Local oscillations in different models of the coherent bcc–hcp boundary in ⁴He and metals

Abstract

Small local vibrations of the order parameter (the relative displacement of atomic planes) on the coherent phase boundary (PB) in the bcc-hcp 4 He crystal are investigated theoretically. Dynamical differential equations for small values of the perturbations of the order parameter are obtained. On the coherent PB bcc-hcp for double-and triple-well models the shape and the spectrum are found for small local vibrations of the order parameter. Characteristic frequencies are found and estimated. It is shown that the bcc-hcp boundary in the 4 He crystal is a very soft system. This fact may explain the high degree of damping of 3 He excitations in nuclear magnetic resonance (NMR) experiments.

Quantum Behavior of the Twin Boundary and the Stacking Fault in hcp Helium Crystals

“…Here U is (y, z) is part of the isotropic potential (9) in the plane which is perpendicular to the shift direction, U an1 (x) is the anisotropic and nonlinear part of the potential in the direction Ox of the shift. In turn, the potential U an1 (x) can be divided into two parts.…”

“…In the limit ξ = ±ξ 0 this equation transforms into isotropic formula (9) inside hcp phase. Inside the boundary the potential is considerably softer in direction Ox because k b (ξ ) < k is .…”

“…See above discussion before Eq. (9). In isotropic harmonic approximation [20,21] the atomic potential can be presented as [22] …”

“…It was shown that the three OPs and one OP descriptions of PB and TB are uniquely related. Local oscillation spectra of one OP in different models of coherent bcc-hcp boundary in 4 He were investigated in [9] as a soft system with discrete levels.…”

Twin Boundary in hcp Crystals: Quantum and Thermal Behavior

“…The three-OP and one-OP descriptions of PB and TB are uniquely related. In different models of coherent bcc-hcp boundary, the local oscillations spectra of OP in 4 He were investigated in [9].…”