Microscopic strain, local structural heterogeneity and the energetics of silicate solid solutions

Carpenter, Michael A.; Ballaran, Tiziana Boffa; Atkinson, A. J.

doi:10.1080/01411599908208011

Cited by 24 publications

(12 citation statements)

References 23 publications

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“…This thermal expansion excess of the C2/c intermediate composition samples at high-T is consistent with the observation by Boffa Ballaran (2003); Carpenter et al (1999);and Carpenter (2002). They firstly interpreted the sharpening of some FTIR absorption bands (i.e., Δcorr 150 ) as substantial local decrease of strain heterogeneity, on the basis of the elastic trace element substitution model proposed by Blundy and Wood (1994) and van Westrenen et al (2001van Westrenen et al ( , 2003.…”

Section: Thermal Expansion Coefficients Behaviorsupporting

confidence: 80%

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Volume thermal expansion along the jadeite–diopside join

et al. 2014

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7.1(1.7) × 10 −10 × X 2 Jd ] obtained from the α V at room-T (i.e., α V303K,1bar ) allows us to predict the room-T volume thermal expansion for Fe-free C2/c clinopyroxenes with intermediate composition along the binary join Jd-Di. The observed α V value for P2/n omphacite α V(303K,1bar) = 2.58 (5) × 10 −5 K −1 was compared with that recalculated for disordered C2/c omphacite published by Pandolfo et al. (Phys Chem Miner 1-10, 2012) Despite the large e.s.d.'s for the latter, the difference of both values at room-T is small, indicating that convergent ordering has practically no influence on the room-T thermal expansion. However, at high-T, the smaller thermal expansion coefficient for the C2/c sample with respect to the P2/n one with identical composition could provide further evidence for its reduced stability relative to the ordered one.

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Section: Thermal Expansion Coefficients Behaviorsupporting

confidence: 80%

“…However, several parameters need to be accounted (see Holland 1990, Boffa Ballaran 2003Carpenter et al 1999;Carpenter 2002) in order to perform reliable thermodynamics calculation on the two phase stability.…”

Section: Thermal Expansion Coefficients Behaviormentioning

confidence: 99%

Volume thermal expansion along the jadeite–diopside join

et al. 2014

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“…There are limitations to the elastic model. The model requires that the elastic strain fields due to individual atomic exchanges overlap; this assumption breaks down in dilute alloys (Wood and Blundy 1997;Carpenter et al 1999). Rigid rotations of structural units are not considered, although such effects may be accommodated by excess pressure terms (Sect.…”

Section: Discussionmentioning

confidence: 99%

“…It is assumed that the proportion of each endmember is sufficiently large that the exchanging atoms have overlapping strain fields, and, therefore, cannot be treated as impurities . In very dilute solid solutions, elastic strain energies are local and should be treated as such (Wood and Blundy 1997;Carpenter et al 1999).…”

Section: The Elastic Modelmentioning

confidence: 99%

The elastic solid solution model for minerals at high pressures and temperatures

Myhill

2018

Contrib Mineral Petrol

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Non-ideality in mineral solid solutions affects their elastic and thermodynamic properties, their thermobaric stability, and the equilibrium phase relations in multiphase assemblages. At a given composition and state of order, non-ideality in minerals is typically modelled via excesses in Gibbs free energy which are either constant or linear with respect to pressure and temperature. This approach has been extremely successful when modelling near-ideal solutions. However, when the lattice parameters of the solution endmembers differ significantly, extrapolations of thermodynamic properties to high pressures using these models may result in significant errors. In this paper, I investigate the effect of parameterising solution models in terms of the Helmholtz free energy, treating volume (or lattice parameters) rather than pressure as an independent variable. This approach has been previously applied to models of order-disorder, but the implications for the thermodynamics and elasticity of solid solutions have not been fully explored. Solid solution models based on the Helmholtz free energy are intuitive at a microscopic level, as they automatically include the energetic contribution from elastic deformation of the endmember lattices. A chemical contribution must also be included in such models, which arises from atomic exchange within the solution. Derivations are provided for the thermodynamic properties of n-endmember solutions. Examples of the use of the elastic model are presented for the alkali halides, pyroxene, garnet, and bridgmanite solid solutions. Elastic theory provides insights into the microscopic origins of non-ideality in a range of solutions, and can make accurate predictions of excess enthalpies, entropies, and volumes as a function of volume and temperature. In solutions where experimental data are sparse or contradictory, the Helmholtz free energy approach can be used to assess the magnitude of excess properties and their variation as a function of pressure and temperature. The formulation is expected to be useful for geochemical and geophysical studies of the Earth and other planetary bodies.

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“…More direct evidence for the existence of local strain heterogeneities in perovskites is provided by line broadening in infrared absorption spectra, 36 while in silicates the heterogeneities appear to be eliminated by cation ordering. [37][38][39][40][41][42][43] It is therefore proposed that similar local strain fields are induced by cation disordering in La 0.6 Sr 0.1 TiO 3 , and that it is these local heterogeneities which are responsible for the suppression of strain-order-parameter coupling. A slight increase in the widths of superlattice reflections from the disordered sample, relative to those from the ordered sample, suggests smaller antiphase domain sizes and may imply that domain growth is also hindered by the disordering.…”

Section: Discussionmentioning

confidence: 99%

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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Microscopic strain, local structural heterogeneity and the energetics of silicate solid solutions

Cited by 24 publications

References 23 publications

Volume thermal expansion along the jadeite–diopside join

Volume thermal expansion along the jadeite–diopside join

The elastic solid solution model for minerals at high pressures and temperatures

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

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