Linear Compressibility Research Articles

Theoretical Investigation of Zero Linear Compressibility on Metal Squarates MC4O4 (M = Pb and Ba)

Zero linear compressibility (ZLC) and zero thermal expansion (ZTE) are unique and rare properties because of their excellent resistance to pressure and temperature, respectively. Metamaterials possessing both ZLC and ZTE will have promising application prospects. Herein, we conducted density functional theory studies on MC4O4 (M = Pb and Ba), which have “dumbbell”-like structures with ZTE property reported previously. The results show that the two compounds exhibit ZLC over the studied pressure range of 0 to 10 GPa along the c-axis, which is also the reported ZTE direction. Meanwhile, the ZLC can be furtherly tuned in value by replacing the metal element. The predicted ZLC phenomena in ZTE materials provide inspirations for designing and discovering new ZLC + ZTE metamaterials.

A novel design of mechanical metamaterial incorporating multiple negative indexes

Mechanical metamaterials that combine multiple negative properties are rare, but have great appeal for applications in multipurpose devices. Herein, a novel metamaterial incorporating negative Poisson’s ratio, negative compressibility, and negative thermal expansion or swelling was proposed. The unit cell was designed by simulating the bond structure of lead monoxide crystals using elastic beams. Analytical models for the mechanical responses of the unit cell were established, and expressions for Young’s modulus, thermal expansion, Poisson’s ratio, and compressibility were derived and confirmed by numerical simulations. The results showed that the metamaterial not only displayed a negative Poisson’s ratio but also had negative linear and area compressibilities as well as negative linear, area, and volume thermal expansions if the geometric parameters were properly adjusted. Furthermore, metamaterials with negative linearity and area swelling were obtained experimentally by replacing the thermal expansion of the material with the water absorption expansion of a hydrogel. Such metamaterials with multiple negative indexes are expected to contribute to the feasibility of advanced multifunctional devices with mechanical, pressure, temperature, and moisture sensitivities.

Extreme flexibility and unusual piezomechanical properties of zinc-alkyl-based metal-organic frameworks: A first principles study

The behavior of three Zn-alkyl-based MOFs, ZnGA (Zn-Glutarate), ZnAA (Zn-Adipate), and ZAG-4 (Zinc Alky Gate), under hydrostatic compression has been investigated using first-principles DFT simulation, which has proven its reliability in previous studies. Due to the lack of the high pressure experimental data for ZnGA and ZnAA, the reliability of the simulation parameters was tested by taking ZAG-4, whose structural flexibility has been previously reported experimentally and computationally, as a benchmark. All three structures were found to exhibit elastic deformation under pressure up to 15 GPa, due to the flexibility of the alkyl chains that allow the structures to move without disrupting the metal-ligand coordination. Interestingly, the structures exhibit different mechanical properties, with ZAG-4 showing negative linear compressibility (NLC), ZnGA showing positive linear compressibility (PLC), and ZnAA showing zero linear compressibility (ZLC). The NLC in ZAG-4 is attributed to the proton transfer between phosphonate oxygen and water in the structure as previously reported, while the ZLC in ZnAA is due to a dumbbell-like structural motif formed by substructures displaying both NLC and PLC.

Pressure-induced Structural Phase Transition and New Superconducting Phase in UTe2

We report on the crystal structure and electronic properties of the heavy fermion superconductor UTe2 at high pressure up to 11 GPa, as investigated by X-ray diffraction and electrical resistivity experiments. The X-ray diffraction measurements under high pressure using a synchrotron light source reveal anisotropic linear compressibility of the unit cell up to 3.5 GPa, while a pressure-induced structural phase transition is observed above PO–T ∼ 3.5–4 GPa at room temperature, where the body-centered orthorhombic crystal structure with the space group Immm changes into a body-centered tetragonal structure with the space group I4/mmm. The molar volume drops abruptly at PO–T, while the distance between the first-nearest neighbor of U atoms, dU–U, increases, implying a switch from the heavy electronic states to the weakly correlated electronic states. Surprisingly, a new superconducting phase at pressures higher than 7 GPa was detected at Tsc > 2 K with a relatively low upper-critical field, Hc2(0). The resistivity above 3.5 GPa, thus, in the high-pressure tetragonal phase, shows a large drop below 230 K, which may also be related to a considerable change from the heavy electronic states to the weakly correlated electronic states.

Chirality-Dependent Structural Transformation in Chiral 2D Perovskites under High Pressure.

Chiral perovskites have attracted considerable attention owing to their potential applications in spintronic- and polarization-based optoelectronic devices. However, the structural chirality/asymmetry transfer mechanism between chiral organic ammoniums and achiral inorganic frameworks is still equivocal, especially under extreme conditions, as the systematic structural differences between chiral and achiral perovskites have been rarely explored. Herein, we successfully synthesized a pair of new enantiomeric chiral perovskite (S/R-3PYEA)PbI4 (3PYEA2+ = C5NH5C2H4NH32+) and an achiral perovskite (rac-3PYEA)PbI4. Hydrostatic pressure was used, for the first time, to systematically investigate the differences in the structural evolution and optical behavior between (S/R-3PYEA)PbI4 and (rac-3PYEA)PbI4. At approximately 7.0 GPa, (S/R-3PYEA)PbI4 exhibits a chirality-dependent structural transformation with a bandgap "red jump" and dramatic piezochromism from translucent red to opaque black. Upon further compression, a previously unreported chirality-induced negative linear compressibility (NLC) is achieved in (S/R-3PYEA)PbI4. High-pressure structural characterizations and first-principles calculations demonstrate that pressure-driven homodirectional tilting of homochiral ammonium cations strengthens the interactions between S/R-3PYEA2+ and Pb-I frameworks, inducing the formation of new asymmetric hydrogen bonds N-H···I-Pb in (S/R-3PYEA)PbI4. The enhanced asymmetric H-bonding interactions further break the symmetry of (S/R-3PYEA)PbI4 and trigger a greater degree of in-plane and out-of-plane distortion of [PbI6]4- octahedra, which are responsible for chirality-dependent structural phase transition and NLC, respectively. Nevertheless, the balanced H-bonds incurred by equal proportions of S-3PYEA2+ and R-3PYEA2+ counteract the tilting force, leading to the absence of chirality-dependent structural transition, spectral "red jump", and NLC in (rac-3PYEA)PbI4.

SbSeI'nin Anizotropik Elastik Özelliklerine Basıncın Etkileri: DFT Hesaplaması

The mechanical and elastic properties of SbSeI compound under hydrostatic pressure of 0-40 kBar were investigated for the first time. Quantum Espresso software (QE) was used for all calculations. Elastic constants (Cij) were calculated using the ElaStic package distributed with the QE software and using the energy calculation method in this package. According to the elastic constants obtained, the SbSeI compound was found to be mechanically stable. The results obtained at ambient pressure were found to be in perfect agreement with the literature data. Mechanical properties (bulk modulus, shear modulus, Young's modulus, and Poisson’s ratio), anisotropy, linear compressibility, Debye temperatures, Vickers hardness, and minimum thermal conductivity of the SbSeI compound were calculated using these constants. As a result of the calculations, it was seen that the SbSeI compound is a soft (Vickers hardness < 10 GPa) and anisotropic material.

Equations of State and Crystal Structures of KCaPO4, KSrPO4, and K2Ce(PO4)2 under High Pressure: Discovery of a New Polymorph of KCaPO4.

We have studied by means of angle-dispersive powder synchrotron X-ray diffraction the structural behavior of KCaPO4, SrKPO4, and K2Ce(PO4)2 under high pressure up to 26, 25, and 22 GPa, respectively. For KCaPO4, we have also accurately determined the crystal structure under ambient conditions, which differs from the structure previously reported. Arguments supporting our structural determination will be discussed. We have found that KCaPO4 undergoes a reversible phase transition. The onset of the transition is at 5.6 GPa. It involves a symmetry decrease. The low-pressure phase is described by space group P3̅m1 and the high-pressure phase by space group Pnma. For KSrPO4 and K2Ce(PO4)2, no evidence of phase transitions has been found up to the highest pressure covered by the experiments. For the three compounds, the linear compressibility for the different crystallographic axes and the pressure-volume equation of states are reported and compared with those of other phosphates. The three studied compounds are among the most compressible phosphates. The results of the study improve the knowledge about the high-pressure behavior of complex phosphates.

Crystal structure of calcium-ferrite type NaAlSiO4 up to 45 GPa

Abstract Alkali-rich aluminous high-pressure phases including calcium-ferrite (CF) type NaAlSiO4 are thought to constitute ~20% by volume of subducted mid-ocean ridge basalt (MORB) under lower mantle conditions. As a potentially significant host for incompatible elements in the deep mantle, knowledge of the crystal structure and physical properties of CF-type phases is therefore important to understanding the crystal chemistry of alkali storage and recycling in the Earth’s mantle. We determined the evolution of the crystal structure of pure CF-NaAlSiO4 and Fe-bearing CF-NaAlSiO4 at pressures up to ~45 GPa using synchrotron-based, single-crystal X-ray diffraction. Using the high-pressure lattice parameters, we also determined a third-order Birch-Murnaghan equation of state, with V0 = 241.6(1) Å3, KT0 = 220(4) GPa, and KT0′ = 2.6(3) for Fe-free CF, and V0 = 244.2(2) Å3, KT0 = 211(6) GPa, and KT0′ = 2.6(3) for Fe-bearing CF. The addition of Fe into CF-NaAlSiO4 resulted in a 10 ± 5% decrease in the stiffest direction of linear compressibility along the c-axis, leading to stronger elastic anisotropy compared with the Fe-free CF phase. The NaO8 polyhedra volume is 2.6 times larger and about 60% more compressible than the octahedral (Al,Si)O6 sites, with K0NaO8 = 127 GPa and K0(Al,Si)O6 ~304 GPa. Raman spectra of the pure CF-type NaAlSiO4 sample shows that the pressure coefficient of the mean vibrational mode, 1.60(7) cm–1/GPa, is slightly higher than 1.36(6) cm−1/GPa obtained for the Fe-bearing CF-NaAlSiO4 sample. The ability of CF-type phases to contain incompatible elements such as Na beyond the stability field of jadeite requires larger and less-compressible NaO8 polyhedra. Detailed high-pressure crystallographic information for the CF phases provides knowledge on how large alkali metals are hosted in alumina framework structures with stability well into the lowermost mantle.

Mechanical and lattice vibrational investigations of nanostructured AlxIn1-xPySbzAs1-y-z alloys

The compositional dependence of the polarities, elastic constants, elastic moduli, Poisson's ratio, and linear compressibility has been computed for zinc blende AlxIn1-xPySbzAs1-y-z alloys with composition y ranging from 0 to 1. Also, the compositional influence of the bond-stretching force constant, bond-bending force constant, internal strain parameter, Cauchy ratio, effective charge, the Born ratio, anisotropy factor, and sound velocity has been determined. The experimental data and the studied properties for the novel studied alloy lattice matched to the InP substrate show a good level of agreement. The empirical pseudo-potential approach and the virtual crystal approximation have been employed in this work. The obtained results are predicted to help understand the elastic characteristics of AlxIn1-xPySbzAs1-y-z and for applications in optoelectronics.

Spacer-Dependent and Pressure-Tuned Structures and Optoelectronic Properties of 2D Hybrid Halide Perovskites.

Compared with their 3D counterparts, 2D hybrid organic-inorganic halide perovskites (HOIPs) exhibit enhanced chemical stabilities and superior optoelectronic properties, which can be further tuned by the application of external pressure. Here, we report the first high-pressure study on CMA2PbI4 (CMA = cylcohexanemethylammonium), a 2D HOIP with a soft organic spacer cation containing a flexible cyclohexyl ring, using UV-visible absorption, photoluminescence (PL) and vibrational spectroscopy, and synchrotron X-ray microdiffraction, all aided with density functional theory (DFT) calculations. Substantial anisotropic compression behavior is observed, as characterized by unprecedented negative linear compressibility along the b axis. Moreover, the pressure dependence of optoelectronic properties is found to be in strong contrast with those of 2D HOIPs with rigid spacer cations. DFT calculations help to understand the compression mechanisms that lead to pressure-induced bandgap narrowing. These findings highlight the important role of soft spacer cations in the pressure-tuned optoelectronic properties and provide guidance to the design of new 2D HOIPs.

The uniaxial zero thermal expansion and zero linear compressibility in distorted Prussian blue analogue RbCuCo(CN)6.

The uniaxial zero thermal expansion (ZTE) in distorted Prussian blue analogue (PBA) RbCuCo(CN)6 is reproduced by employing first-principles calculations, which agrees well with the experimental data. Also, the zero linear compressibility (ZLC) behavior in RbCuCo(CN)6 can be found. The special Jahn-Teller distortion introduced by Cu2+ in RbCuCo(CN)6 is noticed by investigating the change of the local structure with temperature and hydrostatic pressure. The lattice thermal conductivity (LTC) and phonon group velocity of RbCuCo(CN)6 are studied, where the LTC and phonon group velocity are significantly anisotropic. Especially, RbCuCo(CN)6 exhibits a quite low LTC, and its c-axis shows a characteristic of glasslike LTC at low temperatures. Our work facilitates a deep understanding of the coexistence mechanisms of uniaxial ZTE and ZLC properties in RbCuCo(CN)6.

Исследование сжимаемости цианамидов металлов и влияния давления на их электронные свойства

Based on the density functional theory, the effect of pressure on the structure and electronic properties of crystalline metal cyanamides Zn(CN2) and NaSc(CN2)2 has been studied. The negative linear compressibility of Zn(CN2) was revealed and its correlation with microscopic changes in the atomic structure under pressure was established. It is shown that NaSc(CN2)2 has a low compressibility (0.2 TPa-1) in a direction close to that of cyanamide anions. Based on the quantum topological analysis of the electron density, interatomic interactions were studied and it was found that the Zn-N and Sc-N bonds have a partially covalent character. The band gaps of Zn(CN2) and NaSc(CN2)2 at pressures up to 1 GPa have been determined and found to correspond to the UV range of 224-271 nm.

Multiple responses of 1,6-diphenyl-1,3,5-hexatriene to mechanical stimulation: emission enhancement, piezochromism and negative linear compressibility.

The properties of mechanoresponsive materials are mainly affected by intermolecular interaction, in which anisotropic grinding and hydrostatic high-pressure compression are the powerful tools used for modulation. Upon applying high pressure to 1,6-diphenyl-1,3,5-hexatriene (DPH), the reduced molecular symmetry results in the originally forbidden S0 → S1 transition to become allowed that then leads to a 13-times emission enhancement, and π-π interactions result in piezochromism (red-shifted up to 100 nm). With increasing pressure, high-pressure-stiffened H⋯C/C⋯H and H⋯H interactions enable the DPH molecules to generate a NLC mechanical response (9-15 GPa) with Kb = -5.8764 TPa-1 along the b-axis. As a contrast, upon destroying the intermolecular interactions by grinding, the DPH luminescence blue-shifts from cyan to blue. Based on this research, we investigate a new pressure-induced emission enhancement (PIEE) mechanism and enabled NLC phenomena by controlling weak intermolecular interactions. In-depth research of the evolution of intermolecular interactions has important reference value for developing new fluorescence materials and structural materials.

Ab Initio Study of H-Bond Dynamics in Three-Component Crystals Comprising (DABCOH+ )n Polycationic Chains.

In this work, the dynamic character of hydrogen-bond (H-bond) networks in two three-component crystals comprising polycationic chains was described. The first studied system was 1,4-diazabicyclo[2.2.2]octan-1-ium (DABCOH+ ) sulfamate monohydrate, known for its large negative linear compressibility. The second analyzed material was the newly obtained polar salt co-crystal: 1,4-diazabicyclo[2.2.2]octan-1-ium sulfamate urea. X-ray diffraction measurements enabled us to study the H-bond systems in both crystals using the graph set analysis. Obtained structures served as the initial models for Born-Oppenheimer molecular dynamics computations. A detailed study of intermolecular interactions and power spectra was conducted. The analysis of time and space correlations between the changes in H-bonds enabled the detection of proton transfer occurring in both systems at 300 K. Further study of those dynamic phenomena was done using the Energy Decomposition Analysis for selected trajectory fragments. Our work should improve the understanding of dielectric and ferroelectric properties of hybrid organic-inorganic materials.

Penta-graphene and phagraphene: thermal expansion, linear compressibility, and Poisson’s ratio

Nonplanar penta-graphene and planar phagraphene, which are connected by carbon pentagons and penta–hexa–hepta carbon rings, respectively, are two allotropes of graphene. Graphene as a star material in two-dimensional materials has been widely studied. However, the studies around penta-graphene and phagraphene are still insufficient. We are interested in both materials’ response to temperature, hydrostatic pressure, and stress. In this work, the thermal expansion, linear compressibility, and Poisson’s ratio of penta-graphene and phagraphene have been investigated systematically. It is found that both materials can exhibit abnormal negative thermal expansion behavior, while their linear compressibility behavior is normal. The negative Poisson’s ratio behavior only occurs in penta-graphene, which is consistent with other work. Through an analysis of the lattice vibrations and associated mode Grüneisen parameters, it is found that there are anomalies in the phonon spectra of both penta-graphene and phagraphene. It is noted that acoustic phonons contribute most to their respective anomalies, especially the transverse acoustic mode. The librational motion of the lowest-frequency optical phonon of both materials is identified and also associated with their novel properties. In general, the unique topological arrangement of carbon atoms can play a decisive role in determining the performances of penta-graphene and phagraphene.

Comparative first-principles study of the (TiZrHfNbTa)B2 high entropy solid solution and its constituent binary diborides

The stability, electronic and phonon structures, optical, mechanical and thermodynamic properties of the random high entropy (TiZrHfNbTa)B2 solid solution (alloy) were studied in comparison with those of TiB2, ZrB2, HfB2, NbB2 and TaB2 using first-principles calculations. The mixing enthalpy of −0.842 kJ/mol of atoms for the high entropy diboride points to that it is stable against decomposition into the constituting binary diborides. All the diborides studied are thermodynamically, mechanically and dynamically stable. The dielectric function, reflectivity and extinction coefficient of the diboride compounds were comprehensively studied. Both (TiZrHfNbTa)B2 and binary diborides are found to be good reflective materials in infrared, visible and ultraviolet regions. The calculated elastic moduli, B/G ratio, Vickers hardness, fracture toughness and Debye temperature of (TiZrHfNbTa)B2 are medium between largest and lowest ones of the constituents, approximately obey the rule of mixture. Calculations of the stress-shear strain relations for (TiZrHfNbTa)B2 point to the possibility of the activation of both basal and prismatic slip systems. The elastic moduli and linear compressibility exhibit the spatial anisotropy inherent to hexagonal structures. The thermodynamic characteristics of the diborides studied are well reproduced in a temperature range up to 800–1000 K.

ZIF-75 under Pressure: Negative Linear Compressibility and Pressure-Induced Instability

The behavior of the crystal structure of the zeolitic imidazolate framework ZIF-75 under pressure was studied by means of periodic density functional theory methods. Experimentally, it was shown that this material is tetragonal, space group I41/a at room temperature. However, according to the calculations, at zero temperature this material is monoclinic, space group C2/c. Irrespective of the symmetry of the material, the results show that ZIF-75 exhibits a negative linear compressibility effect and is unstable under relatively small applied pressures of the order of 0.1 GPa.

Chemical Bonding Effects and Physical Properties of Noncentrosymmetric Hexagonal Fluorocarbonates ABCO3F (A: K, Rb, Cs; B: Mg, Ca, Sr, Zn, Cd).

The present work applied the methods of density functional theory and the van der Waals interaction PBE + D3(BJ) on the basis of localized orbitals of the CRYSTAL17 package. It featured the effect of interactions between structural elements of fluorocarbonates ABCO3F (A: K, Rb, Cs; B: Mg, Ca, Sr, Zn, Cd) on their elastic and vibrational properties. The hexagonal structures proved to consist of alternating ···B-CO3··· and ···A-F··· layers in planes ab, interconnected along axis c by infinite chains ···F-B-F···, where cations formed polyhedra AOnF3 and BOmF2. The calculations included the band energy structure, the total and partial density of electron states, the energy and band widths of the upper ns- and np-states of alkali and alkaline-earth metals, as well as nd-zinc and nd-cadmium. For hydrostatic compression, we calculated the parameters of the Birch–Murnaghan equation of state and the linear compressibility moduli along the crystal axes and bond lines. We also defined the elastic constants of single crystals to obtain the Voigt–Reuss–Hill approximations for the elastic moduli of polycrystalline materials. The study also revealed the relationship between the elastic properties and the nature of the chemical bond. Hybrid functional B3LYP made it possible to calculate the modes of normal long-wavelength oscillations, which provided the spectra of infrared absorption and Raman scattering. Intramolecular modes ν1 and ν4 with one or two maxima were found to be intense, and their relative positions depended on the lengths of nonequivalent C–O bonds.

Covalent bond shortening and distortion induced by pressurization of thorium, uranium, and neptunium tetrakis aryloxides

Covalency involving the 5f orbitals is regularly invoked to explain the reactivity, structure and spectroscopic properties of the actinides, but the ionic versus covalent nature of metal-ligand bonding in actinide complexes remains controversial. The tetrakis 2,6-di-tert-butylphenoxide complexes of Th, U and Np form an isostructural series of crystal structures containing approximately tetrahedral MO4 cores. We show that up to 3 GPa the Th and U crystal structures show negative linear compressibility as the OMO angles distort. At 3 GPa the angles snap back to their original values, reverting to a tetrahedral geometry with an abrupt shortening of the M-O distances by up to 0.1 Å. The Np complex shows similar but smaller effects, transforming above 2.4 GPa. Electronic structure calculations associate the M-O bond shortening with a change in covalency resulting from increased contributions to the M-O bonding by the metal 6d and 5f orbitals, the combination promoting MO4 flexibility at little cost in energy.

A 2D FDEM-based THM coupling scheme for modeling deformation and fracturing of the rock mass under THM effects

Deformation and fracturing of the rock mass are heavily affected by complex thermal-hydraulic-mechanical (THM) processes in the subsurface environment. This study develops a THM coupling formulation based on the 2D combined finite-discrete element method (FDEM) to investigate the rock deformation and fracturing behavior driven by coupled THM phenomena in the rock mass. The coupled scheme consists of three subsolvers, i.e., a hydraulic solver, thermal solver, and mechanical solver. In the developed hydraulic solver, a flow network searching algorithm is proposed based on the pore network models and the special mesh discretization in the FDEM. The laminar viscous flow in the flow network is solved using the cubic law approximation, and the fluid pressure field is determined by a linear compressibility model. The developed thermal solver accounts for the complex thermal transport processes decomposed into conduction in the solid and the fluid, advection by fluid flow, and fluid-solid thermal convective transfer. The coupled THM formulation is implemented by iterating the three subsolvers using an explicit, partitioned scheme. This approach is then progressively verified by a series of benchmark problems. Finally, the deformation and branching of a single fracture embedded in the rock mass due to cold fluid injection are simulated, in which the gradual aseismic fracture slip/opening, as well as the branch fracture initiation and propagation, and their potential impact on seismic events are discussed. The results show the potential of the developed numerical tool in modeling the coupled THM process-driven deformation and fracturing of the rock mass. Improvements in the implementation are needed, such as improvements in modeling the thermo-poroelastic effects and temperature- and pressure-dependent physical properties.