The Structure of Bismuth at Low Temperatures

Abstract

A precision determination of the displacement parameter of zone-refined bismuth containing less than 0�3 parts per million of spectroscopically detectable impurity has been carried out as a function of temperature. Procedures were used that minimize uncertainties in integrated intensities due to extinction, absorption, temperature factor, dispersion and f-curve errors, and statistical errors. The parameter bId, where d is the spacing of the (Ill) rhombohedral planes of one sub-lattice and b is the displacement of the other sub-lattice (111) planes from these, is 0�40437�0�00008 at 4�2 oK, 0�40403�0�00008 at 78 oK, and 0�4041:1:0�0005 at 296�2 oK; the rhombohedral. parameter, u, corresponding to these values is, respectively, 0�23406, 0�23400, and. 0�23401. The small but presumably significant dependence on temperature at low temperatures is in disagreement with predictions of a theory of Blount and Cohen and. may signify a lessening of resistance to the atom displacement from simple cubic, due to thermal expansion of the structure. Powder patterns yielded 57.314, 57�28., and 57�23. � for the rhombohedral angle at 4�2, 78, and 304 oK respectively.