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.