Beryllium Silicate,Be2SiO4 (phenakite) – a Novel Trigonal SRS‐Active Crystal

In single crystals of the beryllium silicate Be₂SiO₄ with trigonal symmetry , known also as the mineral phenakite, χ⁽³⁾‐nonlinear lasing by stimulated Raman scattering (SRS) is investigated. All observed Stokes and anti‐Stokes lasing components are identified and ascribed to a single SRS‐promoting vibration mode with ω_SRS ≈876 cm⁻¹. With picosecond single‐wavelength pumping at one micrometer the generation of an octave‐spanning Stokes and anti‐Stokes comb is observed.     

Calcium and strontium thio­sulfate,CaS2O3·6H2O and SrS2O3·5H2O

In contrast to former morphological studies, the results presented here show that calcium(II) thio­sulfate hexahydrate, CaS₂O₃·6H₂O, crystallizes centrosymmetrically in the pinacoidal class (point group ). The structure is characterized by chains, parallel to [100], of alternating S₂O₃ and Ca(H₂O)₆O₂ groups sharing common O atoms. The composition of each chain link is [Ca(H₂O)₆(S₂O₃)]. The geometry is analysed and compared in detail with the structural features of monoclinic strontium(II) thio­sulfate pentahydrate, SrS₂O₃·5H₂O, which forms layers, parallel to (100), of alternating S₂O₃ and Sr(H₂O)₄O₅ groups connected via common O atoms and O–O edges. Each layer contains [Sr(H₂O)₃O(S₂O₃)]_∞ as the unique repeat unit.     

Three novel non‐centrosymmetric compounds of glycine: glycine lithium sulfate,glycine nickel dichloride dihydrate and glycine zinc sulfate trihydrate

The crystal structures of three compounds of glycine and inorganic materials are presented and discussed. The ortho­rhombic structure of glycinesulfatodilithium(I), [Li₂(SO₄)(C₂H₅NO₂)]_n, consists of corrugated sheets of [LiO₄] and [SO₄] tetrahedra. The glycine mol­ecules are located between these sheets. The main features of the monoclinic structure of di­aqua­di­chloro­glycinenickel(II), [NiCl₂(C₂H₅NO₂)(H₂O)₂]_n, are helical chains of [NiO₄Cl₂] octahedra connected by glycine mol­ecules. The orthorhombic structure of tri­aqua­glycinesulfatozinc(II), [Zn(SO₄)(C₂H₅NO₂)(H₂O)₃]_n, is made up of [O₃SOZnO₅] clusters. These clusters are linked by glycine mol­ecules into zigzag chains. All three compounds are examples of non‐centrosymmetric glycine compounds.     

Logarithmic Finite-Size Correction in Non-neutral Two-Component Plasma on Sphere

We consider a general two-component plasma of classical pointlike charges \(+e\) (e is say the elementary charge) and \(-Z e\) (valency \(Z=1,2,\ldots \)), living on the surface of a sphere of radius R. The system is in thermal equilibrium at the inverse temperature \(\beta \), in the stability region against collapse of oppositely charged particle pairs \(\beta e^2 < 2/Z\). We study the effect of the system excess charge Qe on the finite-size expansion of the (dimensionless) grand potential \(\beta \varOmega \). By combining the stereographic projection of the sphere onto an infinite plane, the linear response theory and the planar results for the second moments of the species density correlation functions we show that for any \(\beta e^2 < 2/Z\) the large-R expansion of the grand potential is of the form \(\beta \varOmega \sim A_V R^2 + \left[ \chi /6 - \beta (Qe)^2/2\right] \ln R\), where \(A_V\) is the non-universal coefficient of the volume (bulk) part and the Euler number of the sphere \(\chi =2\). The same formula, containing also a non-universal surface term proportional to R, was obtained previously for the disc domain (\(\chi =1\)), in the case of the symmetric \((Z=1)\) two-component plasma at the collapse point \(\beta e^2=2\) and the jellium model \((Z\rightarrow 0)\) of identical e-charges in a fixed neutralizing background charge density at any coupling \(\beta e^2\) being an even integer. Our result thus indicates that the prefactor to the logarithmic finite-size expansion does not depend on the composition of the Coulomb fluid and its non-universal part \(-\beta (Qe)^2/2\) is independent of the geometry of the confining domain.     

Three-dimensional lattice ground states for Riesz and Lennard-Jones–type energies

The Riesz potential $f_s(r)=r^{-s}$ is known to be an important building block of many interactions, including Lennard-Jones–type potentials $f_{n,m}^{\mathrm{LJ}}(r):=a{r}^{-n}-b{r}^{-m}$, $n>m$ that are widely used in molecular simulations. In this paper, we investigate analytically and numerically the minimizers among three-dimensional lattices of Riesz and Lennard-Jones energies. We discuss the minimality of the body-centered-cubic (BCC) lattice, face-centered-cubic (FCC) lattice, simple hexagonal (SH) lattices, and hexagonal close-packing (HCP) structure, globally and at fixed density. In the Riesz case, new evidence of the global minimality at fixed density of the BCC lattice is shown for and the HCP lattice is computed to have higher energy than the FCC (for $s>3/2$) and BCC (for ) lattices. In the Lennard-Jones case with exponents , the ground state among lattices is confirmed to be an FCC lattice whereas an HCP phase occurs once added to the investigated structures. Furthermore, phase transitions of type “FCC-SH” and “FCC-HCP-SH” (when the HCP lattice is added) as the inverse density V increases are observed for a large spectrum of exponents $(n,m)$. In the SH phase, the variation of the ratio Δ between the interlayer distance d and the lattice parameter a is studied as V increases. In the critical region of exponents , the SH phase with an extreme value of the anisotropy parameter Δ dominates. If one limits oneself to rigid lattices, the BCC-FCC-HCP phase diagram is found. For , the BCC lattice is the only energy minimizer. Choosing , the FCC and SH latices become minimizers.