Anharmonic Effects on the Thermodynamic Properties of Quartz from First Principles Calculations

The simple chemistry and structure of quartz together with its abundance in nature and its piezoelectric properties make convenient its employment for several applications, from engineering to Earth sciences. For these purposes, the quartz equations of state, thermoelastic and thermodynamic properties have been studied since decades. Alpha quartz is stable up to 2.5 GPa at room temperature where it converts to coesite, and at ambient pressure up to 847 K where it transforms to the beta phase. In particular, the displacive phase transition at 847 K at ambient pressure is driven by intrinsic anharmonicity effects (soft-mode phase transition) and its precise mechanism is difficult to be investigated experimentally. Therefore, we studied these anharmonic effects by means of ab initio calculations in the framework of the statistical thermodynamics approach. We determined the principal thermodynamic quantities accounting for the intrinsic anharmonicity and compared them against experimental data. Our results up to 700 K show a very good agreement with experiments. The same procedures and algorithms illustrated here can also be applied to determine the thermodynamic properties of other crystalline phases possibly affected by intrinsic anharmonic effects, that could partially invalidate the standard quasi-harmonic approach.

Coherent vibrational dynamics reveals lattice anharmonicity in organic–inorganic halide perovskite nanocrystals

The halide ions of organic-inorganic hybrid perovskites can strongly influence the interaction between the central organic moiety and the inorganic metal halide octahedral units and thus their lattice vibrations. Here, we report the halide-ion-dependent vibrational coherences in formamidinium lead halide (FAPbX3, X = Br, I) perovskite nanocrystals (PNCs) via the combination of femtosecond pump–probe spectroscopy and density functional theory calculations. We find that the FAPbX3 PNCs generate halide-dependent coherent vibronic wave packets upon above-bandgap non-resonant excitation. More importantly, we observe several higher harmonics of the fundamental modes for FAPbI3 PNCs as compared to FAPbBr3 PNCs. This is likely due to the weaker interaction between the central FA moiety and the inorganic cage for FAPbI3 PNCs, and thus the PbI64− unit can vibrate more freely. This weakening reveals the intrinsic anharmonicity in the Pb-I framework, and thus facilitating the energy transfer into overtone and combination bands. These findings not only unveil the superior stability of Br–based PNCs over I–based PNCs but are also important for a better understanding of their electronic and polaronic properties.

In situ Infrared Spectra for Hydrous Forsterite up to 1243 K: Hydration Effect on Thermodynamic Properties

Hydrogen substitution has significant effect on the physical properties of olivine, the most abundant mineral in the upper mantle. We collected high-temperature polarized Fourier Transform infrared (FTIR) spectra on hydrous forsterite (Mg-pure olivine) crystals, which were synthesized at 12 GPa, 1473–1673 K. The modes at 3612, 3578, 3566, 3551 cm−1 show comparable negative temperature dependence, and the magnitude of (∂vi/∂T)P decreases dramatically with frequency increasing. Whereas, the peak at 3477 cm−1, which is attributed to protonation along the O1...O2 edge on the Si tetrahedron, has a positive temperature dependence. The absorbance intensities of all these OH bands remained almost the same when quenched to room temperature. On the other hand, we also evaluate the hydration effect on the thermodynamic properties (heat capacities). For the anhydrous forsterite sample, the intrinsic anharmonicity could significantly increase the heat capacity by 5~6% when extrapolated to 2000 K. Hydration further increase such difference to ~9%, in both the cases of M-substitution or Si-substitution. Hence, hydration in olivine has significant impact on the anharmonic contribution to the thermodynamic properties, as well as Equations of State and equilibrium isotope fractionation β-factor at high-P,T conditions in the deep mantle.

Lattice thermal expansion of complex oxides with intrinsic anharmonicity

The lattice thermal expansion of crystalline solids cannot be adequately modeled by Grüneisen approximation using either Einstein single harmonic frequency or Debye frequency spectrum because a true phonon spectrum does not follow either of the two kinds. The Debye model misfits to many observations due to the fact that real solids comprises of axial anisotropy, lattice waves with dispersion at the Brillouin zone boundaries, low/high frequency optical vibrations in excess of the Debye spectrum. The actual frequency distribution is a complicated function of frequency instead of a simple parabolic Debye spectrum. The frequency distribution can be simplified using power series [1] leading to singularities before and after the Debye cutoff frequency. Using multiple Debye or Einstein oscillators, or their mixtures, is also common practice to better describe the lattice expansion, however, these models extremely suffer from intrinsic anharmonicity in particular at high temperatures. It was demonstrated that even the noble monoatomic solids required inclusion of anharmonic terms in the harmonic model to better explain the observed values [2]. Worse even, when anharmonicity becomes dominant due to formation of vacancies and defects, anomalies of hard/soft modes or change of stereochemical activities of lone electron pairs (LEPs) as function of temperature. Herein we approach an extended Grüneisen approximation that includes harmonic, quasiharmonic and intrinsic anharmonic potentials to describe the internal energy of the crystal as function of temperature. The model has been applied to several complex oxides with LEPs (Bi2Ga4O9[3]) along with axial negative thermal expansion (PbFeBO4) and rigid-unit-modes (KAsW2O9) reported here. The metric parameters were obtained from quality data collected from temperature-dependent neutron and X-ray powder diffractions.