Study of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ω</mml:mi></mml:math>phase in Zr-Nb alloys by Mössbauer and x-ray diffuse scattering

Abstract

The $\ensuremath{\omega}$ phase transformation in Zr-Nb alloys has been studied by measuring x-ray and M\"ossbauer diffuse scattering from single crystals with compositions ranging from 8- to 30-wt% Nb. We present an extensive two-dimensional mapping of the x-ray diffuse scattering for all compositions. The distinct features of these experimental observations are (a) the x-ray $\ensuremath{\omega}$ reflections are displaced, in general, toward a lower angle from the hexagonal positions, (b) the M\"ossbauer elastic scattering is shifted toward a lower angle while the inelastic portions are centered at the exact hexagonal positions. Our intensity calculations indicate that no single model, based either on an independent-particle approach or a wave model, accounts for the observed scattering features. The displacement of x-ray peaks seems to be consistent with two effects: a phononlike distortion with a wave vector ${k}_{m}$ slightly larger than ${k}_{\ensuremath{\omega}}$ (the exact value) and a Bain-type lattice expansion. A possible mechanism behind the M\"ossbauer elastic peak shifts is presented based on energetic considerations. The metastable athermal $\ensuremath{\omega}$ may be viewed as the result of time-dependent fluctuations of the bcc lattice into $\ensuremath{\omega}$ like regions. The size and time dependences are strongly composition dependent. At 15-wt% Nb and lower, $\ensuremath{\omega}$ regions are quite large and long lived, and they are essentially crystalline in nature. At high concentrations, the $\ensuremath{\omega}$ domain fluctuations are small and short lived.