Effect Of Thermal Vibrations Research Articles

Atomistic origin, temperature dependence, and responsibilities of surface energetics: An extended broken-bond rule

There has long been confusion regarding the origin and temperature dependence of surface energetics and its responsibility for the processes and phenomena at a surface. From the perspective of bonds broken and its consequences on the remaining bonds of the undercoordinated surface atoms, we suggested herewith two essential concepts supplementing to the existing definition of surface energy for clarification purposes. One is the energy-density-gain per unit volume in surface skin and the other is the remaining cohesive-energy per discrete atom upon bond order loss once the surface is formed. The former governs the strength and elasticity while the latter dominates the thermal and structural stability of the surface. The shortened and strengthened bonds between the undercoordinated atoms dictate surface energetics and the effects of thermal expansion and vibration dominate their temperature dependence. Reproduction of the measured size and temperature dependency has led to information about the bond energy, which may go beyond traditional approaches and evidence the validity of the approaches.

Effect of thermal vibrations and their correlations on grazing scattering of atoms from crystal surfaces

The influence of thermal vibrations of target atoms and their correlations on grazing scattering of keV atoms from crystal surfaces is investigated. Classical 2D and 3D trajectory calculations are performed and thermal vibrations are included using the Debye model as well as its high-temperature limit and uncorrelated thermal vibrations. Ion beam triangulation, rainbow structures for scattering along low-indexed directions of the surface plane, and polar angular distributions for impact along high-indexed directions are studied. We demonstrate that ion beam triangulation can be analyzed using uncorrelated thermal vibrations, while a realistic description of angular distributions requires more detailed modeling. For the peak positions of rainbow structures thermal vibrations play a minor role and they are well described by 2D simulations based on continuum potentials.

First-principles calculation of phase equilibria and phase separation of the Fe-Ni alloy system

Theoretical investigation of the phase equilibria of the Fe-Ni alloy has been performed by combining the FLAPW total energy calculations and the Cluster Variation Method through the Cluster Expansion Method. The calculations have proved the stabilization of the L1 2 phase at 1:3 stoichiometry, which is in agreement with the experimental result, and predicted the existence of L1 0 as a stable phase below 550 K; this L1 0 phase has been missing in the conventional phase diagram. The calculations are extended to the Fe-rich region that is characterized by a wide range phase separation and has drawn considerable attention because of the intriguing Invar property associated with a Fe concentration of 65%. To reveal the origin of the phase separation, a P-V curve in an entire concentration range is derived by the second derivative of free energy functional of the disordered phase with respect to the volume. The calculation confirmed that the phase separation is caused by the breakdown of the mechanical-stability criterion. The newly calculated phase separation line combined with the L1 0 and L1 2 order-disordered phase boundaries provides phase equilibria in the wider concentration range of the system. Furthermore, a coefficient of thermal expansion (CTE) is attempted by incorporating the thermal vibration effect through harmonic approximation of the Debye-Gruneisen model. The Invar behavior has been reproduced, and the origin of this anomalous volume change has been discussed.

Finite difference method calculations of X-ray absorption fine structure for copper

Abstract The finite difference method is extended to calculate X-ray absorption fine structure (XAFS) for solid state copper. These extensions include the incorporation of a Monte Carlo frozen phonon technique to simulate the effect of thermal vibrations under a correlated Debye–Waller model, and the inclusion of broadening effects from inelastic processes. Spectra are obtained over an energy range in excess of 300 eV above the K absorption edge—more than twice the greatest energy range previously reported for a solid state calculation using this method. We find this method is highly sensitive to values of the photoelectron inelastic mean free path, allowing us to probe the accuracy of current models of this parameter, particularly at low energies. We therefore find that experimental data for the photoelectron inelastic mean free path can be obtained by this method. Our results compare favourably with high precision measurements of the X-ray mass attenuation coefficient for copper, reaching agreement to within 3%, and improving previous results using the finite difference method by an order of magnitude.

Equation of state and elastic properties of beryllium from first principles calculations

The electronic and structural properties of beryllium were investigated under high pressure using first principle pseudopotential calculations within the generalized gradient approximation (GGA). Our results including pressures, elastic constants, Debye temperatures for two crystal structures (a hexagonal close packed and β body-centred cubic) are compared with the experimental and other theoretical data over a wide density range. Calculated phonon spectra allow us to explain the anomalous behavior of the hcp-bcc transition under pressure. An equation of state (EOS) for the hcp phase at finite temperatures is derived taking into account the anharmonicity effects of thermal lattice vibrations. The resulting 300 K isotherm and Hugoniot curve, as well as the evolution of the shear modulus under pressure and temperature, are in good agreement with available experimental and theoretical data.

Damage Mechanics Modeling of Concurrent Thermal and Vibration Loading on Electronics Packaging

The problem of concurrent thermal and vibration loading has not been thoroughly studied even though it is common in electronic packaging applications. Here we attempt to address such a problem using a damage mechanics based constitutive model. Damage mechanics constitutive model for eutectic Pb/Sn solder alloys is used to simulate the damage effects of concurrent cyclic thermal loads and vibrations on Ball Grid Array (BGA) packages. The model is implemented into the commercial finite element code ABAQUS through its user defined material subroutine capability. For the integration algorithm we have used a return mapping scheme, which dramatically improves the convergency rate as compared to previous implementations of the same model. Results are examined in terms of accumulation of plastic strain within the solder connections. It is shown that the simplistic Miner’s rule can not accurately account for the combined effect of both loadings acting concurrently.

First principles study of tantalum thermodynamics by the statistical moment method

The thermodynamic properties of bcc tantalum are studied using the analytic statistical moment method and the first principles PAW–LDA (projector augmented wave method with local density approximation) scheme. The equation of states at finite temperatures are derived taking into account the anharmonicity effects of thermal lattice vibrations. The calculated thermodynamic quantities of bcc Ta crystals are in good agreement with the experimental results.

Investigation of thermodynamic properties of cerium dioxide by statistical moment method

The thermodynamic properties of the cerium dioxide (CeO2) are studied using the statistical moment method, including the anharmonicity effects of thermal lattice vibrations. The free energy, linear thermal expansion coefficient, bulk modulus, specific heats at the constant volume and those at the constant pressure, CV and CP, are derived in closed analytic forms in terms of the power moments of the atomic displacements. The temperature dependence of the thermodynamic quantities of cerium dioxide is calculated using three different interatomic potentials. The influence of dipole polarization effects on the thermodynamic properties and thermodynamic stability of cerium dioxide have been studied in detail.

A Band Transport Model for Highly Ordered Discotic Mesophases

A band-transport model is described for a highly ordered discotic liquid crystal system. The effects of thermal vibrations and defects in the ordering of the system are considered. Defects are modeled as quantum tunnel barriers. Simulated data is presented and used to draw conclusions about the nature of the parameters that affect carrier mobility.

Theoretical Investigation of Fe-Based Phase Equilibria from the First-Principles

Theoretical investigation of the phase equilibira of three kinds of Fe-based alloys, Fe-Ni, Fe-Pd and Fe-Pt systems is attempted by combining FLAPW total energy calculations and Cluster Variation Method. It is revealed that the magnetism plays a crucial role in the phase stability and spin polarized calculation is indispensable. The experimental L10-disorder transition temperatures are reproduced with fairly high accuracy. Thermal vibration effects incorporated based on the Debye-Gruneisen model further improve the calculated transition temperatures. Furthermore, the influence of the various effective cluster interactions on phase stability is calculated systematically.

Model for the voltage and temperature dependence of the soft breakdown current in ultrathin gate oxides

The voltage and temperature dependence of the soft breakdown conduction mechanism in metal-oxide-semiconductor capacitors and transistors with ultrathin dielectric layers is investigated. A physical derivation of the quantum point contact model and its parameters is presented, which incorporates the smearing of the Fermi function at the electrodes as well as the effect of thermal vibrations of the constriction’s bottleneck. The model also takes into account the boundary conditions at the two ends of the breakdown path by considering the semiconductor band bending occurring in the nondamaged surrounding device area. Good agreement between model and experimental curves is found. Because of its analytical nature, the proposed model can be implemented in circuit simulators.

Electrical conductivity in the antiferromagnetic insulating phase of V2O3

The electrical conductivity of ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ in the antiferromagnetic insulating (AFI) phase has been measured on multidomain and single-domain crystals over a conductivity range of more than five orders of magnitude, and for the temperature range 160--40 K. The intrinsic mechanism for conductivity in the AFI phase for a single-domain sample of well-defined orientation was determined, using a special experimental setup that minimized mechanical stresses. The conductivity in the AFI phase of the unstressed, single-domain crystal was comparable to the conductivity of the multidomain crystal, but the two samples differ in their temperature dependence. The results were interpreted by analyzing the effect of thermal lattice vibrations on the resonance integral. The polaron localization radius was found to be of the order of the lattice vibration amplitudes.

Interpretation of high pressure experimental data in mgb2: a challenge to current theories

We review various anomalies seen in Raman spectroscopy, superconducting transition temperature T c and electrical resistance at room temperature and high pressure in the new high temperature superconductor MgB2. In order to explore the possibility of the anomalies being caused by an electronic topological transition (ETT), we have carried out detailed electronic structure studies of the band structure under pressure. Our calculations are done in the presence of a frozen-in phonon displacement that mimics the effects of thermal vibrations of the B-atoms at room temperature. Our results clearly establish the occurrence of a phonon-assisted ETT near 18 GPa. The dimensionless electron–phonon coupling λ is also found to be anomalous in its pressure variation at the same pressure. We also indicate why a detailed explanation of the phonon Raman anomaly needs the inclusion of effects arising from a non-linear electron–phonon coupling.

Hcp-bcc structural phase transformation of titanium: Analytic model calculations

We show that the hcp $(\ensuremath{\alpha})\ensuremath{\rightarrow}\mathrm{bcc}\phantom{\rule{0.3em}{0ex}}(\ensuremath{\beta})$ structural phase transformation of titanium occurs via anharmonicity effect of thermal lattice vibrations. The full-potential linear muffin-tin orbital method in the local density approximation with the generalized gradient correction is used to derive the embedded atom potential for Ti, which allows us the analytic and realistic calculations of the thermodynamic quantities. We also discuss the similar phase transformation but slightly different mechanism occurring in zirconium in terms of the anharmonicity of thermal lattice vibrations.

High-pressure anomaly in the normal state ofMgB2

The E 2g mode phonon frequency anomaly, observed in high-pressure Raman measurements for the high-temperature superconductor MgB 2 and conjectured to arise due to a phonon-assisted electronic topological transition (ETT), has been corroborated by us with the details of electronic structure calculations of this compound. The present studies have been carried out with a B-atom displacement of the frozen-in E 2g -mode phonon that mimics the effects of thermal vibrations. We found a splitting of the doubly degenerate σ band along the Γ-A direction. The splitting of the band reduces with pressure, causing an ETT at 18 GPa. This ETT is expected to cause anomaly in the E 2g phonon mode by influencing the ionic system. Our calculated electron-phonon coupling constant λ , for the distorted lattice with a frozen-in displacement, also depicts an anomalous variation around 18 GPa.

Ultrarelativistic nuclei in a crystal channel: Coulomb scattering, coherence, and absorption

We incorporate the effect of lattice thermal vibrations into the Glauber-theory description of particle and nucleus-crystal Coulomb interactions at high energy. We show that taking the lattice thermal vibrations into account produces a strong absorption effect: the phase shift function of the multiple-diffraction scattering on a chain of N identical atoms acquires a large imaginary part, and the radius of the absorption region in the impact parameter plane grows logarithmically with N. Consequences of this observation for the elastic and quasi-elastic Coulomb scattering are discussed. The practically interesting example of the coherent Coulomb excitation of ultrarelativistic particles and nuclei passing through a crystal is considered in detail.

Effect of anisotropic temperature factors on convergent-beam electron diffraction intensities and measurement of the local change in the oxygen concentration of YBa2Cu3O y

The local oxygen concentration of the high-T c superconductor YBa2Cu3O y was measured from large-angle convergent-beam electron diffraction patterns using a transmission electron microscope equipped with a field emission gun with an in-column-type energy filter. The anisotropic effect of thermal vibrations of atoms was considered in the analysis of the oxygen concentration, based on the many-beam dynamic theory. The observed fluctuation in the oxygen concentration can explain the peak effect in the J c–H curve, the critical current density J c plotted as a function of applied magnetic field H.

First-principles study on thermal vibration effects ofMgH2

We report the results of the first-principles calculation on the atomic displacement parameters, the crystal structure factors, and the charge density distributions of $\mathrm{Mg}{\mathrm{H}}_{2}$ at finite temperature. Our calculations have been performed with the ultrasoft pseudopotential method and the linear response approach based on the density-functional perturbation theory (DFPT). The thermal vibration effects have been taken into consideration using phonon dispersions predicted by the DFPT and the harmonic approximation. To obtain the crystal structure factors, the pseudo charge density has been converted to the all electron one by utilizing the projector augmented wave formalism. The computed atomic displacement parameters of the hydrogen atom in $\mathrm{Mg}{\mathrm{H}}_{2}$ are in good agreement with the inelastic neutron data. The crystal structure factors at $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ predicted from the atomic form factors and the Debye-Waller factors have been compared with those obtained from the synchrotron x-ray diffraction measurement. They are in good agreement for lower diffraction vector indices $hkl$, but there are slightly differences in higher $hkl$. We also discuss the temperature dependence of the charge density distribution. It is confirmed that thermal vibration is more effective to the H atom than the Mg atom. The ionic charge which is estimated from the number of electrons within the sphere around the H atom is well in agreement with the experimental result by the maximum entropy method.

First-Principles Calculation of <i>L</i>1<SUB>0</SUB>-Disorder Phase Boundary in Fe-Pd System

L10-disorder phase boundaries for Fe-Pd system are calculated by combining first-principles FLAPW electronic structure calculation with Cluster Variation Method. The total energy calculation at the ground state well predicted the global tendencies of the phase diagram. The calculated transition temperature of L10-disorder based on the free energy formulated by Cluster Variation Method is in good agreement with experimental one. The incorporation of thermal vibration effects further improves the agreement. The shift of the congruent composition from the stoichiometry is, however, not realized by the present calculation.

Calculation of thermodynamic quantities of metals and alloys by statistical moment method

The thermodynamic quantities of metals and alloys are studied using the moment method in the quantum statistical mechanics, going beyond the quasi-harmonic approximations. Including the power moments of the atomic displacements up to the fourth order, the free energy, specific heats Cv and Cp, mean square atomic displacements and thermal lattice expansion coefficients are derived explicitly in terms of the second and fourth order vibrational coupling constants. The thermodynamic quantities are calculated both for cubic (fcc and bcc) and closed packed hexagonal (hcp) metals. The Lennard–Jones type of potentials as well as the effective interatomic potentials derived from the tight-binding (TB) total energy calculation scheme are used. The calculated thermodynamic quantities are favorably compared with the experimental results. For the calculations of alloys, we investigate the effects of thermal lattice vibration on the long range order (LRO) parameter and order–disorder transitions of the ordered binary alloys.