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Journal Article

Distribution of REE between amphibole and pyroxenes in the lithospheric mantle: An assessment from the lattice strain model Available to Purchase

Chunguang Wang, Yan Liang, Wenliang Xu, Chenguang Sun, Kei Shimizu
Published: 01 November 2024
American Mineralogist (2024) 109 (11): 1921–1933.
DOI: https://doi.org/10.2138/am-2022-8831
... between orthopyroxene and amphibole and between clinopyroxene and amphibole. These models were formulated on the basis of parameterized lattice strain models of mineral-melt REE partitioning for orthopyroxene, clinopyroxene, and amphibole, and they were calibrated using major element and REE data...
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Journal Article

Eu speciation in apatite at 1 bar: An experimental study of valence-state partitioning by XANES, lattice strain, and Eu/Eu* in basaltic systems Available to Purchase

Nicholas D. Tailby, Dustin Trail, Bruce Watson, Antonio Lanzirotti, Matthew Newville, Yanling Wang
Published: 01 May 2023
American Mineralogist (2023) 108 (5): 789–813.
DOI: https://doi.org/10.2138/am-2022-8388
... ± 0.16 . The second technique involves analysis of Sm, Eu, and Gd in both apatite and coexisting basaltic melt (glass), and is defined by: ( Eu E u * ) D Sm × Gd = 1 1 + 10 - 0.15 ± 0.03 × l o g ⁡ ( f o 2 ) - 2.46 ± 0.41 . The third technique is based on the lattice strain model and also requires...
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View PDF for article title, Eu speciation in apatite at 1 bar: An experimental study of valence-state partitioning by XANES, <span class="search-highlight">lattice</span> <span class="search-highlight">strain</span>, and Eu&#x2F;Eu* in basaltic systems
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Journal Article

Lead diffusion in CaTiO 3 : A combined study using Rutherford backscattering and TOF-SIMS for depth profiling to reveal the role of lattice strain in diffusion processes Available to Purchase

Christopher Beyer, Ralf Dohmen, Detlef Rogalla, Hans-Werner Becker, Katharina Marquardt, Christian Vollmer, Ulrich Hagemann, Nils Hartmann, Sumit Chakraborty
Published: 01 April 2019
American Mineralogist (2019) 104 (4): 557–568.
DOI: https://doi.org/10.2138/am-2019-6730
.... We forward modeled the depth profiles of the thin film and powder source anneals using a numerical finite difference scheme ( Crank 1979 ). A detailed outline and description of this method is given in Costa et al. (2008) for example. Perovskite diffusion experimental lattice strain...
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View PDF for article title, Lead diffusion in CaTiO 3 : A combined study using Rutherford backscattering and TOF-SIMS for depth profiling to reveal the role of <span class="search-highlight">lattice</span> <span class="search-highlight">strain</span> in diffusion processes
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Journal Article

Parameterized lattice strain models for REE partitioning between amphibole and silicate melt Available to Purchase

Kei Shimizu, Yan Liang, Chenguang Sun, Colin R.M. Jackson, Alberto E. Saal
Published: 01 November 2017
American Mineralogist (2017) 102 (11): 2254–2267.
DOI: https://doi.org/10.2138/am-2017-6110
... published experimental REE and Y partitioning data between amphibole and silicate melt, the lattice strain model, and nonlinear least-squares regression method to parameterize key partitioning parameters in the lattice strain model ( D 0 , r 0 , and E ) as a function of pressure, temperature, and both...
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View PDF for article title, Parameterized <span class="search-highlight">lattice</span> <span class="search-highlight">strain</span> models for REE partitioning between amphibole and silicate melt
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Journal Article

Crystallinity, crystallite size and lattice strain of illite-muscovite and chlorite; comparison of XRD and TEM data for diagenetic to epizonal pelites Available to Purchase

Peter Arkai, Richard J. Merriman, Brinley Roberts, Donald R. Peacor, Maria Toth
Published: 01 October 1996
European Journal of Mineralogy (1996) 8 (5): 1119–1137.
View PDF for article title, Crystallinity, crystallite size and <span class="search-highlight">lattice</span> <span class="search-highlight">strain</span> of illite-muscovite and chlorite; comparison of XRD and TEM data for diagenetic to epizonal pelites
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Journal Article

Determining (Al,Si) distribution and strain in alkali feldspars using lattice parameters and diffraction-peak positions; a review Available to Purchase

Herbert Kroll, Paul H. Ribbe
Published: 01 June 1987
American Mineralogist (1987) 72 (5-6): 491–506.
...Herbert Kroll; Paul H. Ribbe Abstract Al contents (t i ) of the T i tetrahedral sites have been estimated from (T i -O) bond lengths of 38 K-rich alkali feldspars. These data were used together with lattice parameters and selected difFraction-peak positions (in degrees 2 θ , Cu K α 1 , radiation...
View PDF for article title, Determining (Al,Si) distribution and <span class="search-highlight">strain</span> in alkali feldspars using <span class="search-highlight">lattice</span> parameters and diffraction-peak positions; a review
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Image
Lattice strain vs. sample strain data (symbols) for the four deformation sequences. The solid lines show the self-consistent elastic model for each lattice plane calculated for the pressure and temperature conditions of each sequence. The uncertainty in lattice strain is ±0.001, which is illustrated by an error bar placed to the right side of each deformation sequence.

Lattice strain vs. sample strain data (symbols) for the four deformation se... Open Access

Published: 01 February 2019
Figure 1. Lattice strain vs. sample strain data (symbols) for the four deformation sequences. The solid lines show the self-consistent elastic model for each lattice plane calculated for the pressure and temperature conditions of each sequence. The uncertainty in lattice strain is ±0.001, which
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Lattice strain vs. sample strain data (symbols) for the four deformation sequences. The lines show the self-consistent models calculated to match the data. The slip system activity is plotted below each. The slip systems included in each group are listed in Table 2. The uncertainty in lattice strain is ±0.001, which is illustrated by an error bar placed to the right side of each deformation sequence.

Lattice strain vs. sample strain data (symbols) for the four deformation se... Open Access

Published: 01 February 2019
Figure 2. Lattice strain vs. sample strain data (symbols) for the four deformation sequences. The lines show the self-consistent models calculated to match the data. The slip system activity is plotted below each. The slip systems included in each group are listed in Table 2 . The uncertainty
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Lattice strain vs. sample strain for experiments Fay_33 (682 °C) and Fay_37 (26 °C). Compression produces a decrease in the lattice spacing and negative lattice strain. Lattice strains in the transverse direction (measured at ψ = 90°) are positive. For Fay_37 negative values plotted with larger symbols are for diffraction measured at ψ = 180°, smaller symbols indicate diffraction measured at ψ = 0°. For Fay_33 the average of the values measured at ψ = 180° and ψ = 0° are plotted. For reference, the gray band indicates the self-consistent elastic slope for all reflections plotted. Variations between individual reflections as well as the difference between the high-temperature and room-temperature slope, fit within the thickness of the band.

Lattice strain vs. sample strain for experiments Fay_33 (682 °C) and Fay_37... Open Access

Published: 01 July 2015
Figure 3 Lattice strain vs. sample strain for experiments Fay_33 (682 °C) and Fay_37 (26 °C). Compression produces a decrease in the lattice spacing and negative lattice strain. Lattice strains in the transverse direction (measured at ψ = 90°) are positive. For Fay_37 negative values plotted
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EPSC simulation of lattice strain vs. sample strain for the operation of the {110}[001] slip system. Compression produces a decrease in the lattice spacing and negative lattice strain. Lattice strains in the transverse direction are positive. The onset of plastic deformation begins at −0.023 strain. The model was calculated with 900 steps; for clarity, only selected points are plotted.

EPSC simulation of lattice strain vs. sample strain for the operation of th... Open Access

Published: 01 July 2015
Figure 4 EPSC simulation of lattice strain vs. sample strain for the operation of the {110}[001] slip system. Compression produces a decrease in the lattice spacing and negative lattice strain. Lattice strains in the transverse direction are positive. The onset of plastic deformation begins
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Lattice strain at 14% sample strain for EPSC simulations of the operation of individual olivine slip systems as well as a purely elastic simulation and the simulation of the kink band formation. Since the (001)[100] and (100)[001] slip systems have identical Schmidt factors, they are plotted together.

Lattice strain at 14% sample strain for EPSC simulations of the operation o... Open Access

Published: 01 July 2015
Figure 5 Lattice strain at 14% sample strain for EPSC simulations of the operation of individual olivine slip systems as well as a purely elastic simulation and the simulation of the kink band formation. Since the (001)[100] and (100)[001] slip systems have identical Schmidt factors
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Lattice strain at 14% sample strain for EPSC simulations of the operation of various slip systems. Note that as more slip systems are added to the simulation, the level of lattice strain for all reflections declines.

Lattice strain at 14% sample strain for EPSC simulations of the operation o... Open Access

Published: 01 July 2015
Figure 7 Lattice strain at 14% sample strain for EPSC simulations of the operation of various slip systems. Note that as more slip systems are added to the simulation, the level of lattice strain for all reflections declines.
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Lattice strain model fits from experiments. (a) REE3+ partition coefficients with lattice strain models from apatite in all individual experiment data of monovalent [VI]REE3+ from this study (black circles), compared with data reported from basanite and tholeiitic andesite by Watson and Green (1981). Note that Ce is included in the model data set because partitioning data indicates no influence from Ce4+ over the observed experimental conditions. Error bars reported in 1σ or where absent smaller than symbols. (b) REE3+ partition coefficients with lattice strain models from apatite four representative experiments using both EPMA (closed circles, dashed lattice strain curve) and LA-ICP-MS (open triangles, solid lattice strain curve) techniques. Note the two techniques record similar partitioning values, similar error and similar lattice strain model topology. (c) Lattice strain fits from experiments containing coexisting apatite and merrillite (ApREE-01a and ApREE-04), showing relative REE3+ partitioning among the two phosphate phases coexisting with basalt (diamonds correspond to merrillite and circles correspond to apatite). Note data obtained from EPMA, while merrillite ionic radii correspond to 8-coordinated sites of the dominant Ca sites within the mineral with elements in the Figure including La, Ce, Sm, Gd, and Lu (from right to left). (d) REE3+ partition coefficients with lattice strain models from merrillite based on EPMA (including experiments ApREE-01a and ApREE-04, solid circles, dashed curves) and LA-ICP-MS (experiment ApREE-03a, open triangles, solid curve). Note that though the two techniques show similar topology and error, though direct comparison of data are not possible.

Lattice strain model fits from experiments. ( a ) REE 3+ partition coeffic... Available to Purchase

Published: 01 May 2023
Figure 11. Lattice strain model fits from experiments. ( a ) REE 3+ partition coefficients with lattice strain models from apatite in all individual experiment data of monovalent [VI] REE 3+ from this study (black circles), compared with data reported from basanite and tholeiitic andesite
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(a) Comparison of (Eu/Eu*) in apatite as determined by lattice strain [i.e., (Eu/Eu*)Dlattice strain] vs. (Eu/Eu*) as determined by the concentration of neighboring REEs Sm-Gd [i.e., (Eu/Eu*)DSm-Gd]. Open symbols represent LAICP-MS data and closed symbols represent EPMA data. (b) Comparison of (Eu/Eu*) as determined by neighboring REEs Sm-Gd vs. Eu/ΣEu determined from XANES for experiments where both analytical techniques have been applied. (c) Comparison of REE concentration reported in REE2O3 (including La2O3, Ce2O3, Sm2O3, Eu2O3, Gd2O3, Lu2O3) analyses from glass as determined by LA-ICP-MS and EPMA. (d) Comparison of REE2O3 analyses (same elemental oxides as listed in Fig. 15c) from apatite grains within an individual experiment as determined by LA-ICP-MS and EPMA. Error bars represent 1σ. Note: dashed curves in graphs (a and d) represent 1:1 curve across the two analytical techniques being compared (i.e., EPMA vs. LA-ICP-MS, etc.).

( a ) Comparison of (Eu/Eu*) in apatite as determined by lattice strain [i.... Available to Purchase

Published: 01 May 2023
Figure 14. ( a ) Comparison of (Eu/Eu*) in apatite as determined by lattice strain [i.e., ( Eu/ Eu* ) D lattice strain ] vs. (Eu/Eu*) as determined by the concentration of neighboring REEs Sm-Gd [i.e., ( Eu/ Eu* ) D Sm-Gd ]. Open symbols represent LAICP-MS
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Lattice strain models illustrating “1-site” (a and b) and “2-site” (c and d) fits to partitioning data. Effective ionic radii taken from Shannon (1976) based on a coordination number of 8. Partition coefficients for Mn and Eu were omitted from parabola fitting. Note that “1-site” fits to data underestimate Ba partition coefficients by approximately an order of magnitude and fail to explain the increase in partition coefficient between Ce and La.

Lattice strain models illustrating “1-site” ( a and b ) and “2-site” ( c ... Available to Purchase

Published: 01 March 2023
Figure 6. Lattice strain models illustrating “1-site” ( a and b ) and “2-site” ( c and d ) fits to partitioning data. Effective ionic radii taken from Shannon (1976) based on a coordination number of 8. Partition coefficients for Mn and Eu were omitted from parabola fitting. Note that “1
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Comparison of experimental partition coefficients with a lattice strain model (LSM) based on average values for E and r0 (see text). Except for four experiments, the measured ratios of DSrAnh−Sil/DCaAnh−Sil (a) all agree closely with those predicted (0.63–0.53 at 1200–800 °C) by the model. Four anomalous points in a are likely a result of changes to melt CaO content during anhydrite crystallization, and lack of sufficient re-equilibration between early-grown anhydrite and silicate melt in low-temperature experiments. Ratios of DLuAnh−Sil/DLaAnh−Sil also agree closely with the lattice strain model (b). Uncertainties are 1 s.d. (Color online.)

Comparison of experimental partition coefficients with a lattice strain mod... Available to Purchase

Published: 01 March 2023
Figure 7. Comparison of experimental partition coefficients with a lattice strain model (LSM) based on average values for E and r 0 (see text). Except for four experiments, the measured ratios of D Sr A n h − S i l / D Ca A n h − S i l ( a ) all agree
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Site parameters and estimated Youngs moduli for lattice strain calculations... Open Access

Published: 01 February 2020
Table 6. Site parameters and estimated Youngs moduli for lattice strain calculations. Site CN Element Z r 0 (Å) d (Å) a d – 1.38 (Å) b Z / d 3 E (Gpa) c Mineral d Reference N 4 IX Na 1 1.24 2.65 1.27 0.054 80 Eudialyte Johnsen
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Projected chondrite-normalised REE patterns based on lattice strain partitioning models for eudialyte s.s. and oneillite-subgroup variations on the M1 site, as shown in Fig. 8 and 9. Note that melt compositions and absolute partitioning coefficients are unknown, and so the patterns are purely theoretical. Typical REE patterns for eudialyte-group minerals observed in nature are slightly LREE enriched with flat HREE patterns, with or without Eu anomalies. Europium anomalies are neglected in projected patterns, and depend on parental melt signatures (Schilling et al., 2011).

Projected chondrite-normalised REE patterns based on lattice strain parti... Open Access

Published: 01 February 2020
Fig. 10. Projected chondrite-normalised REE patterns based on lattice strain partitioning models for eudialyte s.s . and oneillite-subgroup variations on the M 1 site, as shown in Fig. 8 and 9 . Note that melt compositions and absolute partitioning coefficients are unknown, and so
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PARAMETERS OF THE LATTICE-STRAIN MODEL OBTAINED BY FITTING THE EXPERIMENTAL... Available to Purchase

Published: 30 May 2018
TABLE 4. PARAMETERS OF THE LATTICE-STRAIN MODEL OBTAINED BY FITTING THE EXPERIMENTAL DATA AND VALUES CALCULATED WITH THE WOOD & BLUNDY (1997) EQUATIONS
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Finite lattice strain (rectangular plots) and orientation (semi-circular plots) of principal strain axes of C2/c LiM1Me3+Si2O6 pyroxenes, plus two P21/cM1Ni and M1Cr reported as empty symbols, induced by chemical substitution (left column of graphs), temperature and pressure (middle and right columns of graphs). The lattice strain induced by the ideal substitution was calculated from M2LiM1AlSi2O6 to LiM1Me3+Si2O6, where Me is a progressive large cation, i.e., M1Al vs. M1In; cell parameters of Li(Al,Fe3+)Si2O6 are from this study, LiNiSi2O6 from Tribaudino et al. (2009), LiTiSi2O6 from Kopnin et al. (2003), Li(Cr,Ga,V,Sc,In)Si2O6 from Redhammer and Roth (2004a). Cell parameters of LiAlSi2O6 and LiFe3+Si2O6 at high-T are from Cameron et al. (1973) and Redhammer et al. (2001), respectively. Cell parameters of LiAlSi2O6 at high-P are from Arlt and Angel (2000). (Color online.)

Finite lattice strain (rectangular plots) and orientation (semi-circular pl... Available to Purchase

Published: 01 November 2016
Figure 8 Finite lattice strain (rectangular plots) and orientation (semi-circular plots) of principal strain axes of C 2/ c Li M1 Me 3+ Si 2 O 6 pyroxenes, plus two P 2 1 / c M1 Ni and M1 Cr reported as empty symbols, induced by chemical substitution (left column of graphs), temperature