Structure of seven W surfaces

We present a theoretical study of the structure of seven W surfaces, using a modified fourth moment approximation to tight-binding theory. The seven W surfaces include three low-index surfaces ((100), (110) and (111)) and four high-index ((210), (211), (310) and (321)) surfaces. Perpendicular to the surface, most surfaces followed an oscillatory pattern of contraction and expansion, but the (111) and (321) surfaces relaxed with successive contractions of the first and second interplanar spacing, followed by an expansion of the third interplanar spacing. Also, the (100) surface and high-index (210), (211), (310) and (321) surfaces formed reconstructions with the top layers shifting parallel to the surface. The details of the atomic rearrangement can be understood with a simple bonding coordination argument.