PART I – Papers - Temperature Dependence of Elastic Moduli of Ruthenium, Rhenium, Cobalt, Dysprosium and Erbium; a Study of the Elastic Anisotropy-Phase Transformation Relationship

Measurements of the temperature dependence of the elastic moduli in single crystals of hep ruthenium, rhenium, cobalt, dysprosium, and erbium were carried out for various temperature ranges so as to investigate the correlation, suggested by prior work, between the shear anisotropy ratio, A = C44/C66, and the occurrence of the hcp — bee phase transformation. These measurements confirm the suggestion that A has a positive temperature dependence in that group of hcp metals that undergo thermally induced transfornzations to the bee structure and a negative or zero temperature dependence in the other hcp metals. It appears, from indirect evidence, that the hcp -fee transformation in cobalt is preceded by a highly negative temperature dependence of A. These results indicate that elastic anisotropy is an important factor in determining the temperatures at which martensitic phase transformations occur. Two possible roles for elastic anisotropy are proposed: 1) the shear-modulus ratio within the habit planes must be nearly similar for the two phases and 2) a large anisotropy decreases the stress necessary for the movement of the transfornzation dislocations. FUCHS' calculations of the elastic moduli in the alkali metals have shown that the high shear-anisotropy ratios, c/c', in certain bee metals and alloys are the result of large negative contributions to c' = (c11 - c12)/2 arising from the nearest-neighbor repulsive forces.' On this basis, and following Zener,2 the association between high c/c' ratios and the martensitic phase transformations that occur upon cooling certain bee metals is explained as a unique characteristic of the bee structure. Recent measurements of the elastic moduli in hcp titanium and zirconium show, however, that a high elastic anisotropy also exists in these hcp structures at the temperatures at which they transform to bee upon heating3. If there exists a direct and consistent correlation between the elastic anisotropy in close-packed structures and the occurrence of transformations to the bee phases then there is evidently a need to re-examine the conclusions of Zener theory. Elastic anisotropy may also be the result of the effects of temperature on the stability of the low-temperature close-packed structures or it may play an important role in the mech- anism of the martensitic transformations. The present measurements were aimed at establishing the phenomenological correlation between elastic shear anisotropy in hcp structures and the thermally induced hcp —bee transformations that occur in the majority of the twenty-three hcp metals, as shown in Table I. Prior to the present work the temperature dependence of the anisotropy ratio, A = c44/c66, was known at various temperatures for nine of the metals listed. The data showed a negative temperature dependence of A for cadmium, zinc, magnesium, and cobalt, which do not transform to bee, and a positive temperature dependence of A for thallium, zirconium, titanium, hafnium, and yttrium. The correlation was, however, ambiguous in that these two groups of metals are also separated with respect to the c/a ratios as noted in Table I. There remained the possibility that the temperature dependence of A is a function of c/a and not consistently associated with the transformation. The measurements of the elastic moduli in rhenium and ruthenium, in which hcp —bee transformations do not occur, were needed to help decide this question. The studies of dysprosium and erbium were undertaken to determine whether the correlation holds for the heavy rare earth metals.