Effects of lattice dispersion and elastic anisotropy on the thermal properties of bcc metals

Two new parameters which take into account the effects of elastic anisotropy and phonon dispersion on lattice specific heat in the case of sodium and potassium have been evaluated. A new graded mesh method which uses a 162-direction approximation in (1/16) part of the Brillouin Zone (BZ) has been considered to evaluate the two parameters.     

Calculated elastic constants of dilute alloys based on bcc metals

The elastic constants of dilute alloys based on bcc metals have been calculated using the Green’s function method obtaining explicit expressions for change in elastic constants in terms oft-matrix. The crystal impurity problem is discussed within an impurity model containing central and non-central force constant changes extended up to second neighbours of the impurity. The effect of volume change on elastic constants and a contribution from electron pressure term are considered. Numerical results for changes in three elastic moduli have been presented for a number of dilute alloys based on Mo, Nb, W, Ta and V.     

Peierls potential for crowdions in the bcc transition metals

We present the first derivation of the analytic expression for the Peierls-Nabarro potential for crowdion migration using the double sine-Gordon model. The analysis is guided by the group-specific trend in the shapes of the periodic lattice potentials calculated for the body-centered-cubic transition metals in groups 5B and 6B of the periodic table. We combine density-functional calculations of the crowdion's profile and environment with an extended version of the analytical Frenkel-Kontorova model, and determine the effective potential experienced by the defect's center of mass. This reveals important underlying differences between the metals in these groups, which are inaccessible to either the numerical or analytical approaches alone, and accounts for the previously unexplained significantly higher crowdion migration temperatures observed in the metals of group 6B relative to those of group 5B.     

Phonon dispersion for the bcc metals Mo and Cr

In this paper the phonon dispersion for the bcc metals Mo and Cr is calculated based on the pair potentials obtained from cohesive energies and the Slater-Kirkwood- type three body interaction. In the calculation of the pair potentials the Möbius transform in the number theory is used and the cohesive energy is evaluated by the LMTO method. The results show a good agreement with inelastic neutron scattering data and indicate that the three-body interaction is necessary to account for the phonon dispersion.     

The elastic moduli,the volume contribution and the Cauchy ratio ford andf shell metals

The elastic constants of nine transition metals and four rare-earths and actinides are calculated using the ion-ion interaction defined by us recently. The volume contribution to elastic moduli is calculated by exploiting the density dependence of the screening function. The calculated volume contribution to bulk modulus is found to vary between 17.1% and 62.4% for a number of metals, which is quite significant and play an important role for describing quantitatively the violation of the Cauchy ratio for these metals.     

Effects of lattice dispersion and elastic anisotropy on the thermal properties of fcc metals

New parameters which separately take into account the effects of elastic anisotropy and phonon dispersion on the lattice specific heat in the case of fcc metals have been evaluated. A new graded mesh method which uses 162-direction approximation in (1/16) part of the Brillouin zone has been developed to evaluate the two new parameters.     

Modified Cheveau model for the lattice waves in bcc metals: An application to phonon dispersion and Grüneisen parameter

The force model proposed in the preceeding paper for the fcc metals is further extended for the bcc lattice. The computed values of Grüneisen parameters and the phonon frequencies for potassium show a fairly good agreement with the experimental results.     

One- and two-dimensional lattice sums for the three-dimensional Helmholtz equation

The accurate and efficient computation of lattice sums for the three-dimensional Helmholtz equation is considered for the cases where the underlying lattice is one- or two-dimensional. We demonstrate, using careful numerical computations, that the reduction method, in which the sums for a two-dimensional lattice are expressed as a sum of one-dimensional lattice sums leads to an order-of-magnitude improvement in performance over the well-known Ewald method. In the process we clarify and improve on a number of results originally formulated by Twersky in the 1970s.     

Temperature dependence of elastic moduli for solid C60

The attenuation and velocity of ultrasonic waves (at a frequency of ～4 MHz) along the 〈111〉 and 〈100〉 directions in solid C₆₀ single-crystal samples are measured in the temperature range 100–300 K. The temperature dependences of the complete set of elastic constants for C₆₀ fullerite are determined from the experimental data. It is shown that the specific features in the behavior of the elastic moduli near the orientational phase transition temperature are associated with different contributions of the relaxation processes to the effective elastic moduli. The activation volume and deformation potentials for the ground and excited states of the C₆₀ low-temperature phase are evaluated from the results obtained in this work and the data available in the literature.     

Asymptotic behavior of Mayer cluster sums for the one-dimensional Ising model

The properties of the high-field polynomialsL _n (u) for the one-dimensional spin 1/2 Ising model are investigated. [The polynomialsL _n (u) are essentially lattice gas analogues of the Mayer cluster integralsb _n (T) for a continuum gas.] It is shown thatu ^?1 L _n (u) can be expressed in terms of a shifted Jacobi polynomial of degreen?1. From this result it follows thatu ^?1 L _n (u); n=1, 2,... is a set of orthogonal polynomials in the interval (0, 1) with a weight functionω(u)=u, andu ^?1 L _n (u) hasn?1 simple zerosu _n (v); v=1, 2,...,n?1 which all lie in the interval 0<u<1. Next the detailed behavior ofL _n (u) asn→∞ is studied. In particular, various asymptotic expansions forL _n (u) are derived which areuniformly valid in the intervalsu<0, 0<u<1, andu>1. These expansions are then used to analyze the asymptotic properties of the zeros {u _n (v); v=1, 2,...,n?1}. It is found that $$\begin{array}{*{20}c} {u_n (v) \sim \tfrac{1}{4}({{j_{1,v} } \mathord{\left/ {\vphantom {{j_{1,v} } n}} \right. \kern-\nulldelimiterspace} n})^2 [1 - ({{j_{1,v}^2 } \mathord{\left/ {\vphantom {{j_{1,v}^2 } {12}}} \right. \kern-\nulldelimiterspace} {12}})n^{ - 1} + ({{j_{1,v}^2 } \mathord{\left/ {\vphantom {{j_{1,v}^2 } {700)( - 3 + 2j_{1,v}^2 )n^{ - 4} }}} \right. \kern-\nulldelimiterspace} {700)( - 3 + 2j_{1,v}^2 )n^{ - 4} }}} \\ { + ({{j_{1,v}^2 } \mathord{\left/ {\vphantom {{j_{1,v}^2 } {20160)(40 + 4j_{1,v}^2 - j_{1,v}^4 }}} \right. \kern-\nulldelimiterspace} {20160)(40 + 4j_{1,v}^2 - j_{1,v}^4 }})n^{ - 6} + \cdot \cdot \cdot ]} \\ {u_n (n - v) \sim 1 - ({{j_{0,v}^2 } \mathord{\left/ {\vphantom {{j_{0,v}^2 } 4}} \right. \kern-\nulldelimiterspace} 4})n^{ - 2} + ({{j_{0,v}^2 } \mathord{\left/ {\vphantom {{j_{0,v}^2 } {48)( - 2 + j_{0,v}^2 )n^{ - 4} }}} \right. \kern-\nulldelimiterspace} {48)( - 2 + j_{0,v}^2 )n^{ - 4} }}} \\ { + ({{j_{0,v}^2 } \mathord{\left/ {\vphantom {{j_{0,v}^2 } {2880)(2 + 9j_{0,v}^2 - 2j_{0,v}^4 )n^{ - 6} + \cdot \cdot \cdot }}} \right. \kern-\nulldelimiterspace} {2880)(2 + 9j_{0,v}^2 - 2j_{0,v}^4 )n^{ - 6} + \cdot \cdot \cdot }}} \\ \end{array} $$ asn→∞v fixed, wherej _k,v denotes thevth zero of the Bessel functionJ _k(^z)     

New estimates for macroscopic elastic moduli of random polycrystalline aggregates

Elastic behaviour of random polycrystals, the shape and crystalline orientations of the constituent grains of which are uncorrelated, is considered. A geometrical restriction in earlier derived bounds on the aggregates’ elastic moduli is released leading to new estimates for the general random aggregates. The bounds are expected to predict the scatter ranges for the observed macroscopic moduli. Application to a number of cubic crystals’ aggregates indicates that their moduli are determinable within the accuracy of up to 2 or 3 significant digits in most cases.     

Model for lattice dynamics of fcc metals

A lattice dynamical model which satisfies the requirement of static force equilibrium of fcc crystals is proposed. It incorporates central, angular and electron-ion interactions. The calculated dispersion curves for copper are in good agreement with neutron scattering data.     

Stability analysis for flow past a cylinder via lattice Boltzmann method and dynamic mode decomposition

A combination of the lattice Boltzmann method and the most recently developed dynamic mode decomposition is proposed for stability analysis.The simulations are performed on a graphical processing unit.Stability of the flow past a cylinder at supercritical state,Re = 50,is studied by the combination for both the exponential growing and the limit cycle regimes.The Ritz values,energy spectrum,and modes for both regimes are presented and compared with the Koopman eigenvalues.For harmonic-like periodic flow in the limit cycle,global analysis from the combination gives the same results as those from the Koopman analysis.For transient flow as in the exponential growth regime,the combination can provide more reasonable results.It is demonstrated that the combination of the lattice Boltzmann method and the dynamic mode decomposition is powerful and can be used for stability analysis for more complex flows.     

Second pressure derivatives of the elastic moduli of fused quartz

The first and second pressure derivatives of the elastic moduli of fused quartz have been determined by ultrasonic measurements of the sound velocity as a function of pressure. The second derivatives are positive in sign and are larger in magnitude than those in crystalline materials. The data are used to calculate the equation of state and the volume dependence of the Grüneisen constant.     

On the cluster approach for calculating electronic energies of solid surfaces

A scheme for calculating electronic energy states of infinite solid surface systems by a cluster approach under the framework of the method of linear combinations of atomic orbitals is presented. The basis functions consist of atomic-like orbitals confined within a cluster whereas the Hamiltonian is that of the infinite solid. The latter circumvents the difficulty arising from the auxiliary boundary of the cluster which is not the true surface of the solid. All the multicenter integrals appearing in the Hamiltonian matrix can be evaluated exactly by means of the technique of Gaussian orbitals. This cluster-basis method is applied to the chlorine-adsorbed silicon (111) surface using several different clusters. The results are compared with those of the same Hamiltonian with basis functions extending over the entire solid in the Bloch-sum form. Criteria for optimal selection of clusters are suggested.     

Calculation of the bond energy and elastic moduli of magnesium

The bond energy, equilibrium lattice parameters, and elastic moduli of magnesium are calculated by the method described in [1].