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

Abstract

The 180 • twin boundary (stacking fault) is investigated in the hexagonal close-packed (hcp) lattice. It is shown that the interatomic interaction between neighbors within the boundary lowers symmetry as compared with that in hcp phase. An initial spherical form (hcp phase) is elongated along the shift direction of the atomic planes inside the boundary. We find the wave functions of the helium atom for (i) the spherical oscillator (within the hcp phase) and (ii) an anisotropic one (inside the boundary). To estimate the parameters of the thermodynamic potential we apply the model of spheres and ellipsoids for the isosurfaces of the probability. Method of the successive approximations is applied for the self-consistent description of the distorted wave functions of atoms. It is shown that the quantum behavior of the boundary atoms causes the following effects: (i) increasing of degree of overlap of the atomic wave functions within the twin boundaries, (ii) increasing of the quantum diffusion inside the twin boundaries, (iii) decreasing of energy and broadening of the boundary in comparison with the classical case.

Twin Boundary in hcp Crystals: Quantum and Thermal Behavior

“…Therefore, only term U pn x; ξ ðÞ changes inside TB which is shown in Figure 2. The analysis (see [14]) of the term U pn x; ξ ðÞ allows to write the anisotropic atomic potential Eq. (10) in the following simple form: where k b ξ ðÞis rigidity coefficient inside TB, U 0 ξ ðÞis a varied bottom level, and c ξ ðÞ x is the linear part.…”

“…where ε is the eccentricity of the ellipse. Earlier in the paper [14], we introduced the quantum deformation parameter q q . Here we generalize the parameter q q to the cases of either quantum or thermal motion of an atom and introduce the isosurface deformation parameter q.…”

“…In Table 2, evaluations of different parameters are shown according to Table 1 and relation Eqs. (14), (39), (42), and (43); the sources are shown in round brackets on top of columns.…”

“…In the quantum case, we can evaluate the minimal increase of the exchange integral due to the increase of overlapping wave functions caused by the elliptic deformations [14]:…”

“…The present work is devoted to the development of the self-consistent description of quantum behavior of 4 He atoms in twin boundary proposed in work [14]. We apply this treatment to quantum and thermal description of twin boundary in some metals.…”