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![First thumbnail for: Temperature-dependent absorption of biotite: small...]()
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![Sketch of a polaron formed due to a direct transition across the energy gap Eg in M(1,2,3)Fe-bearing amphiboles (a) and of polaron hopping along the TO4-MO6 strips (b). The crystallographic-axes compass refers to C2/m. The dipole moment of the polaron, represented by the thick arrow in a, is parallel to the I-beam because it arises from an electronic transition between hybridized orbitals of Fe and O within a plane perpendicular to the c axis, which couples with a phonon having polarity along the c axis (see Mihailova et al. 2021). (Color online.)]()
![Schematic illustration of polaron dynamics in silicate glasses, with the structural units depicted based on the melt polymerization (O2− coordination) model of Hess (1980). M is a divalent network-modifying cation; M–h· is a trivalent network-modifying cation. (a) Formation of a polaron in a transition metal-bearing silicate glass via oxidation: (1) unreacted glass; (2) formation of a polaron as two divalent network-modifiers become trivalent network-modifiers as atmospheric oxygen accepts two electrons. The structural distortion so created follows the migration of the h·. (b) Migration of a polaron, and the associated (counter) motion of the network-modifying cation, in a transition metal-bearing silicate glass.]()
![(a) Arrhenius diagram showing H+ diffusion rates in clinopyroxene [Jaipur diopside for the proton-polaron mechanism (Woods et al. 2000; Ferriss et al. 2016) and synthetic diopside for the proton vacancy mechanism (Sundvall et al. 2009)] and orthopyroxene [Kilbourne Hole enstatite for the proton-polaron mechanism (Stalder and Skogby 2003) and synthetic enstatite for the proton-vacancy mechanism (Stalder and Behrens 2006)] overlaid on the olivine mechanisms (Mackwell and Kohlstedt 1990; Demouchy and Mackwell 2006; Ferriss et al. 2018). Olivine DFeMg is shown for comparison (Dohmen and Chakraborty 2007a, 2007b). Isotropic data (or experimental data sets where only one crystallographic axis has an Arrhenius relationship constrained) have one line, while anisotropic diffusivities have multiple lines for different crystallographic axes. Experimental constraints between 700–1000 °C (shown at the top of the figure) were used to extrapolate using the log-linear Arrhenius relationships. (b) Clinopyroxene proton-polaron and (c) orthopyroxene proton-polaron Arrhenius relationships are shown with 95% confidence interval error envelopes (shaded fields) calculated from experimental data. (Color online.)]()
![First thumbnail for: The effect of A-site cations on charge-carrier mob...]()
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![Model results for proton-polaron diffusion mechanisms (squares) compared to possible proton-vacancy diffusion mechanisms (diamonds) for 1 and 3 mm pyroxene models. Proton-polaron models (square symbols) are as shown in Figure 5. Models representing the proton-vacancy mechanism utilize Sundvall et al. (2009) (purple diamonds) for Cpx and Stalder and Behrens (2006) (red symbols) for Opx. Legend abbreviations are: F16 = Ferriss et al. 2016; S09 = Sundvall et al. 2009; S03 = Stalder and Skogby 2003; S06 = Stalder and Behrens 2006. (Color online.)]()
![(a) Arrhenius diagram showing H+ diffusion rates in olivine for the proton polaron mechanism [solid gray lines = Mackwell and Kohlstedt (1990)], proton vacancy mechanism [dashed gray lines = Demouchy and Mackwell (2006)], and total H+ diffusion [green lines = Ferriss et al. (2018)]. Olivine DFeMg (yellow region) is shown for comparison (Dohmen and Chakraborty 2007a, 2007b). Anisotropic diffusivities are labeled for each principal crystallographic axis. Experimental constraints between 800–1000 °C (shown at the top of the figure) were used to extrapolate using the log-linear Arrhenius relationships. Uncertainties associated with this extrapolation are represented by 95% confidence interval error envelopes (shaded fields) calculated from experimental data for the (b) proton vacancy mechanism, (c) proton polaron mechanism, and (d) “total” H diffusion. (Color online.)]()
![First thumbnail for: Bond-length fluctuation in the orthorhombic 3 × 3 ...]()
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![A scheme of small polaron around Mg sites. The lattice is locally distorted by excess charge of FeMg•, which attract anions and repulse cations.]()
![Modeled diffusion durations (log time, minutes) for 100% re-equilibration of 1 and 3 mm grains from 600–1000 °C. Results reflect both low-H and high-H models, as the 100% re-equilibration timescales are insensitive to the choice of boundary condition. Clinopyroxene (purple squares) and orthopyroxene (red squares) proton-polaron models utilize Fe-bearing diffusivities (Woods et al. 2000; Ferriss et al. 2016; Stalder and Skogby 2003). Three olivine models are shown: the fast proton polaron mechanism (ol PP = dark gray circles; Mackwell and Kohlstedt 1990), the slower proton vacancy mechanism (ol PV = light gray circles; Demouchy and Mackwell 2006), and the intermediate total H+ diffusion expression (ol tot = green circles; Ferriss et al. 2018). Upper and lower bounds of error envelopes calculated for experimental data are represented by the lines and reflect the potential uncertainty in the modeled re-equilibration timescale. (Color online.)]()
![Calculated absorption spectra for photon-assisted hopping (PAH) of small polarons using Equation (4) with parameter values as given in the text and temperatures as denoted compared to the spectrum at 293 K for Miask biotite (a) and difference spectra as described (b).]()
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![Evolution of polaron diffusivities determined from equation (15), DhXFe, for various iron contents: grey lines. Full square: effective diffusivity of a reaction involving metal vacancies (Guillaumou et al. 1999; Ingrin and Skogby 2000). Other symbols are the same as in Figure 13.]()
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![First thumbnail for: Electrical conductivity of diaspore, δ-AlOOH and ε...]()
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![1D transects with diffusion time from the Cpx proton-polaron high-H boundary condition model for a 3 mm diameter grain at 1200 °C. These 1D traverses were extracted parallel to the b-axis in the ideal 2D section shown in Figure 3. After only 1.25 min of diffusion, the core composition shows a factor of two increase in water content and is 40% re-equilibrated with the boundary condition. After ~3 min, the core concentration has reached 99% re-equilibration, which is the effective %re-equilibration (indicated by the dashed line at 99) where distinguishing zoning profiles between the core and rim of the crystal becomes difficult due to error on typical NAM water measurements (see discussion in Online Material1). If analytical precision is even poorer (e.g., 10% error), zoning profiles are only resolvable until 86% reequilibration (dashed line at 86). For this high-H boundary condition, the 1% uncertainty is 7.5 ppm and the 10% uncertainty is 75 ppm (Table 1).]()
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Journal Article
Temperature-dependent absorption of biotite: small-polaron hopping and other fundamental electronic excitations Available to Purchase
Journal: European Journal of Mineralogy
Publisher: GeoScienceWorld Journals
Published: 01 September 2012
European Journal of Mineralogy (2012) 24 (5): 817–822.
...Claus H. Rüscher Abstract Temperature-dependent absorption investigations between 10 and 823 K reveal photon-assisted hopping (PAH) of small polarons in biotites as the dominating excitation in the near-infrared spectral range. These data show a transfer of oscillator strength of the PAH of small...
FIGURES
Image
Sketch of a polaron formed due to a direct transition across the energy gap... Available to Purchase
in The effect of A-site cations on charge-carrier mobility in Fe-rich amphiboles
> American Mineralogist
Published: 01 September 2024
Figure 2. Sketch of a polaron formed due to a direct transition across the energy gap E g in M (1,2,3) Fe-bearing amphiboles ( a ) and of polaron hopping along the T O 4 - M O 6 strips ( b ). The crystallographic-axes compass refers to C 2/ m . The dipole moment of the polaron, represented
Image
Schematic illustration of polaron dynamics in silicate glasses, with the st... Available to Purchase
in Iron concentration and the physical processes of dynamic oxidation in an alkaline earth aluminosilicate glass
> American Mineralogist
Published: 01 March 2000
F igure 3. Schematic illustration of polaron dynamics in silicate glasses, with the structural units depicted based on the melt polymerization (O 2− coordination) model of Hess (1980) . M is a divalent network-modifying cation; M–h · is a trivalent network-modifying cation. ( a ) Formation
Image
![(a) Arrhenius diagram showing H+ diffusion rates in clinopyroxene [Jaipur diopside for the proton-polaron mechanism (Woods et al. 2000; Ferriss et al. 2016) and synthetic diopside for the proton vacancy mechanism (Sundvall et al. 2009)] and orthopyroxene [Kilbourne Hole enstatite for the proton-polaron mechanism (Stalder and Skogby 2003) and synthetic enstatite for the proton-vacancy mechanism (Stalder and Behrens 2006)] overlaid on the olivine mechanisms (Mackwell and Kohlstedt 1990; Demouchy and Mackwell 2006; Ferriss et al. 2018). Olivine DFeMg is shown for comparison (Dohmen and Chakraborty 2007a, 2007b). Isotropic data (or experimental data sets where only one crystallographic axis has an Arrhenius relationship constrained) have one line, while anisotropic diffusivities have multiple lines for different crystallographic axes. Experimental constraints between 700–1000 °C (shown at the top of the figure) were used to extrapolate using the log-linear Arrhenius relationships. (b) Clinopyroxene proton-polaron and (c) orthopyroxene proton-polaron Arrhenius relationships are shown with 95% confidence interval error envelopes (shaded fields) calculated from experimental data. (Color online.)](https://gsw.silverchair-cdn.com/gsw/Content_public/Journal/ammin/106/5/10.2138_am-2021-7435/1/s_am-2021-7435_fig02.png?Expires=2147483647&Signature=CeaMXwvNj7FgCecUxWFBxbgf32YERLbHF4DukVMFSrqjkDJlCKFZAGy8uO9T0aK~jQ9APYGP5PPbYX2AWBHapa0Ak5kHF-pwH-39azTtjBQp95~Us-LiQPUUrCNwZnPAqmndokBNsZTmLKvuYwmM26-XT-Q6DUjl9kdGmqLnBCMsHdo1Pgi7MPM3tvmU8OccTLME7E3nfS0JfjHsAupFpQ6FTrjmvAQe2Pa~elIr0CYveE05tFQyyX6SoSVE9FoeBIFLsRHfxabRtZaHJDdlguTHS-9~~dUgaJlvQO-YGJ44thWfLb7WpRkxSSWdYD-dKDHECtablbvaYCgZrJudTQ__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
( a ) Arrhenius diagram showing H + diffusion rates in clinopyroxene [Jaip... Available to Purchase
in The potential for aqueous fluid-rock and silicate melt-rock interactions to re-equilibrate hydrogen in peridotite nominally anhydrous minerals
> American Mineralogist
Published: 01 May 2021
Figure 2. ( a ) Arrhenius diagram showing H + diffusion rates in clinopyroxene [Jaipur diopside for the proton-polaron mechanism ( Woods et al. 2000 ; Ferriss et al. 2016 ) and synthetic diopside for the proton vacancy mechanism ( Sundvall et al. 2009 )] and orthopyroxene [Kilbourne Hole
Journal Article
The effect of A-site cations on charge-carrier mobility in Fe-rich amphiboles Available to Purchase
Journal: American Mineralogist
Publisher: Mineralogical Society of America
Published: 01 September 2024
American Mineralogist (2024) 109 (9): 1545–1553.
...Figure 2. Sketch of a polaron formed due to a direct transition across the energy gap E g in M (1,2,3) Fe-bearing amphiboles ( a ) and of polaron hopping along the T O 4 - M O 6 strips ( b ). The crystallographic-axes compass refers to C 2/ m . The dipole moment of the polaron, represented...
FIGURES
Includes: Supplemental Content
Image
Model results for proton-polaron diffusion mechanisms (squares) compared to... Available to Purchase
in The potential for aqueous fluid-rock and silicate melt-rock interactions to re-equilibrate hydrogen in peridotite nominally anhydrous minerals
> American Mineralogist
Published: 01 May 2021
Figure 6. Model results for proton-polaron diffusion mechanisms (squares) compared to possible proton-vacancy diffusion mechanisms (diamonds) for 1 and 3 mm pyroxene models. Proton-polaron models (square symbols) are as shown in Figure 5 . Models representing the proton-vacancy mechanism utilize
Image
![(a) Arrhenius diagram showing H+ diffusion rates in olivine for the proton polaron mechanism [solid gray lines = Mackwell and Kohlstedt (1990)], proton vacancy mechanism [dashed gray lines = Demouchy and Mackwell (2006)], and total H+ diffusion [green lines = Ferriss et al. (2018)]. Olivine DFeMg (yellow region) is shown for comparison (Dohmen and Chakraborty 2007a, 2007b). Anisotropic diffusivities are labeled for each principal crystallographic axis. Experimental constraints between 800–1000 °C (shown at the top of the figure) were used to extrapolate using the log-linear Arrhenius relationships. Uncertainties associated with this extrapolation are represented by 95% confidence interval error envelopes (shaded fields) calculated from experimental data for the (b) proton vacancy mechanism, (c) proton polaron mechanism, and (d) “total” H diffusion. (Color online.)](https://gsw.silverchair-cdn.com/gsw/Content_public/Journal/ammin/106/5/10.2138_am-2021-7435/1/s_am-2021-7435_fig01.png?Expires=2147483647&Signature=nz2~-ldUPn0Vypq0sk4pKoAPgk8CVfMcsFiUBkcbQo72--TWVnQIy-EsmeVrjw-wngDEz9hWmvWEGpI9d0OPTDMkVv5tJ~QzlGF1P0W5HN63PtrTwhN9XKNe~x6vn7wrOTIK7L8AQmiw8CMGHSuiMU~e0KeGVFXdDefPeOsFBgxMCvGopcksiV4z835ab9KOPl9fflICdIY2y9u3yv0lmx7pybmmqty~jW~e8fwKIHX0G3KDFLQPXzpCkgdOYWXPle44aO1~LLgAtsuGTMmhTH917pK3hyeMzTFHC~zAgVm5EVMESC9p7iqpbFx5TvLjUUEONFEvceFJrbRwTg46fQ__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
( a ) Arrhenius diagram showing H + diffusion rates in olivine for the pro... Available to Purchase
in The potential for aqueous fluid-rock and silicate melt-rock interactions to re-equilibrate hydrogen in peridotite nominally anhydrous minerals
> American Mineralogist
Published: 01 May 2021
Figure 1. ( a ) Arrhenius diagram showing H + diffusion rates in olivine for the proton polaron mechanism [solid gray lines = Mackwell and Kohlstedt (1990) ], proton vacancy mechanism [dashed gray lines = Demouchy and Mackwell (2006) ], and total H + diffusion [green lines = Ferriss et al
Journal Article
Bond-length fluctuation in the orthorhombic 3 × 3 × 1 superstructure of LiMn 2 O 4 spinel Open Access
Journal: American Mineralogist
Publisher: Mineralogical Society of America
Published: 01 August 2014
American Mineralogist (2014) 99 (8-9): 1528–1536.
... are assumed to exchange their oxidation states dynamically between 3+ and 4+ in a time ratio of ~3:1, forming a polaron centered at a Mn 4 O 4 heterocubane cluster with orbital and spin orders. The high-temperature cubic form contains an inherent positional disordering of oxygen ions. The effect...
FIGURES
Image
A scheme of small polaron around Mg sites. The lattice is locally distorted... Available to Purchase
in Electrical conductivity of the major upper mantle minerals: a review
> Russian Geology and Geophysics
Published: 01 December 2009
Fig. 2. A scheme of small polaron around Mg sites. The lattice is locally distorted by excess charge of Fe Mg • , which attract anions and repulse cations.
Image
Modeled diffusion durations (log time, minutes) for 100% re-equilibration o... Available to Purchase
in The potential for aqueous fluid-rock and silicate melt-rock interactions to re-equilibrate hydrogen in peridotite nominally anhydrous minerals
> American Mineralogist
Published: 01 May 2021
) and orthopyroxene (red squares) proton-polaron models utilize Fe-bearing diffusivities ( Woods et al. 2000 ; Ferriss et al. 2016 ; Stalder and Skogby 2003 ). Three olivine models are shown: the fast proton polaron mechanism (ol PP = dark gray circles; Mackwell and Kohlstedt 1990 ), the slower proton vacancy
Image
Calculated absorption spectra for photon-assisted hopping (PAH) of small po... Available to Purchase
in Temperature-dependent absorption of biotite: small-polaron hopping and other fundamental electronic excitations
> European Journal of Mineralogy
Published: 01 September 2012
Fig. 4 Calculated absorption spectra for photon-assisted hopping (PAH) of small polarons using Equation (4) with parameter values as given in the text and temperatures as denoted compared to the spectrum at 293 K for Miask biotite (a) and difference spectra as described (b).
Journal Article
Reduced charge transfer in mixed-spin ferropericlase inferred from its high-pressure refractive index Available to Purchase
Journal: American Mineralogist
Publisher: Mineralogical Society of America
Published: 01 July 2024
American Mineralogist (2024) 109 (7): 1145–1152.
... that charge transport by small polaron is reduced in mixed-spin ferropericlase, providing fundamental insights into the factor-of-three lower electrical conductivity of ferropericlase at ~50–70 GPa. All high-pressure experiments were performed using symmetrical DACs equipped with diamond pairs featuring...
FIGURES
Includes: Supplemental Content
Journal Article
The potential for aqueous fluid-rock and silicate melt-rock interactions to re-equilibrate hydrogen in peridotite nominally anhydrous minerals Available to Purchase
Journal: American Mineralogist
Publisher: Mineralogical Society of America
Published: 01 May 2021
American Mineralogist (2021) 106 (5): 701–714.
...Figure 2. ( a ) Arrhenius diagram showing H + diffusion rates in clinopyroxene [Jaipur diopside for the proton-polaron mechanism ( Woods et al. 2000 ; Ferriss et al. 2016 ) and synthetic diopside for the proton vacancy mechanism ( Sundvall et al. 2009 )] and orthopyroxene [Kilbourne Hole...
FIGURES
Image
Evolution of polaron diffusivities determined from equation (15), D h ... Available to Purchase
Published: 01 January 2006
Figure 14. Evolution of polaron diffusivities determined from equation (15), D h X Fe , for various iron contents: grey lines. Full square: effective diffusivity of a reaction involving metal vacancies ( Guillaumou et al. 1999 ; Ingrin and Skogby 2000 ). Other symbols are the same
Journal Article
High-pressure electrical conductivity and elasticity of iron-bearing δ-AlOOH Available to Purchase
Journal: American Mineralogist
Publisher: Mineralogical Society of America
Published: 01 May 2023
American Mineralogist (2023) 108 (5): 950–958.
..., suggesting that both small polaron and proton conduction mechanisms dominate in iron-bearing δ-AlOOH. Furthermore, the high-pressure electrical conductivity profiles are comparable between δ-(Al 0.95 Fe 0.05 )OOH and δ-(Al 0.52 Fe 0.48 )OOH, indicating that high-iron content only marginally influences...
FIGURES
Journal Article
Electrical conductivity of diaspore, δ-AlOOH and ε-FeOOH Available to Purchase
Journal: American Mineralogist
Publisher: Mineralogical Society of America
Published: 01 May 2021
American Mineralogist (2021) 106 (5): 774–781.
... pressure could enhance the proton migration by reducing the potential barrier, thereby raising the electrical conductivity. Small polaron conduction may contribute to the conductivity of ε-FeOOH to generate higher conductivity than δ-AlOOH. Furthermore, hydrogen bond symmetrization will also play...
FIGURES
Journal Article
Radiation-induced defects in montebrasite: An electron paramagnetic resonance study of O – hole and Ti 3+ electron centers Available to Purchase
Journal: American Mineralogist
Publisher: Mineralogical Society of America
Published: 01 July 2020
American Mineralogist (2020) 105 (7): 1051–1059.
..., quartz, and tourmaline. The color centers in these minerals are often related to O − hole centers, where the color is produced by bound small polarons inducing absorption bands in the near UV to the visible spectral range. In this work, colorless montebrasite specimens from Minas Gerais state, Brazil...
FIGURES
Image
1D transects with diffusion time from the Cpx proton-polaron high-H boundar... Available to Purchase
in The potential for aqueous fluid-rock and silicate melt-rock interactions to re-equilibrate hydrogen in peridotite nominally anhydrous minerals
> American Mineralogist
Published: 01 May 2021
Figure 8. 1D transects with diffusion time from the Cpx proton-polaron high-H boundary condition model for a 3 mm diameter grain at 1200 °C. These 1D traverses were extracted parallel to the b -axis in the ideal 2D section shown in Figure 3 . After only 1.25 min of diffusion, the core
Journal Article
Electrical conductivity of hydrous wadsleyite Available to Purchase
Journal: European Journal of Mineralogy
Publisher: GeoScienceWorld Journals
Published: 01 June 2009
European Journal of Mineralogy (2009) 21 (3): 615–622.
... in wadsleyite the electrical conductivity increases at a rate higher than observed in previous studies. The activation enthalpy in the temperature range studied where proton conduction dominates is low (0.66 eV) suggesting an inevitable crossover to small polaron conduction at moderately higher temperatures...
FIGURES
Journal Article
The electrical conductivity of dry polycrystalline olivine compacts at high temperatures and pressures Available to Purchase
Journal: Mineralogical Magazine
Published: 01 October 2010
Mineralogical Magazine (2010) 74 (5): 849–857.
... and oxygen fugacity can be described as log 10 (σ) = (2.47±0.085) + (0.096±0.023)×log 10 f O 2 +(−0.55±0.011)/ T , which presents the exponential factor q (∼0.096). Our observations demonstrate that the primary conduction mechanism for polycrystalline olivine compacts is a small polaron. A large body...
FIGURES
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