Thermodynamics of sodium feldspar II: Experimental results and numerical calculations

Salje, Ekhard K. H.; Kuscholke, B.; Wruck, B.; Kroll, Herbert

doi:10.1007/bf01046834

Cited by 138 publications

(90 citation statements)

References 8 publications

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“…The same method applies to other forms of coupling between the order parameters and the spontaneous strain; see Salje et al (1985), Salje & Devarajan (1986) and Salje (1990) for details of the mathematical form of G(Q) and the resulting (Q 1 , Q 2 ) versus T topologies. The derivation of order parameter coupling shows that Landau-like models are very well suited to dealing with the interactions between multiple phase-transition processes.…”

Section: Phase Transitions and Spontaneous Strainmentioning

confidence: 99%

“…As a result, phase transitions whose underlying mechanisms are clearly of an order±disorder type may have macroscopic behaviour which is Landau-like, and hence apparently displacive. Examples of this behaviour include cation ordering in minerals, such as (Al, Si) ordering in feldspars (Salje et al, 1985;Salje et al, 1993), (Fe, Mg, Mn) ordering in olivine (Redfern, 1998;Redfern et al, 2000), (Al, Fe) and (Ca, Na) ordering in omphacite (Carpenter et al, 1990a). Similarly, the behaviours of many ferroelectric and antiferroelectric systems, such as BaTiO 3 (Zalar et al, 2003), squaric acid (Dalal et al, 1998) Salje (1990) described such crystals as`co-elastic'.…”

Section: Phase Transitions and Spontaneous Strainmentioning

confidence: 99%

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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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Section: Phase Transitions and Spontaneous Strainmentioning

confidence: 99%

Section: Phase Transitions and Spontaneous Strainmentioning

confidence: 99%

Ferroelastic phase transitions: structure and microstructure

Salje

Hayward

Lee

2004

Acta Crystallogr A Found Crystallogr

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“…The implication is that the coupling coefficient 4 might itself be explicitly dependent on q 2 . In the lowest order permitted by symmetry, 4 could be replaced by 4 Јq 2 2 , such that 4 = 0 when q 2 = 0. A term of the form 4 Јe t q 2 2 q 5 2 then appears in Eq.…”

Section: Discussionmentioning

confidence: 99%

“…5͑a͒. The tilting transition appears to be close to tricritical in character, since 4 varies approximately linearly with temperature for both samples ͓q 5 4 ϰ ͑T c2 * − T͒; Fig. 5͑b͔͒.…”

Section: Structure Refinementmentioning

confidence: 99%

“…This effect is well known in minerals such as albite ͑NaAlSi 3 O 8 ͒ and anorthite ͑CaAl 2 Si 2 O 8 ͒, where changes in Al/Si ordering among crystallographic sites induced at high temperatures can have a significant influence on subsequent displacive phase transitions. [3][4][5][6][7] The effect is also known in ferroelectric materials where cation disordering can cause the ferroelectric transition to become diffuse. [8][9][10] The same concept does not seem to have been applied to ferroelastic transitions in perovskites, however, and the purpose of the present paper is to describe an octahedral tilting transition for which the ferroelastic response displays a strong and unexpected sensitivity to ordering of cations and vacancies on A sites of the perovskite structure.…”

Section: Introductionmentioning

confidence: 99%

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Suppression of strain coupling in perovskiteLa0.6Sr0.1TiO3by cation disorder

et al. 2007

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An octahedral tilting transition has been investigated in two samples of La 0.6 Sr 0.1 TiO 3 by powder neutron diffraction. One ͑slowly cooled͒ sample had a degree of cation/vacancy ordering on the A sites and was tetragonal, P4/mmm, at high temperatures. The second ͑quenched͒ sample had disordered cations and cubic, Pm3m, symmetry at high temperatures. On cooling, both underwent the same R-point tilting transition at ϳ560-570 K, to give symmetry changes P4/mmm ↔ Cmmm and Pm3m ↔ I4/mcm, respectively. From the evolution of the tilt angles, the transition appears to be close to tricritical in both cases. As expected from a Landau expansion in the two order parameters, the transition temperature was found to be only weakly dependent on the degree of cation order. In contrast with the expectation of standard patterns of strain to order parameter coupling, however, the tilted ͑tetragonal͒ form of the disordered sample remained metrically cubic, implying that coupling of the tetragonal shear strain with the octahedral tilting was suppressed. It is proposed that cation disordering causes the development of local strain heterogeneities in crystals of La 0.6 Sr 0.1 TiO 3 which prevent a coherent, long-range shear strain from developing. Manipulation of the degree of cation order in perovskites with carefully selected compositions might therefore provide a means by which the magnitudes of ferroelastic strains could be engineered according to the requirement of particular applications.

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Phase Transitions in Minerals: From Equilibrium Properties Towards Kinetic Behaviour Progress Report

Salje

1992

Ber Bunsenges Phys Chem

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Landau theory is derived from a simple atomistic model. The Gibbs free energy can be written in the displacive limit as magnified image where Ts = 1/2Θs is the saturation temperature due to quantum fluctuations. The coefficients A, B,… and degeneracies of the order parameter are determined by the conventional symmetry constraints. For T > Θs, G is the classic Landau potential. Solutions for non‐displacive systems and coupled order parameters are discussed. – The theory is applied to some model‐minerals such as quartz, Na‐feldspar, and calcite as typical examples. It is argued that the structural complexity of minerals is often related to several thermodynamic degrees of freedom. The transition leads to coupling phenomena, which are reviewed in some detail. – Non‐equilibrium features in crystals which are “nearly” in thermodynamic equilibrium are domain walls. It is shows that domain walls react very sensitively to small changes in the thermodynamic state of the material. New structural configurations are generated in the wall which do not exist in the bulk. – Kinetic processes with continuous order parameters can be analysed using a general rate equation which contains δG/δQ (G is often a Landau potential, Q is the order parameters) as a driving force. This theory draws, thus, a connection between the equilibrium Landau‐type theories and kinetic rate theories.

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Thermodynamics of sodium feldspar II: Experimental results and numerical calculations

Cited by 138 publications

References 8 publications

Ferroelastic phase transitions: structure and microstructure

Ferroelastic phase transitions: structure and microstructure

Suppression of strain coupling in perovskiteLa0.6Sr0.1TiO3by cation disorder

Phase Transitions in Minerals: From Equilibrium Properties Towards Kinetic Behaviour Progress Report

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