Showing papers on "Lattice energy published in 2013"

Understanding the role of vibrations, exact exchange, and many-body van der Waals interactions in the cohesive properties of molecular crystals

Abstract: The development and application of computational methods for studying molecular crystals, particularly density-functional theory (DFT), is a large and ever-growing field, driven by their numerous applications. Here we expand on our recent study of the importance of many-body van der Waals interactions in molecular crystals [A. M. Reilly and A. Tkatchenko, J. Phys. Chem. Lett. 4, 1028 (2013)], with a larger database of 23 molecular crystals. Particular attention has been paid to the role of the vibrational contributions that are required to compare experiment sublimation enthalpies with calculated lattice energies, employing both phonon calculations and experimental heat-capacity data to provide harmonic and anharmonic estimates of the vibrational contributions. Exact exchange, which is rarely considered in DFT studies of molecular crystals, is shown to have a significant contribution to lattice energies, systematically improving agreement between theory and experiment. When the vibrational and exact-exchange contributions are coupled with a many-body approach to dispersion, DFT yields a mean absolute error (3.92 kJ/mol) within the coveted "chemical accuracy" target (4.2 kJ/mol). The role of many-body dispersion for structures has also been investigated for a subset of the database, showing good performance compared to X-ray and neutron diffraction crystal structures. The results show that the approach employed here can reach the demanding accuracy of crystal-structure prediction and organic material design with minimal empiricism.

Defect chemistry and lithium-ion migration in polymorphs of the cathode material Li2MnSiO4

Abstract: The search for new low-cost and safe cathodes for next-generation lithium batteries has led to increasing interest in silicate materials. Here, a systematic comparison of crystal properties, defect chemistry and Li-ion migration behaviour of four polymorphs of Li2MnSiO4 is reported based on the results of atomistic simulations. The four polymorphs examined have Pmn21, Pmnb, P21/n, and Pn symmetry. Lattice energies of all four polymorphs are very similar, with only a small energy preference for the two orthorhombic phases over the monoclinic phases, which explains the difficulty experimentalists have had preparing pure-phase samples. Defect formation energies of the polymorphs are also similar, with antisite Li/Mn defects the most energetically favourable. Detailed analysis of the Li-ion migration energy surfaces reveals high activation energies (around 0.9 to 1.7 eV) and curved trajectories. All four polymorphs are thus expected to be poor Li-ion conductors, requiring synthesis as nanoparticles to facilitate sufficient Li transfer. The results accord well with experimental reports on the structure, relative phase stabilities and electrochemical performance of materials in this system.

Towards ab initio screening of co-crystal formation through lattice energy calculations and crystal structure prediction of nicotinamide, isonicotinamide, picolinamide and paracetamol multi-component crystals

Abstract: Co-crystallisation of a drug with another molecule to form a new crystalline material is an appealing route to enhance physical properties Despite mounting research effort, there is still considerable uncertainty whether a given co-crystal will form Previous attempts to use lattice energy calculations to investigate whether a potential co-crystal is thermodynamically more stable than its pure co-former crystals have been inconclusive In the present study, dispersion-corrected density functional theory is used to minimise the lattice energies of all known co-crystals and salts of nicotinamide, isonicotinamide and picolinamide, and their corresponding neutral co-formers (excluding any organometallic compounds) Out of the resulting 102 co-crystals and salts, 99 (97%) are found to be more stable than their corresponding co-formers In addition, full crystal structure prediction studies show that two paracetamol co-crystals are very unstable in comparison to their co-formers, thus explaining why these co-crystals have not been observed experimentally These results demonstrate that a simple yet accurate thermodynamic approach can predict reliably whether a co-crystal can be formed

Sulfonamide Molecular Crystals: Structure, Sublimation Thermodynamic Characteristics, Molecular Packing, Hydrogen Bonds Networks

Abstract: The crystal structures of ten sulfonamides have been determined by X-ray diffraction. On the basis of our previous data, the obtained results and literature data crystal properties including molecular conformational states, packing architecture, and hydrogen bond networks were comparatively analyzed using graph set notations. Conformational flexibility of the bridge connecting two phenyl rings was studied. It was found out that the most frequently occurring graphs for compounds with a single hydrogen bond are infinite chains with four atoms included. The molecular packing architecture of the selected crystals may be conditionally divided into three different groups. The idea underlying such classification is the difference in structure and composition of molecular layers that can be singled out for most packings. The influence of various molecular fragments on crystal lattice energy was analyzed. A correlation between melting points and fragmental molecular interactions in the crystal lattices was obtaine...

Capturing the crystal: prediction of enthalpy of sublimation, crystal lattice energy, and melting points of organic compounds.

Abstract: Accurate computational prediction of melting points and aqueous solubilities of organic compounds would be very useful but is notoriously difficult Predicting the lattice energies of compounds is key to understanding and predicting their melting behavior and ultimately their solubility behavior We report robust, predictive, quantitative structure–property relationship (QSPR) models for enthalpies of sublimation, crystal lattice energies, and melting points for a very large and structurally diverse set of small organic compounds Sparse Bayesian feature selection and machine learning methods were employed to select the most relevant molecular descriptors for the model and to generate parsimonious quantitative models The final enthalpy of sublimation model is a four-parameter multilinear equation that has an r2 value of 096 and an average absolute error of 79 ± 03 kJmol–1 The melting point model can predict this property with a standard error of 45° ± 1 K and r2 value of 079 Given the size and div

Study of Halogen-Mediated Weak Interactions in a Series of Halogen-Substituted Azobenzenes

Abstract: The azobenzenes, known for their various importance in the industry, have been chosen as model compounds to understand the role of weak interactions involving the C–X (X = F, Cl, and Br) bond using single-crystal X-ray diffraction technique, especially in the absence of other stronger intermolecular forces such as hydrogen bonds. The fluorinated compounds have been found to pack in the lattice by utilizing C–H···F hydrogen bonds, whereas the chlorinated and brominated analogues have been found to prefer C–X···X–C, C–X···π, and π···π interactions while packing in the lattice. The stabilization energy offered by the C–H···F hydrogen bonds and the C–X···X–C interactions have been estimated by computational methods using Gaussian 09, and the topological properties have been determined by using the AIM2000 package. The lattice energy decomposition has been done using semiclassical density sums (SCDS) PIXEL method. Our studies indicate that the stabilization energy offered by each C–H···F hydrogen bond lies in ...

Quantitative insights into energy contributions of intermolecular interactions in fluorine and trifluoromethyl substituted isomeric N-phenylacetamides and N-methylbenzamides

Abstract: The presence of the C–F bond in organic molecules, particularly in the context of generating different intermolecular interactions of the type C–F⋯F–C, C–H⋯F and C–F⋯π is of extreme significance in the realm of structural chemistry. These interactions generate different packing motifs in the formation of the crystal. It is of interest to evaluate the energetic contributions of such weak interactions to evaluate their important role in crystal packing. In this respect, a library of twelve compounds containing a strong donor and acceptor, along with the presence of a C–F bond in different electronic environments (fluorine atom connected to C(sp2) and C(sp3) carbon atom) have been synthesized and characterized using single crystal X-ray diffraction studies at low temperature. In addition, the non-fluorinated counterpart has also been synthesized. These crystal structures have been analyzed to understand the contribution of weak interactions involving organic fluorine in the crystal packing. Furthermore, the stabilizing–destabilizing roles of such interactions in terms of favourable energetics have been quantified with inputs from calculations performed using PIXEL. It is observed that most of the interactions involving fluorine are of a dispersive character, and in some cases the interaction is also coulombic in origin. These results have been compared with ab initio quantum-chemical calculations (DFT-D3/B-97D level) performed using TURBOMOLE. In addition, the lattice energies of all the compounds have been evaluated, and the total contribution partitioned into the corresponding coulombic, polarization, dispersion and exchange contributions using the CLP module. The results correlate well with thermochemical data experimentally determined for these compounds.

Absorbing a Little Water: The Structural, Thermodynamic, and Kinetic Relationship between Pyrogallol and Its Tetarto-Hydrate

Abstract: The anhydrate and the stoichiometric tetarto-hydrate of pyrogallol (0.25 mol water per mol pyrogallol) are both storage stable at ambient conditions, provided that they are phase pure, with the system being at equilibrium at aw (water activity) = 0.15 at 25 °C. Structures have been derived from single crystal and powder X-ray diffraction data for the anhydrate and hydrate, respectively. It is notable that the tetarto-hydrate forms a tetragonal structure with water in channels, a framework that although stabilized by water, is found as a higher energy structure on a computationally generated crystal energy landscape, which has the anhydrate crystal structure as the most stable form. Thus, a combination of slurry experiments, X-ray diffraction, spectroscopy, moisture (de)sorption, and thermo-analytical methods with the computationally generated crystal energy landscape and lattice energy calculations provides a consistent picture of the finely balanced hydration behavior of pyrogallol. In addition, two mono...

Polymorphism and solvatomorphism of bicalutamide

Abstract: Single crystals of the crystallosolvate [bicalutamide + DMSO] with 1:1 stoichiometry were grown, and their structures were solved by X-ray diffraction methods. Polymorphic modifications I and II, the amorphous state, and the DMSO crystallosolvate of bicalutamide were prepared and thermochemistry of fusion processes was studied by DSC technique. The temperature dependence of the saturated vapor pressure of polymorphic form I was obtained and the thermodynamic characteristics of the sublimation process including the crystal lattice energy were calculated. The solution enthalpies of the forms under consideration and the crystallosolvate were acquired by the solution calorimetry procedure. The phase transition enthalpies estimated for form I, form II, and the amorphous state followed the rank order: form I— > form II, form I— > amorphous state, and form II— > amorphous state. The crystal lattice energy of polymorphic form II was determined using the results of sublimation and solution calorimetric experiments. The difference between the crystal lattice energy of the crystallosolvate and unsolvated phases was observed. The dissolution kinetics of forms I, II, the amorphous state, and DMSO solvate in water were investigated.

Thermodynamics of Nanoscale Calcium and Strontium Titanate Perovskites

Abstract: The surface enthalpies of nanocrystalline CaTiO3 and SrTiO3 perovskites were determined using high-temperature oxide melt solution calorimetry in conjunction with water adsorption calorimetry. The nanocrystalline samples were synthesized by a hydrothermal method and characterized using powder X-ray diffraction, FTIR spectroscopy, and Brunauer–Emmett–Teller surface area measurements. The integral heats of water vapor adsorption on the surfaces of nanocrystalline CaTiO3 and SrTiO3 are � 78.63 � 4.71 kJ/mol and � 69.97 � 4.43 kJ/mol, respectively. The energies of the hydrous and anhydrous surfaces are 2.49 � 0.12 J/m 2 and 2.79 � 0.13 J/m 2 for CaTiO3 and 2.55 � 0.15 J/m 2 and 2.85 � 0.15 J/m 2 for SrTiO3, respectively. The stability of the perovskite compounds in this study is discussed according to the lattice energy and tolerance factor approach. The energetics of different perovskites suggest that the formation enthalpy becomes more exothermic and surface energy increases with an increase in ionic radius of the “A” site cation (Ca, Sr, and Ba), or with the tolerance factor. PbTiO3 shows a lower surface energy, weaker water binding, and a less exothermic enthalpy of formation than the alkaline-earth perovskites.

Lattice plane control of liquid crystal blue phase

Abstract: A correlation between the orientation of the lattice plane of liquid crystal blue phase (BP) and the surface free energy of the solid substrates which were coated with a polyimide thin layer or treated by a silane coupling reagent was investigated. The lattice plane was identified from the optical texture observation and the reflection spectra of BP. It was confirmed that the orientation of the lattice plane of BP was closely related to the surface free energy of the substrate. In particular, the area fraction of the lattice plane {110} of BP I increased as the polar component (γp) decreased.

A dispersion-corrected density functional theory case study on ethyl acetate conformers, dimer, and molecular crystal

Abstract: We present a dispersion-corrected density functional theory case study on recently reported apparently difficult systems (Boese et al. in Chem Phys Chem 14:799, 2013). The relative stability of the trans, gauche, and cis conformers of ethyl acetate, the dissociation energy of the (trans–trans) dimer, and the structure and electronic lattice energy of the corresponding molecular crystal are calculated. We utilize the generalized gradient approximation density functionals PBE and BLYP, the hybrid functional B3LYP, and the double-hybrid functional B2PLYP. It is shown that all semilocal density functionals must be corrected for missing long-range electron correlation, a.k.a. London dispersion interaction. The performance of the ab initio dispersion correction DFT-D3 is excellent and significantly improves the results compared to the uncorrected functionals and compared to the older more empirical DFT-D2 correction. The three-body dispersion contribution to the lattice energy is 7 %, while its impact on the crystal geometry and the conformer energies is negligible. A nonlocal correction approach termed DFT-NL is also tested and shows good performance comparable to the DFT-D3 results. Overall, it is shown that dispersion-corrected density functional theory can accurately describe the properties of ethyl acetate in various states ranging from single-molecule conformers to the infinite periodic molecular crystal.

An embedded atom method potential of beryllium

Abstract: We present an embedded atom method (EAM) potential for hexagonal beryllium, with a pair function in the form of a Morse potential and a Johnson embedding function with exponential electron density. The cohesive energy, elastic constants, lattice parameters and relaxed vacancy formation energy were used to fit the potential. The fitted-potential was validated by a comparison to first-principles and, wherever available, experimental results for the lattice energies of various crystal structures: vacancy cluster, interstitial formation and surface. Using a large cutoff distance of 5 Å, which includes interactions to approximately the eighth neighbor shell of beryllium, allows our potential to reproduce these quantities considerably better than previous EAM potentials. The accuracy obtained by our potential is similar to or in some cases even better than available modified EAM potentials, while being computationally less intensive.

Obtaining the lattice energy of the anthracene crystal by modern yet affordable first-principles methods.

Abstract: The non-covalent interactions in organic molecules are known to drive their self-assembly to form molecular crystals. We compare, in the case of anthracene and against experimental (electronic-only) sublimation energy, how modern quantum-chemical methods are able to calculate this cohesive energy taking into account all the interactions between occurring dimers in both first-and second-shells. These include both O(N6)- and O(N5)-scaling methods, Local Pair Natural Orbital-parameterized Coupled-Cluster Single and Double, and Spin-Component-Scaled-Moller-Plesset perturbation theory at second-order, respectively, as well as the most modern family of conceived density functionals: double-hybrid expressions in several variants (B2-PLYP, mPW2-PLYP, PWPB95) with customized dispersion corrections (–D3 and –NL). All-in-all, it is shown that these methods behave very accurately producing errors in the 1–2 kJ/mol range with respect to the experimental value taken into account the experimental uncertainty. These meth...

Short π-Stacking in N-Rich Ionic Aromatic Compounds

Abstract: Reaction of N-rich conjugated bis(3,4-diamino-1,2,4-triazole)s with dilute hydrochloric acid affords bis(3,4-diamino-1,2,4-triazol-2-ium)chlorides. These compounds form layered structures in which planar layers of molecules are parallelly stacked. The π-stacking distance of the layers is relatively short, as compared with all-carbon-containing aromatic compounds, ranging between 3.00 and 3.22 A at 173 K, and several contacts shorter than the sum of van der Waals radii are observed in the crystal structures. The features of the crystal structures are discussed in terms of the high nitrogen content of the compounds and of the H-bonding patterns. Periodic ab initio theoretical calculations of the crystal structures have allowed decomposing the lattice energy into various contributions in order to put up the relevance of van der Waals interactions for the π-stacking. In particular, it is found that van der Waals interactions account for about 10% of the total lattice energy and about 50% of the stacking energ...

Ca[LiAlN2]: A Quaternary Nitridoaluminate

Abstract: Ca[LiAlN2] was synthesized from LiAlH4, LiN3, calcium, and lithium metal as fluxing agent in welded-shut tantalum crucibles at 900 °C. The compound crystallizes in the form of transparent colorless platelets that undergo hydrolysis in air and under moisture. The crystal structure [P21/c (no. 14), a = 5.7587(12) A, b = 6.8773(14) A, c = 5.7960(12) A, β = 90.28(3)°, Z = 4] was solved from single-crystal X-ray diffraction data and was confirmed with Rietveld refinement methods and lattice-energy calculations (Madelung part of lattice energy, MAPLE). Ca[LiAlN2] forms layers of edge- and vertex-sharing AlN4 tetrahedra isotypic with LiCaGaN2. Li+ ions are positioned in tetrahedral voids within the [Al2N2N4/2] layers resulting in a highly condensed structure of Al- and Li-centered polyhedra.

Lattice summations for spread out particles: applications to neutral and charged systems.

Abstract: This work is concerned with the lattice energy of periodic assemblies of mass and charge distributions of the form, exp (−αp2), where α is an adjustable positive variable and p is the vector from the lattice site or average position. The energy of interaction between two distributions is the density-weighted integral of the interactions between the volume elements of each distribution. Reciprocal space lattice summation formulas derived for particles represented by gaussian smeared-out density distributions are applied to the gaussian potential and a bounded version of the soft-sphere potential for a range of exponents. Two types of spatial broadening are considered, continuous or physical broadening (PB) and broadening resulting from the time average of point particle positions, so-called “time” broadening (TB). For neutral mass distributions a reciprocal space lattice summation formula is derived which is applied to the bounded soft-sphere potential. For the charged systems, the methodology described i...

Thermoanalytical and spectroscopic studies on different crystal forms of nevirapine

Abstract: This study is aimed at exploring the utility of thermoanalytical methods in the characterization of various polymorphs and solvates of nevirapine. The different forms obtained by recrystallization of nevirapine from various solvents showed morphological differences in SEM. The presence of polymorphic forms is suggested by single sharp melting endotherm different from original sample in DSC and no mass loss in TG, while appearance of desolvation peak in TG indicated the formation of solvates. The higher desolvation temperatures of all the solvates than their respective boiling point indicate tighter binding of solvent. The changes in the crystal lattice were demonstrated by X-ray powder diffraction studies. The enthalpy of fusion rule indicated the existence of monotropy in polymorphic pairs I/O and II/O, while I/II is enantiotropically related. The enthalpy of solution, an indirect measure of the lattice energy of a solid, was well correlated with the crystallinity of all the solid forms obtained. The magnitude of ΔH sol was found to be −14.26 kJ mol−1 for Form V and −8.29 kJ mol−1 for Form O, exhibiting maximum ease of molecular release from the lattice in Form V. The transition temperature was found to be higher than the melting of both the forms except for polymorphic pair I/II providing complementary evidence for the existence of monotropy as well as enantiotropy in these polymorphic pairs.

Lattice Enthalpy Drives Hubbard U to Zero

Abstract: In the equation U = I – A for the Mott energy, the electron-hole interaction of the successor state is missing. Adding the attractive term, the energy for disproportionation (Hubbard U), may adopt any sign. The missing term is related to the Born effect, the Madelung correction and the Lattice Enthalpy.

Titania nanorods curve to lower their energy

Abstract: Spontaneous formation of curved nanorods is generally unexpected, since curvature introduces strain energy. However, electron microscopy shows that under hydrothermal conditions, some nanorods grown by oriented attachment of small anatase particles on {101} surfaces are curved and dislocation free. Molecular dynamics simulations show that the lattice energy of a curved anatase rod is actually lower than that of a linear rod due to more attractive long-range interatomic Coulombic interactions among atoms in the curved rod. The thermodynamic driving force stemming from lattice energy could be harnessed to produce asymmetric morphologies unexpected from classical Ostwald ripening with unusual shapes and properties.

Localization and relaxation of singlet exciton formation in conjugated polymers under photoexcitation.

Abstract: This paper employs a molecular dynamics approach to uncover the time profile of exciton formation, which can be divided into two stages: localization of electron–hole pairs and relaxation process (nuclear and electronic). Under photoexcitation, an electron–hole pair is formed by an electronic transition, and the pair in turn becomes localized through the electron–lattice interaction, which triggers the total energy to shift violently and oscillate. The oscillation during the first 40 fs induces the excitation to step into the second stage, i.e., relaxation. After the relaxation process of about 850 fs, the total energy, lattice energy, and electron energy reach certain values whereas the lattice configuration and electron remain localized, indicating the formation of a singlet exciton.

Density, Viscosity and Conductivity of Protic Ionic Liquid N,N -DimethylethanolammoniumPropionate

Abstract: The density, viscosity, and conductivity of protic ionic liquid (PIL) N,N-dimethylethanolammonium propionate (DMEOAP) were determined in the temperature range of 283.15−333.15 K. The influence of temperature on density, viscosity, and conductivity is discussed. The thermal expansion coefficient, molecular volume, standard molar entropy, and lattice energy of DMEOAP were calculated using empirical and semiempirical equations. The molar conductivity of DMEOAP was determined from density and conductivity data. The temperature dependence of viscosity and conductivity data was fitted using the Vogel-FulcherTammann (VFT) equation. The relationship between molar conductivity and viscosity was determined by the Walden rule.

Crystal structure and packing energy calculations of (+)-6-aminopenicillanic acid.

Abstract: The X-ray single-crystal structure of (2S,5R,6R)-6-amino-3,3-dimethyl-7-oxo-4-thia-1-aza­bicyclo­[3.2.0]heptane-2-carb­oxy­lic acid, commonly known as (+)-6-amino­penicillanic acid (C8H12N2O3S) and a precursor of a variety of semi-synthetic penicillins, has been determined from synchrotron data at 150 K. The structure represents an ordered zwitterion and the crystals are nonmerohedrally twinned. The crystal structure is composed of a three-dimensional network built by three charge-assisted hydrogen bonds between the ammonium and carboxyl­ate groups. The complementary analysis of the crystal packing by the PIXEL method brings to light the nature and ranking of the energetically most stabilizing inter­molecular inter­action energies. In accordance with the zwitterionic nature of the structure, PIXEL lattice energy calculations confirm the predominance of the Coulombic term (−379.1 kJ mol−1) ahead of the polarization (−141.4 kJ mol−1), dispersion (−133.7 kJ mol−1) and repulsion (266.3 kJ mol−1) contributions.

Structure and interactions in benzamide molecular crystals

Abstract: In this study, we resolved discrepancies concerning the experimentally determined structure of benzamide molecular crystals from dispersion-corrected density functional calculations. A clear energy ranking was obtained for the two candidates of the stable (P1) modification of benzamide. This was rationalised by subtle differences of the molecular interactions in the molecular crystal. The potential energy of the different structures was dominated by the interplay of intermolecular attraction and molecular torsion/deformation to accommodate favourable hydrogen-bonded networks. Using suitable proxies arranged in pseudo-crystalline set-ups, we discriminated the contribution of electrostatics, π–π interactions and intra-molecular interactions to the lattice energies.

"In-silico seeding": Isostructurality and pseudoisostructurality in a family of aspirin derivatives

Abstract: Novel crystal packings of the aspirin molecule and 17 molecules that are related to aspirin by substitution are studied using a computational approach. The packings are created by taking a crystal structure for which the crystal packing and molecular geometry have been determined experimentally and replacing the native molecule with a different one. The resulting crystal structures are optimized using molecular mechanics, followed by a quantum mechanical method based on density functional theory and including a correction for dispersive interactions. There are 21 known, experimental, crystal structures for the molecules considered, some of which are polymorphic. For any given molecule, the lowest, calculated lattice energy is always found to be that of a crystal structure which corresponds to experiment. For the three polymorphic molecules, the second lowest lattice energy is also found to correspond to an experimental structure. The agreement between the observation of a particular packing and its low ra...

Thermodynamics of the Solvation of Potassium Thiocyanate in Mixed EtOH-H 2 O Solvents at 301.15 K

Abstract: The Gibbs free energies as very important thermodynamic p roperty were evaluated for potassium thiocyanate (KSCN) in mixed ethanol (EtOH-H2O) solvents at 301.15 K fro m the experimental solubility measarments. The ratio of the ionic radii between potassium and thiocyanate ions was used to divide the total Gibbs free energy of the salt into its indiv idual contribution in the mixtu res used. Libration Gibbs free energy associated with mov ing KSCN in standard gas state to standard state in solution was evaluated according to specific cycle for the solvation process using the solubility products. Also the lattice energy for solid KSCN (Cr) was calculated and used for further evaluation. The conventional Gibbs free energ ies for the cation (K + ) and anion (SCN - ) were estimated theoretically and also the Gibbs free energy of (SCN - ) gas was evaluated and all values were discussed. The present work is concerned with relative(conventional) and absolute Gibbs free energies of the solvation of ions used.

Atomistic simulation of the lattice constants and lattice vibrations in RCo2 and Nd1− x R x Co2 (R = rare earth)

Abstract: The lattice parameters and phase stability of RCo2 and Nd1−x R x Co2 (R = rare earth) are evaluated by using interatomic pair potentials based on Chen's lattice inversion method. The calculated results demonstrate that the concentration dependence of a approximately follows Vegard's law by a = xa 1 + (1−x)a 0, where a 0 and a 1 are the lattice constants of NdCo2 and RCo2. The results are in good agreement with experiments. The properties related to lattice vibration, such as phonon density of states, specific heat and vibrational entropy, are also evaluated. The method utilized in the present investigation offers a rather easy and direct way to study the structural and vibrational properties of rare earth compounds.

Correlation between standard enthalpy of formation, structural parameters and ionicity for alkali halides

Abstract: The standard enthalpy of formation (∆H ) is considered to be an interesting and useful parameter for the correlation of various properties of alkali halides. The interrelation between ∆H and structural parameters for the halides of Li, Na, K and Rb has been thoroughly analyzed. When the cationic component element is kept constant in a homologous series of alkali halides, the negative value of ∆H was observed to decrease linearly with increasing interionic distance (d). Accordingly, the following empirical equation ∆H = α + + βd (where α and β are empirical constants) was established. However, for common anionic series of alkali halides, an opposing non-linear trend was observed, with the exception of common fluorides. The correlation study on the standard enthalpy of formation was extended in term of the radius ratio and also discussed in the light of ionization energy of the metal, electron affinity of the halogen, size of the ions, ionic character of the bond and the lattice energy of the compound.