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

Abstract

The low-frequency mechanical properties of pure and Ca-doped lead orthophosphate, (Pb 1Àx Ca 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 hightemperature 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 &3À5ºC 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 &15ºC 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 À150ºC in either sample, although a pronounced peak in attenuation, P5, at T & À100ºC 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.

Elastic and anelastic anomalies in (Ca,Sr)TiO3 perovskites: Analogue behaviour for silicate perovskites

“…If it is now assumed, following the work of Harrison andRedfern (2002) andHarrison et al (2003), that the properties and behaviour of twin walls in tetragonal CST and rhombohedral LaAlO 3 perovskites are not fundamentally different from those of any other perovskites which undergo octahedral tilting transitions, some generalisations can be made M a n u s c r i p t 16 about the likely seismic properties of silicate perovskites. Experimental data for CaSiO 3 place the Pm 3m  I4/mcm transition in the vicinity of the lower mantle geotherm (Ono et al, 2004a;Kurashina et al, 2004;Caracas et al, 2005;Jung and Oganov, 2005;Li et al 2006a, b;Adams and Oganov, 2006;and references therein).…”

“…In general, the magnitude of anelastic softening due to twin wall movements under applied stresses depends largely on the restoring force they experience when they become M a n u s c r i p t 14 displaced from their stress-free configurations, while the magnitude of dissipation depends largely on viscous drag as they move (Combs and Yip, 1983;Huang et al, 1992;Harrison and Redfern, 2002;Harrison et al, 2003Harrison et al, , 2004. Between T1 and the freezing interval, tetragonal crystals are most likely to be in the domain wall sliding regime of Natterman et al…”

Structural evolution, strain and elasticity of perovskites at high pressures and temperatures

“…The spontaneous strain orientation for one twin is different from that of an adjacent twin, so movement of the wall separating them can change the total macroscopic strain of the crystal. If the twin wall moves in response to an applied shear stress, the total resulting strain can become substantially greater than would occur by simple lattice bending and the crystal will be anomalously soft (Schranz et al, 1999;Kityk et al, 2000aKityk et al, , 2000bBinder and Knorr, 2001;Lemanov et al, 2002;Harrison and Redfern, 2002;Harrison et al, 2003Harrison et al, , 2004aHarrison et al, , 2004bHarrison et al, , 2004c. This mechanism of softening involves some dissipation of energy and is anelastic in character.…”

“…Details of the dissipation mechanism at MHz frequencies are not known, but twin wall movements could be a more localised bulging between pinning points rather than the macroscopic displacements observed by Harrison et al (2004aHarrison et al ( , 2004bHarrison et al ( , 2004c. At high temperatures resonance peaks in RUS spectra from polycrystalline tetragonal CST samples disappear, implying complete attenuation (Q ≈ 0).…”

“…It was recognised from the early days of elastic constant measurements on SrTiO 3 that the displacement of transformation twin walls in response to an applied shear stress can give rise to additional softening and attenuation effects (Rehwald, 1971;Fossheim and Berre, 1972). These can be large in magnitude, giving rise to so called superelasticity (Schranz et al, 1999;Kityk et al, 2000aKityk et al, , 2000bBinder and Knorr, 2001;Lemanov et al, 2002;Harrison and Redfern, 2002;Harrison et al, 2003Harrison et al, , 2004aHarrison et al, , 2004bHarrison et al, , 2004c. Equivalent behaviour in silicate perovskites cannot be investigated directly because of the high confining pressure required to stabilise them, but a useful analogue system is the binary solid solution CaTiO 3 SrTiO 3 (CST).…”