Variant Selection in Zr Alloys: How Many Variants Generated from one Beta Grain?
The elastic energy of a set of the twelve variants generated during the b ® a transformation of zirconium, with volume fractions fi, i=1..12, is derived with simplifying assumptions and the conditions on the fi to reach the energy minimum are established analytically. The minimum number of variants needed to reach this minimum is shown to be 6, and in this case, the variants have very specific volume fractions. Another result is that the maximum volume fraction of any variant is 1/3.
C. Esling, M. Humbert, R.A. Schwarzer and F. Wagner
P. Barbéris et al., "Variant Selection in Zr Alloys: How Many Variants Generated from one Beta Grain? ", Solid State Phenomena, Vol. 105, pp. 133-138, 2005