Icosahedral order, disclinations and the order parameter in simple metallic glasses

Abstract

This paper deals with the problem of the order parameter for simple metallic glasses. It is shown that the structure of metallic glasses is characterized by the tensor order parameter, βij. This field is associated with an internal geometry, which is characterized by a zero curvature tensor. It is shown that the field should be regarded as the distortion field, well known in the general theory of elasticity. An essential feature of the field is the lack of integrability conditions and the fact that the order parameter cannot be reduced to a vector. The direct consequence of this feature is the existence of dislocations and disclinations. The problem of the elastic energy density of the defects is solved by means of the hypothesis that the ideal unstressed state of the glass is realized in curved space.