Equation of state predictions for ScF3 and CaZrF6 with neural network-driven molecular dynamics.

In silico property prediction based on density functional theory (DFT) is increasingly performed for crystalline materials. Whether quantitative agreement with experiment can be achieved with current methods is often an unresolved question, and may require detailed examination of physical effects such as electron correlation, reciprocal space sampling, phonon anharmonicity, and nuclear quantum effects (NQE), among others. In this work, we attempt first-principles equation of state prediction for the crystalline materials ScF3 and CaZrF6, which are known to exhibit negative thermal expansion (NTE) over a broad temperature range. We develop neural network (NN) potentials for both ScF3 and CaZrF6 trained to extensive DFT data, and conduct direct molecular dynamics prediction of the equation(s) of state over a broad temperature/pressure range. The NN potentials serve as surrogates of the DFT Hamiltonian with enhanced computational efficiency allowing for simulations with larger supercells and inclusion of NQE utilizing path integral approaches. The conclusion of the study is mixed: while some equation of state behavior is predicted in semiquantitative agreement with experiment, the pressure-induced softening phenomenon observed for ScF3 is not captured in our simulations. We show that NQE have a moderate effect on NTE at low temperature but does not significantly contribute to equation of state predictions at increasing temperature. Overall, while the NN potentials are valuable for property prediction of these NTE (and related) materials, we infer that a higher level of electron correlation, beyond the generalized gradient approximation density functional employed here, is necessary for achieving quantitative agreement with experiment.

Controlling the Phase Behavior of Low and Negative Thermal Expansion ReO3-Type Fluorides using Interstitial Anions: Sc1-xZrxF3+x.

Density measurements suggest that the incorporation of ZrF4 into the cubic ReO3-type structure of Sc1-xZrxF3+x is associated with the creation of anion interstitials. X-ray total scattering measurements are consistent with the conversion of corner-sharing octahedra to edge-sharing polyhedra as the solid solutions become richer in ZrF4. The cubic (Pm3̅m) to rhombohedral (R3̅c) cooperative octahedral tilting transition seen for ScF3 moves to a higher pressure as increasing amounts of zirconium are added, and it is eventually suppressed completely (x = 0.4 and 0.5) so that the cubic phase persists to high pressure until an amorphization occurs. All the samples studied (x = 0.0, 0.1, 0.2, 0.3, 0.4, and 0.5) display pressure-induced softening, and increasing the zirconium content leads to a higher zero-pressure bulk modulus. The incorporation of "excess fluoride" into ReO3-type fluorides is a powerful tool for suppressing the generally unwanted phase transitions seen when subjecting these materials to stress.

Thermal Expansion and Response to Pressure of Double-ReO3-Type Fluorides NaMVF6 (M = Nb, Ta).

Several II-IV double-ReO3-type (DROT) fluorides are known to exhibit strong negative thermal expansion (NTE) over a wide temperature range while retaining a cubic structure down to 120 K or lower. CaZrF6, CaNbF6, CaTiF6, and MgZrF6, embody these properties. In contrast to the behavior of these II-IV materials, the I-V DROT material, NaSbF6, has been reported to display a phase transition from rhombohedral to cubic above 300 K and positive thermal expansion both above and below the transition. In this work, NaNbF6 and NaTaF6 are shown to undergo first-order cubic-to-rhombohedral transitions on cooling to ∼130 K. Above this transition, NaNbF6 shows modest NTE between 160 and 250 K, whereas NaTaF6 exhibits near-zero thermal expansion over the range 210-270 K. These I-V systems are elastically softer than their II-IV counterparts, with a zero pressure bulk modulus, K0, of 14.6(8) GPa and first derivative of the bulk modulus with respect to pressure, K0', of -18(3) for cubic NaNbF6, and K0 = 14.47(3) GPa and K0'= -21.56(7) for cubic NaTaF6. When subject to ∼0.3 GPa at 300 K, both compounds exhibit a phase transition from Fm3̅m to R3̅. The R3̅ phases exhibit negative linear compressibility over a limited pressure range. A further transition with phase coexistence occurs at ∼2.5-3.0 GPa for NaNbF6 and ∼4.5 GPa for NaTaF6. Compression of NaNbF6 in helium at room temperature and below provides no evidence for helium penetration into the structure to form a perovskite with helium on the A-site, as was previously reported for CaZrF6.

Tuning Thermal Expansion in Metal-Organic Frameworks Using a Mixed Linker Solid Solution Approach.

Several metal-organic frameworks are known to display negative thermal expansion (NTE). However, unlike traditional NTE material classes, there have been no reports where the thermal expansion of a MOF has been tuned continuously from negative to positive through the formation of single-phase solid solutions. In the system Zn-DMOF-TMx, Zn2[(bdc)2-2x(TM-bdabco)2x][dabco], the introduction of increasing amounts of TM-bdc, with four methyl groups decorating the benzene dicarboxylate linker, leads to a smooth transition from negative to positive thermal expansion in the a-b plane of this tetragonal material. The temperature at which zero thermal expansion occurs evolves from ∼186 K for the Zn-DMOF parent structure (x = 0) to ∼325 K for Zn-DMOF-TM (x = 1.0). The formation of mixed linker solid solutions is likely a general strategy for the control of thermal expansion in MOFs.

Negative Thermal Expansion, Response to Pressure and Phase Transitions in CaTiF6.

Strong volume negative thermal expansion over a wide temperature range typically only occurs in ReO3-type fluorides that retain an ideal cubic structure to very low temperatures, such as ScF3, CaZrF6, CaHfF6, and CaNbF6. CaTiF6 was examined in an effort to expand this small family of materials. However, it undergoes a cubic ( Fm3̅ m) to rhombohedral ( R3̅) transition on cooling to ∼120 K, with a minimum volume coefficient of thermal expansion (CTE) close to -42 ppm K-1 at 180 K and a CTE of about -32 ppm K-1 at room temperature. On compression at ambient temperature, the material remains cubic to ∼0.25 GPa with K0 = 29(1) GPa and K'0 = -50(5). Cubic CaTiF6 is elastically softer and shows more pronounced pressure induced softening, than both CaZrF6 and CaNbF6. In sharp contrast to both CaZrF6 and CaNbF6, CaTiF6 undergoes a first-order pressure induced octahedral tilting transition to a rhombohedral phase ( R3̅) on compression above 0.25 GPa, which is closely related to that seen in ScF3. Just above the transition pressure, this phase is elastically very soft with a bulk modulus of only ∼4 GPa as octahedral tilting associated with a reduction in the Ca-F-Ti angles provides a low energy pathway for volume reduction. This volume reduction mechanism leads to highly anisotropic elastic properties, with the rhombohedral phase displaying both a low bulk modulus and negative linear compressibility parallel to the crystallographic c-axis for pressures below ∼2.5 GPa. At ∼3 GPa, a further phase transition to a poorly ordered phase occurs.

Synthesis of Defect Perovskites (He2-x□x)(CaZr)F6 by Inserting Helium into the Negative Thermal Expansion Material CaZrF6.

Defect perovskites (He2-x□x)(CaZr)F6 can be prepared by inserting helium into CaZrF6 at high pressure. They can be recovered to ambient pressure at low temperature. There are no prior examples of perovskites with noble gases on the A-sites. The insertion of helium gas into CaZrF6 both elastically stiffens the material and reduces the magnitude of its negative thermal expansion. It also suppresses the onset of structural disorder, which is seen on compression in other media. Measurements of the gas released on warming to room temperature and Rietveld analyses of neutron diffraction data at low temperature indicate that exposure to helium gas at 500 MPa leads to a stoichiometry close to (He1□1)(CaZr)F6. Helium has a much higher solubility in CaZrF6 than silica glass or crystobalite. An analogue with composition (H2)2(CaZr)F6 would have a volumetric hydrogen storage capacity greater than current US DOE targets. We anticipate that other hybrid perovskites with small neutral molecules on the A-site can also be prepared and that they will display a rich structural chemistry.

Synthesis and Properties of the Helium Clathrate and Defect Perovskite [He2-x □ x ][CaNb]F6.

The defect double perovskite [He2-x □ x ][CaNb]F6, with helium on its A-site, can be prepared by the insertion of helium into ReO3-type CaNbF6 at high pressure. Upon cooling from 300 to 100 K under 0.4 GPa helium, ∼60% of the A-sites become occupied. Helium uptake was quantified by both neutron powder diffraction and gas insertion and release measurements. After the conversion of gauge pressure to fugacity, the uptake of helium by CaNbF6 can be described by a Langmuir isotherm. The enthalpy of absorption for helium in [He2-x □ x ][CaNb]F6 is estimated to be ∼+3(1) kJ mol-1, implying that its formation is entropically favored. Helium is able to diffuse through the material on a time scale of minutes at temperatures down to ∼150 K but is trapped at 100 K and below. The insertion of helium into CaNbF6 reduces the magnitude of its negative thermal expansion, increases the bulk modulus, and modifies its phase behavior. On compressing pristine CaNbF6, at 50 and 100 K, a cubic (Fm3̅m) to rhombohedral (R3̅) phase transition was observed at <0.20 GPa. However, a helium-containing sample remained cubic at 0.4 GPa and 50 K. CaNbF6, compressed in helium at room temperature, remained cubic to >3.7 GPa, the limit of our X-ray diffraction measurements, in contrast to prior reports that upon compression in a nonpenetrating medium, a phase transition is detected at ∼0.4 GPa.

Orientational order-dependent thermal expansion and compressibility of ZrW2O8 and ZrMo2O8.

The role of MO4 (M = W, Mo) orientational disorder in the thermal expansion and compressibility of ZrW2O8 and ZrMo2O8 was investigated via in situ powder X-ray diffraction at elevated temperature and pressure. A dramatic reduction in the bulk modulus of α-ZrW2O8, which has ordered WO4 tetrahedra at room temperature, from 65 GPa at room temperature to 47 GPa at 386 K was observed to be concomitant with the onset of a reversible WO4 orientational disordering upon compression. Additionally, the coefficient of thermal expansion (CTE) of the α phase became more negative upon compression within the temperature range in which pressure-dependent disorder was observed; αl, over the range 298 to 386 K, was ~-11 ppm K(-1) at 35 MPa but ~-16 ppm K(-1) at 276 MPa. No softening upon heating or change in CTE upon compression was observed for ZrW2O8 above the order → disorder phase transition temperature. Cubic ZrMo2O8 has a disordered arrangement of MoO4 tetrahedra at all temperatures and pressures accessed in this study. Its bulk modulus was independent of temperature, and its CTE was insensitive to pressure, much like ß-ZrW2O8. The stability/metastability of the cubic and orthorhombic phases upon heating above room temperature and compression is discussed, with a focus on changes in the thermodynamics and kinetics of the cubic ↔ orthorhombic transition.

Pronounced negative thermal expansion from a simple structure: cubic ScF(3).

Scandium trifluoride maintains a cubic ReO(3) type structure down to at least 10 K, although the pressure at which its cubic to rhombohedral phase transition occurs drops from >0.5 GPa at ∼300 K to 0.1-0.2 GPa at 50 K. At low temperatures it shows strong negative thermal expansion (NTE) (60-110 K, α(l) ≈ -14 ppm K(-1)). On heating, its coefficient of thermal expansion (CTE) smoothly increases, leading to a room temperature CTE that is similar to that of ZrW(2)O(8) and positive thermal expansion above ∼1100 K. While the cubic ReO(3) structure type is often used as a simple illustration of how negative thermal expansion can arise from the thermally induced rocking of rigid structural units, ScF(3) is the first material with this structure to provide a clear experimental illustration of this mechanism for NTE.