Binary Mixed Crystals Research Articles

Multiphased mixed crystals: Interconnection of the conductivity activation energy with bulk properties

Using the miscible alkali halides, viz. NαBr and KCl, multiphased binary and ternary mixed crystals have recently been grown. Such crystals are important because of their potential applications, for example, for the construction of laser optical windows. The temperature dependence of their conductivity and the corresponding activation energy E have also been recently reported for various compositions. Here, we show that, upon combining experimental data alone, an interesting correlation emerges, which indicates that the energy E varies linearly with BΩ, where B stands for the measured bulk modulus of the multiphased mixed crystals and Ω denotes the mean volume per atom. This conforms with an early model that interconnects the Gibbs energy for the formation and migration of defects in solids with bulk properties.

Estimating the temperature dependence of the dielectric constant of multiphased mixed crystals

Measurements of the dielectric constant of multiphased binary and ternary mixed alkali halides, which have found a multitude of applications in optical and electronic devices, have been recently reported in the temperature range from room temperature to 423 K. It was found that the temperature variation in the binary mixed crystal (NaCl)0.587 (KBr)0.413 is drastically larger than in any other. We show that this variation can be quantitatively reproduced by means of a simple model, which does not contain any adjustable parameter and solely makes use of the properties of the end members, viz., NaCl and KBr.

A tentative model for estimating the compressibility of multiphased mixed crystals

The growth of multiphased binary and ternary mixed crystals by the melt method using the miscible alkali halides, viz., NaBr and KCl, along with the experimental determination of their compressibility, have been recently reported. These materials are particularly useful for the construction of laser optical windows. Here, we suggest a theoretical model that enables the estimation of the compressibility of the multiphased mixed crystals in terms of the elastic data of the end members alone. The calculated values are in reasonable agreement with the experimental ones. The model makes use of an early suggestion that interconnects the Gibbs energy for the formation and migration of defects in solids, with bulk properties, and has been found of value in a large variety of solids.

Studies on multiphased mixed crystals grown from NaBr and KCl

We have grown multiphased binary and ternary mixed crystals by the melt method using the miscible alkali halides, viz. NaBr and KCl and physically characterized. Thermal parameters like Debye–Waller factor, Debye temperature, Debye frequency and mean square amplitude of vibration were determined using the X-ray powder diffraction intensity data. DC and AC electrical measurements were carried out by using the parallel plate capacitor method at various temperatures. Activation energies (DC and AC), mean jump frequency, compressibility and mean sound velocity were also determined. The results obtained are reported here.

Thermodynamic study on competitive solubilization of cholesterol and β-sitosterol in bile salt micelles

Differences in the preferential solubilization of cholesterol and competitive solubilizates ( β-sitosterol and aromatic compounds) in bile salt micelles was systematically studied by changing the molar ratio of cholesterol to competitive solubilizates. The cholesterol solubility in a mixed binary system (cholesterol and β-sitosterol) was almost half that of the cholesterol alone system, regardless of the excess β-sitosterol quantity added. On the other hand, the mutual solubilities of cholesterol and pyrene were not inhibited by their presence in binary mixed crystals. Finally, the cholesterol solubility was measured by changing the alkyl chain length of n-alkylbenzenes. When tetradecylbenzene was added to the bile solution, the cholesterol solubility decreased slightly and was below the original cholesterol solubility. Based on Gibbs energy change (Δ G°) for solubilization, chemicals that inhibit cholesterol solubility in their combined crystal systems showed a larger negative Δ G° value than cholesterol alone.

Disorder-Induced Optical Nonlinearlity in Mixed Crystals

The disorder-induced transient optical four-wave mixing for a Frenkel exciton in a binary mixed crystal is theoretically investigated. We have clarified the role of static disorder in a wide range of disorder strength by using the coherent potential approximation. It is found that the weak disorder gives rise to exciton dephasing, and the strong disorder induces a photon echo signal. The crossover from homogeneous to inhomogeneous broadening with increasing disorder strength is systematically analyzed. In the case of off-resonant excitation, we find an oscillatory echolike signal inherent in the disorder-induced optical nonlinearity.

Growth and transport properties of tin monosulphoselenide single crystals

The binary and ternary mixed single crystals of the orthorhombic IV–VI family in the form of SnS x Se 1− x (where x=0, 0.25, 0.50, 0.75 and 1) were grown by direct vapor transport technique. The lattice parameters of each grown crystal were determined from the X-ray diffraction analysis. The grown crystals were examined under the optical zoom microscope for their surface microstructure study. The low-temperature resistivity measurements were carried out in the temperature range 123–303 K using four-probe method. The Hall coefficient, carrier concentration and Hall mobility of each sample was determined from Hall effect measurements at room temperature. From the optical absorption spectra obtained in the range 1000–1500 nm, optical band gap of each sample was determined at room temperature. The results obtained are reported systematically.

Uniform Thermodynamic Description of the Orientationally Disordered Mixed Crystals of a Group of Neopentane Derivatives

The experimental systems considered in this paper are isobaric binary plastic-crystalline mixed crystals of neopentane derivatives, and their properties studied are (i) solid−liquid phase behavior and (ii) the thermodynamic mixing properties, actually the excess enthalpy, entropy, and volume. More in particular, 10 systems are considered, nine being face-centered cubic and one body-centered cubic, and their components are derived from neopentane, C(CH3)4, by substituting one or more −CH3 groups by one or more −CH2OH groups and/or one −NO2 or −NH2 groups. The (mean) number of −CH2OH groups per molecule appears to have a dominating influence with regard to melting temperature and degree of compactness. The values of the excess properties vary from system to system, whereas their quotients are system-independent. For the group of fcc systems, the quotient of excess enthalpy and excess entropy (compensation temperature) has the uniform value of 630 K, and the quotient of excess enthalpy and excess volume the value of about 0.5 GPa.

Perfect families of mixed crystals: the “ordered’' crystalline forms of n-alkanes

The experimental systems considered in this paper are isobaric binary mixed crystals of n-alkanes in the crystalline forms Op, Mdci and Mdep, which, on the temperature scale, precede mixed crystals in the rotator forms. The properties studied are the thermodynamic mixing properties, actually the excess enthalpy and excess entropy. For 14 binary systems in the range C17 to C28, quantitative thermodynamic data have been obtained by studying the transition to the rotator forms, for which the thermodynamic mixing properties had been determined earlier. The most important outcome of the investigation is that the complete set of systems is characterised by (i) a uniform ratio between excess enthalpy and excess entropy, having the value of 335 K, and (ii) a uniform dependence of the excess enthalpy on relative difference between number of carbon atoms in the molecules of the components of the system.

Perfect families of mixed crystals: The rotator I N-alkane case

The experimental systems considered in this paper are isobaric binary mixed crystals, and their properties studied are the thermodynamic mixing properties, actually the excess enthalpy and excess entropy. More in particular, the excess behavior is examined for families of systems where the components of each of the member systems belong to a group of chemically coherent substances. The accent is on a group of 18 systems composed of n-alkanes in the range from C11H24 to C26H54, such that the components of an individual system are either neighbors or next nearest neighbors. In these systems mixed crystalline solid forms are stable in which the molecules have rotational freedom around their long axis. One of these forms is rotator I, and it is this form for which thermodynamic mixing properties have been determined. The magnitudes of the excess enthalpy and excess entropy are system-dependent and can be correlated to the geometric mismatch, i.e., the relative difference in number of carbon atoms of the molecules of the components of the system. The quotient of the two excess properties, on the other hand, is shown to be system-independent: it corresponds to a temperature which is characteristic of the family as a whole. For the rotator n-alkane family, its value is 320 K. The result obtained for the n-alkanes gives support to the treatment (of a similar nature) we applied earlier to the common-ion alkali halide systems and the p-dihalobenzenes. We propose to refer to such groups of systems of mixed crystals as a “perfect family of mixed crystals.”

Raman Spectra and Intermolecular Vibrational Coupling Behaviour of Binary Mixed Crystals of (dppm)M(CO)4 Complexes (M=Cr, Mo, W)

Raman Spectra and Intermolecular Vibrational Coupling Behaviour of Binary Mixed Crystals of (dppm)M(CO)4 Complexes (M=Cr, Mo, W)

Raman Spectra and Intermolecular Vibrational Coupling Behaviour of Binary Mixed Crystals of dppmMCO4 Complexes M=Cr, Mo, W

The Raman spectra of binary mixed crystals of (dppm)M(CO)4 complexes [dppm=bis(diphenyl-phosphino)methane, M=Cr, Mo, W] in the ν(CO) region are interpreted in terms of one-mode and two-mode behaviours, resulting from the presence and absence of intermolecular vibrational coupling in the unit cell, respectively. The behaviour of the spectral features in the mixed crystals is successfully correlated with the occurrence of factor group splitting in the individual spectra of the pure compounds. An unexpected wavenumber shift effect depending on crystal composition was detected. An explanation is proposed based on the breakdown of translational symmetry in mixed crystals and consequent invalidity of the k=0 rule.

Thermodynamics of Binary Mixed Crystals in the Sub-quasi-chemical/Debye Approximation

A new statistical model for the description of the thermodynamic properties of binary mixed crystals is discussed. The model is based on an asymmetrical analogue of the quasi-chemical approximation and the Debye model of a solid. With two interchange -energy parameters and two interchange-Debye-temperature parameters, all important thermodynamic functions, at constant volume, of the binary mixed crystal can be calculated as a function of temperature and composition. The binary system {( 1 - x)Nai + xKI}(s) is used for illustration of the model.

Graphical Representation of Solid‐Solute Phase Equilibria in Aqueous Solution

AbstractSolid‐solute phase diagrams are useful tools for the depiction of stable and metastable equilibria between binary mixed crystals with common ions and aqueous solutions. Generalized Gibbs‐Duhem equations provide the common basis and suggest natural co‐ordinates for the graphical representation of thermodynamic variables. Diagrams applicable even to highly soluble electrolytes can be constructed by plotting the osmotic coefficient of the solvent times the total molality πΣm vs. the mole fractions x of the dissolved and solid components, respectively. According to Schmalzried and Pelton's topological classification the resulting phase diagrams are of Type II. They can be used for practical purposes, e.g., to predict the separability of the components by fractional crystallization.

Effect of disorder on quantum localization in 2D AxB1−x binary crystals

A 2D square lattice with nearest neighbor interactions (V0) and periodic boundary conditions is used to analyze the quantum localization of eigenstates of a binary mixed crystal in the split-band limit. The lattice sites are randomly occupied either by A molecules with energy EA = Δ at concentration x or by B molecules with energy EB = −Δ at concentration 1 − x. Because of the random distribution of the molecules the general Hamiltonian implicitly accounts for both diagonal and off-diagonal disorders. The full diagonalization of the Hamiltonian provides all eigenstates in the energy domains of A and B from which the inverse participation ratios (IPR) and their band averages ⟨L⟩E are evaluated and configurationally averaged. The two limiting cases Δ ⩾ V0 and Δ ≅ V0 are investigated and compared. In the latter case it is shown that the statistical fluctuations are smoothed out relative to that of the infinite split-band. Furthermore, our results show a gradual decrease of the band averages when increasing x and a strong dependence on Δ.

Self-Trapping in Mixed Crystal. II. Concentration Dependence

We studied self-trapping of a Frenkel exciton in a binary mixed crystal A x B 1- x with randomness in the exciton atomic (e i ) and the transfer ( t i j ) energies, and the short range exciton-lattice interaction D i . The concentration dependence of the energies of relaxed excitons and the emission energies are calculated for self-trapped ( S i ) states at i =A or B site and free (F) states using the coherent potential approximation. Extrinsic self-trapping and the F-S transition are discussed with phase diagrams obtained for various parameters Δ=e B -e A , D i , the exciton band width T i ( i =A, B) and the concentration x . The results are compared with recent experiments on mixed ionic crystals and II-VI compound semiconductors.

Lattice Relaxation of Self-Trapped Excitons in Binary Mixed Crystals of KCl and KBr

Change of emission bands in KCl 1- x Br x mixed crystals has been investigated at liquid helium temperature (LHeT) to make clear the nature of lattice relaxation of the self-trapped exciton (STE). When x <0.03, two emission bands appear at 3.60 eV and 4.88 eV. These emission bands have been confirmed to originate from a triplet state and a singlet state of localized excitons created at Br - dimer centers, respectively. With increase of x , the 4.88 eV band shifts gradually toward the low energy side to become finally the σ emission band in KBr ( x =1.0), but the 3.60 eV band diminishes on the way. Instead, a new emission band, which appears in the lower energy side, is connected to the π emission band in KBr. The discontinuity between the 3.60 eV band and the π band has been attributed to an additional lattice distortion characteristic to the initial state of the π emission. An off-center displacement of the Br 2 - core of the STE is suggested as a candidate for the type of the additional distortion.

Relaxed States of Indirect Excitons in Mixed Crystals of Thallous Halides

By measurements of luminescence and the Urbach tail of indirect absorption, exciton states were investigated in mixed crystals of thallous halides for a wide range of compositions. From the estimation of the steepness coefficients of the Urbach tail in TlCl x Br 1- x mixed crystals, the relaxed exciton state was found to change from the self-trapped state to the free state at x =0.7-0.6, consistent with the results of the emission studied before. On the other hand, the indirect excitons in TlBr x I 1- x (0.3< x <1) were found, upon analysis of the emission band and the steepness coefficient of the Urbach tail, to relax always to the self-trapped states, which become shallow with increasing iodine concentration. Exciton states in mixed thallous halides are discussed together with a theoretical study on a binary mixed crystal and in relation to percolation of minority-halogen ion clusters.

Band tails in the density of states of mixed crystals

AbstractThe Saxon‐Hutner theorem proves the existence of band tails in the density of states for a wide class of models of mixed crystals. These band tails are discussed in detail by Lifshitz. They are not obtained, however, in self‐consistent theories like the coheren, potential approximation or in the theory of Klauder. The non‐existence of band tails in the self‐consistent theories is related to a wrong percolation behaviour of the self‐energy and it is proved that a recently proposed alternative theory results in a density of states which fulfils the Saxon‐Hutner theorem. Further it is shown that the density of states of binary mixed crystals exhibits all Van Hove singularities of both pure constituents.

A study on the composition of a binary mixed crystal

The formation of centres of a new phase in a one-component system has already been investigated in detail, both theoretically and experimentally. In the present work, for a two-component melt system, the free energy required for the formation of a spherical nucleus having a molecules of component A and b molecules of component B has been studied. At the saddle point the values of a ∗, b ∗ and ΔG ∗ have been computed applying the binomial approximation. From the graphical analysis, the composition of the melt for which the composition of the nucleus becomes equal is determined. The LiBr-LiCl binary system has been chosen for the above study.