The surface enthalpy of NaC1 has been redetermined from heats of solution of salt samples of different specific s~~r f a c e areas. Special care was talcen in the preparation of these sanlples t o avoid contamination by nitrate and excess s o d~u n~. The value obtained, 276 c r g s /~m .~, diifers from t h a t reported by Benson and Benson, viz. 305 e r g s /~m .~, for samples containing some nitrate impurity.
Rapidly converging lattice sums for the electrostatic and van der Waals contributions to the surface energy of a generalized sodium chloride crystal have been derived. As special cases numerical values of these sums for the {100} and {110} faces of a NaCl-type crystal and for the {110} face of a CsCl-type crystal were computed. Surface energies for {100} faces of NaCl-type alkali halides and for {110} faces of both NaCl-and CsCl-type alkali halides have been calculated.
The surface free energy for the interface between crystalline sodium chloride and a saturated alcoholic solution was determined from the solubility of sodium chloride in absolute ethyl alcohol as a function of the particle size of the salt. At 298°K. a value of 171 ergs/cm.2 was found. A general discussion of the validity of the Ostwald equation, which relates solubility and particle size, is presented.
A simple modification to a previously described search method for the computation of chemical equilibria is presented. The modification consists of an automatic correction for any drift which normally arises with the search method. The drift correction also obviates the need for starting estimates which obey atom balance conditions. The modified method is both faster and mme convenient to use than the method described previously.his note is a supplement to an earlier paper"', T which describes a simple technique for the computation of chemical equilibria, suitable for use on computers of limited memory space and in cases where the initial estimate of the equilibrium composition was so poor that second order method^'*'^*^' became troublesome from the point of view of initial convergence'"7'. The method described in"' allowed a large number of condensed phases to be included without difficulty, and could be used for non-ideal systems.The main price paid for these advantages was that the method was very slow. The technique made use of a steepest descent minimization of the Gibbs free energy F with a deliberately fixed (and small) step size. In operation, the method started from an estimate of the equilibrium composition which satisfied the atom balance equations, then approached the minimum in steps, each of which led to a composition closer to the equilibrium, but which satisfied the original atom balance equations. As a result of round-off and other errors the successive compositions obtained during the search for the minimum tended to drift away from values which satisfied the desired atom balance conditions unless a small step size was used. It was this need to use a small step size which slowed down the method.While, as pointed out in"', it is possible t o reduce this drifting tendency considerably by using high order integration methods, the resulting program will be found far too large for a small computer, thus losing one of the two chief advantages of the method.The purpose of this note is to describe a simple modification of the original method, which, at the cost of a very slight increase in program size, automatically corrects for any drift which may arise. The resulting program is still well within the capacity of a small computer, and allows a much larger step to be used, 1Present address: Scientific On presente une modification simple B une mkthode dkiB dkcrite pour calculer les Cquilibres chimiques; elle consiste en une correction automatique de tout Ccart qui se produit normalernent dans la dite mbthode. La correction en question klimine le besoin de faire des estimks sujets aux conditions d'kquilibre des atomes. La mkthode modifiCe est plus rapide et plus facile A utiliser que celle qu'on a prCckdemment dkcrite.thus greatly increasing the speed of operation. A subsidiary convenience is that the starting estimates need no longer obey the desired atom balance conditions. TheoryUsing the notation of'", let it be assumed that a set of estimates n, (i = 1, . . . N ) , of the equilibrium values of the nu...
A simple method for evaluating the Madelung constant of a CsCl-type crystal is described. The Madelung constants of CaF2-type and ZnS-type lattices are computed to ten decimal places from linear relations between the Madelung constants of these and NaCl- and CsCl-type crystals.
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