Universal equation of state

Compressibility Studies of Copper Selenides Obtained by Cation Exchange Reaction Revealing the New CsCl Phase

In this study, we conducted a high-pressure investigation of Cu2-xSe nanostructures with pyramid- and plate-like morphologies, created through cation exchange from zinc-blende CdSe nanocrystals and wurtzite CdSe nanoplatelets respectively. Using a diamond anvil cell setup at the APS synchrotron, we observed the phase transitions in the Cu2-xSe nanostructures up to 40 GPa, identifying a novel CsCl-type lattice with Pm3̅m symmetry above 4 GPa. This CsCl-type structure, previously unreported in copper selenides, was partially retained after decompression. Our results indicate that the initial crystalline structure of CdSe does not affect the stability of Cu2-xSe nanostructures formed via cation exchange. Both morphologies of Cu2-xSe sintered under compression, potentially contributing to the stabilization of the high-pressure phase through interfacial defects. These findings are significant for discovering new phases with potential applications in future technologies.

Nanomechanical properties of SSTSAA microcrystals are dominated by the inter-sheet packing

Amyloid fibrils have been associated with human disease for many decades, but it has also become apparent that they play a functional, non-disease-related role in e.g. bacteria and mammals. Moreover, they have been shown to possess interesting mechanical properties that can be harnessed for future man-made applications. Here, the mechanical behaviour of SSTSAA microcrystals has been investigated. The SSTSAA peptide organization in these microcrystals has been related to that in the corresponding amyloid fibrils. Using high-pressure X-ray diffraction experiments, the bulk modulus K, which is the reciprocal of the compressibility β, has been calculated to be 2.48 GPa. This indicates that the fibrils are tightly packed, although the packing of most native globular proteins is even better. It is shown that the value of the bulk modulus is mainly determined by the compression along the c-axis, that relates to the inter-sheet distance in the fibrils. These findings corroborate earlier data obtained by AFM and molecular dynamics simulations that showed that mechanical resistance varies according to the direction of the applied strain, which can be related to packing and hydrogen bond contributions. Pressure experiments provide complementary information to these techniques and help to acquire a full mechanical characterization of biomolecular assemblies. This article is part of the theme issue 'Exploring the length scales, timescales and chemistry of challenging materials (Part 2)'.

Negative linear compressibility in Se at ultra-high pressure above 120 GPa

A series of in situ synchrotron X-ray diffraction (XRD) measurements were carried out, combined with first-principles calculations, to study structural phase transitions of selenium at high pressures and room temperature. Several phase transitions were observed, among which an isostructural phase transition was found at around 120 GPa for the first time. Evolved from the rhombohedral (space group R 3 m) structure (Se-V), the new phase (Se-V') exhibited an interesting increase of lattice parameter a at pressures from 120 to 148 GPa, known as negative linear compressibility (NLC). The discovery of NLC behavior observed in this work is mainly attributed to the accuracy and fine steps controlled by the membrane system for in situ XRD data collected with an exposure time of 0.5 s. After 140 GPa, a body-centered cubic (b.c.c.) structure Se-VI (space group Im 3 m) was formed, which remains stable up to 210 GPa, the highest pressure achieved in this study. The bulk moduli of phases Se-V, Se-V' and Se-VI were estimated to be 83 ± 2, 321 ± 2 and 266 ± 7 GPa, respectively, according to the P-V curve fit by the third-order Birch-Murnaghan equation of state. The Se-V' phase shows a bulk modulus almost 4 times larger than that of the Se-V phase, which is mainly due to the effect of its NLC. NLC in a higher pressure range is always more significant in terms of fundamental mechanism and new materials discovery, yet it has barely been reported at pressures above 100 GPa. This will hopefully inspire future studies on potential NLC behaviors in other materials at ultra-high pressure.

Quasi-harmonic approximation of lattice dynamics and thermodynamic properties of half Heusler ScXSb (x= Ni, Pd, Pt) from first principles

We report the lattice dynamics and thermodynamic properties of ScXSb (X= Ni, Pd, Pt) half Heusler compounds. Calculations for the structural and electronic properties were performed based on the Perdew-Burke-Ernzerhof-generalized gradient approximation density functional theory. We used the linear response density functional perturbation theory for computations addressing the elastic property, lattice dynamics, and thermodynamic properties. Results for the equilibrium lattice parameter are in reasonable agreement with reports in the existing literature. The electronic band structure behavior and bandgap agree with relevant results in research. The elastic parameters and phonon dispersions establish the mechanical stability of the compounds. Deductions from the tone of the mode-Grüneisen parameter, specific heat capacity at constant pressure and volume, and thermal expansion favor ScNiSb as the most promising material for thermal conductivity at high temperatures in the three compounds studied. The three compounds obey the Dulong-Petit law at high temperatures. Results for the Dulong-Petit limit is consistent with expectations for solid materials at high temperatures.

Dendrite formation in silicon anodes of lithium-ion batteries

Rechargeable lithium-ion batteries require a vigorous improvement if we want to use them massively for high energy applications. Silicon and metal lithium anodes are excellent alternatives because of their large theoretical capacity when compared to graphite used in practically all rechargeable Li-ion batteries. However, several problems need to be addressed satisfactorily before a major fabrication effort can be launched; for instance, the growth of lithium dendrites is one of the most important to take care due to safety issues. In this work we attempt to predict the mechanism of dendrite growth by simulating possible behaviors of charge distributions in the anode of an already cracked solid electrolyte interphase of a nanobattery, which is under the application of an external field representing the charging of the battery; thus, elucidating the conditions for dendrite growth. The extremely slow drift velocity of the Li-ions of ∼1 mm per hour in a typical commercial Li-ion battery, makes the growth of a dendrite take a few hours; however, once a Li-ion arrives at an active site of the anode, it takes an extremely short time of ∼1 ps to react. This large difference in time-scales allows us to perform the molecular dynamics simulation of the ions at much larger drift velocities, so we can have valuable results in reasonable computational times. The conditions before the growth are assumed and conditions that do not lead to the growth are ignored. We performed molecular dynamics simulations of a pre-lithiated silicon anode with a Li : Si ratio of 21 : 5, corresponding to a fully charged battery. We simulate the dendrite growth by testing a few charge distributions in a nanosized square representing a crack of the solid electrolyte interphase, which is where the electrolyte solution comes into direct contact with the LiSi alloy anode. Depending on the selected charge distributions for such an anode surface, the dendrites grow during the simulation when an external field is applied. We found that dendrites grow when strong deviations of charge distributions take place on the surface of the crack. Results from this work are important in finding ways to constrain lithium dendrite growth using tailored coatings or pre-coatings covering the LiSi alloy anode.

Dendrite formation conditions on a SEI crack exposing the silicon anode to the electrolyte during the charging of a LIB.

Understanding the Unusual Response to High Pressure in KBe2BO3F2

Strong anisotropic compression with pressure on the remarkable non-linear optical material KBe₂BO₃F₂ has been observed with the linear compression coefficient along the c axis found to be about 40 times larger than that along the a axis. An unusual non-monotonic pressure response was observed for the a lattice parameter. The derived bulk modulus of 31 ± 1 GPa indicates that KBe₂BO₃F₂ is a very soft oxide material yet with stable structure up to 45 GPa. A combination of high-pressure synchrotron powder X-ray diffraction, high-pressure Raman spectroscopy, and Density Functional Theory calculations points to the mechanism for the unusual pressure response being due to the competition between the K-F bond length and K-F-K bond angle and the coupling between the stretching and twisting vibration modes.

A first-principles study of the avalanche pressure of alpha zirconium

The critical swelling pressure, the avalanche pressure, is P_a = −15 GPa for alpha zirconium.

Pressure effect on stabilities of self-interstitials in HCP-zirconium

The self-interstitial atoms (SIAs) mediate the evolution of micro-structures which is crucial in understanding the instabilities of hexagonal close packed (HCP) structures. Taking zirconium as a prototype, we investigate the pressure effect on the stabilities of SIAs using first-principles calculations based on density-functional theory. We found that the pressure greatly affects the stability of the SIAs. The SIAs in basal planes are more stable under pressure. The SIA configuration of the lowest formation energy changes from basal octahedral (BO) to octahedral (O) at a pressure of 21 GPa. The lowest formation enthalpy configuration switches from BO to S (split-dumbbell) at the pressure of 30 GPa. The formation volumes of SIAs decrease monotonically in response to an increase in pressure. Our results reveal that it is important to take pressure effects into account when predicting the micro-structural evolution of HCP structures.

High-pressure phase transitions in the rare-earth orthoferrite LaFeO3

Sequential Rietveld refinements were applied on high-pressure synchrotron powder X-ray diffraction measurements of lanthanum ferrite (LaFeO3) revealing two phase transitions on the room-temperature isotherm up to a pressure of 48 GPa. The first structural phase transition of second order occurs at a pressure of 21.1 GPa, changing the space group fromPbnmtoIbmm. The second transition, involving a isostructural first-order phase transition, occurs at approximately 38 GPa, indicating a high-spin to low-spin transition of the Fe3+ion. Following the behavior of the volume up to the hydrostatic limit of methanol–ethanol it was possible to use inverted equations of state (EoS) to determine a bulk modulus ofB0= 172 GPa and a corresponding pressure derivative ofB′0= 4.3. In addition, the linearized version of the inverted EoS were used to determine the corresponding moduli and pressure derivatives for each lattice direction.

Applicability of isothermal unrealistic two-parameter equations of state for solids

The aim of the present study, an extension of a recent one (Bose Roy and Bose Roy 2005 J. Phys.: Condens. Matter 17 6193), is to assess and compare the curve-fitting utility of the isothermal unrealistic two-parameter equations of state for solids (EOS), proposed at different stages in the development of the EOS field, for the purposes of smoothing and interpolation of pressure-volume data, and extraction of accurate values of the isothermal bulk modulus and its pressure derivative. To this end, 21 such EOSs are considered, formulated by/labelled as Born-Mie (1920), Born-Mayer (1932), Bardeen (1938), Slater-Morse (1939), Birch-Murnaghan (1947), Pack-Evans-James (1948), Lagrangian (1951), Davydov (1956), Davis and Gordon (1967), Onat and Vaisnys (1967), Grover-Getting-Kennedy (1973), Brennan-Stacey (1979), Walzer-Ullmann-Pan'kov (1979), Rydberg (1981), Dodson (1987), Holzapfel (1991), Parsafar-Mason (1994), Shanker-Kushwah-Kumar (1997), Poirier-Tarantola (1998), Deng-Yan (2002) and Kun-Loa-Syassen (2003). Furthermore, all these EOSs are compared with our three-parameter EOS, as well as its two-parameter counterpart proposed in this work. We have applied all the EOS models, with no constraint on the parameters, to the accurate and model-independent isotherms of nine solids. The applicability has been assessed in terms of an unbiased composite test, comprising fitting accuracy, agreement of the fit parameters with experiment, stability of the fit parameters with variation in the compression/pressure ranges and on the basis of the number of wiggles of the data deviation curves about the fit parameters. Furthermore, a rigorous method is devised to scale the relative adequacy of the EOSs with respect to the test parameters. A number of remarkable findings emerge from the present study. Surprisingly, both the old EOSs, the Born-Mie and the Pack-Evans-James, are significantly better in their curve-fitting capability than the Birch-Murnaghan EOS which has been widely used and continues to be used for curve-fitting purposes as a standard EOS in the literature. The Born-Mayer as well as the Walzer-Ullmann-Pan'kov models also fit isotherms better than the Birch. The performance of the EOS based on the Rydberg potential-that has been rediscovered by Rose et al (1984 Phys. Rev. B 29 2963), and strongly promoted by Vinet et al (1989 J. Phys.: Condens. Matter 1 1941) as the so-called universal equation of state, and is currently used as a standard EOS along with that of the Birch-is very poor, on a comparative scale. Furthermore, the curve-fitting capability of our original three-parameter EOS, and more importantly its two-parameter counterpart, is superior to all the isothermal unrealistic two-parameter EOSs so far proposed in the literature.

A novel method for static equation-of state-development: Equation of state of a cross-linked poly(dimethylsiloxane) (PDMS) network to 10 GPa

Pressure-volume-temperature (PVT) equation-of-state (EOS) information for polymers and polymeric composites is valuable for predicting their response to extreme conditions. An obstacle in determining equations of state for polymeric materials is the lack of a simple, static experimental method for acquiring PVT data for solid networks and liquids at pressures greater than several kilobars. Here, we report a novel approach in determining static EOS for polymers using high-pressure diamond-anvil cells coupled with optical microscopy and image analysis. Results are presented for a cross-linked poly(dimethylsiloxane) polymer, Sylgard 184. Static isothermal results were fitted to empirical and semiempirical equations of state, including the Tait, Birch-Murnaghan, and Vinet forms. Static PV data were also converted to pseudoshock velocity-pseudoparticle velocity (U(s)-u(p)) for comparison to dynamic Hugoniot data. A linear Rankine-Hugoniot fit U(s)=s(T)u(p)+c(T) gives c(T)=1.572 km/s and s(T)=1.703. s(T) is related to the pressure derivative of the bulk modulus B(0) (') by s(T)=(B(0) (')+1)/4 and B(0) (')=5.8. A comparison of the static and shock data is given, along with an estimate of the Grüneisen parameter, and a discussion of the free volume content in the polymer network, and limitations of this novel method.

Density and composition of the lower mantle

The observed density distribution of the lower mantle is compared with density measurements of the (M g,Fe)SiO 3 perovskite and (Mg,Fe)O magnesiowtistite highpressure phases as functions of pressure, tem perature and composition. We find that for plausible bounds on the composition of the upper mantle (ratio of magnesium to iron + magnesium components x M g ^ 0.88) and the temperature in the lower mantle ( T ^ 2000 K), the high-pressure mineral assemblage of upper-mantle composition is at least 2 .6 ( ± 1 ) % less dense than the lower m antle over the depth range 1000-2000 km. Thus, we find that a model of uniform m antle composition is incompatible with the existing mineralogical and geophysical data. Instead, we expect that the mantle is stratified, with the upper and lower m antle convecting separately, and we estimate that the compositional density difference between these regions is about 5 ( + 2) %. The stratification may not be perfect (‘leaky layering’), but significant intermixing and homogenization of the upper and lower m antle over geological timescales are precluded.