Ferroelastic orientation states and domain walls in lead phosphate type crystals

Bismayer, U.; Mathes, Dagmar; Bosbach, Dirk; Putnis, Andrew; Tendeloo, Gustaaf Van; Novak, Jurica; Salje, Ekhard K. H.

doi:10.1180/002646100549328

Cited by 18 publications

(18 citation statements)

References 28 publications

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“…Wall widths of 10À20 lattice spacing are sufficient to generate high attenuation in the one-dimensional simulations of Combs and Yip (1983). Similar widths are observed in a wide range of ferroelastic materials (Chrosch and Salje, 1999), including lead orthophosphate (Wruck et al, 1994;Bismayer et al, 2000).…”

Section: Discussionmentioning

confidence: 65%

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

2004

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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.

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Section: Discussionmentioning

confidence: 65%

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

2004

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“…This definition was chosen in close analogy with the equivalent definitions of ferroelectricity and ferromagneticity [1][2][3][4][5][6][7]. The non-linear relationship between strain and stress is exemplified in the ferroelastic hysteresis.…”

Section: Introductionmentioning

confidence: 99%

On the dynamics of ferroelastic domain boundaries under thermal and elastic forcing

Salje

2010

Phase Transitions

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Experimental observations and some theoretical models for the propagation of ferroelastic domain boundaries and phase fronts are reviewed. While the static configurations of domains and domain walls are reasonably well understood in ferroelastics (and specifically in shape memory alloys), one finds that the dynamic features have been less thoroughly investigated. In most cases, a smooth movement of domain walls in the ballistic limit is observed, accelerated propagation seems not to exist in the time and space limits of most experiments. Pattern formation occurs when the local order parameter is conserved over a length scale which is different from the ferroelastic correlation length. Currently, only few spiky elastic measurements and domain wall jamming in ferroelastics have been reported. Emphasis is given to disordered systems in which the occurrence of 'jerky elasticity' can be expected.

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“…Minerals that undergo phase transformations are likely to show microstructures with twin structures as a typical ®nger-print for ferroelastic behaviour (Salje, 1990(Salje, , 2000Bosbach et al, 1997;Roewer et al, 1997;Salje et al, 2000). The interaction between twin walls leads to the formation of corner domains, needle domains and comb patterns.…”

Section: Theoretical Basismentioning

confidence: 99%

Ferroelastic phase transitions: structure and microstructure

Salje

Hayward

Lee

2004

Acta Crystallogr A Found Crystallogr

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Landau-type theories describe the observed behaviour of phase transitions in ferroelastic and co-elastic minerals and materials with a high degree of accuracy. In this review, the derivation of the Landau potential G = 1 2 A S [coth( S /T) À coth( S /T C )]Q 2 + 1 4 BQ 4 + F F F is derived as a solution of the general 0 4 model. The coupling between the order parameter and spontaneous strain of a phase transition brings the behaviour of many phase transitions to the mean-®eld limit, even when the atomistic mechanism of the transition is spin-like. Strain coupling is also a common mechanism for the coupling between multiple order parameters in a single system. As well as changes on the crystal structure scale, phase transitions modify the microstructure of materials, leading to anomalous mesoscopic features at domain boundaries. The mesostructure of a domain wall is studied experimentally using X-ray diffraction, and interpreted theoretically using Ginzburg±Landau theory. One important consequence of twin mesostructures is their modi®ed transport properties relative to the bulk. Domain wall motion also provides a mechanism for superelastic behaviour in ferroelastics. At surfaces, the relaxations that occur can be described in terms of order parameters and Landau theory. This leads to an exponential pro®le of surface relaxations. This in turn leads to an exponential interaction energy between surfaces, which can, if large enough, destabilize symmetrical morphologies in favour of a platelet morphology. Surface relaxations may also affect the behaviour of twin walls as they intersect surfaces, since the surface relaxation may lead to an incompatibility of the two domains at the surface, generating large strains at the relaxation. Landau theory may also be extended to describe the kinetics of phase transitions. Time-dependent Landau theory may be used to describe the kinetics of order±disorder phase transitions in which the order parameter is homogeneous. However, the time-dependent Landau theory equations also have microstructural solutions, explaining the formation of microstructures such as tweed.

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Ferroelastic orientation states and domain walls in lead phosphate type crystals

Cited by 18 publications

References 28 publications

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

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

On the dynamics of ferroelastic domain boundaries under thermal and elastic forcing

Ferroelastic phase transitions: structure and microstructure

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