Verifying Larché–Cahn elasticity, a milestone of 20th-century thermodynamics

Shi, Shan; Markmann, Jürgen; Weißmüller, J.

doi:10.1073/pnas.1809355115

Cited by 19 publications

(20 citation statements)

References 55 publications

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“…Expressions for binary crystal structures are now available which extends the scope to a broad range of common crystal structures. In the future, it will be interesting to quantify the link to the thermodynamic description by Larché and Cahn and to calculate open system elastic constants 55 based on the long wavelength acoustic limit 39 . The additional finding of optical phonon modes goes beyond the theory of hydrodynamics.…”

Section: Discussionmentioning

confidence: 99%

Elasticity of disordered binary crystals

2020

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The properties of crystals consisting of several components can be widely tuned. Often solid solutions are produced, where substitutional or interstitional disorder determines the crystal thermodynamic and mechanical properties. The chemical and structural disorder impedes the study of the elasticity of such solid solutions, since standard procedures like potential expansions cannot be applied. We present a generalization of a density-functional based approach recently developed for one-component crystals to multi-component crystals. It yields expressions for the elastic constants valid in solid solutions with arbitrary amounts of point defects and up to the melting temperature. Further, both acoustic and optical phonon eigenfrequencies can be computed in linear response from the equilibrium particle densities and established classical density functionals. As a proof of principle, dispersion relations are computed for two different binary crystals: A random fcc crystal as an example for a substitutional, and a disordered sodium chloride structure as an example of an interstitial solid solution. In cases where one of the components couples only weakly to the others, the dispersion relations develop characteristic signatures. The acoustic branches become flat in much of the first Brillouin zone, and a crossover between acoustic and optic branches takes place at a wavelength which can far exceed the lattice spacing.

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Section: Discussionmentioning

confidence: 99%

Elasticity of disordered binary crystals

2020

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“…The work of Larché and Cahn (1973, 1978a, 1978b, 1982 has been hailed as "a milestone of twentieth century thermodynamics" (Shi et al, 2018). It has been applied successfully to the study of epitaxial thin films (e.g., Guyer & Voorhees, 1996;Lian et al, 2021;Spencer et al, 1991;Wang et al, 2006), lithium ion batteries (e.g., Bower et al, 2011;Cui et al, 2012;Meca et al, 2016;Sethuraman et al, 2010;Shi et al, 2018), and coherent precipitates in alloys (e.g., Kamachali et al, 2014Kamachali et al, , 2018Schwarze et al, 2017;Voorhees & Johnson, 1989). Here we briefly review the key concepts that underlie our work, noting that other recent studies also discuss these concepts from a variety of perspectives (e.g., Powell et al, 2018Powell et al, , 2019Voorhees & Johnson, 2004;Wheeler, 2018).…”

Section: Larché-cahn Theorymentioning

confidence: 99%

“…The work of Larché and Cahn (1973, 1978a, 1978b, 1982, 1985) has been hailed as “a milestone of twentieth century thermodynamics” (Shi et al., 2018). It has been applied successfully to the study of epitaxial thin films (e.g., Guyer & Voorhees, 1996; Lian et al., 2021; Spencer et al., 1991; Wang et al., 2006), lithium ion batteries (e.g., Bower et al., 2011; Cui et al., 2012; Meca et al., 2016; Sethuraman et al., 2010; Shi et al., 2018), and coherent precipitates in alloys (e.g., Kamachali et al., 2014, 2018; Schwarze et al., 2017; Voorhees & Johnson, 1989).…”

Section: Larché‐cahn Theorymentioning

confidence: 99%

Quantifying the Effects of Non‐Hydrostatic Stress on Multi‐Component Minerals

2022

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Mineral compositions are used to infer pressures, temperatures, and timescales of geological processes. The thermodynamic techniques underlying these inferences assume a uniform, constant pressure. Nonetheless, convergent margins generate significant non‐hydrostatic (unequal) stresses, violating the uniform pressure assumption and creating uncertainty. Materials scientists F. Larché and J. Cahn derived an equation suitable for non‐hydrostatically stressed geologic environments that links stress and equilibrium composition in elastic, multi‐component crystals. However, previous works have shown that for binary solid solutions with ideal mixing behavior, hundreds of MPa to GPa‐level stresses are required to shift mineral compositions by a few hundredths of a mole fraction, limiting the equation's applicability. Here, we apply Larché and Cahn's equation to garnet, clinopyroxene, and plagioclase solid solutions, incorporating for the first time non‐ideal mixing behavior and more than two endmembers. We show that non‐ideal mixing increases predicted stress‐induced composition changes by up to an order of magnitude. Further, incorporating additional solid solution endmembers changes the predicted stress‐induced composition shifts of the other endmembers being considered. Finally, we demonstrate that Larché and Cahn's approach yields positive entropy production, a requirement for any real process to occur. Our findings reveal that stresses between tens and a few hundred MPa can shift mineral compositions by several hundredths of a mole fraction. Consequently, mineral compositions could plausibly be used to infer stress states. We suggest that stress‐composition effects could develop via intracrystalline diffusion in any high‐grade metamorphic setting, but are most likely in hot, dry, and strong rocks such as lower crustal granulites.

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“…A key complicating factor is the mutual interplay between these phenomena, i.e., the chemo-mechanical coupling between diffusing solutes and the stress fields around a precipitate, amplified by the small size of the precipitates. The importance of the chemo-mechanical coupling has been discussed in various contexts [ 1 , 2 , 3 , 4 , 5 , 6 ]. Recent theoretical and experimental studies have revealed that the mutual interactions between stress fields and solutal gradients at the precipitation front can alter precipitates’ growth and ripening kinetics [ 7 , 8 , 9 , 10 ].…”

Section: Introductionmentioning

confidence: 99%

Simulation of the θ′ Precipitation Process with Interfacial Anisotropy Effects in Al-Cu Alloys

Bilal

Häusler

et al. 2021

Materials

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The effects of anisotropic interfacial properties and heterogeneous elasticity on the growth and ripening of plate-like θ’-phase (Al2Cu) in Al-1.69 at.% Cu alloy are studied. Multi-phase-field simulations are conducted and discussed in comparison with aging experiments. The precipitate/matrix interface is considered to be anisotropic in terms of its energy and mobility. We find that the additional incorporation of an anisotropic interfacial mobility in conjunction with the elastic anisotropy result in substantially larger aspect ratios of the precipitates closer to the experimental observations. The anisotropy of the interfacial energy shows comparably small effect on the precipitate’s aspect ratio but changes the interface’s shape at the rim. The effect of the chemo-mechanical coupling, i.e., the composition dependence of the elastic constants, is studied as well. We show that the inverse ripening phenomenon, recently evidenced for δ’ precipitates in Al-Li alloys (Park et al. Sci. Rep. 2019, 9, 3981), does not establish for the θ’ precipitates. This is because of the anisotropic stress fields built around the θ’ precipitates, stemming from the precipitate’s shape and the interaction among different variants of the θ’ precipitate, that disturb the chemo-mechanical effects. These results show that the chemo-mechanical effects on the precipitation ripening strongly depend on the degree of sphericity and elastic isotropy of the precipitate and matrix phases.

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Verifying Larché–Cahn elasticity, a milestone of 20th-century thermodynamics

Cited by 19 publications

References 55 publications

Elasticity of disordered binary crystals

Elasticity of disordered binary crystals

Quantifying the Effects of Non‐Hydrostatic Stress on Multi‐Component Minerals

Simulation of the θ′ Precipitation Process with Interfacial Anisotropy Effects in Al-Cu Alloys

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