Novel type of phase transition to incommensurate structure in quartz and in berlinite

It is shown that the β-incommensurate transitions which take place in quartz at ${\mathrm{T}}_{\mathrm{S}}$≃846 K and in berlinite at ${\mathrm{T}}_{\mathrm{S}}$≃870 K are of a novel type which has recently been discussed theoretically. This transition has features in common with both instability and nucleation types. The wave vector q of the incommensurate phase rotates continuously away from the symmetry axis as the temperature is lowered below ${\mathrm{T}}_{\mathrm{S}}$. Renormalization-group and scaling arguments are presented, suggesting that the perpendicular component of the wave vector should vary as ${\mathrm{q}}_{\mathrm{\perp }}$∼${\mathrm{t}}^{\nu }$, where t=(${\mathrm{T}}_{\mathrm{S}}$-T)/${\mathrm{T}}_{\mathrm{S}}$ and ν is the critical exponent associated with the correlation length.