CaSO4 and its pressure-induced phase transitions. A density functional theory study

Theoretical investigations concerning possible calcium sulfate, CaSO(4), high-pressure polymorphs have been carried out. Total-energy calculations and geometry optimizations have been performed by using density functional theory at the B3LYP level for all crystal structures considered. The following sequence of pressure-driven structural transitions has been found: anhydrite, Cmcm (in parentheses the transition pressure) → monazite-type, P2(1)/n (5 GPa) → barite-type, Pnma (8 GPa), and scheelite-type, I4(1)/a (8 GPa). The equation of state of the different polymorphs is determined, while their corresponding vibrational properties have been calculated and compared with previous theoretical results and experimental data.     

New results for phase transitions from catastrophe theory

Catastrophe theory predicts that in certain limits universal relations should exist between barrier heights, curvatures and the positions of local maxima and minima on a potential or free energy surface. In the present work we investigate these relations for both first- and second-order phase transitions, revealing that the ideal ratios often hold quite well over a wide range of conditions. This elementary catastrophe theory is illustrated for the melting transition of an atomic cluster, the isotropic-to-nematic transition in a liquid crystal, and the ferromagnetic-to-paramagnetic phase transition in the two-dimensional Ising model.     

Cobalt in NaBH4 hydrolysis

Cobalt-catalyzed hydrolysis of sodium borohydride (NaBH(4)) has attracted great attention since the hydride is believed to be promising hydrogen storage material. Cobalt is an efficient metal catalyst and has already proven to be a potential alternative to noble metals. Nevertheless it is not stable. Indeed it transforms into a Co- and B-based material when on contact with NaBH(4). Through ex situ characterizations (e.g. ICP, XRD, XPS and SEM), the Co- and B-based material has been supposed to be either a cobalt boride Co(x)B (with x from 1 to 3) or a Co-B alloy. This contradiction is the topic of the present paper. Herein, the literature dedicated to the Co-catalyzed NaBH(4) hydrolysis is exhaustively surveyed. The results of the ex situ characterizations are largely discussed, for example that: (i) the ex situ characterized Co(x)B or Co-B might be different from the in situ formed Co- and B-based catalyst; (ii) there is no clear evidence of the formation of either Co(x)B or Co-B; (iii) the in situ formed catalyst would change in accordance with a cycle in the course of the hydrolysis; and (iv) in situ characterizations are clearly required but their setting up is a challenge. These conclusions, among others, are argued.     

Multivariable kinetic theory of the first order phase transitions

The problem of calculation of the steady state homogeneous nucleation rate in the multidimensional space of the variables describing a nucleus is considered. Within the framework of the theory proposed, expressions for the nucleation rate and the steady state distribution function of nuclei are derived. The expression for the nucleation rate is invariant with respect to the space dimensionality and, in particular, involves the result of the one-dimensional theory. The distribution function is obtained in the initial, physical variables. In connection with the analysis of restrictions on the current direction, the question of symmetry of the matrix of diffusivities is considered; on the basis of the detailed balance principle it is shown that this matrix is symmetric. The question of normalizing the equilibrium distribution functions is investigated and the physical picture of the equilibrium state is described. The procedure of reducing the multidimensional theory to the one-dimensional one is described.     

A simple theory of liquid—solid phase transitions

A simple phenomenological theory of liquid—solid phase transitions, based on the use of perturbation theory about a hard-sphere fluid, is examined. A temperature dependent hard-sphere diameter is determined which permits the prediction of solid and liquid densities and melting pressures. Calculations presented here for the Lennard-Jones 12-6 fluid show good agreement with the computer simulation results. Provided pair potentials are available, the theory may also be used for other fluids, including liquid metals.     

Pressure-induced phase transitions in PbTiO3: a query for the polarization rotation theory

Our first-principles computations show that the ground state of PbTiO3 under hydrostatic pressure transforms discontinuously from P4mm to R3c at 9 GPa. Spontaneous polarization decreases with increasing pressure so that the R3c phase transforms to the centrosymmetric Rc phase at around 27 GPa. The first-order phase transition between the tetragonal and rhombohedral phases is exceptional since there is no evidence for a bridging phase. The essential feature of the R3c and Rc phases is that they allow the oxygen octahedron to increase its volume VB at the expense of the cuboctahedral volume VA around a Pb ion. This is further supported by the fact that neither the R3m nor Cm phase, which keep the VA/VB ratio constant, is a ground state within the pressure range between 0 and 40 GPa. Thus, tetragonal strain is dominant up to 9 GPa, whereas at higher pressures, efficient compression through oxygen octahedra tilting plays the central role for PbTiO3. Previously predicted pressure induced colossal enhancement of piezoelectricity in PbTiO3 corresponds to unstable Cm and R3m phases. This suggests that the phase instability, in contrast to the polarization rotation, is responsible for the large piezoelectric properties observed in systems like Pb(Zr,Ti)O3 in the vicinity of the morphotropic phase boundary.     

Towards a molecular theory of phase transitions in fatty acid monolayers

A molecular theory of phase transitions in fatty acid monolayers at the air/water interface is proposed based on rotational ordering of molecules about their longitudinal axes. The first order statistical mechanical lattice model of Bell, Mingins, and Taylor (BMT ) which is an equilibrium diluted Ising model is used to describe the monolayer behavior of some simple aliphatic carboxylic acids. The interaction energy parameters in the BMT model are adjusted to give reasonable agreement with the experimentally observed chain length dependence, and the energies thus obtained are compared with those calculated for interacting aliphatic carboxylic acid dimers by the technique of perturbative configuration interaction using localized orbitals (PCILO ). It is concluded that intermolecular rotational ordering due to the anisotropy of the intermolecular potential plays a significant role in simple fatty acid monolayer phase behavior. A possible experimental test of the model is briefly described.     

The crystal structure and phase transitions of LiBaPO4

Polymorphism in lithium barium phosphate (LiBaPO₄) was investigated by synchrotron X-ray diffraction (sXRD) and high temperature X-ray diffraction (HT-XRD). Two modifications were isolated using different cooling rates from the synthesis temperature to room temperature. The slowly-cooled sample exhibited a monoclinic structure with a Cc space group (denoted as M-LiBaPO₄) while the quenched sample belonged to a trigonal system with a P31c space group (denoted as T-LiBaPO₄). In both structures, LiO₄ and PO₄ tetrahedra are linked alternatively by sharing each corner in the lattice, forming tridymite-type six-membered rings. The voids in the anionic framework are filled by Ba atoms. The monoclinic distortion in M-LiBaPO₄ can be attributed to “polyhedral tilting” which shifts the axial bridging oxygens from the centroid of the PO₄ tetrahedron, breaking the three-fold symmetry in the trigonal structure. The HT-XRD data upon heating from 298 to 1373 K indicate successive structural transitions as follows; M-LiBaPO₄ (Cc) → T-LiBaPO₄ (P31c) → H-LiBaPO₄ (P6₃) → O-LiBaPO₄ (Pmcn). H-LiBaPO₄ and O-LiBaPO₄ denote the phases exhibiting the hexagonal and orthorhombic systems, respectively. The thermal evolution of the crystal structure of LiBaPO₄ is quite similar to that of LiKSO₄. The sequences of space group change in both compounds are nearly identical and only the transition temperatures differ.     

Distinct phase transitions and dielectric anomalies in two 4-methylanilinium salts

Solid-state phase transitions of 4-methylanilinium perchlorate (4-CH 3 C 6 H 4 NH 3 ·ClO 4 , 1) and tetrafluoroborate (4-CH 3 C 6 H 4 - NH 3 ·BF 4 , 2) were investigated with variable-temperature X-ray single-crystal structure analysis and thermal studies. Both 1 and 2 undergo first-order phase transitions and exhibit distinct dielectric anomalies at 385 and 247 K, respectively.     

Membrane distillation: theory and experiments

A theoretical approach is presented that describes membrane distillation processes due to the simultaneous action (in a proactive or in a counteractive way) of temperature and concentration differences through porous hydrophobic membranes. The model developed emphasizes the importance of the boundary layers, shows the existence of a coupling term between the two thermodynamic forces acting on the system, and permits the definition and characterization of the so-called steady states. In order to check the model, two membranes have been studied in different experimental conditions. The influence of some relevant parameters, such as solution concentration, stirring rate, mean temperature and temperature difference has been considered and the theoretical predictions of the model have been applied to the obtained results. The accordance may be considered good.     

化学反应中的双稳性的临界现象及Landau相变理论

本文通过两个典型事例,即Langmuir形式的交换过程和Schlogle用以模拟一级相变的自催化反应,阐明化学反应系统的双稳性临界现象同样可以纳入Landau相变理论的模式。从而进一步揭示了双稳系统一级相变线临界点的二级(连续)相变特征,同时也揭示了作为远离平衡的化学反应双稳性临界现象的共性,以至于在更大范围内临界现象的共性。将相变的Landau理论,由原来的处于热平衡的凝聚物质推广到范围更宽广,表现更为丰富多彩的远离平衡系统的临界现象。     

Cooling rate effect on the phase transitions in a polymer liquid crystal: DSC and real-time MAXS and WAXD experiments

The importance of the cooling rate for the structural transformations in a main-chain poly(hexamethylene-4,4′-bibenzoate) has been presented. Detailed analysis of the phase transitions, main structural parameters and their temperature changes has been performed by differential scanning calorimetry, real-time middle-angle X-ray scattering and wide-angle X-ray diffraction methods. The thermodynamic nature of the initial transformation into a smectic A phase has been discussed. The material in the smectic state is supposed to be organized in smectic domains. The crystallization from the smectic phase depends strongly on the kinetics. The crystallization inside the smectic domains results into different final structures determined by the cooling rate applied. At the highest cooling rates, only one crystalline form has been observed. Different possible modifications have been discussed for the case: either a γ-polymorphic form or still some mesophase of high order, as a frozen metastable state. There is a possibility that the phase might be also identified as a condis crystal. At decreasing cooling rates, a new crystalline form, named α∗, appears together with the first one. Lowering the cooling rate, the volume fraction of the α∗-polymorph gradually increases, at the expenses of the first form. The interesting feature of the new observed α∗-polymorph is that it has some similarities with α- and δ-phases of the same material. Contrary to the previous observations, no γ?α^∗ transformation has been observed neither during the course of single crystallization nor during the subsequent heating. A model describing the gradual transformation of the material during its temperature treatment has been proposed.     

Surface phase transitions in one-dimensional channels arranged in a triangular cross-sectional structure: theory and Monte Carlo simulations

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a submonolayer lattice-gas of interacting monomers adsorbed on one-dimensional channels arranged in a triangular cross-sectional structure. Two kinds of lateral interaction energies have been considered: (1) w(L), interaction energy between nearest-neighbor particles adsorbed along a single channel and (2) w(T), interaction energy between particles adsorbed across nearest-neighbor channels. We focus on the case of repulsive transverse interactions (w(T)>0), where a rich variety of structural orderings are observed in the adlayer, depending on the value of the parameters k(B)Tw(T) (being k(B) the Boltzmann constant) and w(L)w(T). For w(L)w(T)=0, successive planes are uncorrelated, the system is equivalent to the triangular lattice, and the well-known ([square root] 3 x [square root] 3) [([square root] 3 x ([square root] 3)(*)] ordered phase is found at low temperatures and a coverage, theta, of 13. In the more general case (w(L)/w(T) not equal 0), a competition between interactions along a single channel and a transverse coupling between sites in neighboring channels leads to a three-dimensional adsorbed layer. Consequently, the ([square root] 3 x ([square root] 3) and (([square root] 3 x ([square root] 3)(*) structures "propagate" along the channels and new ordered phases appear in the adlayer. Each ordered phase is separated from the disordered state by a continuous order-disorder phase transition occurring at a critical temperature, T(c), which presents an interesting dependence with w(L)/w(T). The Monte Carlo technique was combined with the recently reported free energy minimization criterion approach (FEMCA) [F. Roma et al., Phys. Rev. B 68, 205407 (2003)] to predict the critical temperatures of the order-disorder transformation. The excellent qualitative agreement between simulated data and FEMCA results allows us to interpret the physical meaning of the mechanisms underlying the observed transitions.     

Electrokinetic filtration in clays: theory and experiments

The main aspects and results of some electrokinetic filtration tests are presented. Both theory and tests show the key role played by the electrochemical boundary phenomena, such as the electrode reactions, and by the mineralogy of the soil. The aforementioned results show the necessity to run long duration tests. Indeed the macroscopic properties of the soil can change widely during the tests, therefore affecting the expected results in terms of environmental remediation or consolidation but also in terms of energy consumption and efficiency.     

Raman spectra and phase transitions in single crystal (NH4)2ZnCl4

Raman spectra of single crystal (NH₄)₂ZnCl₄ at 300 and 105K at different polarizations are reported and analysed in view of previously reported structural data. The experimental observations suggest that the free oriented gas model is applicable for group theoretical analysis of the vibrational modes in this system at room temperature. It is also concluded that the space group for the room temperature phase III is C²_s instead of C⁹_2v. The temperature dependence of thermosensitive bands shows discontinuities at 267 and 194 K. The structure in the new phase VI below 194 K is suggested to be triclinic.     

On cell theory in relation to isostructural phase transitions due to core collapse

Qualitative features of phase diagrams for isostructural (fcc-fcc) solid-solid transitions are accounted for by a perturbative version of cell theory using a model “step” potential allowing for core collapse.     

Effect of glycerol and dimethyl sulfoxide on the phase behavior of lysozyme: theory and experiments

Salt, glycerol, and dimethyl sulfoxide (DMSO) are used to modify the properties of protein solutions. We experimentally determined the effect of these additives on the phase behavior of lysozyme solutions. Upon the addition of glycerol and DMSO, the fluid-solid transition and the gas-liquid coexistence curve (binodal) shift to lower temperatures and the gap between them increases. The experimentally observed trends are consistent with our theoretical predictions based on the thermodynamic perturbation theory and the Derjaguin-Landau-Verwey-Overbeek model for the lysozyme-lysozyme pair interactions. The values of the parameters describing the interactions, namely the refractive indices, dielectric constants, Hamaker constant and cut-off length, are extracted from literature or are experimentally determined by independent experiments, including static light scattering, to determine the second virial coefficient. We observe that both, glycerol and DMSO, render the potential more repulsive, while sodium chloride reduces the repulsion.     

The Novel Reduction Systems: NaBH4-SbCl3 OR NaBH4-BiCl3 for Conversion of Nitroarenes to Primary Amines

Nitroarenes can be conveniently reduced to primary amines in good to excellent yields by sodium borohydride in the presence of bismuth chloride or antimony chloride.     

Model for phase coexistence in phase transitions

We propose a general model for describing the phenomena of phase coexistence in relation to pressure induced phase transformations by means of the T–P distribution in statistical thermodynamics. Using the well‐known B1–B2 transition in NaCl as a prototype, we demonstrate how phase coexistence gives rise to the changes in the bulk modulus and the equation‐of‐state across the transition. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004