Kanzaki Forces Research Articles

Lattice Statics of a Hydrogen Centre in Magnesium

In this work we consider the static perturbation of the hexagonal lattice of magnesium by one stored hydrogen atom. Equations are given to evaluate the equilibrium positions of the ions in the disturbed crystal. The effect of the hydrogen atom is described by a so-called Kanzaki force, an additional force in the ideal lattice. The force between two ions of the ideal lattice is assumed to obey the harmonic approximation. The force constants are calculated form an effective ion-ion potential. The static Green tensor, which is the inverse of the tensor of force constants, is calculated and with its aid the equations of lattice statics are transformed. The transformed equations are solved under the assumption of a Kanzaki force acting only upon the nearest and next-nearest neighbors of the hydrogen atom at a tetrahedral interstitial site. Finally we calculate the volume change Δ V and compare the result with the experimental value.

Magnetic and static lattice perturbation in dilute FeSb alloys from diffuse scattering of unpolarised and polarised neutrons

The neutron diffuse elastic cross sections of dilute Fe1-cSbc alloys have been deduced from polarised and unpolarised neutron measurements. The magnetic cross sections are proportional to the concentration whereas the nuclear and the nuclear-magnetic cross sections present an abnormal concentration dependence. The data are analysed in terms of magnetic perturbation and static lattice distortions, the short-range order contribution being negligible. The magnetic perturbation corresponds to a model of 'isolated' impurities where the magnetic moment on antimony is small and negative (-0.2+or-0.3 mu B) and the average magnetic moment on iron increases with Sb concentration with a slope d mu Fe/dc=1.2 mu B atom-1. The results concerning the nuclear terms can be qualitatively explained by the contribution of large static lattice distortions around Sb atoms described in a Kanzaki force model. The unusual concentration variation is mainly attributed to the presence of direct defect-defect interactions.

A lattice-dynamics model of an oscillating screw dislocation

The concept of the Boyer-Hardy source-force, or Kanzaki force, for a static screw dislocation is extended to describe a moving dislocation — in a simple cubic, nearest neighbour, harmonic lattice (snapping-bond model) — and together with the phonon Green's function is used to derive expressions for the atomic displacements and time-averaged energy disspation, viz. the rate of energy transfer from the moving dislocation to the lattice vibrations. For the case in which the dislocation oscillates harmonically in time, an expression for the energy dissipation is derived which, for megahertz frequencies and lower, is then reduced to a finite sum and finite integration, and is evaluated to lowest (zeroth) order in the frequency. The way in which the method may be extended to describe a lattice containing a low concentration c of point defects in a random array is then outlined, and it is shown how the change in energy dissipation, to lowest order, is proportional to c. The method developed here is such that it can, in principle, be further generalized in a completely unambiguous fashion, to allow for a non-linear or anharmonic atomic force-law in the dynamic source-force of the dislocation as well as a temperature dependent phonon damping in the Green's function.

Electronic and elastic structure of hydrogen in metals

The present work consists of an attempt to treat hydrogen in metals on a fundamental level. Starting with the full many-body hamiltonian we derive a one-electron Schrödinger equation. The ground state solution represents the electronic structure of interstitial hydrogen, and the corresponding eigen-value acts as a potential for the proton movement and determines the forces exerted on the neighbouring ions (Kanzaki forces). The self-consistent reaction of the host lattice results in the displacement field and the equilibrium energy. We give as an example the calculation of a single hydrogen atom in magnesium.

Calculation of relaxation volumes, dipole tensors and Kanzaki forces for point defects

The relaxation volumes and dipole tensors associated with point defects in metals are commonly deduced from the results of lattice statistics and computer simulation calculations. Often an approximation introduced by Hardy for weakly disturbing defects is applied in such deductions. However, for strongly disturbing defects such as interstitials, and even in some models vacancies, this approximation breaks down. A more rigorous treatment of the problem which avoids these difficulties is presented.

Defect pressure, formation volume, and temperature dependence of formation properties of point defects in ionic solids

The concept of local defect pressure is developed and is applied to determine the elastic relaxation about point defects in ionic solids. The method is superior to that of Kanzaki forces for treatment of Coulomb and many-atom interactions. The lattice sums for the Coulomb interaction and the relaxation volume of Schottky defects in NaCl and KCl in the static limit are given ; the use of neutral Evjen cubes rather than charged Mott-Littleton regions is found unavoidable for a complete and satisfactory atomistic treatment of charged defects in ionic solids. In both alkali and silver halides, the temperature dependence of the volume and the enthalpy of formation of equilibrium defects is understood in terms of the temperature dependence of the shear moduli. The high-temperature anomalies of defect formation volume, tracer diffusion, and ionic conductivity of the silver halides is traced to an intrinsic property of the Frenkel defect caused by an exceptional temperature dependence of elastic properties of the perfect crystal.

Lattice distortions due to deuterium in niobium

The quasielastic diffuse scattering of neutrons from deuterium interstitials in niobium has been measured and compared to data calculated from a Kanzaki force model with central forces acting on nearest and next-nearest neighbours. It is found that the cubic symmetry of the long range distortion field of H in Nb is already established in the immediate neighbourhood of the defect.

The Dislocation Loop in an Anisotropic Medium and Its Interaction with an Interstitial Atom

AbstractSeveral explicit expressions for the distortion field of an elliptical dislocation loop in a general anisotropic medium are presented. These are used to evaluate the interaction energy between an interstitial dislocation loop in copper and a nearby interstitial atom. The interstitial atom is represented by either a simple spherical inclusion or by realistic Kanzaki forces for its dumb‐bell configuration. The effects of both the microscopic anisotropy of the point defect and of the elastic anisotropy of the body on the form and magnitude of the interaction energy is thus exposed.