Application of Path-integral for Studying EXAFS Cumulants

In this work, the path-integral effective potential (PIEP) method has been applied to re-study the temperature dependence of extended X-ray absorption fine structure (EXAFS) cumulants of materials. Using the trial density matrix and effective potential expression, we derived the analytical expressions of the first three EXAFS cumulants in the first shell of materials. The cumulant relation is also calculated to determine the temperature range in which the PIEP method could be applied. Our results are compared with available experimental data as well as with those calculated by the first-order perturbation approach in anharmonic Einstein model and the reasonable agreements are achieved

Investigation of the EXAFS Cumulants of Silicon and Germanium Semiconductors by Statistical Moment Method: Pressure Dependence

Pressure dependence of Extended X-ray Absorption Fine Structure (EXAFS) cumulants of silicon and germanium have been investigated using the statistical moment method (SMM). Analytical expressions of the first and second cumulants of silicon and germanium have been derived. The equations of states for silicon and germanium semiconductors have been also obtained using which the pressure dependence of lattice constants and volume of these semiconductors have been estimated. Numerical results using the developed theories for these semiconductors are found to be in good and reasonable agreement with those of the other theories and with experiment

Pressure Dependence of EXAFS Debye-Waller Factors in Crystals

In present article the pressure dependence of Debye-Waller factors in crystals has been investigated by using statistical moment method and anharmonic correlated Einstein model. These two methods provide similar results which indicate that the Debye-Waller factors of crystals decreases slightly under high pressure. Our numerical results for several crystals are compared to other theoretical and experimental values and showed a good agreement

High pressure melting curves of silver, gold and copper

In this work, based on the Lindemann's formula of melting and the pressure-dependent Grüneisen parameter, we have investigated the pressure effect on melting temperature of silver, gold and copper metals. The analytical expression of melting temperature as a function of volume compression has been derived. Our results are compared with available experimental data as well as with previous theoretical studies and the good and reasonable agreements are found. We also proposed the potential of this approach on predicting melting of copper at very high pressure

Mobility of carrier in the single-side and double-side doped square quantum wells

We present a theoretical study of the effect from doping of quantum wells (QWs) on enhancement of the mobility in one-side (1S) and two-side (2S) doped square infinite quantum well. Within the variational approach, we introduce the enhancement factor defined by the ratio of the overall mobility in the 2S doped square quantum wells to that in the 1S doped counterpart with the same sheet carrier density and interface profiles. The enhancement is fixed by the sample parameters such as well width and sheet carrier density. We propose two-side doping as an efficient way to upgrade the quality of QWs. Our theory is able to well reproduce the recent experimental data about low-temperature transport of electrons and holes in one-side and two-side doped square QWs

Pressure effects on the thermodynamic and mechanical properties of zinc-blende ZnTe compound

In this paper, the moment method in statistical mechanics has been employed to study the pressure effects on thermodynamic and mechanical properties of zinc-blende zinc telluride using many-body potential. We have derived the analytical expressions of the pressure-dependent lattice parameter, volume compression as well as mean-square displacement of zinc-blende type compound. Numerical calculations performed for ZnTe compound up to 12 GPa are found to be in good and reasonable agreement with available experimental data as well as with previous theoretical studies. These results have been used to evaluate the bulk modulus and its first pressure derivative of ZnTe. The present moment method has taken into account the quantum zero-point vibrations at low temperature and the higher-order anharmonic terms in the atomic displacements. This research shows the advantage of moment method on extensively studying thermo-mechanical properties of materials under high pressures

Mechanical properties of metallic thin films: theoretical approach

The statistical moment method in statistical mechanics was developed to investigate the mechanical properties of free-standing metallic thin films at ambient conditions including the anharmonicity effects of thermal lattice vibrations. Analytical expressions of isothermal areal modulus BT, Young’s modulus E and shear modulus G were derived in terms of the power moments of the atomic displacements. Numerical calculations have been performed for metallic Ni, Au and Al thin films, and compared with those of bulk metals. This method is physically transparent and it successfully described the temperature effects on mechanical properties of metallic thin films

Investigation of elastic moduli and constants of zinc-blende Al

The elastic moduli and elastic constants of the ternary semiconductor alloy AlyGa1-yAs at finite temperature have been investigated using the statistical moment method. The Young, shear, bulk moduli and elastic constants C11, C12, C44 of the zinc-blende AlyGa1−yAs crystal are calculated as functions of Al composition and temperature. Numerical calculations have been performed and compared with those of the experimental and other theoretical results showing the reasonable agreements. Our study shows that elastic moduli and C11, C12 constants of zinc-blende AlyGa1−yAs alloy are decreasing functions of the temperature and Al composition; C44 constant is a decreasing function of the Al composition

Pressure effects on thermo-mechanical properties of intermetallic B2-type FeAl alloy

The pressure effects on thermo-mechanical properties of B2-type FeAl compound have been investigated based on the moment method in statistical mechanics. We derive analytical expressions of equation-of-state, isothermal bulk modulus and specific heats at constant volume and constant pressure of B2-type iron aluminide intermetallic compound. Numerical calculations for lattice parameter, isothermal bulk modulus, Young’s modulus, shear modulus and specific heat at constant pressure of B2-type Fe-40 at.% Al have been performed up to pressure of 10 GPa. Our research shows that the elastic moduli are linear proportional to pressure and the specific heat at constant pressure diminishes strongly at temperature below 300 K. The present statistical moment method results are compared with available experimental data as well as ab initio calculations when possible to verify the developed theory. This research proposes the potential of the moment method in the investigation of thermo-mechanical properties of materials under pressure

Investigation of melting point, Debye frequency and temperature of iron at high pressure

The Debye model has been developed to investigate the pressure effects on melting point, Debye frequency and Debye temperature of iron metal. The analytical expressions of these thermodynamic quantities have been derived as functions of crystal volume compressibility. The pressure dependence of them is studied based on the well-established equation-of-state which includes the contributions of the anharmonic and electronic thermal pressures. We performed numerical calculations for iron up to pressure 350 GPa and compared with experimental data when possible. Our results show that the Debye frequency and Debye temperature increase rapidly with compression, and beyond 150 GPa they behave like linear functions of pressure. From the pressure-dependent melting point of iron, we deduce the temperatures of the Earth’s inner-outer core boundary (ICB) and core-mantle boundary (CMB). The temperatures of the Earth’s ICB and CMB are predicted lower than 5540(±170) K and about 4060 K, respectively