Some thermodynamic aspects of the growth of strained crystals

Brice, J.C.

doi:10.1016/0022-0248(75)90241-9

Cited by 302 publications

(137 citation statements)

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“…The model is based on the observations of Onuma et al (1968), who showed that the behaviour of D i versus r i for series of homovalent cations is near parabolic with maxima corresponding to the size of the crystal lattice site(s) on which substitution occurs. It combines these observations with the lattice strain model of Brice (1975), relating lattice strain energy U strain associated with the insertion of a trace element with radius r i into a site with ideal radius r 0 , to the elasticity of the site (Young's modulus, E) and the size misfit between substituent and ideal site cations (r i -r 0 ):…”

Section: Lattice Strain Modelmentioning

confidence: 99%

Experimental and computational study of trace element distribution between orthopyroxene and anhydrous silicate melt: substitution mechanisms and the effect of iron

Parker¹,

Liebscher

Frei

et al. 2009

Contrib Mineral Petrol

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Although orthopyroxene (Opx) is present during a wide range of magmatic differentiation processes in the terrestrial and lunar mantle, its effect on melt trace element contents is not well quantified. We present results of a combined experimental and computational study of trace element partitioning between Opx and anhydrous silicate melts. Experiments were performed in air at atmospheric pressure and temperatures ranging from 1,326 to 1,420°C in the system CaO-MgO-Al 2 O 3 -SiO 2 and subsystem CaOMgO-SiO 2 . We provide experimental partition coefficients for a wide range of trace elements (large ion lithophile: Li, Be, B, K, Rb, Sr, Cs, Ba, Th, U; rare earth elements, REE: La, $ 0:058, and are all virtually independent of temperature. Cr and Co are the only compatible trace elements at the studied conditions. To elucidate charge-balancing mechanisms for incorporation of REE into Opx and to assess the possible influence of Fe on Opx-melt partitioning, we compare our experimental results with computer simulations. In these simulations, we examine major and minor trace element incorporation into the end-members enstatite (Mg 2 Si 2 O 6 ) and ferrosilite (Fe 2 Si 2 O 6 ). Calculated solution energies show that R 2? cations are more soluble in Opx than R 3? cations of similar size, consistent with experimental partitioning data. In addition, simulations show charge balancing of R 3? cations by coupled substitution with Li ? on the M1 site that is energetically favoured over coupled substitution involving Al-Si exchange on the tetrahedrally coordinated site. We derived best-fit values for ideal ionic radii r 0 , maximum partition coefficients D 0 , and apparent Young's moduli E for substitutions onto the Opx M1 and M2 sites. Experimental r 0 values for R 3? substitutions are 0.66-0.67 Å for M1 and 0.82-0.87 Å for M2. Simulations for enstatite result in r 0 = 0.71-0.73 Å for M1 and *0.79-0.87 Å for M2. Ferrosilite r 0 values are systematically larger by *0.05 Å for both M1 and M2. The latter is opposite to experimental literature data, which appear to show a slight decrease in r M2 0 in the presence of Fe. Additional systematic studies in Febearing systems are required to resolve this inconsistency and to develop predictive Opx-melt partitioning models for use in terrestrial and lunar magmatic differentiation models.

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Section: Lattice Strain Modelmentioning

confidence: 99%

Experimental and computational study of trace element distribution between orthopyroxene and anhydrous silicate melt: substitution mechanisms and the effect of iron

Parker¹,

Liebscher

Frei

et al. 2009

Contrib Mineral Petrol

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“…Semiempirical partitioning models, such as the lattice strain model [41,42], aim to determine a set of partition coefficients ( ) for ion where, for example, the partitioning of a trace ion between fluid and mineral is described by…”

Section: The Lattice Strainmentioning

confidence: 99%

“…In the rhombohedral crystal structure of calcite, Ca 2+ has a 6-fold coordination, which corresponds to a Shannon radius of 1.00Å, whereas the REE 3+ have ionic radii varying between 1.032Å (La) and 0.861Å (Lu). The lattice strain model is based on the Brice equation [41], and it considers the partitioning of an element as a function of its ionic radius, charge, and the elastic properties of the mineral lattice site (i.e., Young's modulus). When the REE partition from an aqueous solution into a mineral like calcite, strain occurs on the crystal lattice because of this slight size and charge mismatch between REE 3+ and Ca 2+ .…”

Section: The Lattice Strainmentioning

confidence: 99%

“…Experimental studies of REE partitioning between fluidcalcite [28,30,40] and fluid-fluorite [29] have been carried out at temperatures <100 ∘ C. In the study of van Hinsberg et al [29], the partitioning behavior of the REE between fluid-fluorite yielded predictable results according to the REE ionic radii, and their experimental data were fit to the lattice strain model [41,42]. This model was later applied to the partitioning of REE between fluid-calcite for a set of selected REE by Voigt et al [30].…”

Section: Introductionmentioning

confidence: 99%

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Rare Earth Elements in Mineral Deposits: Speciation in Hydrothermal Fluids and Partitioning in Calcite

Perry

Gysi

2018

Geofluids

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is properly cited.Studying the speciation and mineral-fluid partitioning of the rare earth elements (REE) allows us to delineate the key processes responsible for the formation of economic REE mineral deposits in natural systems. Hydrothermal REE-bearing calcite is typically hosted in carbonatites and alkaline rocks, such as the giant Bayan Obo REE deposit in China and potential REE deposits such as Bear Lodge, WY. The compositions of these hydrothermal veins yield valuable information regarding pressure ( ), temperature ( ), salinity, and other physicochemical conditions under which the REE can be fractionated and concentrated in crustal fluids. This study presents numerical simulation results of the speciation of REE in aqueous NaCl-H 2 O-CO 2 -bearing hydrothermal fluids and a new partitioning model between calcite and fluids at different --conditions. Results show that, in a high CO 2 and low salinity system, bicarbonate/carbonate are the main transporting ligands for the REE, but predominance shifts to chloride complexes in systems with high CO 2 and high salinity. Hydroxyl REE complexes may be important for the solubility and transport of the REE in alkaline fluids. These numerical predictions allow us to make quantitative interpretations of hydrothermal processes in REE mineral deposits, particularly in carbonatites, and show where future experimental work will be essential in improving our modeling capabilities for these ore-forming processes.

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“…Following Olin and Wolff (2010), we employ a method of identifying equilibrium mineral-melt pairs from natural samples that is independent of textural context. We then present titanite/melt D values for Y, Zr, Nb, REE, Hf, Ta, Th and U and use the data to estimate 7-fold coordination radii for REE 3+ not reported by Shannon (1976), and to approximately predict titanite/melt partitioning behavior of Ra, Ac and Pa. We then assess the results, paying particular attention to behaviors (melt structure effects, fractionation of cations of identical charge and radius) that are not predicted by the lattice strain model of Brice (1975) and Blundy and Wood (1994).…”

Section: Introductionmentioning

confidence: 99%

Partitioning of rare earth and high field strength elements between titanite and phonolitic liquid

Olin

Wolff

2012

Lithos

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We present the results of a LA-ICPMS study of titanites and associated glasses from the mixed-magma phonolitic Fasnia Member of the Diego Hernández Formation, Tenerife, Canary Islands. We employ a method of identifying equilibrium mineral-melt pairs from natural samples using REE contents and a linear form of the lattice strain model equation (Blundy and Wood, 1994), where the Young's modulus (E M ) for the 7-fold coordinated site is an output variable. For felsic magmas that contain crystals potentially derived from a variety of environments within the system, this approach is more rigorous than the use of solely textural criteria such as mineral-glass proximity.We then estimate titanite/melt partition coefficients for Y, Zr, Nb, REE, Hf, Ta, U and Th. In common with prior studies, we find that middle REE partition more strongly into titanite than either light or heavy REE, and that REE partitioning behavior in titanite is reasonably predicted by the lattice strain model. Titanite also fractionates Y from Ho, Zr from Hf, and Nb from Ta. Comparison with experimental data indicates that melt structure effects on partitioning are significant, most particularly in very highly polymerized melts. We use the data to estimate 7-fold coordination radii for trivalent Pr, Nd, Ho, Tm and Lu, and to make approximate predictions of titanite/melt partitioning of Ra, Ac and Pa. Interpolation of data for heavy REE does not predict the behavior of Y, indicating that factors other than charge and radius are involved in partitioning. Variations in Y/Ho induced by magmatic processes appear to be negatively correlated with temperature, and are expected to be greatest in near-minimum melts.

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Some thermodynamic aspects of the growth of strained crystals

Cited by 302 publications

References 4 publications

Experimental and computational study of trace element distribution between orthopyroxene and anhydrous silicate melt: substitution mechanisms and the effect of iron

Experimental and computational study of trace element distribution between orthopyroxene and anhydrous silicate melt: substitution mechanisms and the effect of iron

Rare Earth Elements in Mineral Deposits: Speciation in Hydrothermal Fluids and Partitioning in Calcite

Partitioning of rare earth and high field strength elements between titanite and phonolitic liquid

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