**Abstract**

The 180° twin boundary (TB) (stacking fault) is investigated in the hexagonal close-packed (hcp) light materials. It is shown that atomic symmetry inside the twin boundary is lower than in hcp phase due to interatomic interaction between neighbors. In the case of quantum or thermal behavior, for the isosurfaces, an initial spherical form (in hcp phase) transforms into ellipsoid (in the boundary). We introduce the isosurface deformation parameter. The self-consistent description is developed to estimate the parameters of the thermodynamic potential, and the models of hard spheres and ellipsoids are used. It is shown that the quantum or thermal behavior of the boundary atoms causes the following effects: (i) the increase of degree of overlap of the atomic wave functions or trajectories within the twin boundaries, (ii) the increase of diffusion inside the twin boundaries, and (iii) the decrease of energy and broadening of the quantum boundary in comparison with the classical case.

**Keywords:** solid helium, twin boundary, stacking fault, hard ellipsoids, quantum diffusion **PACS numbers:** 61.72.Mm, 61.72.Nn, 64.75.Gh, 66.30.Ma

## **1. Introduction**

Helium crystals have unique quantum properties and are useful for the investigation of dynamic and kinetic behavior of atomic crystals [1]. In experiments, the structure phase transition between body-centered cubic (bcc) and hcp phase was found for both metals and solid <sup>4</sup> He [2, 3]. The coherent phase boundary (PB) and twin boundary (TB) or stacking fault (SF) was investigated theoretically in the frame of one order parameter (OP) model [4, 5]. The two-OP theory of PB [6, 7] was developed on the basis of the Burgers mechanism. In work [5] we proposed the three-OP theory that combines Sanati [6, 7] and Kaschenko [8] treatments; so we take into account the changes of volume and pressure under the phase transition. 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 <sup>4</sup> He were investigated in [9].

In the experiment [10], a glass formation under deformation of solid helium was investigated. Usually the deformation of crystals generates the different defects [11], including stacking faults. In the nuclear magnetic resonance (NMR) experiments [12], the great role of the interface in increasing the quantum diffusion was found. In work [13] for single hcp crystal <sup>4</sup> He, the stacking fault energy was measured.

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