleigh wave scattering are studied as possible energy loss processes. The effects of electric subbanding near the surface are included. τ_ε is calculated for T_e ? 15 K in the electric quantum limit. We find that a single θ = 12.0 K Rayleigh phonon fits theory to experiment for a single electron inversion density (N_inv) case, but can not provide a fit simultaneously for more than one N_inv value. Theory and experiment disagree when Rayleigh wave acoustic scattering is assumed.     

Influence of thickness,width and temperature on critical current density of Nb thin film structures

The density of critical currents j_C in Nb thin films with thickness smaller than 15 nm and width between 100 nm and 10 μm has been measured in a wide temperature range. We have found that the temperature dependencies of j_C in sub-micrometer wide bridges at 0.7T_C < T < T_C are well described by the Ginzburg–Landau de-pairing critical current. In wider bridges already at T < 0.9T_C the j_C value is significantly reduced due to the penetration and de-pinning of magnetic vortices.     

Surface electromigration of In on vicinal Si(0 0 1)

Surface mass transport of In film on vicinal Si(0 0 1) has been systematically investigated by a scanning Auger electron microscopy (SAM), low energy electron diffraction (LEED) and atomic force microscopy (AFM). It was observed that the temperature dependence of the mass transport shows the critical phenomenon. Above a critical temperature T_c, surface electromigration of the In film toward the cathode side dominated the surface mass transport on the vicinal Si(0 0 1) surface. The LEED and AFM observations revealed that the In film surface on the vicinal Si(0 0 1) consists of 3×4 terraces and (3 1 0) facets. The area ratio of the facet to the terrace exhibited abrupt an increase at T_c. It is believed that the change of the mass transport is related to the abrupt change of the area ratio of the facet to the terrace. Both the critical temperature T_c and the spread due to the surface electromigration of the In film depended on the configuration of the DC current direction and the step edge.     

On the surface properties and baric fragmentation of iron

The dependence of the specific surface energy (??) on the normalized volume (V/V ₀) and temperature (T) for the body-centered cubic (BCC) lattice of iron has been studied on the basis of the Mie-Lennard-Jones potential of interatomic interaction. It is shown that below the definite value of the normalized volume (V/V ₀)_fr the specific surface energy of the BCC-Fe lattice passes to the negative range of values: ??(V/V ₀)_fr = 0, and the (V/V ₀)_fr value increases almost linearly with temperature. In the case of compression, when (V/V ₀) < (V/V ₀)_fr, the exothermal process of crystal fragmentation into dendritic domains with the maximum possible specific intercrystalline surface takes place. In the case of nanofragmentation, surface pressure (P _sf) emerges, leading to self-packing of the formed nanocrystals. The dependence of the ??(V/V ₀) and P _sf (V/V ₀) functions on the size and shape of the BCC-Fe nanocrystals has been studied at different temperature values T = 1500?C3500 K. It has been shown that the P _sf function increases with a decrease in the size; this occurs more strongly, the more the nanocrystal deviates from the most thermodynamically stable cubic shape. The dimensional compression of the lattice parameter of BCC-Fe nanocrystals has been studied. The specific (per volume unit) amount of heat released during fragmentation of the BCC-Fe lattice at high pressures and temperatures has been estimated.     

Combinatorial and Topological Analysis of the Ising Chain in a Field

We present an alternative solution of the Ising chain in a field under free and periodic boundary conditions, in the microcanonical, canonical, and grand canonical ensembles, from a unified combinatorial and topological perspective. In particular, the computation of the per-site entropy as a function of the energy unveils a residual value for critical values of the magnetic field, a phenomenon for which we provide a topological interpretation and a connection with the Fibonacci sequence. We also show that, in the thermodynamic limit, the per-site microcanonical entropy is equal to the logarithm of the per-site Euler characteristic. The canonical and grand canonical partition functions are identified as combinatorial generating functions of the microcanonical problem, which allows us to evaluate them. A detailed analysis of the magnetic field-dependent thermodynamics, including positive and negative temperatures, reveals interesting features. Finally, we emphasize that our combinatorial approach to the canonical ensemble allows exact computation of the thermally averaged value <????> of the Euler characteristic associated with the spin configurations of the chain, which is discontinuous at the critical fields, and whose thermal behavior is expected to determine the phase transition of the model. Indeed, our results show that the conjecture <????>?(T _C)?=?0, where T _C is the critical temperature, is valid for the Ising chain.     

Superconducting behavior of amorphous Zr70Cu30

Measurement of the Meissner penetration depth, λ(T) were made in amorphous Zr₇₀Cu₃₀ samples. The results indicate that this amorphous alloy behaves as a BCS superconductor with 2Δ(0)?kT_c = 3.8, where Δ(0) is the superconducting energy gap at T=0 and T_c the critical temperature. It is also concluded that the low energy excitation, TLS, characteristics of amorphous material does not contribute to T_c.     

Adhesion studies of latex film surfaces on the meso- and nanoscale

In this paper the effects of surface roughness and annealing temperature (T) of latex coating films on adhesion are discussed for the different stages of the film formation process. The surface free energy of latex films was assessed in terms of practical work of adhesion (W) (or adherence) using a custom-built adhesion-testing device (ATD), atomic force microscopy (AFM), and contact angle measurements. For preannealed latex films surface roughness averages (R_a) were determined from AFM height images and were related to the values of W obtained from ATD measurements at room temperature. The results obtained using these tests exhibiting surface behavior on different length scales indicate a dependence of the measured adhesion on surface roughness and temperature, as well as on the length scale of the measurements.First preannealed samples were studied, which were obtained by heat treatment above the respective glass transition temperatures (T_g). Increasing the temperature of preannealing resulted in a decrease of the adherence observed in ATD experiments at room temperature. However, on the nanoscale, using AFM, no significant variation of the adherence was observed. This observation can be explained by roughness arguments. Preannealing decreases roughness which results in lower adherence values measured by ATD while for essentially single asperity AFM experiments roughness has an insignificant effect. Specimens were also annealed over a constant period of time (90 min) at different temperatures. At the end of the heat treatment, adhesion was measured at the treatment temperature by ATD. The amplified effect of temperature observed in this case on adherence is attributed to the combination of roughness decrease and increasing test temperature. In a third set of experiments completely annealed samples were studied by ATD as well as by AFM as a function of temperature. With increasing T values ATD showed a decrease in adherence, which is attributed to a decreasing surface free energy of the annealed films at elevated T values. AFM, on the other hand, showed an opposite trend which is assigned to increasing penetration of the tip into the tip/wetting polymer samples versus increasing temperature. Finally, annealing isotherms as a function of time were investigated by ATD in situ at different temperatures. This last set of experiments allowed us to optimize annealing time and temperature to achieve complete curing.     

Defect interaction and solid electrolyte transition in AgI-based materials

The first-order phase transition that leads to the superionic phase in AgI-based materials is studied by dc-conductivity measurements and a free energy model. By properly adjusting the model parameters, an abrupt change of disordering concentration, Δη?, is predicted at a transition temperature, T_t. The temperature dependence of the dc-conductivity, σ(T), is well fitted to the η?(T) equilibrium configuration obtained from the trial free energy function. The reported comparative study was done using an AgI–KI modified sample. The model also predicts a transition temperature, T_c for a continuous phase transition (Δη? = 0).     

Detection of various phases in liquids from the hypersound velocity and damping near closed phase-separation regions of solutions

Theoretical analysis revealed that experimental results obtained in our studies on hypersound propagation in a guaiacol-glycerol solution in the vicinity of the closed phase-separation region, double critical point, and special point, as well as the origin of these regions, can be explained by the presence of two different phases (I and II) of the solution with phase-transition temperature T ₀. Temperature T ₀ coincides with the temperature at the center of closed phase-separation regions, as well as with the double critical point and with the special point. In (Frenkel) phase I, molecules are in potential wells whose depth exceeds the thermal energy of a molecule, while thermal energy in (gaslike) phase II is higher than the potential well depth. At the lower critical point, the thermodynamic potential of phase I is equal to the thermodynamic potential of the phase-separated solution. At the upper critical point, the thermodynamic potential of phase II is equal to the thermodynamic potential of the phase-separated solution. The observed broad dome of the hypersound absorption coefficient near T ₀ can be explained by the contribution associated with fluctuations of the order parameter corresponding to the transition from phase I to phase II. The difference in the temperature coefficients of hypersound velocity on different sides of T ₀ and some other effects are also explained.     

Some parameters of superconductors with an extreme singularity in the density of state: (s+d) model

We study some parameters of superconductors with δ-function type singularities in the electronic density of states (DOS), exhibiting (s+d)-wave symmetry of the order parameter. Starting with a pure s-wave pairing potential V_s, the critical temperature T_c at first slightly increases with increasing the d-wave interaction potential V_d, being determined by this interaction only for stronger V_d values. The ratio R=2|Δ(0)|/k_BT_c of the mean value of the zero temperature energy gap |Δ(0)| to T_c increases with increasing V_d, reaching a maximum which depends on the mixing interaction term. The maximum values of R are comparable with very high values obtained in some gap measurements. The jump in the specific heat at critical temperature is by a factor 2.4 higher for the extreme singularity of pure s-wave symmetry, as compared with the BCS theory with constant DOS. Such higher values of the jump are in agreement with the experimentally observed values, as well as with the calculations determined by extended saddle points in the electronic bands. By switching the d-wave channel, the value of the jump decreases. The results show the usefulness of calculations with δ-type singularities as a limiting case of very strong singularities in the DOS.