Spontaneous strain variations through the low temperature phase transitions of deuterated lawsonite

High resolution neutron powder diffraction has been used to determine lattice parameter variations of deuterated lawsonite across the Cmcm <----> Pmcn and Pmcn <----> P2(1)cn phase transitions, in the temperature interval 1.6-505 K. The variations are reversible through heating and cooling cycles. Strain analysis, based on a displacive model of the transitions with saturation temperatures to describe the temperature-independent behavior as T --> 0 K, shows that the data are consistent with a tricritical transition at 271 2 K and a second-order transition at 155 +/- 1 K. Comparisons with strains from published dilatation data for a natural (hydrogenated) sample highlight aspects of the transitions that are most dependent on the behavior of protons in the structure. Replacing H by D causes the low temperature transition point to be increased by similar to27 K and an anomaly in the strain evolution of the Pmcn transition to increase from similar to225 to similar to250 K. The transition point of the high-temperature transition remains the same within +/- similar to2 K. We conclude that proton ordering and displacive contributions are both important in the 271 K transition, though with the displacive component providing the initial symmetry-breaking mechanism. Structural changes that are more dependent on the behavior of H or D become important similar to20-50 K below this. Strains for the Pmcn <----> P2(1)cn transition are consistent with a transition driven by a single order parameter. The data are used to determine values for strain/order parameter coupling coefficients for calculation of elastic anomalies due to the phase transitions.