A new high-pressure polymorph of Ti2O3: implication for high-pressure phase transition in sesquioxides

The post-corundum phase transition has been investigated in Ti₂O₃ on the basis of synchrotron X-ray diffraction in a diamond anvil cell and transmission electron microscopy. The new polymorph of Ti₂O₃ was found at about 19 GPa and 1850 K, and this phase was stable even at about 40 GPa. A new polymorph of Ti₂O₃ can be indexed on a Pnma orthorhombic cell, and the unit-cell parameters are a=7.6965 (19) Å, b=2.8009 (9) Å, c=7.9300 (23) Å, V=170.95 (15) Å³ at 19 GPa, and a=7.8240 (2) Å, b=2.8502 (1) Å, c=8.1209 (3) Å, V=181.10 (1) Å³ at ambient conditions. The Birch–Murnaghan equation of state yields K ₀=206 (3) GPa and K′₀=4 (fixed) for corundum phase, and K ₀=296 (4) GPa and K′₀=4 (fixed) for the post-corundum phase. The molar volume decreases by 12% across the phase transition at around 20 GPa. The structural identification was carried out on a recovered sample by the Rietveld method, and a new polymorph of Ti₂O₃ can be identified as Th₂S₃-type rather than U₂S₃-type structure. The transition from corundum-type to Th₂S₃-type structure accompanies the drastic change of the form of polyhedron: from TiO₆ octahedron in the corundum-type to TiO₇ polyhedron in the Th₂S₃-type structures.     

First-principles study of structural,elastic, electronic and thermodynamic properties of topological insulator Bi2Se3 under pressure

The structural, elastic, electronic and thermodynamic properties of the rhombohedral topological insulator Bi₂Se₃ are investigated by the generalized gradient approximation (GGA) with the Wu–Cohen (WC) exchange-correlation functional. The calculated lattice constants agree well with the available experimental and other theoretical data. Our GGA calculations indicate that Bi₂Se₃ is a 3D topological insulator with a band gap of 0.287 eV, which are well consistent with the experimental value of 0.3 eV. The pressure dependence of the elastic constants C_ij, bulk modulus B, shear modulus G, Young’s modulus E, and Poisson’s ratio σ of Bi₂Se₃ are also obtained successfully. The bulk modulus obtained from elastic constants is 53.5 GPa, which agrees well with the experimental value of 53 GPa. We also investigate the shear sound velocity V_S, longitudinal sound velocity V_L, and Debye temperature Θ_E from our elastic constants, as well as the thermodynamic properties from quasi-harmonic Debye model. We obtain that the heat capacity C_v and the thermal expansion coefficient α at 0 GPa and 300 K are 120.78 J mol^?1 K^?1 and 4.70 × 10^?5 K^?1, respectively.     

Pressure-induced phase transformation of CsPbI3 by X-ray diffraction and Raman spectroscopy

The structural transformation of cesium lead iodine (CsPbI₃) has been investigated in diamond anvil cells up to ～15 GPa at room temperature by employing synchrotron radiation X-ray diffraction and Raman spectroscopy. One reversible transformation from orthorhombic (Pnma) to monoclinic (P2₁/m) phase has been observed at 3.9 GPa. Isothermal pressure–volume relationship of orthorhombic CsPbI₃ is well fitted by the third-order Birch–Murnaghan equation of state with K₀ = 14(3) GPa, K′₀ = 6(2) and V₀ = 891(7) ų. The ultralow value of bulk modulus K₀ demonstrates the high compressible nature of CsPbI₃, similar to those of organic–inorganic metal halide perovskites. The present results provide essential information on the intrinsic properties and stability of CsPbI₃, which may be applied in photovoltaic devices.     

In situ high-pressure X-ray diffraction experiments and ab initio calculations of Co2P

In situ high-pressure experiments of Co2P are carried out by means of angle dispersive X-ray diffraction with diamond anvil cell technique. No phase transition is observed in the present pressure range up to 15 GPa at room temperature, even at high temperature and 15 GPa. Results of compression for Co2P are well presented by the second-order Birch-Murnaghan equation of state with V0 = 130.99(2)3 (1=0.1 nm) and K0 = 160(3) GPa. Axial compressibilities are described by compressional modulus of the axis: Ka = 123(2) GPa, Kb = 167(8) GPa and Kc = 220(7) GPa. Theoretical calculations further support the experimental results and indicate that C23-type Co2P is stable at high pressure compared with the C22-type phase.     

An in situ high-pressure X-ray diffraction experiment of hydroxyapophyllite

The compression behavior of a natural hydroxyapophyllite is investigated up to about 10.01 GPa at 300 K using in situ angle-dispersive X-ray diffraction and a diamond anvil cell at High Pressure Experiment Station, Beijing Synchrotron Radiation Facility (BSRF). Over this pressure range, no phase change or disproportionation is observed. The isothermal equation of state is determined for the first time. The values of zero-pressure volume V₀, isothermal bulk modulus K₀, and K₀' refined with a third-order Birch-Murnaghan equation of state are V₀=1276.3±0.9 ų, K₀=71±3 GPa, and K₀'=8±1. Furthermore, we confirm that the values of linear compressibility β along a and c directions of hydroxyapophyllite are elastically anisotropic.     

Spin-lattice relaxation of the Vk-center in LiF

The angular and temperature dependences of the spin-lattice relaxation (SLR) rate of V_k-centers in LiF doped with Mg or Ag have been investigated. In the temperature interval 4.2–100 K the results can be fitted by the formula $\text{τ}{}^{\mathrm{?1}}\text{= A(θ)T + Be}{}^{\mathrm{<mtext>?\Delta </mtext><mtext>T</mtext>}}$ with A(0°) = 0.11 sec^?1K^?1, A(90°) = 1.3 sec^?1K^?1, B = 3 × 10⁵sec^?1 and Δ = (175 ± 15)K.A mechanism for the SLR is considered, assuming the modulation of the hyperfine interaction by phononinduced transitions between the ground and excited states of the resonant molecular vibrations of the V_k-center. This mechanism is found to explain the value, the temperature dependence and the isotropy of τ^?1 in the interval T = 20–100 K.The one-phonon SLR mechanisms of the V_k-center in the T < 10 K region are discussed.     

A new acentric borate of K2Ba[B4O5(OH)4]2·10H2O: synthesis,structure and nonlinear optical property

A new acentric mixed metal borate of composition K₂Ba[B₄O₅(OH)₄]₂·10H₂O, has been successfully obtained by slow evaporation solution method. The compound crystallizes in the Orthorhombic space group Pna21 (No.33) with a = 16.8668(7) Å, b = 13.0903(5) Å, c = 11.5529(5) Å and Z = 4. [B₄O₅(OH)₄]^2? clusters serve as fundamental building unit linking with BaO₈, K1O₆, K2O₇ by common O atoms to form three-dimensional layer structure. The second harmonic generation measurements in the powder samples reveal that the compound exhibits approximately 0.5 times that of KH₂PO₄ (KDP) and phase matching.     

In-situ X-ray diffraction study on β-CrOOH at high pressure and high-temperature

ABSTRACT

High pressure hydrous phases with distorted rutile-type structure have attracted much interest as potential water reservoirs in the Earth’s mantle. An in-situ X-ray diffraction study of β-CrOOH was performed at high pressures of up to 6.2?GPa and high-temperatures of up to 700?K in order to clarify the temperature effect on compression behaviors of β-CrOOH. The P-V-T data fitted to a Birch–Murnaghan equation of state yielded the following results: isothermal bulk modulus K_T0?=?191(4)?GPa, temperature derivative (?K_T/?T)_P?=??0.04(2)?GPa?K^?1, and volumetric thermal expansion coefficient α?=?3.3(2)?×?10^?5?K^?1. In this study, at 300?K, the a-axis became less compressible at pressures above 1–2?GPa. We found that the pressure where the slopes of a/b and a/c ratios turned positive increased with temperature. This is the first experimental study indicating the temperature dependence of the change in the axial compressibility in distorted rutile-type M³⁺OOH.     

Conformational and Structural Analysis of 6‐(4‐Methoxy‐phenyl)‐1,5,7a‐triphenyl‐tetrahydro‐imidazo[1,5‐b][1,2,4]oxadiazol‐2‐one

Abstract

The cis stereochemistry of 6‐(4‐methoxy‐phenyl)‐1,5,7a‐triphenyl‐tetrahydro‐imidazo[1,5‐b][1,2,4]oxadiazol‐2‐one was studied by use of a PM3 semi‐empirical quantum mechanical model, and x‐ray crystallographic analysis. It crystallizes in the monoclinic space group P2 ₁ /n with a = 10.812(1) Å, b = 16.464(2) Å, c = 13.379(1) Å, α = 90.00°, β = 98.39(1)°, γ = 90.00°, V = 2356.07(4) Å³, Z = 4, D _calc = 1.3067 g cm^?3, F(0 0 0) = 976.41, and μ = 0.086 mm^?1. The structure was solved by direct methods and refined to R = 0.066 for 1257 independent reflections [I > 4σ (I)]. The results from x‐ray diffraction were seen to be generally consistent with the results from previously reported spectroscopic investigations, beside theoretical calculations, except for conformations of five‐membered fused heterocycles. Two inter‐ and intramolecular weak interactions in addition to carbon atoms (C1 and C3) with different chiralities were found in the structure. The conformational study was performed by randomly scanning the potential energy surface belonging to the title compound with respect to selected torsion angles.     

P–V–T equation of state of rhodium oxyhydroxide

A high pressure X-ray diffraction study of RhOOH was carried out up to 17.44?GPa to investigate the compression behavior of an oxyhydroxide with an InOOH-related structure. A fit to the third-order Birch–Murnaghan equation of state gave K₀?=?208?±?6?GPa, and K′?=?9.4?±?1.3. The temperature derivative of the bulk modulus was found to be ?K/?T?=??0.06?±?0.02?GPa K^?1. The refined parameters for volume thermal expansion were α₀?=?2.7?±?0.3?×?10^?5 K^?1; α₁?=?1.7?±?1.1?×?10^?8 K^?2 in the polynomial form (α(T)?=?α_0?+?α₁(T?300)). Our results show that RhOOH is very incompressible, and has a higher bulk modulus than other InOOH-structured oxyhydroxides (e.g. δ-AlOOH, ε-FeOOH, and γ-MnOOH).     

Polymer/clay nanocomposites based on MMT/ODA intercalates

Natural Na-montmorillonite (MMT) with the formula (Na_0.67K_0.01Ca_0.02)(Al_2.90Mg_0.59 Fe³⁺ _0.49Ti_0.01)(Si_7.92Al_0.08)O₂₀(OH)₄was intercalated with octadecylamine (C₁₈H₃₉N) (ODA) with varied MMT/ODA ratios. The basal spacings d(00l) of natural and intercalated Na-MMT with ODA were determined by XRD analysis. The set of basal diffractions: d(001) = 56 Å, d(002) = 28 Å, d(003) = 18 Å, d(004) = 14 Å, d(005) = 11 Å for the saturated Na-MMT/ODA intercalate indicates existence of highly ordered periodic structure with the ODA double-layer intercalated in the silicate interlayer spacing. Molecular modeling calculations were applied to the Na-MMT/ODA saturated intercalation system. Stable structure with d-spacing 53 Å has been calculated which is in a good agreement with the experimental data. Such structure gives good conditions for the organosilicate layered structure exfoliation and nanocomposite production. Na-MMT/ODA intercalates were compounded with polypropylene. In accordance with theoretical predictions, XRD analysis applied to compounded structures have proved that a high degree of the organoclay exfoliation was achieved.     

Semiempirical determination of the atom-surface interaction

We discuss three methods of determining V(z), the lateral average (G = 0 Fourier component) of the atom-surface interaction, from the bound state spectrum found in beam scattering. One method uses the Rydberg-Klein-Rees technique, which yields the width of the potential (i.e., separation of classical turning points) as a function of energy. This method incorporates also the known asymptotic form V ～ ?C₃z^?3, whereC₃ is derived from the polarizability and dielectric function of atom and solid, respectively. The second method uses a hybrid potential, constructed from a Morse potential with shifted zero of energy connected to the asymptotic form,?C₃z^?3, requiring continuity of V and $\text{d}\text{V}\text{d}\text{z}$. The third potential is a Lennard-Jones 3–9 interaction. Results are presented for H and He scattering from LiF and NaF.     

L p -Boundedness of the Wave Operator for the One Dimensional Schrödinger Operator

Given a one dimensional perturbed Schrödinger operator H =  ? d ²/dx ² + V(x), we consider the associated wave operators W  _± , defined as the strong L ² limits $\lim_{s\to\pm\infty}e^{isH}e^{-isH_{0}}Given a one dimensional perturbed Schr?dinger operator H = − d ²/dx ² + V(x), we consider the associated wave operators W _± , defined as the strong L ² limits . We prove that W _± are bounded operators on L ^p for all 1 < p < ∞, provided , or else and 0 is not a resonance. For p = ∞ we obtain an estimate in terms of the Hilbert transform. Some applications to dispersive estimates for equations with variable rough coefficients are given.     

Phase transformations of Fe3N-Fe4N iron nitrides at pressures up to 30 GPa studied by in situ X-ray diffractometry

The parameters of the equation of state of the stable ?-Fe₃N _x (where x = 0.8) nitride in the Fe-N system have been determined at pressures up to 30 GPa and temperatures up to 1273 K. The parameters V ₀ = 81.48(2) Å^?3, K _T = 162(3) GPa, K _T = 4.0 = 1.66(2), γ₀ = 555 K, and q = 1 have been determined for ?-Fe₃N_0.8 by the approximation of the P-V-T data with the Vinet equation of state and the thermal parameters within the Mie-Grüneisen-Debye formalism. No anomalous change in the volume of the cell owing to possible magnetic transitions has been revealed. The instability of Fe₄N at high pressures and Fe₃N in the presence of a deficit of nitrogen in the system has been established. The stable phase in the temperature range of 300–673 K and the pressure range of 20–30 GPa is ?-Fe₃N rather than ?-Fe₃N_0.8.     

Infrared transitions of C2D6 from v 4 to the interacting system v 4+ v 6, v 4+ v8, v 3+ 2v 4: rotational analysis,and torsional splitting in the v 3+ 2v 4 and v 3+ v 4 states

The hot infrared transitions of C₂D₆ from the υ₄(A_1u ) to the υ₄ + υ₆(A_2g ) and υ₄ + υ₈(E _g ) vibrational states, observed from 960 to 1180 cm^?1, have been rotationally analysed on a high-resolution Fourier transform spectrum (full width at half-maximum about 0·0030 cm^?1). The vibration-rotation interactions affecting the upper vibrational states are very similar to those of the corresponding cold system. A strong x,y Coriolis interaction between υ₄ + υ₆ and υ₄ + υ₈, with K-level crossing, generates large displacements of the rotational components of both vibrational states, tuning them to additional local resonances in several spectral regions. Thus l resonances with Δl = ±2, Δk = ±1 occur within υ₄ + υ₈. A x,y Coriolis-type resonance between υ₄ + υ₈(?l,K ? 1) and υ₃ + 2υ₄(K) occurs at K = 11,12,13, and a further coupling of υ₄ + υ₈(+l,K + 1) and υ₃ + 2υ₄(K + 3) is most effective at K = 11 and 12. These resonances induce torsional splittings on the perturbed levels of υ₄ + υ₈ and allow us to determine the torsional splittings in the υ₃ + 2υ₄ state. The vibration-rotation constants of υ₄ + υ₆, υ₄ + υ₈ and υ₃ + 2υ₄, several interaction parameters and the torsional splitting of υ₃ + 2υ₄ have been determined by least-squares fit of 1391 observed transition wavenumbers, with an overall standard deviation σ = 0·75 × 10^?3 cm^?1. The vibrational wavenumbers found for the four torsional components of (υ₃ + 2υ₄)? υ₄ are υ(E_3d) = 1040·961 82(809)cm^?1, υ(A_3d) = 1041·218 27(865)cm^?1, υ(E_3s) = 1041·225 23(662)cm^?1 and υ(A_1s) = 1041·407 77(633)cm^?1. These are anomalous for both the order of the torsional components and the magnitudes of their separations. We believe that this is mainly due to the interactions of υ₃ + 2υ₄ with the torsional manifolds with υ₃ = 0 and υ₃ = 2, through the vibration-torsion Hamiltonian term (?V ₆/?q ₃)q ₃cos (6γ)]/2. The further observation of a few doublets of υ₈ and υ₃ + υ₄ at resonance provides information on the torsional splitting of the latter state.     

Equation of state of liquid Fe–17 wt%Si to 12 GPa

Equation of state (EOS) of liquid Fe–17 wt%Si has been investigated at a temperature of 1773 K and pressures up to 12 GPa by the sink/float technique using composite spheres. The EOS of liquid Fe–17 wt%Si, in the form of the second order Birch–Murnaghan equation, produces K _0T=68±2 GPa when K′_0T=4.0. Considering the effect of temperature and pressure on K _0T, extrapolation of this EOS to Earth's outer core conditions reveals that the addition of Si to liquid Fe decreases its density ρ and increases its compressional wave velocity V _P , indicating that Si is a possible light element candidate in the outer core. The possible existence of Si in the cores of other planetary bodies is also discussed.     

Degree Complexity of Birational Maps Related to Matrix Inversion

For a q × q matrix x = (x _{i, j} ) we let ${J(x)=(x_{i,j}^{-1})}For a q × q matrix x = (x _{i, j} ) we let J(x)=(x_i,j^-1){J(x)=(x_{i,j}^{-1})} be the Hadamard inverse, which takes the reciprocal of the elements of x. We let I(x)=(x_i,j)^-1{I(x)=(x_{i,j})^{-1}} denote the matrix inverse, and we define K=I°J{K=I\circ J} to be the birational map obtained from the composition of these two involutions. We consider the iterates Kⁿ=K°?°K{K^n=K\circ\cdots\circ K} and determine the degree complexity of K, which is the exponential rate of degree growth d(K)=lim_n?￥( deg(Kⁿ) )^1/n{\delta(K)=\lim_{n\to\infty}\left( deg(K^n) \right)^{1/n}} of the degrees of the iterates. Earlier studies of this map were restricted to cyclic matrices, in which case K may be represented by a simpler map. Here we show that for general matrices the value of δ(K) is equal to the value conjectured by Anglès d’Auriac, Maillard and Viallet.     

Amorphous germanium II. Structural properties

The coherent X-ray scattering for momentum transfer, k, between 0·025 and 15·0 Å^?1 has been measured for a series of sputtered amorphous Ge films prepared at various substrate temperatures, T _s, between 0 and 350°C. Differences in the radial distribution function (RDF) of films of different T _s have been determined by an accurate differential scattering technique. The small angle scattering (SAS) of the films is less than 100 electron units for k < 1 Å^?1. From a combination of SAS, RDF and scanning electron microscope studies, it is concluded that an observed increase in film density with increasing T _s occurs through a reduction in the number of voids about 7 Å or less in diameter. No variation of bond length with T _s is found. With increasing T _s, there is an increase in first and second-neighbour coordination and a reduction in bond angle distortion.

The rate of change of coordination, C, with density, ρ₀, is found to be d ln C/d ln ρ₀ = 0·6±0·2. Using a new, general theory of the dependence of the RDF on the dihedral angle distribution, P(θ), it is shown that with increasing T _s there is an increased probability of dihedral angles corresponding to the staggered configuration. For all films, the experimental RDF between r = 4·5 and 6·2 Å agrees with a nearly random P(θ) distribution. Comparison of experimental RDF's of crystalline and amorphous Ge indicates the static distortion of the first-neighbour bond length has a standard deviation of only about 0·04 Å.