Equation of state and thermodynamics of fcc transition metals: A pseudopotential approach

A simple pseudopotential model is used for the calculation of the phonon spectra at the equilibrium volume and under pressure. The model is based on the secondorder perturbation theory with the local pseudopotential acting on thes electrons while thed electrons contribution is simulated by the repulsive Born-Mayer interatomic potential. Pressure influence on the lattice properties was studied for small compressions (mode Grüneisen parameters) as well as for ultrahigh pressure (equation of state up to 1 TPa). Results of the lattice dynamics calculations were used for determining temperature dependence of the lattice heat capacity and of the macroscopic Grüneisen parameter. The Kohn anomaly at the small wave vectors obtained previously in palladium, platinum and rhodium affects strongly the temperature dependence at low temperature.     

The Effect of Temperature on Lattice Mechanical Properties of Noble and Transition Metals

A simple pseudopotential model is used for the calculation of the temperature dependence of lattice mechanical properties which also depend on the phonon density of states such as lattice heat capacity C _V , Debye temperature _D, harmonic contribution to free energy, thermal pressure, isothermal bulk modulus corrected to the fourth order, volume thermal expansion coefficient , Debye-Waller factor, mean-square displacement, Debye-Waller temperature parameter, and X-ray characteristic temperature _M of Cu, Ag, Au, Ni, Pd, Pt, Rh, and Ir. The contribution of d-like electrons is taken into account by introducing repulsive short-range Born-Mayer-like term. Very recently proposed screening function due to Sarkar et al. has been used to obtain the screened form factor. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings show the ability of our model potential to reproduce wide class of properties in noble and transition metals.     

Lattice mechanical properties of noble and transition metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is used to study the interatomic interactions, phonon dispersion curves (inq and r-space analysis), phonon density of states, mode Grüneisen parameters, dynamical elastic constants (C ₁₁,C ₁₂ andC ₄₄), bulk modulus (B), shear modulus (C′), deviation from Cauchy relation (C ₁₂–C ₄₄), Poisson’s ratio (σ), Young’s modulus (Y), behavior of phonon frequencies in the elastic limit independent of the direction (Y ₁), limiting value in the [110] direction (Y ₂), degree of elastic anisotropy (A), maximum frequencyω _max, mean frequency 〈ω〉, 〈ω ²〉^1/2=(〈ω〉/〈ω ⁻¹〉)^1/2, fundamental frequency 〈ω ²〉, and propagation velocities of the elastic constants in Cu, Ag, Au, Ni, Pd, and Pt. The contribution of s-like electrons is calculated in the second-order perturbation theory for the model potential while that of d-like electrons is taken into account by introducing repulsive short-range Born-Mayer like term. Very recently proposed screening function due to Sarkar et al. has been used to obtain the screened form factor. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings has proved the ability of our model potential for predicting a large number of physical properties of transition metals.     

Lattice Dynamics of Some Fcc F-Shell Metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is used to study the binding energy, equation of state, ion-ion interaction, phonon dispersion curves (q-space and r-space analysis), phonon density of states, Debye temperature, mode Grüneisen parameters, dynamical elastic constants, Debye-Waller factor, mean-square displacement, Debye-Waller temperature parameter and propagation velocities of elastic waves of some fcc f-shell metals La, Yb, Ce, and Th. The contribution of the s-like electrons is calculated in the second-order perturbation theory for the model potential while d- and f-like electron is taken into account by introduction of repulsive short-range Born-Mayer term. Very recently proposed screening function due to Sarkar et al. has been used to obtain the screened form factor. The parameter of the potential is evaluated by zero pressure condition. Which is independent of any fitting procedure. An excellent agreement between theoretical investigations and experimental findings prove the ability of the potential for d- and f-shell metals exclusively.     

Electronic contribution to electric field gradient in dilute alloys

A simple relation for calculating the electronic contribution to the electric field gradient in dilute alloys of transition metals is reported and is compared with the conduction electron charge shift model. The dependence of the field gradient on thes andd electrons and the difference in radii between the host and the probe atoms is considered for calculating the field gradient. It is found that thed electrons are the major contributors to the field gradient.     

Electric field gradient in transitional dilute alloys

The electric field gradient (EFG) and the asymmetry parameter (η) due to transition metal impurities in the host metals Al, Cu and V are investigated. The valence EFG is formulated using dielectric screening theory in conjunction with pseudopotential theory. The size EFG is evaluated in the elastic continuum limit for a screened point charge model of the host metal. The detailed calculations are carried out forAl (Sc, Fe, Cr),Cu (Ni, Pd, Pt) andV (Ti, Cr, Fe, Nb, Ta, W) alloys.     

Thermopower calculation for anisotropic normal metals

The thermopower of the divalent normal metals has been calculated in a single OPW approximation, using pseudopotential form factors and a realistic phonon spectra. The calculation emphases the contribution of the phonon drag term. The results are compared with experiments and a simple interpretation is suggested for the evolution of the thermopower anisotropy in the series Be, Mg, Zn and Cd.     

Ab initio phonon dispersion relations of $\mathsf{\alpha}$-Ga

We present the ab initio phonon dispersion relations of -Ga. The calculations are carried out within density functional perturbation theory by using either norm-conserving pseudopotential and 4s and 4p electrons in the valence or ultrasoft pseudopotential and 3d electrons in the valence as well. The inclusion of 3d electrons in the valence turned out to be necessary to better reproduce the experimental frequencies of the stretching modes of the Ga₂ dimers present in the -Ga structure.Received: 29 July 2003, Published online: 19 November 2003PACS: 63.20.Dj Phonon states and bands, normal modes, and phonon dispersion - 71.15.Nc Total energy and cohesive energy calculations - 71.15.Mb Density functional theory, local density approximation, gradient and other corrections     

Theoretical examination of electron–phonon interaction and superconductivity in the hexagonal pnictide SrPtAs

We have calculated the structural and electronic properties of SrPtAs in a hexagonal KZnAs-type of crystal structure using a generalized gradient approximation of the density functional theory and the ab initio planewave pseudopotential method. These results are used to further calculate the phonon dispersions curves and the phonon density of states using a linear response approach based on the density functional theory. Using the electronic and phonon results, the electron–phonon coupling is computed to be of the intermediate strength of 0.78. In large part, this is contributed by the phonon modes dominated by the vibrations of Pt and As atoms. The superconducting critical temperature is estimated to be 1.9 K, in good accord with its experimental value of 2.4 K.     

Tc map and superconductivity of simple metals at high pressure

We calculate T_c map in region of weak electron–phonon coupling based on simple phonon spectrum. By using linear-response method and density functional theory, we calculate phonon spectra and Eliashberg functions of simple metals under pressure. Based on the evolutions of superconducting parameters of simple metals on the T_c map with increasing pressure, we find that there are two different responses to pressure for simple metals: (1) enhancing electron–phonon interaction λ such as for La and Li, (2) increasing phonon frequency such as for Pb, Pt. The λ threshold effect is found, which origins from the competition between electron–phonon interaction and electron–electron Coulomb interaction and is the reason why T_c of most superconductors of simple metals are higher than 0.1 K.     

On the electron band structure of liquid metals

The electronic structure and the density of states of simple liquid metals is discussed on the basis of a nonlocal and energy-dependent pseudopotential of the Phillips-Kleinman type. As an example we treat lithium. To calculate this pseudopotential we need to know the states and the eigenvalues of the liquid metal ion cores. For these quantities we use: first, the core data of the free atom; second, of the free ion; third, the data we have determined from the measured phonon dispersion curves. The deviations between the band structures, the density of states as calculated with these pseudopotentials and those of free electrons are considerable.     

A pseudopotential calculation of the phonon spectrum of aluminium

The phonon dispersion curves for Al are calculated from a theory based on Coulomb interactions among the ions and a local pseudopotential interaction between ions and conduction electrons. Conduction electron correlations are taken into account according to a theory of Singwiet al. ^1,2. A dielectric constant is constructed which satisfies the compressibility sum rule. This is especially important for longitudinal phonons. The agreement of the computed frequencies with the experimental dispersion curves of Stedman and Nilsson³ is good. Sites, sizes and widths of Kohn anomalies in the dispersion curves are also calculated. As expected the theoretical curves show larger anomalies than the experimental data. Finally a comparison is made with the recent calculations of Wallace⁴.     

Magnetic 4d systems studied by implanted ions

By application of the perturbed -ray distribution method following heavy-ion reactions and recoil implantation techniques, we have found an experimental way of producing and investigating magnetic 4d states in metals. Strong 4d magnetism has been found for 4d ions in alkali metal hosts and in Pd hosts. In alkali metals, 4d ions reflect the phenomena of well-defined ionic ground states, orbital magnetism, mixed valence, and crystal field splittings smaller than theLS coupling. Magnetic 4d states in alkali metals cannot be described by one-electron approaches based on Anderson-type models, but requires an analysis in terms of many electron ionic configurations exhibiting basic features common to the physics of stable and unstable f stales in metals. In contrast, the local moment formation of 4d and 3d ions in Pd is governed by inter-atomic interactions of the magnetic d states with host d-band electrons, giving rise to spin magnetic behavior of the 4d impurity and to strong spin polarizations of the 4d electrons of the Pd host. Thus, the magnetism and electronic structure of 4d ions in metals exhibit qualitative differences in alkali metal hosts compared to Pd. The existence of magnetic 4d systems strongly depends on the 4d ion species and the host matrix, and on spin fluctuation rates or the corresponding Kondo temperatures. The results can be directly compared to theoretical work and also to the magnetic behavior of 3d ions in sp metal hosts and in hosts with d-band electrons.     

Untersuchung der Zustandsdichte und der charakteristischen Energieverluste von Ir,Rh, Pt und Pd mit Isochromatenmessungen

X-ray isochromats of the above metals measured with high resolution are presented. Assuming a rigid band model for the four metals they give — with some usual approximations — the qualitative form of the density of states. It turns out that the densities of statesZ(ε) at the Fermi limits decrease in the succession Ir, Rh, Pt, Pd. This is in contradiction to low temperature measurements of the electronic specific heatc _e which for the same succession give an appreciable raising inZ(ε). It is assumed that this discrepancy is caused by a special coupling of the electrons to the transverse phonons. In consequence of this,Z(ε) of the renormalized electron system measured byc _e can be very different from that of the bare electrons measured by the isochromats. Assuming that the transition temperature of elemental superconductors is related according to BCS-theory to the latter density of states the absence of superconductivity of Rh, Pt and Pd can be understood. In addition the isochromats give values for the characteristic energy losses of the four metals.     

New results on diffusion in fcc metals

The Kondo model for the diffusion of light particles in metals has provided a satisfactory explanation for the low temperature diffusion rates for muons in the fcc metals Cu and Al. Explicit experiments which show the strong dependence of muon behaviour on the presence of conduction electrons have now been performed belowT=1 K in Al. Challenging new diffusion studies on fcc metals such as Pt are also presented.     

Lattice dynamics of a Pd0.90Rh0.10 crystal

Using inelastic neutron scattering, the phonon dispersion relations along the [100], [110] and [111] directions of a single crystal of Pd_0.90Rh_0.10 have been measured at 296K. From these results and phonon data for Pd, the phonon frequency shifts,(q), and the self-energy function, _j (q, _j (q)), have been determined for all branches. The frequency changes exhibit large wave vector and polarization dependence and behave non linearly with the increase concentration of Rh. The seventh neighbour tensor Born-von Kármán model has been fitted to the experimental phonon dispersion curves, and the force constants and elastic constants calculated. Correlations between the phonon anomalies, displayed in the slope ofT ₁ [110] branch, and the structure of the generalized susceptibility function, ₀(q), for Pd were discussed. From which follows the influence of the electron-electron interaction on theT ₁ [110] branch in Pd and Pd-Rh alloys.     

Pseudopotential in metals and alloys

In this communication, the pseudopotential investigation of, the various properties of non-transition metals and alloys, is discussed. Various one parametric model pseudopotentials, derived from well known spherical functions s_l(x), are employed in the calculations. Many recurrence relations of the s_l(x) function have been described. The effects of exchange and correlation on conduction electrons are also considered separately by using different dielectric screenings in various properties. The ion-ion interaction, force constants, phonon spectrum, temperature coefficient of Knight shift and electronic transport coefficients of certain metals and alloys are evaluated. The results are compared with available experimental values. Generally good agreement is achieved. The screening charge density of certain metals in low and high density region are also determined.     

The use of OPW's in the Lindgren approximation of conduction-core exchange and the lattice dynamical properties of rubidium

This paper reports a first principles nonlocal pseudopotential calculation for the lattice dynamical properties of rubidium metal. In these calculations, an orthogonalized plane wave (OPW) has been used for the first time to represent the conduction state in the Lindgren approximation of conduction-core exchange. A comparison is made of phonon spectra and elastic shear constants using both plane wave (PW) and OPW conduction states. It is found that the OPW results are in excellent agreement with experiment and consistently better than the PW results for both phonon spectra and elastic constant. Similar results are found for other simple alkali metals.     

FCC金属结构稳定性和声子谱的MAEAM研究

应用改进分析型嵌入原子方法(MAEAM)计算fcc金属的结构稳定性和声子谱.考虑更远邻原子之间的相互作用,提出新的两体势函数,并采用新的截尾处理函数和加强光滑连接条件.通过拟合单空位迁移能、结合能、三个独立弹性常数及晶体平衡条件,确定了模型参数.在体积不变条件下,计算金属不同结构的能量,说明Ag、Al、Au、Cu、Ir、Ni、Pd、Pt和Rh的fcc结构比较稳定.它们的能量-体积曲线与Rose方程结果基本-致,进-步说明了体积变化时的结构稳定性.同时发现[100]、[110]和[111]三个方向声子谱的计算结果符合实验值和其它计算结果.