Elastic interactions between hydrogen atoms in metals. I. Lattice forces and displacements
This is the first of a series of papers in which a second-order perturbation theory is derived for the Hamiltonian of a metal hydride. The theory, which is called the fully harmonic lattice approximation, or FHLA, goes beyond the customary harmonic treatment of Horner and Wagner to include second-order terms for the hydrogen-hydrogen and metal-hydrogen potentials. These terms account for the hydrogen-concentration dependences of a metal hydride's volume and elastic constants; their inclusion should result in a better representation of the free-energy and phase-change behavior at high hydrogen concentration. In this paper, the forces between hydrogen atoms and metal atoms are evaluated using the FHLA. Two types of forces result: direct forces, between an isolated hydrogen atom and a metal atom, and indirect forces, which are effective forces between a hydrogen atom and a metal atom caused by the presence of a neighboring hydrogen atom. Both the direct and indirect forces each have two components: a permanent part, which is equivalent to the force exerted by a hydrogen atom on a metal atom in the pure (hydrogen-free) metal lattice, and an induced part, which corrects the permanent part for the effects of the hydrogen atom on the metal-metal couplings. These four forces are evaluated for the hydrogen-niobium system. The indirect forces have one-tenth the magnitude and are of opposite sign to the direct forces. The induced component of the force is approximately one-third the size of the permanent component, and opposite to it in sign. The displacements of the metal atoms surrounding an isolated hydrogen atom or a pair of hydrogen atoms are also evaluated. These are compared with the results of previous harmonic-approximation calculations and of experiments on the hydrogen-niobium system.
- Research Organization:
- Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544
- OSTI ID:
- 5601895
- Journal Information:
- Phys. Rev. B: Condens. Matter; (United States), Vol. 33:12
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
NIOBIUM HYDRIDES
INTERATOMIC FORCES
ATOM TRANSPORT
BOUND STATE
ELASTICITY
EMBRITTLEMENT
HAMILTONIANS
MIGRATION LENGTH
PAIRING INTERACTIONS
PERTURBATION THEORY
PHASE STUDIES
DIMENSIONS
HYDRIDES
HYDROGEN COMPOUNDS
INTERACTIONS
LENGTH
MATHEMATICAL OPERATORS
MECHANICAL PROPERTIES
NEUTRAL-PARTICLE TRANSPORT
NIOBIUM COMPOUNDS
QUANTUM OPERATORS
RADIATION TRANSPORT
REFRACTORY METAL COMPOUNDS
TENSILE PROPERTIES
TRANSITION ELEMENT COMPOUNDS
360202* - Ceramics
Cermets
& Refractories- Structure & Phase Studies