Born model repulsive interactions in the alkali halides determined from ultrasonic data

A new interionic potential model is developed by taking into account (i) the effect of three body interactions, (ii) the recent values of van der Waals (vdW) potentials estimated from KirkwoodMuller formula, (iii) the repulsive hardness parameters evaluated from the overlap integrals using the exchange charge model, and (iv) the effect of coupling between overlap repulsive and van der Waals forces in terms of the Drude oscillator model. The modified potential model is capable of predicting correctly the relative stability of two structures viz. NaCl and CsCl structures. The calculated values of transition pressure are found t o present close agreement with experimental data.Ein neues Interionenpotentialmodell wird entwickelt unter Beriicksichtigung von ( 1 ) des Einflusses von Dreikorperwechselwirkungen (2) der neueren Werte der van der W a d s (vdW)-Potentiale, die mit der Kirkwood-Muller-Formel bcrechnet wurden, (3) der repulsiven Harteparamrter aus den tfberlappungsintegralen mit Austauschladungsmodell und (4) des Einflusses der Kopplung zwischen repulsiveu Uberlappungs-und van der Waals-Kraften aus dem Drude-Oszilbtormodell. Das modifizierte Potentialmodell ermoglicht die korrekte Vorhersage der relativen Stabilitat von znei Strukturen, NaCl-und CsC1-Struktur. Die berechneten Werte des Druckubergangs zeigen enge Ubereinstimmung mit experimentellen Werten._..

Section: Resultsmentioning

confidence: 53%

Structural Phase Transition of Alkali Halides Using a Modified Interaction Model

Kumar

Hans

Sharma

et al. 1987

“…The traditional radii due to Pauling, Goldschmidt, and Zachariasen were identified as the free state radii as they were based on size-screening parameters corresponding to the free state [21,221. The electron density radii, on the other hand, have been found to agree very well with the values of radii calculated from the detailed analysis of interionic potentials performed by Fumi and Tosi [5,61 and by Boswarva [20] within the framework of the Born model using ultrasonic data on bulk modulus and its pressure and temperature derivatives [23].…”

Section: Methods Of Analysismentioning

confidence: 62%

Analysis of Ionic Radii, Second Neighbour Interactions, and Electronegativity Difference for Ionic Crystals

Singh¹

1990

Values of ionic radii are determined using the additivity rule and experimental information on X-ray diffraction and electron density measurements for NaCl crystals. The calculated values of ionic radii are found to produce the nearest-neighbour interionic separations close to the experimental values in I-VII, 11-VI, and 111-V compounds. In order to demonstrate the suitability of the calculated radii the interionic distances in tri-atomic compounds are also predicted. The second-neighbour overlap repulsive interactions and electronegativity differences are discussed in terms of ionic radii. The calculated radii are found to correlate very well with the electronegativity differences.Mit der Summenregel und experimentellen Informationen iiber Rontgenbeugungs-und Elektronendichtemessungen werden die Werte der Ionenradien fur NaC1-Kristalle bestimmt. Es wird gefunden, daB die berechneten Werte der Ionenradien Ionenabstande der nlchsten Nachbarn hervorrufen, die in den I-VII, 11-VI-und 111-V-Verbindungen nahe bei den experimentellen Werten liegen. Um die Eignung der berechneten Radien zu demonstrierm, werden auch die Interionenabstande in Dreierverbindungen vorhergesagt. Die abstoBenden Uberlappungs-Wechselwirkungen und die Elektronegativitatsdifferenzen zweiter Nachbarn werden mit den Ionenradien diskutiert. Es wird gefunden, daB die berechneten Radien sehr gut mit den Elektronegativitatsdifferenzen korrelieren.

“…With the help of this relation it has been possible to evaluate higher-order derivatives d2f/dr2 and d3fldr3 needed in the calculations of third-and fourth-order elastic constants. We make an attempt to fit exactly the three elastic constants Cll, C12, C,, and the equilibrium [5,19]. interionic distance r, for twenty alkali halides and four alkaline earth oxides using interionic repulsive interactions up to second neighbours, the vdW interactions for first as well as second neighbours, and three-body interactions simultaneously.…”

Section: Resultsmentioning

confidence: 99%

Thermoelastic Behaviour and Higher‐Order Elastic Constants of Ionic Crystals

Bhende

Bakhshi²,

Shanker³

1985

The relationships are given between thermoelastic properties and higher-order (third and fourth order) elastic constants for twenty alkali halides with NaCl and CsCl structures, and for four alkaline earth oxides viz. MgO, CaO, 6r0, and BaO crystals. Expressions for thermoelastic qwntities such as the Griineisen parameter and its volume derivative, Anderson parameters, and thermal expansion coefficient, are obtained in terms of higher-order elastic constants. These expressions provide a new method for estimating thermoelastic qnantities from higher-order elastic const,ants. Calculations are performed using a n interionic potential model which takes account of three body interactions, van der Waals interactions, and overlap repulsive interactions upto second neighbours. The resuks are discussed and compared with experimental data.Die Beziehungen zwischen den thermoelastischen Eigenschaften und den elastischen Konstanten hoherer Ordnung (dritter und vierter Ordnung) werden fur zwanzig Alkalihalogenide mit NaClund CsC1-Struktur und fur vier Erdalkalioxide, MgO-, CaO-, SrO-und BaO-Kristalle, angegeben. Ausdriicke fur die thermoelastischen GroBen, wie Griineisenparameter und seine Volumenableitung, Andersonparameter, thermischer Ausdehnungskoeffizient, werden mit den elastischen Konstanten hoherer Ordnung erholten. Diese Ausdriicke liefern eine neue Methode zur Rerechnung der thermoelastischen GroIlen a m den elastischen Konstanten hohcrer Ordnung. Die Berechnungen werden mit einem Interionenpotentialmodell durchgefiihrt, das Dreikorperwechselwirkungen, van der Waals-Wecliselwirkungeii und abstol3ende Uberlappungswechselwirkungen bis zu zweiten Nachbarn beriicksichtigt. Die Ergebnisse werden diskutiert und mit experimentellen Werten verglichen.