Quantum diffusion of atomic species in metals (original) (raw)
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Quantum diffusion in transition metals
Journal of the Less …, 1991
The functions governing the temperature dependence of small-polaron diffusion are calculated by using the phonon dispersion relations with high accuracy for octahedral interstitial sites in copper, palladium, nickel and platinum f.c.c. hosts, as well as for tetrahedral and octahedral sites in tantalum, niobium and vanadium hosts. The current experimental data on the diffusion coefficient for hydrogen in b.c.c. tantalum and niobium, and for positive muons in copper are very well reproduced for all temperature ranges. By comparison with exact calculation, very accurate results are also obtained by using an approximate universal function calculated within the Debye approximation, for which we give a closed analytical formula. This allows manual calculations of the diffusion coefficient for light interstitial impurities in transition metals within the small-polaron model.
Quantum theory of interstitial impurities: Energy spectrum, stationary states and deformation field
Solid State Communications, 1985
The Hamiltonian of an impurity field, tightly bound to the host crystal, is diagonalized by a new transformation. The impurities couple strongly with the phonon gas by terms which are linear and quadratic in the ionic displacements of the host. Closed-form expressions for the exact stationary states and energy spectrum follow. The analytical calculation of a number of effects like phonon-assisted tunneling and optical absorption, valid for massive impurities and high concentrations, follow as direct applications.
Atomic displacements in quantum crystals
Physical Review B, 2017
Displacements of atoms and molecules away from lattice sites in helium and parahydrogen solids at low temperature have been studied by means of Quantum Monte Carlo simulations. In the bcc phases of 3 He and 4 He, atomic displacements are largely quantum-mechanical in character, even at melting. The computed Lindemann ratio at melting is found to be in good agreement with experimental results for 4 He. Unlike the case of helium, in solid parahydrogen there exists near melting a significant thermal contribution to molecular vibrations, accounting for roughly half of the total effect. Although the Lindemann ratio at melting is in quantitative agreement with experiment, computed molecular mean square fluctuations feature a clear temperature dependence, in disagreement with recent experimental observations.
Physical Review, 1967
Lattice response functions, such as the thermal conductivity and dielectric susceptibility of an imperfect crystal with rocksalt structure, are evaluated in terms of the irreducible T matrix accounting for the phonon scattering. It is shown that the eBect of defects on thermal conductivity and dielectric susceptibility can be accounted for by expressions which have essentially the same structure. The T matrix for a defect which affects both the mass and the short-range interaction is analyzed according to the irreducible representations of the point group which pertains to the perturbation, and the resonance conditions for F&, F», and F» irreducible representations are considered in detail for any positive impurity in KBr crystals. Hardy s deformation-dipole (DD) model is employed for the description of the host-lattice dynamics. A comparison is made with simplified models, such as diatomic linear chains with nearest-neighbor interaction; it is shown that in polar crystals an eft'ective-force constant has to be used in order to give a reliable description of the short-range interaction between the impurity and the host lattice. An attempt is made to define such effective force constants in the framework of the DD model. The numerical calculations concern positive monovalent impurities in KBr crystals. Fj, F», and F» resonance frequencies are evaluated as a function of the change of mass and nearest-neighbor force constant. For KBr. 'Li+ and KBr'. Ag+ we also evaluate the band shape of the absorption spectrum at infrared frequencies; good agreement is found between the theoretical prediction and the experimental data on KBr. 'Li+. It is shown that some structures actually observed in the spectrum are due to peaks in the projected density of states of the host lattice, and have nothing to do with resonance scattering. Good agreement is found between the impurity-host-lattice interaction as estimated from a Priori calculations and as deduced by fitting the I'» resonance frequency to the experimental data. A simple explanation of the oG-center position of small ions is also suggested. Finally, concentration and stress eGects on the absorption coefBcient are briefly discussed.
Quantum diffusion at intermediate temperatures
Physics Letters A, 1983
A new closed-form expression for the diffusion coefficient, valid in a wide range of temperatures (including the intermediate ones), is obtained in the framework of the theory of quantum diffusion. The new formula fits well the available experimental data on ~+ diffusion in Cu in the whole temperature range. The origin of the discrepancies of previous theoretical expressions with high temperature measurements are explained in detail.
Solid State Physics [Working Title], 2019
In the first sections, we bring into the present context some of our past contributions on the influence of quantum correlations on the formation of tightly bound solids. We discuss the effects of the overlap between neighbor orbitals in diverse situations of interest-involving both bulk and surface states-and call the reader's attention to an exact tight-binding calculation which allows gauging the errors introduced by the underlying hypotheses of the usual tight-binding approximation. We round up this part by reviewing a quantum Monte Carlo method specific for strongly correlated fermion systems. In the last section, we explore some nonequilibrium routes to (not necessarily tightly bound) solid state: we discuss spatiotemporal pattern formation in arrays of FitzHugh-Nagumo (FHN) neurons, akin to resonant crystal structures.
Introduction to Atomic Physics
Iterative International Publishers, 2022
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Theory for Atomic Diffusion on Fixed and Deformable Crystal Lattices
Advances in Continuum Mechanics and Thermodynamics of Material Behavior, 2000
We develop a theoretical framework for the diffusion of a single unconstrained species of atoms on a crystal lattice that provides a generalization of the classical theories of atomic diffusion and diffusion-induced phase separation to account for constitutive nonlinearities, external forces, and the deformation of the lattice. In this framework, we regard atomic diffusion as a microscopic process described by two independent kinematic variables: (i) the atomic flux, which reckons the local motion of atoms relative to the motion of the underlying lattice, and (ii) the time-rate of the atomic density, which encompasses nonlocal interactions between migrating atoms and characterizes the kinematics of phase separation. We introduce generalized forces power-conjugate to each of these rates and require that these forces satisfy ancillary microbalances distinct from the conventional balance involving the forces that expend power over the rate at which the lattice deforms. A mechanical version of the second law, which takes the form of an energy imbalance accounting for all power expenditures (including those due to the atomic diffusion and phase separation), is used to derive restrictions on the constitutive equations. With these restrictions, the microbalance involving the forces conjugate to the atomic flux provides a generalization of the usual constitutive relation between the atomic flux and the gradient of the diffusion potential, a relation that in conjunction with the atomic balance yields a generalized Cahn-Hilliard equation.
Quantum diffusion: effect of defect-localized phonon dynamics
The European Physical Journal B, 2005
The quantum diffusion of lattice defects is considered on the basis of the non-perturbative description of the quadratic defect-lattice coupling. This allows to take explicitly into account the effect of defect-localized phonon dynamics. This effect is especially important in the case of diffusion of vacancies and self-interstitials while a defect displacement to a nearest site is accompanied by a breaking and reconstitution of bonds of nearest atoms. It is shown that the local softening of the lattice by a vacancy due to the breaking of bonds produces an enhancement of the contribution of the low frequency phonons while the local hardening of the lattice by an interstitial atom leads to the opposite effect. As a consequence, at low temperatures the diffusion coefficient of vacancies is much smaller than that of interstitial atoms; the temperature dependences of these coefficients are also different. The obtained results are compared with experimental data for diffusion of vacancies in solid helium.