Phase stability of Cd–Y–Yb quasicrystal and 1/1–1/1–1/1 approximant

The formation range of the Cd–Y–Yb 1/1–1/1–1/1 approximant was determined and its atomic structure was investigated in detail by applying the Rietveld analysis to the powder X-ray diffraction data. The ternary Cd–Y–Yb 1/1–1/1–1/1 approximant is found to be formed only along a unique composition line connecting Cd85.7Yb14.3 and Cd84Y16, where a decrease in the Cd concentration from 85.7 to 84 at.% accompanies an increase in the Y concentration from 0 to 16 at.% and, in turn, an increase in nominal electron concentration e/a from 2.0 to 2.16. This is seemingly at variance with the Hume-Rothery rule which states that the approximant tends to be stabilized along a constant e/a line. However, the present structure analysis clearly showed an increase in the number of vacancies per unit cell with increasing e/a. As a result, the number of valence electrons per unit cell Nu is found to be kept constant at 338.0 ± 2.0. From this we conclude that the ternary Cd–Y–Yb 1/1–1/1–1/1 approximant is formed in accordance with the Hume-Rothery matching rule, which must be restated such that Nu should be employed in place of e/a when the number of vacancies changes with composition.