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Book ChapterDOI

Physikalische Eigenschaften der festen Salze

01 Jan 1972-pp 40-372
About: The article was published on 1972-01-01. It has received 6 citations till now.
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Journal ArticleDOI
TL;DR: In this article, a new set of Pitzer ion interaction model parameters for the binary NaOH-H2O system for concentrations up to over 30 mol·kg−1 and temperatures ranging from 273.15 to 523.15 K were presented.
Abstract: This paper presents a new set of Pitzer ion interaction model parameters for the binary NaOH–H2O system for concentrations up to over 30 mol·kg−1 and temperatures ranging from 273.15 to 523.15 K. Assuming that the electrolyte is only partially dissociated, the model requires the adjustment of (i) the three classical binary interaction parameters β (0), β (1) and C ϕ , (ii) the equilibrium constant of formation of the aqueous complex NaOH0(aq), and iii) one binary (λ NaOH/NaOH) and one ternary (\( \zeta_{{{\text{NaOH}}/{\text{Na}}^{ + } /{\text{OH}}^{-} }} \)) interaction parameter. This approach, which provides much better results than the approach of treating NaOH as a fully dissociated electrolyte, was chosen to extend the description of the system to high temperatures and high concentrations. The temperature functions of the solubility products of anhydrous NaOH(cr) and five hydrated salts, NaOH·nH2O(cr) (where n = 1, 2, 3.11, 3.5, 4α), were determined. In order to evaluate the quality of the new set of parameters, several tests were run on various properties using various literature data. These include the boiling point elevation in the NaOH–H2O system and the phase diagrams of the two ternary systems NaOH–NaCl–H2O and NaOH–LiOH–H2O. Interaction parameters for the two related binary systems NaCl–H2O and LiOH–H2O were taken from previous studies. To ensure consistency, four new mixing parameters were revised (\( \zeta_{{{\text{Na}}^{ + } /{\text{Cl}}^{-} /{\text{NaOH}}}} \) and \( \varPsi_{{{\text{Cl}}^{-} /{\text{OH}}^{-} /{\text{Na}}^{ + } }} \) for the ternary system NaOH–NaCl–H2O and \( \lambda_{{{\text{Li}}^{ + } /{\text{NaOH}}}} \) and \( \varPsi_{{{\text{OH}}^{ - } /{\text{Na}}^{ + } /{\text{Li}}^{ + } }} \) for the ternary system NaOH–LiOH–H2O). Consistent with Pitzer’s equations, our new set of parameters can be used to satisfactorily describe the quaternary Na+–Li+–Cl−–OH−–H2O system to very high concentrations and temperatures.

19 citations


Cites background from "Physikalische Eigenschaften der fes..."

  • ...Kirschstein [54] provided boiling point values for molalities ranging from 1....

    [...]

  • ...…(K ) m NaOH (mol·kgw-1) Figure 6 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 B o ili n g p o in t ra is e ( °C ) m NaOH (mol·kgw-1) Kirschstein (1972) Bialik et al (2008) This study Dühring's law irsc st i [54] i li l. [55] [56] Figure 7 0 1 2 3 4 5 6 7 8 0 10 20 30 40 50 60 70…...

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Dissertation
04 Nov 2015
TL;DR: In this paper, the authors propose a modification of the logiciel PhreeqC, a logiciel of geochimie, which permettait deja le calcul du coefficient osmotique, la capacite calorifique, de l’activite de l'eau and du coefficient d'activite.
Abstract: Les saumures naturelles sont des ressources en eau de plus en plus convoitees et utilisees par les industriels, que ce soit pour la production d’eau potable (dessalement de l’eau de mer…) ou pour la recuperation de substances valorisables (le lithium, le potassium, le magnesium, la silice …). Les saumures industrielles sont aussi souvent utilisees dans differents procedes comme fluides caloporteurs ou lors d’extraction de minerai (phosphore, alumine…). Cependant, ces solutions aqueuses complexes presentent des proprietes thermodynamiques qui s’ecartent de celles des solutions aqueuses diluees (dites ideales). Des approches de calcul specifiques sont alors necessaires pour pouvoir determiner ces proprietes. Cette etude s’interesse au calcul des proprietes thermodynamiques d’exces (coefficient osmotique, capacite calorifique, densite …) de ces systemes. Celles-ci dependent toutes de la derivee de l’energie libre de Gibbs d’exces (G^ex) par rapport a la concentration en sels dissous, a la temperature ou a la pression. Suite a une revue bibliographique des differents modeles thermodynamiques permettant de calculer l’energie libre de Gibbs d’exces, le modele de Pitzer a ete selectionne pour decrire les proprietes d’exces d’un systeme contenant c cations, a anions et n especes neutres. Les proprietes thermiques et volumiques ont ete, dans un premier temps, etablies pour un systeme contenant des especes neutres avant d’etre implementees dans le logiciel PhreeqC, logiciel de geochimie qui permettait deja le calcul du coefficient osmotique, de l’activite de l’eau et du coefficient d’activite. Le logiciel issu de cette modification, PhreeSCALE, permet desormais, lorsque les parametres d’interaction de Pitzer sont connus, de calculer les proprietes d’exces telles que le coefficient osmotique, la capacite calorifique ou la densite d’une saumure en tenant compte de la speciation exacte de la solution. Dans le cas ou les parametres d’interaction sont a determiner, PhreeSCALE peut etre couple a des logiciels d’optimisations pour etablir de nouveaux jeux de parametres, cales sur les proprietes mesurees des solutions. Les applications de cette etude s’appuient sur plusieurs systemes qui sont soit des saumures industrielles, soit des saumures naturelles. Le systeme NaOH-H2O a ete selectionne en raison des salinites elevees dans l’eau (jusqu’a 29 mol.kgw-1 a 25°C). Pour representer au mieux l’ensemble des proprietes sur toute la gamme de concentrations, la dissociation partielle de l’espece NaOH a du etre prise en compte. Les autres systemes etudies sont des saumures chlorurees, plus caracteristiques des saumures naturelles. Une approche par etape a permis d’etablir les parametres d’interaction pour cinq systemes binaires (NaCl, KCl, CaCl2, MgCl2 et BaCl2). Puis, des systemes ternaires et un systeme quinquenaire composes de ces cinq electrolytes, ont ete etudies. Dans chaque cas, la capacite calorifique et la densite ont ete determinees. Finalement des abaques, tenant compte des conditions de temperature et de pression, ont pu etre tracees pour le systeme NaCl-H2O.

5 citations


Cites background or methods from "Physikalische Eigenschaften der fes..."

  • ...Kirschstein [54] provided boiling point values for molalities ranging from 1....

    [...]

  • ...m NaOH (mol·kgw-1) Kirschstein (1972) Bialik et al (2008) This study Dühring's law Kirschstein [54] Bialik et al....

    [...]

  • ...The experimental data are from Kirschstein [54] (open diamonds) and Bialik et al....

    [...]

Journal Article
TL;DR: In this paper, an algorithme generalise permettant le calcul de la constante de Madelung est proposed for des cristaux heteropolaires a maille cubique de formule AxBy.
Abstract: Un algorithme generalise permettant le calcul de la constante de Madelung est propose pour des cristaux heteropolaires a maille cubique de formule AxBy. La definition de la constante de Madelung fait apparaitre les expressions des contributions anioniques et cationiques. Des exemples d'applications sont donnes pour la blende (M=3,7829), la fluorine (M=11,6365) et la cuprite (M=10,2590).

1 citations

01 Jan 1965
TL;DR: Using a torque magnetometer, experimental results were reported on some new magnetic properties in high-purity, optical-quality single crystals of lithium fluoride, potassium chloride, and sodium chloride as mentioned in this paper.
Abstract: Using a torque magnetometer, experimental results are reported on some new magnetic properties in high‐purity, optical‐quality single crystals of lithium fluoride, potassium chloride, and sodium chloride. Since the torque observations are not produced by the gross diamagnetism of these salts, the magnetic centers may be along dislocations because the magnetic susceptibility is observed to possess uniaxial anisotropy. Soft x irradiation increased the observed magnetization. In addition, there is a cooperative interaction among the magnetic centers which gives a remanent magnetization. The temperature dependence of the remanent magnetization is similar to the Bloch spin‐wave concept of ferromagnetism. These new magnetic properties are an order of magnitude smaller when measured in crystals of magnesium fluoride and of calcium fluoride.

1 citations

References
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Book
01 Jan 1954
TL;DR: Born and Huang's classic work on the dynamics of crystal lattices was published over thirty years ago, and it remains the definitive treatment of the subject as mentioned in this paper. But it is not the most complete work on crystal lattice dynamics.
Abstract: Although Born and Huang's classic work on the dynamics of crystal lattices was published over thirty years ago, the book remains the definitive treatment of the subject. It begins with a brief introduction to atomic forces, lattice vibrations and elasticity, and then breaks off into four sections. The first section deals with the general statistical mechanics of ideal lattices, leading to the electric polarizability and to the scattering of light. The second section deals with the properties of long lattice waves, the third with thermal properties, and the fourth with optical properties.

7,756 citations

Journal ArticleDOI
Francis Birch1
TL;DR: In this article, Murnaghan's theory of finite strain is developed for a medium of cubic symmetry subjected to finite hydrostatic compression, plus an arbitrary homogeneous infinitesimal strain.
Abstract: Murnaghan's theory of finite strain is developed for a medium of cubic symmetry subjected to finite hydrostatic compression, plus an arbitrary homogeneous infinitesimal strain. The free energy is developed for cubic symmetry to include terms of the third order in the strain components. The effect of pressure upon the second-order elastic constants is found and compared with experiment, with particular reference to the compressibility; the pressure-volume relation in several approximations is compared with the measurements to 100,000 kg/${\mathrm{cm}}^{2}$. The simplest approximation is shown to give a satisfactory account of most of the experimental data. The results are also compared with some of the calculations based on Born's lattice theory.

4,834 citations

Book
15 Jun 1971
TL;DR: In this paper, the authors present data on the elastic properties of single crystals collected from the literature through mid-1970 and the elastic property of isotropic aggregates which are calculated according to the schemes of Voigt and Reuss for all materials, and Hashin and Shtrikman for materials with cubic symmetry.
Abstract: Data on the elastic properties of single crystals has increased dramatically since Professor Simmons completed his first book in 1965. While this book is a consolidation of his earlier work, it has been extensively updated and revised to include new material and references, is far more complete, and is presented in a more useful form.This is actually a handbook consisting of computer printout in tabular format. It presents data on the elastic properties of single crystals collected from the literature through mid-1970 and the elastic properties of isotropic aggregates which are calculated according to the schemes of Voigt and Reuss for all materials, and Hashin and Shtrikman for materials with cubic symmetry. The tables include about 3000 determinations.At present it is impossible to calculate the elastic properties of a random, macroscopically isotropic aggregate of crystals from the single crystal elastic constants, but bounds may be obtained for the aggregate properties from the single crystal constants. Accordingly the book tabulates the Voigt and Reuss averages for all materials for which single crystal data has been reported. Hashin and Shtrikman have shown that the Voigt and Reuss bounds could be improved, and they have developed expressions for the corresponding bounds of aggregates of cubic crystals.In this book all four bounds (Voigt, Hashin, Shtrikman, and Reuss) are tabulated for cubic materials while Voigt and Reuss bounds only are tabulated for non-cubic materials. The elastic properties of aggregates are those in common use and include Young's modulus, shear modulus, Poisson's ration, bulk modulus, compressibility, velocity of compressional waves, and the velocity of shear waves. Although any two of these properties suffice to uniquely characterize a given material, all are tabulated because different sets are best suited for different uses.

2,913 citations

Journal ArticleDOI
TL;DR: In this article, a short-range repulsive interaction between ions with closed shell electron configurations is investigated, and an approximate interpretation of the Born-Mayer potential in terms of overlap integrals is developed.
Abstract: The simple classical theories of the dielectric constants and compressibility of ionic crystals lead to two relations among the experimental quantities from which arbitrary parameters have been eliminated, the Szigeti relations. Neither is satisfied by the data, indicating the inadequacy of these simple theories. The short-range repulsive interaction between ions with closed shell electron configurations is investigated, and an approximate interpretation of the Born-Mayer potential in terms of overlap integrals is developed. These results are applied to the interaction of model ions consisting of rigid charged shells bound to cores by harmonic restoring forces. Using this model, polarization mechanisms neglected in the simple dielectric constant theory, the "short range interaction polarization," and the "exchange charge polarization" are described. Both arise from charge redistributions occurring when the ions move with resulting changes in electron overlaps. Applied to a crystal, these ion models permit the derivation of generalizations of the Szigeti, Clausius-Mossotti, and Lorenz-Lorentz relations. The $\frac{{e}^{*}}{e}$ of the second Szigeti relation can then be calculated and comparison with the $\frac{{e}^{*}}{e}$ values derived from experimental data imply that the above polarization mechanisms must be at least in part responsible for the deviation of this parameter from unity. The failure of the first Szigeti relation is discussed and attributed to the inadequacy of the treatment of compressibility. The additivity feature of the simple theory and its absence in the refined theory are discussed in relation to the so-called vacuum and crystal ion polarizabilities.

1,988 citations

Journal ArticleDOI
TL;DR: In this article, a method was devised to study the energy spectrum for an excited electron configuration in an ideal crystal, which consists of a single excited electron taken out of a full band of $N$ electrons.
Abstract: In this article, a method is devised to study the energy spectrum for an excited electron configuration in an ideal crystal. The configuration studied consists of a single excited electron taken out of a full band of $N$ electrons. The multiplicity of the state is ${N}^{2}$. It is shown that because of the Coulomb attraction between the electron and its hole ${N}^{\frac{8}{5}}$ states are split off from the bottom of the excited Bloch band; for these states the electron cannot escape its hole completely. The analogy of these levels to the spectrum of an atom or molecule is worked out quantitatively. The bottom of the Bloch band appears as "ionization potential" and the Bloch band itself as the continuum above this threshold energy.

1,639 citations