A New Family of Nonstoichiometric Layered Rare-Earth Tin Antimonides, RESn(x)()Sb(2) (RE = La, Ce, Pr, Nd, Sm): Crystal Structure of LaSn(0.75)Sb(2)

A new class of nonstoichiometric layered ternary rare-earth tin antimonides, RESn(x)()Sb(2) (RE = La, Ce, Pr, Nd, Sm), has been synthesized through reaction of the elements at 950 degrees C. In the lanthanum series LaSn(x)()Sb(2), tin can be incorporated from a maximum content of x approximately 0.7 or 0.8 to as low as x approximately 0.10. The structure of lanthanum tin diantimonide with the maximum tin content, LaSn(0.75)Sb(2), has been determined by single-crystal X-ray diffraction methods. It crystallizes in the orthorhombic space group -Cmcm with a = 4.2425(5) ?, b = 23.121(2) ?, c = 4.5053(6) ?, and Z = 4. The isostructural rare-earth analogues were characterized by powder X-ray diffraction. The structure of LaSn(0.75)Sb(2) comprises layers of composition "LaSb(2)" in which La atoms are coordinated by Sb atoms in a square-antiprismatic geometry. Between these layers reside chains of Sn atoms distributed over three crystallographically independent sites, each partially occupied at about 20%. The structure of LaSn(0.75)Sb(2) can be regarded as resulting from the excision of RE-Sb and Sb-Sb bonds in the related structures of binary rare-earth diantimonides, RESb(2), and then intercalation of Sn atoms between layers.     

Reflection of plane waves from the boundary of a pre-stressed compressible elastic half-space

The effect of pre-stress on the propagation and reflection ofplane waves in an incompressible isotropic elastic half-spacehas been examined recently by the authors (Ogden & Sotiropoulos,1997). In the present paper the corresponding analysis for compressiblematerials is detailed. In the two-dimensional context consideredfor incompressible materials the (homogeneous) plane waves werenecessarily shear waves. By contrast, in the compressible contextpure shear waves can propagate only in specific directions inthe considered principal plane and, in a general direction,a quasi-shear wave may be accompanied by a quasi-longitudinalwave, as is the case in the anisotropic linear theory. The dependenceof the (in-plane) slowness section on the pre-stress (and finitedeformation) and on the choice of constitutive law is elucidated.This information is used to determine the reflection coefficientsfor reflection of either a (quasi-) shear wave or a (quasi-)longitudinal wave from the boundary of the half-space and tocharacterize the different cases which arise depending on thegeometry of the slowness section. The theoretical results are illustrated by numerical calculationsfor the range of possible types of behaviour with referenceforms of strain-energy function and different states of finitedeformation and to the question of stability of the half-space.