On the structural stability of metallic glasses

We discuss the various possibilities advanced to account for the structural stability of metallic glasses. Using a formalism based on the pseudopotential theory and the Gibbs-Bogoliubov inequality we calculate the free energies and free energies of formation for the glassy phase of MgCa at various concentrations and compare these results with those for the corresponding solid and liquid phases of the same system. Subsequently, we attempt to explain the stability of the metallic glasses by noting a matching between the positions of the first peakq _m in the relevant structure factor and the maximumq _s in the relevant screened pseudopotential.The major part of this work was done in the H.H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, England     

Evaluation of Gibbs free energies of formation of Ce–Cd intermetallic compounds using electrochemical techniques

Gibbs free energies of formation of six Ce–Cd intermetallic compounds, CeCd, CeCd₂, CeCd₃, CeCd_58/13, CeCd₆ and CeCd₁₁, were evaluated systematically using electrochemical techniques in the temperature range of 673–923 K in the LiCl–KCl–CeCl₃–CdCl₂ molten salt bath. The linear dependence of the Gibbs free energies of formation on temperature yields to the enthalpies and entropies of formation of these intermetallic compounds. By extrapolating the Gibbs free energy of Ce–Cd intermetallic compounds to the Cd distillation temperature, it was clear that the Gibbs free energy of Ce–Cd intermetallic compounds decreases gradually from CeCd₆ to CeCd₂ and attains minimum value at CeCd₂. This suggests on the Cd distillation from the U–Pu–Ce–Cd alloy that the dissolution of U or Pu into CeCd₂ should be mostly taken into consideration.     

Combinatorics of Dispersionless Integrable Systems and Universality in Random Matrix Theory

It is well-known that the partition function of the unitary ensembles of random matrices is given by a τ-function of the Toda lattice hierarchy and those of the orthogonal and symplectic ensembles are τ-functions of the Pfaff lattice hierarchy. In these cases the asymptotic expansions of the free energies given by the logarithm of the partition functions lead to the dispersionless (i.e. continuous) limits for the Toda and Pfaff lattice hierarchies. There is a universality between all three ensembles of random matrices, one consequence of which is that the leading orders of the free energy for large matrices agree. In this paper, this universality, in the case of Gaussian ensembles, is explicitly demonstrated by computing the leading orders of the free energies in the expansions. We also show that the free energy as the solution of the dispersionless Toda lattice hierarchy gives a solution of the dispersionless Pfaff lattice hierarchy, which implies that this universality holds in general for the leading orders of the unitary, orthogonal, and symplectic ensembles. We also find an explicit formula for the two point function F _nm which represents the number of connected ribbon graphs with two vertices of degrees n and m on a sphere. The derivation is based on the Faber polynomials defined on the spectral curve of the dispersionless Toda lattice hierarchy, and \frac1nmF_nm{\frac{1}{nm}F_{nm}} are the Grunsky coefficients of the Faber polynomials.     

First-principles study of the structural,electronic and optical properties of the cubic triangular quaternary ZnxCdyHg1-x-yTe alloys under hydrostatic pressure

In the present computational study, we have explored the structural, electronic and optical properties of ZnTe, CdTe and HgTe binary compounds and their ternary alloys Zn_xCd_1-xTe, Zn_xHg_1-xTe and Cd_xHg_1-xTe as well as their ordered quaternary Zn_xCd_yHg_1-x-yTe alloys using the full potential linearized augmented plane wave (FP-LAPW) method based on the density functional theory. We have numerically estimated the total energies, the lattice parameters, the bulk moduli and their first pressure derivative using the generalized gradient approximation (GGA). The band structure is computed using the modified Becke-Johnson (TB-mBJ) approximation. Results of our study show a nonlinear dependence of the composition on the lattice constant, bulk modulus and band gap for the binary and ternary compounds as well as for the quaternary alloys. Additionally, the dielectric function, the refractive index and the loss energy were also reported. The pressure effect on the band gap energy and optical properties were also investigated and reported. Our results are in good agreement with experimental values and theoretical data available in the literature.     

Diffusion, Solute Segregations and Interfacial Energies in Some Material: An Overview

We have shown a connection among the three important properties of interfaces, namely, the free energy, diffusion and solute segregation through the conjecture that the interface free energy is the difference between those responsible for diffusion in the lattice and the interface itself. The interface energy is known to decrease upon solute additions. We discuss the methodology and the thermodynamical analysis of the diffusion parameters which enable extraction of the interfacial energies and illustrate them by results obtained in a wide variety of materials. Investigations carried out in pure polycrystalline metals have yielded grain boundary energies comparable to those directly measured. Furthermore, we discuss the role of solute segregation at grain boundaries in alloys in altering diffusion. From the perturbations caused, the solute segregation parameters—the enthalpy and the entropy of binding—have been extracted and levels of solute concentrations estimated. It is shown that similar analyses when applied to complex materials, e.g. the Pb–Sn eutectic alloy, several intermetallic compounds, and oxide systems, also result in acceptable values of interface energies and segregation factors. Finally, some ad-hoc guidelines are provided to alter diffusion in interfaces through solute additions in order to achieve some end use engineering objectives.     

Nonequilibrium energy of Rayleigh waves in half-limited crystals with hot electrons close to the defect surface

Nonequilibrium energies of surface (Rayleigh) lattice oscillations in half-limited crystals with static defects and a two-dimensional layer of hot Fermi and Boltzmann electrons close to the stress free surface were calculated. Substances with electrons heated by an external field retaining their intrinsic temperature for a certain time, T _e ? T, where T is the temperature of the lattice, were considered. As shown earlier, the thermodynamic characteristics of thin films can then be determined by nonequilibrium energy of Rayleigh waves (R-phonons) caused by their interaction with hot electrons. This energy decreases as the widths of the energy spectrum of R-phonons increase. In this work, the earlier calculated spectrum widths are used. These widths are caused by the scattering of R-phonons by electrons and static defects close to the surface (point and extended surface defects, edge dislocations perpendicular to the surface and emerging to it, and random lattice grooves in the lattice plane). In all the calculations, the Keldysh diagram technique transformed for half-limited media was used.     

Atomistic modelling of TiAl I. Bond-order potentials with environmental dependence

Bond-order potentials (BOPs) for L1₀ TiAl have been developed and constructed within a tight-binding framework. In addition to the usual attractive bond-energy contribution arising from the formation of covalent bonds and pairwise contribution describing the overlap repulsion and electrostatic interaction, we have included an environmentally dependent term to represent the strong repulsion experienced by the valence sp electrons in transition metals and their alloys. The latter contribution is crucial for reproducing the negative Cauchy pressures of TiAl and other transition-metal-based intermetallic compounds. The constructed BOPs have been tested in the following ways: firstly, examination of the mechanical stability of the tetragonal L1₀ lattice with respect to large deformations and other crystal structures with the same stoichiometry; secondly, calculation of the γ surface for {111} and related evaluation of the energies of stacking-fault-type defects; thirdly, calculation of energies of the γ-γ interfaces that are present in the lamellar TiAl and energies associated with the formations of point defects in TiAl. The results of all these calculations show very good agreement with various ab-initio calculations. Importantly, we find that this potential is transferable to the different bonding environment in the hexagonal D0₁₉ Ti₃Al. Hence these BOPs are suitable for atomistic study of dislocations and other extended defects not only in L1₀ TiAl but also in Ti₃Al and possibly structures with other titanium-rich stoichiometries.     

Chemical short-range-order effects on stability in δ-Pu–Ga alloys

We present results on the structural stability of Pu_{1? x} Ga _x alloys based on the local spin-density approximation and including non-local corrections to the exchange–correlation functional (generalized gradient approximation). First, we used both the linearized augmented plane-wave and the projector augmented wave (PAW) methods to calculate the energies of formation of five intermediate phases which occur in the Pu–Ga phase diagram. Then, PAW calculations were performed for various superstructures based on the fcc lattice to get the interaction parameters to describe the energetics of the δ-Pu–Ga solid solution. To discuss the effects of the chemical short-range order on the structural stability of the δ-Pu–Ga solid solution as a function of temperature, the cluster variation method configurational entropy has been introduced using the regular tetrahedron approximation. The solid part of the Pu-rich side of the phase diagram involving phase equilibria between the Pu phases, the δ-Pu–Ga solid solution and the Pu₃Ga compound is calculated. We show the importance of chemical short-range order on Ga solubility in δ-Pu.     

On the Convergence of Kikuchi’s Natural Iteration Method

In this article we investigate on the convergence of the natural iteration method, a numerical procedure widely employed in the statistical mechanics of lattice systems, to minimize Kikuchi’s cluster variational free energies. We discuss a sufficient condition for the convergence, based on the coefficients of the cluster entropy expansion, depending on the lattice geometry. We also show that such a condition is satisfied for many lattices usually studied in applications. Finally, we consider a recently proposed class of methods for the minimization of Kikuchi functionals, showing that the natural iteration method turns out as a particular instance of that class.     

Quantum mechanical free energy barrier for an enzymatic reaction

We discuss problems related to in silico studies of enzymes and show that accurate and converged free energy changes for complex chemical reactions can be computed if a method based on a thermodynamic cycle is employed. The method combines the sampling speed of molecular mechanics with the accuracy of a high-level quantum mechanics method. We use the method to compute the free energy barrier for a methyl transfer reaction catalyzed by the enzyme catechol O-methyltransferase at the level of density functional theory. The surrounding protein and solvent are found to have a profound effect on the reaction, and we show that energies can be extrapolated easily from one basis set and exchange-correlation functional to another. Using this procedure we calculate a barrier of 69 kJ/mol, in excellent agreement with the experimental value of 75 kJ/mol.     

Theoretical study of energetic trinitromethyl‐substituted tetrazole and tetrazine derivatives

Density functional theory method was used to study the heats of formation, energetic properties, and thermal stability for a series of trinitromethyl‐substituted tetrazole and tetrazine derivatives with different substituents. It is found that the group ―NO₂, ―NHNO₂, or ―NF₂ play a very important role in increasing the heats of formation of the derivatives. The calculated detonation velocities and pressures indicate that the group ―CF₂NF₂, ―NHNO₂, ―1H‐tetrazolyl, ―2H‐tetrazolyl, or ―1,2,4,5‐tetrazinyl is an effective structural unit for enhancing their detonation performance. An analysis of the bond dissociation energies for several relatively weak bonds indicates that incorporating the group ―NHNO₂ and ―NH₂ into parent ring decreases their thermal stability. Considering the detonation performance and thermal stability, 37 compounds may be considered as the potential high‐energy compounds. Their oxygen balances are close to zero. These results provide basic information for the molecular design of novel high‐energy compounds. Copyright © 2013 John Wiley & Sons, Ltd.     

A theorem concerning twisted and untwisted partition functions in and lattice gauge theories

In order to get a clue to understanding the volume-dependence of vortex free energy (which is defined as the ratio of the twisted against the untwisted partition function), we investigate the relation between vortex free energies defined on lattices of different sizes. An equality is derived through a simple calculation which equates a general linear combination of vortex free energies defined on a lattice to that on a smaller lattice. The couplings in the denominator and in the numerator however shows a discrepancy, and we argue that it vanishes in the thermodynamic limit. Comparison between our result and the work of Tomboulis is also presented. In the appendix we carefully examine the proof of quark confinement by Tomboulis and summarize its loopholes.     

Theoretical investigations of pyridine derivatives as potential high energy density materials

Density function theory has been employed to study pyridine derivatives at the B3LYP/6‐31 G(d,p) and B3P86/6‐31 G(d,p) levels. The crystal structures were obtained by molecular mechanics methods. The heats of formation (HOFs) were predicted based on the isodesmic reactions. Detonation performance was evaluated by using the Kamlet–Jacobs equations based on the calculated densities and HOFs. The thermal stability of the title compounds was investigated by the bond dissociation energies and the energy gaps (ΔE_LUMO?HOMO) predicted. It is found that there are good linear relationships between detonation velocity, detonation pressure, and the number of nitro group. The simulation results reveal that molecule G performs similar to the famous explosive HMX and molecule D outperforms HMX. According to the quantitative standard of energetics and stability as high energy density materials, molecule D essentially satisfies this requirement. These results provide basic information for molecular design of novel high energetic density materials. Copyright © 2012 John Wiley & Sons, Ltd.     

Electronic structural, elastic properties and thermodynamics of Mg17Al12, Mg2Si and Al2Y phases from first-principles calculations

Electronic structures, elastic properties and thermal stabilities of Mg₁₇Al₁₂, Mg₂Si and Al₂Y have been determined from first-principle calculations. The calculated heats of formation and cohesive energies show that Al₂Y has the strongest alloying ability and structural stability. The brittle behavior and structural stability mechanism is also explained through the electronic structures of these intermetallic compounds. The elastic constants are calculated, the bulk moduli, shear moduli, Young's moduli and Poisson ratio value are derived, the brittleness and plasticity of these phases are discussed. Gibbs free energy, Debye temperature and heat capacity are calculated and discussed.     

Ab initio calculation of the phase stability,mechanical properties and electronic structure of ZrCr2 Laves phase compounds

Ab initio calculations have been used to investigate the phase stability, mechanical properties and electronic structure of ZrCr₂ Laves phase compounds, based on the method of augmented plane waves plus local orbitals with the generalized gradient approximation. The calculated lattice constants for the C15, C36 and C14 structures are in good agreement with experimental values. The calculation of heats of formation showed that C15 is a ground-state phase, whereas C36 is an intermediate phase and C14 the high-temperature phase. The elastic constants and elastic moduli for the C15 structure were calculated systematically and compared with experiments and previous theoretical calculations. The intrinsic and extrinsic stacking fault energies are found to be 112 and 98?mJ?m^?2, respectively. The equilibrium separations between Schockley are also predicted using the calculated elastic moduli and stacking fault energies. Finally, the calculated electronic structures of these Laves phases are discussed based on these results.     

A first-principles study on structural stability and mechanical properties of polar intermetallic phases CaZn2 and SrZn2

Structural stability and electronic properties of polar intermetallic CaZn₂ and SrZn₂ in both CeCu₂-type and MgZn₂-type structures have been investigated using first-principles method. The calculated equilibrium lattice parameters agree closely with the available experimental and other theoretical results. In terms of formation enthalpy, it is discovered that the present compounds with CeCu₂-type structure are energetically more stable than that with MgZn₂-type. They are all mechanically stable according to the criteria of elastic stability. In particular, we have investigated the pressure effect on the compressive behaviour and structural stability of each compound. Subsequently, the bulk modulus, shear modulus, Young’s modulus, theoretical hardness, Poisson’s ratio and Debye temperature in the ground state can be estimated using Voigt–Reuss–Hill homogenization method. Mechanical anisotropy is characterized by the anisotropic factors and direction-dependent Young’s modulus. Finally, the electronic structures are determined to reveal the bonding characteristics of considered phases.     

Bulk chemical properties of new elements from one-atom-at-a-time data

For the volatile (oxo)halides of known elements the energies of desorption from the surface of fused silica measured in radiochemical gas-solid chromatographic experiments proved close to the sublimation energies. This could hardly be expected for interaction of isolated molecules with bare surface of ionic SiO₂. Because such regularity shows great promise for evaluation of bulk properties of transactinoid compounds we need to understand the origin of apparent inconsistency. The clue seems to be the real structure of the surface. It is initially rough (from μm down to nm scale), inherently heterogeneous at the molecular level, and contains atoms and groups with excessive energy. Exposing to ambient air produces numerous surface ≡SiOH groups. The halogenating agents employed in transactinoid studies chemically modify such surface: it gets tightly covered by halogen atoms and fragments of the agent molecule attached to the Si and O atoms. Now the molecules of new compounds cannot touch SiO₂ lattice; moreover, in some initially geometric wells (due to roughness), they get surrounded by halogen atoms bonded to the surface — the situation resembling that in their own bulk condensed phase. Hence, there must be sites with desorption energies up to the sublimation energy.     

On the criteria of formation and lattice distortion of perovskite-type complex halides

The famous Goldschmidt's tolerance factor gives us a necessary but not sufficient condition for the formation of perovskite-type compounds (ABX₃). In this work, computerized data analysis has been used to find some complementary criteria for the formation and lattice distortion of perovskite-type complex halides. It has been found that the radius ratio (R_A/R_X) and (R_B/R_X), affecting the stability of BX₆ octahedra and AX₁₂ cubo-octahedra (they are basic units of perovskite structure), are also dominating factors for the formation and lattice distortion of perovskite-type compounds. Besides, it has been found that the transition between the perovskite structure (with corner-sharing BX₆ octahedra) to BaNiO₃ structure (with face-sharing BX₆ octahedra) can be predicted by a criterion based on the relative magnitude of ionic radii and electronegativity. Based on multivariate data analysis, several complementary criteria for the formation and lattice distortion of perovskite-type complex halides have been obtained, and some empirical equations expressing the relationships between the ionic radii (R_A,R_B,R_X) and the lattice constants of perovskite-type complex halides have been found. The physical meaning of these empirical relationships has been discussed based on Pauling's rules of the crystal lattice stability of complex ionic compounds.     

Wall and boundary free energies

The existence of wall or boundary free energies is discussed generally and analyzed explicitly for general lattice systems with scalar (real-valued) spin variables. For systems with ferromagnetic (positive) spin interaction potentials,K, in the bulk andW, for the walls, correlation inequalities and appropriate stability and tempering conditions are used to establish the existence and uniqueness of the limiting free energy per unit area,f _x(K,W), of an infinite planar wall.