Anharmonic Parameters Research Articles

Equilibrium oxygen isotope fractionation in Mg(OH)2-Ca(OH)2-H2O: Implication from in situ high-temperature and high-pressure vibrational spectra

Abstract Equilibrium oxygen isotope fractionations have been extensively studied between H2O and minerals (like brucite-type hydroxides) in isotope geochemistry. In this study, pure 18O-enriched hydroxides were synthesized through reactions between M3N2 (M = Mg and Ca) powders and H218O water. In situ high-temperature (T) and high-pressure (P) Raman and Fourier transform infrared (FTIR) spectra were systematically collected for these phases. The observed 18O-16O effect on the frequency shifts aligns with the theoretical model, and has little impact on the anharmonic O-H potential well. The calculated intrinsic anharmonic parameters (ai) for both lattice and OH-stretching modes are essentially identical between M(16OH)2 and M(18OH)2, satisfying the classical limit for the Helmholtz free energy at extremely high temperature. Based on the measured vibrational data, the equilibrium oxygen isotope fractionation β(T,P) factors were modeled for both hydroxides. Both the intrinsic and external anharmonic contributions are smaller than the experimental uncertainties, and this model is also validated by ab initio calculation. Next, the 103·lnα(T) profiles were computed between brucite/portlandite and H2O, which are consistent with the reported oxygen isotope exchange measurements above 200 °C. Additionally, the discrepancy between this equilibrium model and the precipitation experiment below 120 °C also provides useful information for investigating the mechanism of kinetic isotope fractionation. The predicted 103·lnαbrucite-portlandite(T) curve also agrees well with points inferred from the 18O-16O exchange measurements, while the pressure effect can be ignored for 18O-16O fractionations. Therefore, vibrational spectroscopic measurements, including both Raman and infrared spectroscopies, have valuable applications in studying equilibrium non-metallic isotope fractionations in minerals.

Nonlinear rheological behavior of glass-forming colloidal suspensions under oscillatory shear: Experiment and relation to mode coupling theory predictions

Glass-forming colloids consisting of soft core-shell particles were investigated experimentally under medium and large amplitude oscillatory shear (MAOS and LAOS) using Fourier transform rheology to decompose the stress signal into a series of higher harmonics. The anharmonicity of the stress response under MAOS and LAOS is quantified by the intensity of the third harmonic normalized to the fundamental (I3/1=I3/I1) and within the intrinsic nonlinearity framework of the Q-parameter (Q0=limγ0→0⁡(I3/1/γ02)). Furthermore, the results of the strain amplitude dependence were compared to the literature showing the mechanical anharmonic behavior of the core-shell system being close to the behavior of ultrasoft systems. In the glassy state, I3/1 shows an unusual scaling of I3/1∝γ04 at low frequencies, similar to amorphous polymeric materials when they undergo plastic deformation. For investigating the frequency dependence of the anharmonicity in a specially designed binary mixture to test for critical behavior close to the glass transition as predicted by mode coupling theory (MCT) and extend the measurements to the glassy state, we used the frequency sweep MAOS methodology. Using this time-efficient method, the frequency dependence of a wide range of volume fractions and frequencies was investigated, finding the anharmonicity parameter Q0 to be maximal in the region of the α-relaxation for colloidal liquids. The colloidal glasses do not exhibit a maximum in Q0, but an increase in Q0 with decreasing frequency over the investigated region, as the α-relaxation slows down significantly in colloidal glasses. Predictions from MCT from the literature show agreement with the experimentally determined scaling laws.

Composition effects on equilibrium oxygen isotope fractionation factors between garnets and quartz/calcite/olivine: Implication from vibration frequencies of garnets at high temperatures and high pressures

Garnet-group minerals, with their wide range of compositions, play a significant role in Earth's crust and upper mantle, participating in various petrological and geochemical processes. Oxygen isotope fractionation factors between garnets and other minerals hold crucial implications in these contexts. In this work, vibration frequencies were measured via Raman spectra on five garnet mineral samples in the pyrope-almandine-spessartine ternary system and four synthetic pyrope-grossular solid solutions at temperatures up to 1000 °C and pressures up to 17 GPa. Isobaric (γiP) and isothermal (γiT) mode Grüneisen, as well as anharmonic (ai) parameters, were determined for the observed modes. Our study shows that the vibration bands tend to shift to lower frequencies with increasing temperature and to higher frequencies with increasing pressure. Moreover, the anharmonic correction has been found to contribute positively to equilibrium oxygen isotope fractionation β factors in garnets, typically within 0.5 ‰ above 1000 K. The 103∙lnβ(T) factors calculated from vibration spectra (considering Г points only) align closely with those from theoretical calculations (including all frequencies in the Brillouin zone). Contributions from phonon dispersion (including none-Г points) are typically smaller than the uncertainties propagated from frequency measurements. Additionally, the pressure effect on the oxygen isotope fractionation in garnet, evaluated from the isothermal Grüneisen parameters, is found to be insignificant under crustal and upper mantle conditions, consistent with thermodynamic expectations. Using published oxygen isotope fractionation β factors for quartz and calcite, the equilibrium oxygen isotope fractionation factors (103∙lnα) are calculated between garnets of diverse compositions and any of these phases as functions of temperature, pressure and fraction of garnet endmembers. Considering composition effects helps to reduce the discrepancies among experimental and empirical calibrations of oxygen isotope fractionation factors between garnet and quartz. As an example application, oxygen isotope fractionation factors 103∙lnα(P, T) between garnets and forsterite were calculated under upper mantle conditions. Our findings suggest that these fractionation factors are predominantly dependent on temperature and garnet compositions, with minor influence from pressure. Compared with our calculated fractionation factors between garnet and olivine, the oxygen isotope exchange equilibrium may have been reached in some in kimberlite and mantle xenolith samples between garnet and olivine. However, in other samples, the fractionation factors cannot be explained solely by the composition effect, likely due to metasomatism. Our results underscore the importance of considering garnet compositions when interpreting their oxygen isotope compositions.

Investigation of anharmonic EXAFS parameters of Ag using anharmonic correlated Debye model under the effect of thermal disorders

The effect of thermal disorders on the anharmonic extended X-ray absorption fine structure (EXAFS) parameters of crystalline silver (Ag) has been investigated in the wavenumber and temperature dependencies. The calculation model is developed based on the correlated Debye model using the many-body perturbation (MBP) theory and anharmonic effective (AE) potential. The anharmonicity of the EXAFS signal is caused by the effect of thermal disorders and results from phonon-phonon interactions, with each thermal vibration being quantized and treated as a phonon. The considered EXAFS parameters include the first four cumulants, amplitude reduction, and phase shift of the anharmonic EXAFS signal. The obtained expressions are explicit and can satisfy all their temperature-dependent properties. The numerical results of Ag agree well with those obtained from the experimental data and other calculation models in the temperature range from 0 to 1000 K and the wavenumber range from 0 to 14.14 Å. The obtained results indicate the effectiveness of the present model in investigating the anharmonic EXAFS parameters of Ag from above zero point to near the melting point.

Influence of the relative stiffness of second-neighbor interactions on chaotic discrete breathers in a square lattice

It is known that the modulational instability of a delocalized nonlinear vibrational mode (DNVM) with frequency outside the phonon band can lead to spontaneous energy localization in a nonlinear lattice on chaotic discrete breathers (CDBs). Considering a β-FPUT square lattice with nearest and next-nearest interactions, the appearance of CDBs is analyzed for different stiffnesses of the first- and second-nearest interactions, k1 and k2, keeping the density of the lattice unchanged. There are two DNVMs in the square lattice with frequencies above the phonon spectrum and both are studied. The appearance of CDBs in the lattice is monitored by calculating the time evolution of the energy localization parameter L and the maximum energy of the particles emax. For solid state physics and materials science, the important range of stiffness parameters is k2<k1, since the stiffness of chemical bonds typically decreases with the distance between atoms. It is found that CDBs form in the square lattice when k2>k1/4. This means that they can form in crystals if the stiffness of the second-neighbor bonds is smaller than that of the first-neighbor bonds, but not too small. Depending on the relation between the anharmonicity parameters of the first- and second-neighbor bonds CDBs can have different polarization.

Slow dissipation and spreading in disordered classical systems: A direct comparison between numerics and mathematical bounds.

We study the breakdown of Anderson localization in the one-dimensional nonlinear Klein-Gordon chain, a prototypical example of a disordered classical many-body system. A series of numerical works indicate that an initially localized wave packet spreads polynomially in time, while analytical studies rather suggest a much slower spreading. Here, we focus on the decorrelation time in equilibrium. On the one hand, we provide a mathematical theorem establishing that this time is larger than any inverse power law in the effective anharmonicity parameter λ, and on the other hand our numerics show that it follows a power law for a broad range of values of λ. This numerical behavior is fully consistent with the power law observed numerically in spreading experiments, and we conclude that the state-of-the-art numerics may well be unable to capture the long-time behavior of such classical disordered systems.

The molecular structure and spectroscopic properties of formaldoxime (CH2NOH)

Formaldoxime (CH2NOH) belongs to the possible interstellar molecules. Its isomerization, spectroscopic properties as well as the potential for pumped laser action has long received a lot of attention. Herein, the benchmark database of the spectroscopic constants and anharmonic force fields has been achieved for trans- and cis- formaldoxime. Evaluation is done by using the coupled-cluster theory [CCSD(T)] and density functional theory (B3LYP and B2PLYP), and different basis sets [cc-pVTZ, aug-cc-pVTZ, 6-311+G**, 6-311++G (3df,3pd)] are utilized. The calculated spectroscopic constants commendably reproduce previous experimental results. Besides, a series of vital anharmonic parameters such as vibration-rotation interaction constants, etc, has been provided, which is used for the in-depth study of high-resolution rovibronic spectrum of formaldoxime.

Study of quantum Szilard engine for non-interacting bosons in fractional power-law potentials

Abstract In this article, we have realized the quantum Szilard engine (QZE) for non-interacting bosons. We have adopted the Bose-Einstein statistics for this purpose. We have considered fractional power law potential for this purpose and have used the artifact of the quantization of energy. We have calculated the work and the efficiency for non-interacting bosons in fractional power potential. We have shown the dependence of the number of particles for the work and the efficiency. We also have realized the QZE for a single-particle in a Morse potential revealing how the depth of the potential impacts both work and efficiency. Furthermore, we have examined the influence of temperature and the anharmonicity parameter on the work. Finally, we have conducted a comparative analysis, considering both non-interacting bosons in a fractional power law potential and a single-particle in a Morse potential under harmonic approximation conditions.

Rotational phase transitions in antifluorite-type osmate and iridate compounds

We present temperature-dependent single-crystal diffraction results on seven antifluorite-type A2MeX6 compounds with Me = Os or Ir: K2OsCl6, A 2OsBr6 with A = K, Rb, Cs and NH4, and K2IrX 6 with X = Cl and Br. The structural transitions in this family arise from MeX 6 octahedron rotations that generate a rich variety of symmetries depending on the rotation axis and stacking schemes. In order to search for local distortions in the high-symmetry phase we perform refinements of anharmonic atomic displacement parameters with comprehensive data sets. Even at temperatures close to the onset of structural distortions, these refinements only yield a small improvement indicating only small anharmonic effects. The phase transitions in these antifluorites are essentially of displacive character. However, some harmonic displacement parameters are very large reflecting soft phonon modes with the softening covering large parts of the Brillouin zone. The occurrence of the rotational transitions in the antifluorite-type family can be remarkably well analyzed in terms of a tolerance factor of ionic radii.

Compressibility, thermal expansion and Raman scattering of synthetic whitlockite Ca9Mg(PO3OH)(PO4)6 at high pressures and high temperatures

Abstract In-situ X-ray diffraction and 16 Raman scattering of synthetic whitlockite, Ca9Mg(PO3OH)(PO4)6, have been systematically measured at high pressures and high temperatures, respectively. The results show that whitlockite is stable up to ~ 15 GPa at ambient temperature and undergoes a temperature-induced dehydrogenation to merrillite above 973 K at ambient pressure. The obtained pressure-volume data were fitted using a third-order Birch-Murnaghan equation of state to yield the isothermal bulk modulus as K0 = 79(4) GPa with pressure derivative K0' = 4.3(6). When K0' was fixed at 4, the refined isothermal bulk modulus was 81(1) GPa. The volumetric thermal expansion coefficient (αV) is equal to 4.05(8) × 10-5 K-1. The axial thermal expansion coefficients (αa and αc) are 1.07(5) × 10-5 K-1 and 1.91(6) × 10-5 K-1. Both compressibility and thermal expansion show an axial anisotropy. The effects of pressure and temperature on the Raman spectra of whitlockite have been quantitatively analyzed. The isothermal and isobaric mode Grüneisen parameters, and the intrinsic anharmonic mode parameters of whitlockite were calculated. Some amounts of OH--bearing whitlockite may be preserved and could be discovered in meteorites if whitlockite undergoes a low temperature process.

Lone-pair electron-induced low lattice thermal conductivity and excellent thermoelectric performance of AuX (X = S, Se, Te) monolayers

We present a detailed study on the phonon thermal transport and thermoelectric (TE) properties of gold monochalcogenide AuX (X = S, Se, Te) monolayers via first-principles calculations and the Boltzmann transport theory. At room temperature, the calculated lattice thermal conductivity (κl) values in the x-direction (y-direction) were determined to be 12.66 (3.59), 6.06 (1.23), and 3.02 (0.40) W/(m·K) for the AuS, AuSe, and AuTe monolayers, respectively. The analysis of scattering matrix elements and anharmonic scattering rates suggested that the presence of strong bond anharmonicity leads to low κl values. This anharmonicity was induced by the nonlinear electrostatic repulsive force between lone-pair electrons (LPEs) surrounding the chalcogen atom and adjacent bonding electron. Furthermore, the AuS monolayer exhibited the highest bond anharmonicity among the three monolayers. This can be attributed to the reduced strength of the electrostatic repulsive force when electronegativity decreased from S to Se and Te. Although the AuS monolayer exhibited the strongest bond anharmonicity, its κl was still the largest, demonstrating that among the factors that influence κl, harmonic factors have a greater effect than anharmonic parameters. When the atomic mass was increased, the phonon frequencies, phonon group velocities, and κl decreased. Benefiting from low κl induced by LPEs, the maximum ZT values of p-type doped AuSe and AuTe monolayers exceeded 1.0 and 2.0 at T = 800 K, respectively. These results not only confirmed that the introduction of LPEs can reduce the lattice thermal conductivity and enhance the TE performance of 2D materials, but also demonstrated the promising potential of the 2D AuX family for applications in high-temperature TE devices.

A correlation between hydroxyl vibrations under compression and anharmonicity: glaucophane as a test case

The infrared hydroxyl bands and first hydroxyl combination bands of glaucophane are characterized under pressure. In this weakly hydrogen-bonded mineral, the anharmonicity parameter, as determined from the difference between combinations and the fundamentals, is nearly constant with pressure to 15 GPa, indicating that the ambient pressure value of hydroxyl-bond anharmonicity closely reflects its value at high pressures. Given this near-constancy, the Grüneisen parameters of the hydroxyl stretching vibrations of a wide range of minerals, as derived from the pressure dependence of their O–H stretching frequencies, are correlated with the anharmonic parameter of each vibration, as determined from the ambient pressure offset of the summed frequencies of the fundamental n = 0 to 1 transitions and the frequency of the hydroxyl combination or overtone band corresponding to the n = 0 to 2 transition. This correlation is motivated by (1) the anharmonic origin of the Grüneisen parameter; and (2) the grossly similar form of the interatomic potential governing weak- and medium-strength hydrogen bonding in many minerals. This possible correlation provides a means through which the likely pressure-induced hydroxyl mode shifts of phases might be estimated from ambient pressure near-infrared measurements and emphasizes the importance of near-infrared combination/overtone band measurements. In this context, the combination/overtone bands of high-pressure hydrous phases are almost completely uncharacterized, and thus one probe of their anharmonicity has been neglected. Such information directly constrains the nature of hydrogen bonding in these phases, and hence provides possible insights into both their retention of hydrogen and its mobility. Deviations from the anharmonicity-Grüneisen parameter correlation, when observed (as may be the case in prehnite), could provide insights into anomalous effects on the hydroxyl potential well induced by bifurcated H-bonds, pressure-dependent Davydov splitting, or the influence of neighboring cations.

Spatial Spin-Modulated Structure of Bi1 – xSrxFeO3 – y (x = 0, 0.05, and 0.10) Multiferroics

The room-temperature X-ray and Mössbauer data on the BiFeO3, Bi0.95Sr0.05FeO3 – y, and Bi0.90Sr0.10FeO3 – y multiferroics obtained by solid-phase synthesis are presented. The samples have a rhombohedral crystal structure with the sp. gr. R3c. The lattice parameter ah is invariable, while the parameter ch decreases with increasing strontium content. The 57Fe Mössbauer spectra recorded at a temperature of 295 K have been interpreted within the cycloid spatial spin-modulated structure model. It has been established that the easy-axis magnetic anisotropy is implemented in the investigated multiferroics. The anharmonicity parameter m of the spin-modulated structure has been measured. Upon replacement of trivalent Bi3+ ions in small amounts (x = 0–0.10) with divalent Sr2+ ions, the parameter m increases by a factor of more than 3: from 0.10(4) at x = 0.00 to 0.36(10) at x = 0.10.

Equation of state for Mg3Al2Si3O12 pyrope: Implications for post-garnet transitions and mantle dynamics

Mantle convection is the dominant process driving the upwelling of hot materials and subduction of cold slabs. These processes are density-dependent and influenced by post-spinel and post-garnet transitions in the mantle transition zone (MTZ)/ lower mantle (LM). Knowledge of the Clapeyron slope of these transformations is used to express the dynamics of mantle blocks and is necessary for understanding the deep Earth. Here, we provide the Kunc-Einstein equation of state (EoS) for the pyrope Mg3Al2Si3O12 (Prp) calculated from a joint analysis of the experimentally measured isobaric heat capacity, bulk moduli, thermal expansion, pressure (P), unit cell volume (V), temperature (T) data. Based on our model, the bulk modulus and its pressure derivatives were K0,T0 = 168.5 GPa, K′0,T = 4.77, and V0 = 1501.7 Å. The optimised parameters include two Einstein temperatures, i.e., θ1 = 331 and θ2 = 1093 K, Grüneisen parameter at ambient condition γ0 = 1.77, infinite compression γ∞ = 0 with β = 1.12 and an intrinsic anharmonicity parameter a0 = –20. The value for the thermal expansion coefficient was calculated to be α = 2.33·10−5 K−1, and the thermodynamic Grüneisen parameter was estimated as γth = 1.42. The obtained EoS for Prp and the preliminarily fitted EoS for Al-bearing akimotoite (Al-Aki), in combination with literature data on bridgmanite (Bdm) and corundum (Crn), allowed the calculation of the phase diagram of the system with 75 mol% MgSiO3 + 25 mol% Al2O3 under LM conditions. The transformation from Prp to Bdm + Crn was computed at 24 GPa and 1570 K and exhibited a slightly positive Clapeyron slope (dP/dT = 2.1 MPa/K). The stability field of Al-Aki was detected at T = 1250–1570 K and P = 23–27 GPa. At P values higher than 24–27 GPa, the Al-Aki transforms into a Bdm + Crn assemblage with a highly negative Clapeyron slope. Calculations of sound velocities for the studied phases showed that the transformation from Prp to Bdm + Crn increased Vp and Vs by up to 9 and 20%, respectively. Such a big jump in the sound velocities indicates that the post-garnet transition is a better candidate than the post-Aki transition for producing a double discontinuity at the base of the MTZ, in combination with the transformation of ringwoodite into the Bdm + ferropericlase assemblage. The increase in sound velocities associated with the formation and dissolution of Al-Aki is unlikely to be sensitive to the MTZ. The combination of post-garnet, post-spinel, and post-Aki transitions near 660–720 km depths may have sluggished both the upwelling hot mantle and the subducted cold plates. The stagnant, hot LM material at the base of MTZ warmed the harzburgite and eclogite layers stacked during subduction. The heated MTZ may have been involved in further upwelling.

Effect of La doping on the structure and cycloidal spin ordering in multiferroic BiFeO3.

A series of Bi1-xLaxFeO3 samples with 0.00 ≤ x ≤ 0.30 was synthesized by the sol-gel method. The effects of lanthanum concentration on the phase formation, microstructure and cycloidal spin ordering were studied using X-ray diffraction, scanning electron microscopy and Mössbauer spectroscopy. The crystal structure of the La-doped bismuth ferrite transformed from rhombohedral R3c (x ≤ 0.05) to a mixture of R3c and cubic Pm3m (0.07 ≤ x ≤ 0.15) and finally to a mixture of R3c, Pm3m and orthorhombic Pbam (0.20 ≤ x ≤ 0.30). The Pbam phase, with characteristic porous microstructure shown by microscopy images, was observed in Bi1-xLaxFeO3 compounds for the first time. Based on the Mössbauer spectroscopy, it was found that the cycloidal spin ordering started to disappear at x = 0.07. With increasing La concentration the share of the cycloid decreased from 100% at 0.00 ≤ x ≤ 0.05 to 0% at x = 0.30. At the beginning, for x ≤ 0.02, the anharmonicity parameter, m, of the cycloidal spin ordering was about 0.5, which is typical of a pure BiFeO3 compound. In the range 0.05 ≤ x ≤ 0.25, the m parameter was of the order of 0.1, which indicated the practically harmonic character of the cycloid. The structural transition at x = 0.07 was accompanied by a substantial increase in magnetization.

On relation between renormalized frequency and heat capacity for particles in an anharmonic potential

For free particles in a simple harmonic potential plus a weak anharmonicity, characterized by a set of anharmonic parameters, Newtonian mechanics asserts that there is a renormalization of the natural frequency of the periodic motion; and statistical mechanics claims that the anharmonicity causes a correction to the heat capacity of an ideal gas in the anharmonic potential. The orbital motion and thermal motion depend on the same anharmonic parameters, but in different combinations. These two manners of combinations are fundamentally different, demonstrating that statistical law cannot emerge from the deterministic law for the many-body system.

Lattice thermal conductivity of two-dimensional CrB4 and MoB4 monolayers against Slack’s guideline

Two-dimensional (2D) CrB4 and MoB4 monolayers are typical graphene-like materials with excellent electrical transport properties and high structural stability. Yet, their thermal transport properties are unknown. By first-principles calculations and solving the Boltzmann transport equation iteratively, we report low lattice thermal conductivity (κl) of CrB4 and MoB4 monolayers. At room temperature, κl of CrB4 and MoB4 monolayers are 31.19 and 96.59 W/mK, respectively. This trend is against the well-known Slack’s guideline that the same type of materials with greater atomic mass generally have lower κl. The cause of this anomaly is analyzed from the first-principles harmonic and anharmonic parameters. It is surprising that no obvious correlation is observed between three-phonon scattering rates and mode Grüneisen parameters, despite their common determination by third-order interatomic force constants and one-to-one mode correspondence. The applicability of Grüneisen parameters to searching for novel materials with low κl is discussed from a theoretical viewpoint.

Temperature-dependent elastic constants of thorium dioxide probed using time-domain Brillouin scattering

We report the adiabatic elastic constants of single-crystal thorium dioxide over a temperature range of 77–350 K. Time-domain Brillouin scattering, an all-optical, non-contact picosecond ultrasonic technique, is used to generate and detect coherent acoustic phonons that propagate in the bulk perpendicular to the surface of the crystal. These coherent acoustic lattice vibrations have been monitored in two hydrothermally grown single-crystal thorium dioxide samples along the (100) and (311) crystallographic directions. The three independent elastic constants of the cubic crystal (C11, C12, and C44) are determined from the measured bulk acoustic velocities. The longitudinal wave along the (100) orientation provided a direct measurement of C11. Measurement of C44 and C12 was achieved by enhancing the intensity of quasi-shear mode in a (311) oriented crystal by adjusting the polarization angle relative to the crystal axes. We find the magnitude of softening of the three elastic constants to be ∼2.5% over the measured temperature range. Good agreement is found between the measured elastic constants with previously reported values at room temperature, and between the measured temperature-dependent bulk modulus with calculated values. We find that semi-empirical models capturing lattice anharmonicity adequately reproduce the observed trend. We also determine the acoustic Grüneisen anharmonicity parameter from the experimentally derived temperature-dependent bulk modulus and previously reported temperature-dependent values of volumetric thermal expansion coefficient and heat capacity. This work presents measurements of the temperature-dependent elasticity in single-crystal thorium dioxide at cryogenic temperature and provides a basis for testing ab initio theoretical models and evaluating the impact of anharmonicity on thermophysical properties.

Mechanism for the Combined Li–Na Ionic Conductivity in Sugilite (Fe2Na2K[Li3Si12O30])-Type Compounds

This study explains the ionic conductivity in the mineral sugilite (idealized formula: Fe2Na2K[Li3Si12O30]) by resolving the dynamic disorder of both Li and Na cations using synchrotron X-ray single-crystal diffraction from 298 K to 1023 K. Non-zero anharmonic atomic displacement parameters at Na and Li sites at 1023 K adumbrated long-range charge transport routes for Li and Na cations commonly parallel to the (a–b) plane. Temperature-enhanced diffuse residuals in Fourier maps could unambiguously localize two interstitial sites suitable for Li, as well as three for Na. Each two-dimensional (2D) network of Li and Na interstitials was formed parallel to each other, providing Li and Na hopping pathways. The higher concentration of Na cations hopping in short distances of 2.0962(4)–2.3015(5) Å could be the main reason for the higher bulk conductivity values evaluated by impedance spectra of sugilite in comparison to those of its structural relatives with low Na contents, e.g., the mineral sogdianite ((Zr,Al,Fe)2Na0.36K[Li3Si12O30]). Bond valence sum landscape maps supported the critical role of dynamic disorder of Na+ over densely packed 2D interstitial networks for combined ionic conductivity along with mobile Li+ in sugilite-type compounds.

Equilibrium hydrogen isotope fractionation between portlandite/brucite and water: Implication from the vibrational spectra at elevated temperature and pressure

Minerals in brucite-type structure, including brucite (Mg(OH)2) and portlandite (Ca(OH)2), have been studied as important analogs of hydrous silicate minerals for their thermodynamic properties, including equilibrium hydrogen and oxygen isotope fractionations between minerals and water at elevated temperatures and pressures. In this study, Raman and Fourier transform infrared (FTIR) spectra were collected at high-temperature (T) and high-pressure (P) conditions on synthetic hydrogenated and deuterated portlandite samples (i.e., Ca(OH)2 and Ca(OD)2), and their isobaric and isothermal mode Grüneisen parameters, as well as anharmonic parameters, were then evaluated. These high-precision vibrational spectra enable the evaluation of thermodynamic properties of portlandite (ΔU, CV, CP and ΔS) up to 427 °C, to which anharmonicity has positive contributions. More importantly, they help to determine the isobaric (at P = 1 bar) β factors of brucite and portlandite for equilibrium D/H fractionation considering anharmonic effects, and the D/H fractionation factor (103∙lnα) between brucite/portlandite and water at high-P,T conditions. The calculated equilibrium fractionation factor (lnαbrucite-water) agrees with experimental results in the temperature range from 300 to 647 K (∼27 to ∼374 °C, the critical point of water) within analytical uncertainties estimated using Monte Carlo method. The Ab initio calculation using DFT theory and VASP program was also carried out to obtain phonon spectra for brucite and portlandite with three-split hydrogen sites and to evaluate the dispersion effect, which is found to be smaller than the statistical uncertainty at high temperatures. Our results show that the internal OH-stretching modes in brucite/portlandite play a dominant role in determining the β values, and the anharmonic OH-stretching potential (xi parameter) contributes significantly to the D/H fractionation factor. Because previous studies show that OH-stretching frequencies generally decrease with increasing mass of cation in the metallic hydroxide having similar crystal structure, our results imply that the deuterium isotope may be preferentially enriched in the hydroxide phase with the light cation bonded to the hydroxyl group, which is also consistent with the observed D/H fractionations among hydrous silicates.