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UBC Theses and Dissertations

High resolution positron annihilation study in the -phase region of the copper gallium and copper germanium system McLarnon, James Gordon


A high resolution positron annihilation angular distribution study has been made of a sequence of α-phase alloys, of copper gallium and copper germanium up to electron per atom ratios of about n = 1.25. While the primary study has concerned the variation of the radius of the neck features of the Fermi surface with electron concentration, data has also been obtained for the <110> Fermi cut-off for all alloys and in addition a <100> cut-off has been obtained for the highest concentration copper gallium alloy. The two concentrated alloy systems show different behavior which is in agreement with low concentration studies done on CuGa and CuGe by Coleridge and Templeton. The CuGa neck radius if found to increase at a more rapid rate than predicted by rigid band theory, particularly at the highest concentration studied, whereas the CuGe behavior is below the rigid band predictions. General consistency is obtained between the neck variation and the <110> cut-off change. For the most concentrated CuGa alloy the results allow us to sketch a tentative Fermi surface and also provide convincing proof that the Fermi surface is most unlikely to contact the (200) Brillouin zone boundary even at the limit of the a-phase. This refutes the explanation given by Hume-Rothery and Roaf to account for the occurrence of the Hume-Rothery rules. The present results are compared with the other existing experimental data for these alloys, in particular the optical absorption data of Montgomery and Pells, and it is concluded that, while it is not possible to make any definitive theoretical statements from the present data, the two different measurements provide complementary details of the alloy band structure which would serve as an excellent test of any theory. The recent calculations of Das and Joshi using the coherent potential model has had reasonable success in explaining the optical data for the α-phase of the copper zinc system and it is hoped that the present work will stimulate the application of such theory to the CuGa and CuGe systems.

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