Seismic-frequency attenuation at first-order phase transitions: Dynamical mechanical analysis of pure and Ca-doped lead orthophosphate

The low-frequency mechanical properties of pure and Ca-doped lead orthophosphate, (Pb_1-xCa_x)₃(PO ₄)₂, have been studied using simultaneous dynamical mechanical analysis, X-ray diffraction (XRD), and optical video microscopy in the vicinity of the first-order ferroelastic phase transition. Both samples show mechanical softening at T > T _c, which is attributed to the presence of dynamic short-range order and microdomains. Stress-induced nucleation of the low-temperature ferroelastic phase within the high-temperature paraelastic phase was observed directly via optical microscopy at T ≈ T_c. Phase coexistence is associated with rapid mechanical softening and a peak in attenuation, P1, that varies systematically with heating rate and measuring frequency. A second peak, P2, occurs ≈ 3-5°C below T_c, accompanied by a rapid drop in the rate of mechanical softening. This is attributed to the change in mode of anelastic response from the displacement of the paraelastic/ferroelastic phase interface to the displacement of domain walls within the ferroelastic phase. Both the advancement/retraction of needles (W walls) and wall translation/rotation (W′ walls) modes of anelastic response were identified by optical microscopy and XRD. A third peak, P3, occurring ≈15°C below T_c, is attributed to the freezing-out of local flip disorder within the coarse ferroelastic domains. A fourth peak, P4, occurs at a temperature determined by the amplitude of the dynamic force. This peak is attributed to the crossover between the saturation (high temperature) and the superelastic (low temperature) regimes. Both samples display large superelastic softening due to domain wall sliding in the ferroelastic phase. Softening factors of 20 and 5 are observed in the pure and doped samples, respectively, suggesting that there is a significant increase in the intrinsic elastic constants (and hence the restoring force on a displaced domain wall) with increasing Ca content. No evidence for domain freezing was observed down to -150°C in either sample, although a pronounced peak in attenuation, P5, at T ≈ -100°C is tentatively attributed to the interaction between domain walls and lattice defects. Both samples show similar high values of attenuation within the domain-wall sliding regime. It is concluded that the magnitude of attenuation for ferroelastic materials in this regime is determined by the intrinsic energy dissipation caused by the wall-phonon interaction, and not by the presence of lattice defects. This will have a large impact on attempts to predict the effect of domain walls on seismic properties of mantle minerals at high temperature and pressure.