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H Donald Brooke Jenkins

Publications and source records attributed to H Donald Brooke Jenkins.

16 recordsLinked to original sources
PubMed2006

Volume-based thermodynamics: estimations for 2:2 salts.

The lattice energy of an ionic crystal, U(POT), can be expressed as a linear function of the inverse cube root of its formula unit volume (i.e., Vm(-1/3)); thus, U(POT) approximately 2I(alpha/Vm(1/3) + beta), where alpha and beta are fitted constants and I is the readily calculated ionic strength factor of the lattice. The standard entropy, S, is a linear function of Vm itself: S approximately kVm + c, with fitted constants k and c. The constants alpha and beta have previously been evaluated for salts with charge ratios of 1:1, 1:2, and 2:1 and for the general case q:p, while values of k and c applicable to ionic solids generally have earlier been reported. In this paper, we obtain alpha and beta, k and c, specifically for 2:2 salts (by studying the ionic oxides, sulfates, and carbonates), finding that U(POT)[MX 2:2]/(kJ mol(-1)) approximately 8(119/Vm(1/3) + 60) and S degree [MX 2:2]/(J K(-1) mol(-1)) approximately 1382V(m) + 16.

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PubMed2005

Volumes of solid state ions and their estimation.

Formula unit volume, Vm, has recently been identified as the key link to a number of thermodynamic functions and has given rise to an alternative approach to thermodynamics for modern inorganic materials (volume-based thermodynamics, VBT). In an earlier publication, we reported over 400 ion volumes for commonly encountered cations and anions derived from crystal structure data which can, in turn, be used to generate formula unit volumes for those ionic salts, for which crystal structure data, which is the preferred source of such volume data, is not available. The purpose of the present paper is to report a further 147 supplementary ion volumes. These are compared to ion volumes obtained from the summation of Hofmann's elemental volumes, a convenient and alternative approach for the estimation of Vm. It is shown that many elusive ion volumes can be estimated using these databases in tandem by adopting the newly proposed isomegethic rule and other volume additivity rules. Generation of volume data for new, hypothetical, and counterintuitive ions, as well as for traditional ions, is now a reality, as is demonstrated.

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PubMed2005

Predictive thermodynamics for condensed phases.

Thermodynamic information is central to assessment of the stability and reactivity of materials. However, because of both the demanding nature of experimental thermodynamics and the virtually unlimited number of conceivable compounds, experimental data is often unavailable or, for hypothetical materials, necessarily impossible to obtain. We describe simple procedures for thermodynamic prediction for condensed phases, both ionic and organic covalent, principally via formula unit volumes (or density); our volume-based approach (VBT) provides a new thermodynamic tool for such assessment. These methods, being independent of detailed knowledge of crystal structures, are applicable to liquids and amorphous materials as well as to crystalline solids. Examples of their use are provided.

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PubMed2005

Hexafluoroantimony(V) salts of the cationic Ti(IV) fluoride non metallocene complexes [TiF3(MeCN)3]+ and [TiF2L]2+ (L = 15-Crown-5 and 18-Crown-6). Preparation, characterization and thermodynamic stability.

The cationic titanium fluoride containing complexes [fac-TiF3(MeCN)3][SbF6].MeCN (1), [trans-TiF2(15-Crown-5)][SbF6]2(2) and [trans-TiF2(18-Crown-6)][SbF6]2(2), were prepared by the reaction of TiF4, the molecular ligand and SbF5 in MeCN. Complexes 1-3 were characterized by X-ray single crystal analysis, elemental analysis, IR, NMR and mass spectroscopy. Titanium tetrafluoride reacts with the SbF5 in SO2 with the formation of fac-[TiF3(SO2)3]+, detected by 19F NMR. Application of the volume-based approach to thermodynamics (VBT) offers a means, for the first time, of exploring the energetics surrounding these materials and in the thermodynamic section a discussion of this new approach is provided. It emerges that the basis of the thermodynamic driving force of formation of [TiF3L3][SbF6](s) salts, that enforces the unfavourable [DeltaH degrees =+ 237 (+/-20) kJ mol(-1)] fluoride ion transfer from the Lewis acid TiF4(s) to SbF5(l) to give the hypothetical [TiF3]+[SbF6]-(s), is the higher Ti-L (L = ligand) bond energy in the cationic complexes [TiF3L3]+ as compared to that in the molecular adducts TiF4L2(s) and SbF5L(s) so giving rise to larger enthalpies of complexation of [TiF3]+(g) by 3L(g) compared to those for complexation of TiF4(g) by 2L(g) and SbF5(g) by 1L(g). Formation of the trans-[TiF2(15-Crown-5)]2+ and trans-[TiF2(18-Crown-6)]2+ is accounted for the stabilization of [TiF2]2+ cation by the five donor acceptor Ti-O contacts and the accompanying positive charge delocalization. Cationic titanium(IV) complexes fac-[TiF3MeCN)3-nLn]+(n= 0-3) and cis-[TiF318-Crown-6)]+, trans-[TiF2(Crown)]2+(Crown = 15-Crown-5 and 18-Crown-6) were obtained in MeCN solution by the reaction of fac-[TiF3(MeCN)3]+ and L = Et2, THF, H2 or crown ethers. Complexes fac-[TiF3(MeCN)3-nLn][SbF6] L = Et2, THF, H2O, crown ethers are unstable in MeCN solution and slowly decompose giving molecular complexes cis-TiF4L2, cis-TiF4(Crown), SbF5L, titanium oxofluoride and alkoxide complexes. The structure of the fac-[TiF3(MeCN)3]+ is similar to the fac-[TiCl3(MeCN)3]+ and the complexes trans-[TiF2L]2+ L = 15-Crown-5, 18-Crown-6 have very similar geometries to that of trans-[TiCl2(15-Crown-5)]+ showing that the essential features of coordination are the same for the cationic titanium chloride and fluoride complexes with MeCN and 15-Crown-5, 18-Crown-6.

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PubMed2004

Difference rule-a new thermodynamic principle: prediction of standard thermodynamic data for inorganic solvates.

We present a quite general thermodynamic "difference" rule, derived from thermochemical first principles, quantifying the difference between the standard thermodynamic properties, P, of a solid n-solvate (or n-hydrate), n-S, containing n molecules of solvate, S (water or other) and the corresponding solid parent (unsolvated) salt: [P[n-solvate] - P[parent]]/n = constant = theta(P)[S,s-s], or n-S and other solvate, n'-S: [P[-solvate] - P[n'-solvate]]/(n - n') = [P[n-S ] - P[n'-S]]/(n - n') = constant = theta(P)[S,s-s] where P may be any one of: U(POT) (the lattice potential energy), V(m) (the molecular or formula unit volume), Delta(f)H degrees , Delta(f)S degrees , Delta(f)G degrees or (the standard thermodynamic functions of formation and the absolute entropy), and n can be noninteger. The constants, theta(P)[S,s-s], for each property, P, of solvate of type S, are established by correlation of the available set of experimental data. We also show that, when solid-state data for a particular solvate is sparse, theta(P)[S,s-s] can be reliably predicted from liquid-state values, P[S,l], or even gas-state values, P[S,g]. This rule offers a powerful means for predicting unknown thermodynamic data, extending the compass of currently known thermodynamic information. Systems considered involve the following solvates: H(2)O (hydrates), D(2)O, NH(3), ND(3), (CH(3))(2)O, NaOH, CH(3)OH, C(2)H(5)OH, (CH(2)OH)(2), H(2)S, SO(2), HF, KOH, and (CH(CH(3))(2))(2)O. Detailed examples of usage are given for hydrates and for SO(2).

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PubMed2004

The ionic isomegethic rule and additivity relationships: estimation of ion volumes. A route to the energetics and entropics of new, traditional, hypothetical, and counterintuitive ionic materials.

By virtue of our recently established relationships, knowledge of the formula unit volume, V(m), of a solid ionic material permits estimation of thermodynamic properties such as standard entropy, lattice potential energy, and, hence, enthalpy and Gibbs energy changes for reactions. Accordingly, development of an approach to obtain currently unavailable ion volumes can expose compounds containing these ions to thermodynamic scrutiny, such as predictions regarding stability and synthesis. The isomegethic rule, introduced in this paper, states that the formula unit volumes, V(m), of isomeric ionic salts are approximately the same; this rule then forms the basis for a powerful and successful means of predicting unknown ion volumes (as well as providing a means of validating existing volume and density data) and, thereby, providing solid state thermodynamic data. The rule is exploited to generate unknown ion and (by additivity) corresponding formula unit volumes.

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PubMed2004

Thermodynamic clarification of the curious ferric/potassium ion exchange accompanying the electrochromic redox reactions of prussian blue, iron(III) hexacyanoferrate(II).

The recent Glasser-Jenkins method for lattice-energy prediction, applied to an examination of the solid-state thermodynamics of the cation exchanges that occur in electrochromic reactions of Prussian Blue, provides incisive thermodynamic clarification of an ill-understood ion exchange that accompanies particularly the early electrochromic cycles. A volume of 0.246 +/- 0.017 nm(3) formula unit(-1) for the ferrocyanide ion, Fe(II)[(CN)(6)],(4-) is first established and then used, together with other formula unit-volume data, to evaluate the changes of standard enthalpy, entropy, and Gibbs energy in those ion-exchange reactions. The results impressively show by how much the exchange of interstitial Fe(3+) ions by alkali metal ions, usually exemplified by K+, is thermodynamically favored.

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PubMed2004

The reaction of Li[Al(OR)4] R = OC(CF3)2Ph, OC(CF3)3 with NO/NO2 giving NO[Al(OR)4], Li[NO3] and N2O. The synthesis of NO[Al(OR)4] from Li[Al(OR)4] and NO[SbF6] in sulfur dioxide solution.

NO[Al(OC(CF(3))(2)Ph)(4)] 1 and NO[Al(OC(CF(3))(3))(4)] 2 were obtained by the metathesis reaction of NO[SbF(6)] and the corresponding Li[Al(OR)(4)] salts in liquid sulfur dioxide solution in ca 40% (1) and 85% (2) isolated yield. 1 and 2, as well as Li[NO(3)] and N(2)O, were also given by the reaction of an excess of mixture of (90 mol%) NO, (10 mol%) NO(2) with Li[Al(OR)(4)] followed by extraction with SO(2). The unfavourable disproportionation reaction of 2NO(2)(g) to [NO](+)(g) and [NO(3)](-)(g)[DeltaH degrees = +616.2 kJ mol(-1)] is more than compensated by the disproportionation energy of 3NO(g) to N(2)O(g) and NO(2)(g)[DeltaH degrees =-155.4 kJ mol(-1)] and the lattice energy of Li[NO(3)](s)[U(POT)= 862 kJ mol(-1)]. Evidence is presented that the reaction proceeds via a complex of [Li](+) with NO, NO(2)(or their dimers) and N(2)O. NO(2) and Li[Al(OC(CF(3))(3))(4)] gave [NO(3)(NO)(3)][Al(OC(CF(3))(3))(4)](2), NO[Al(OC(CF(3))(3))(4)] and (NO(2))[Al(OC(CF(3))(3))(4)] products. The aluminium complex [Li[AlF(OC(CF(3))(2)Ph)(3)]](2) 3 was prepared by the thermal decomposition of Li[Al(OC(CF(3))(2)Ph)(4)]. Compounds 1 and 3 were characterized by single crystal X-ray structural analyses, 1-3 by elemental analyses, NMR, IR, Raman and mass spectra. Solid 1 contains [Al(OC(CF(3))(2)Ph)(4)](-) and [NO](+) weakly linked via donor acceptor interactions, while in the SO(2) solution there is an equilibrium between the associated [NO](+)[Al(OC(CF(3))(2)Ph)(4)](-) and separated solvated ions. Solid 2 contains essentially ionic [NO](+) and [Al(OC(CF(3))(3))(4)](-). Complex 3 consists of two [Li[AlF(OC(CF(3))(2)Ph)(3)]] units linked via fluorine lithium contacts. Compound 1 is unstable in the SO(2) solution and decomposes to yield [AlF(OC(CF(3))(2)Ph)(3)](-), [(PhC(CF(3))(2)O)(3)Al(mu-F)Al(OC(CF(3))(2)Ph)(3)](-) anions as well as (NO)C(6)H(4)C(CF(3))(2)OH, while compound 2 is stable in liquid SO(2). The [small nu](NO(+)) in 1 and [NO](+)(toluene)[SbCl(6)] are similar, implying similar basicities of [Al(OC(CF(3))(2)Ph)(4)](-) and toluene.

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PubMed2004

Lattice energies of apatites and the estimation of DeltaH f degrees (PO 4 3-, g).

Experimentally based lattice energies are calculated for the apatite family of double salts M(5)(PO(4))(3)X, where M is a divalent metal cation (Ca, Sr, Ba) and X is hydroxide or a halide. These values are also shown to be estimable, generally to within 4%, using the recently derived Glasser-Jenkins equation, U(POT) = AI(2I/V(m))(1/3), where A = 121.39 kJ mol(-)(1). The apatites exhibiting greater covalent character (e.g., M = Pb, Cd, etc.) are less well reproduced but are within 8% of the experimentally based value. The lattice energy for ionic apatites (having identical lattice ionic strengths, I) takes the particularly simple form U(POT)/kJ mol(-)(1) = 26680/(V(m)/nm(3))(1/3), reproducing cycle values of U(POT) well when V(m) is estimated by ion volume summation and employing a volume for the PO(4)(3)(-) ion (not previously quantified with an associated error) of 0.063 +/- 0.003 nm(3). A value for the enthalpy of formation of the gaseous phosphate ion, DeltaH(f)( ) degrees (PO(4)(3)(-), g), is absent from current thermochemical tabulations. Examination of solution and solid state thermochemical cycles for apatites, however, leads us to a remarkably consistent value of 321.8 +/- 1.2 kJ mol(-)(1). Experimental and estimated lattice energies were used along with other thermodynamic data to determine enthalpies, entropies, and free energies of dissolution for apatites of uncertain stabilities. These dissolution values are compared with the corresponding values for stable apatites and are used to rationalize the relative instability of certain derivatives.

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PubMed2004

Enthalpies of formation of gas-phase N3, N3-, N5+, and N5- from Ab initio molecular orbital theory, stability predictions for N5(+)N3(-) and N5(+)N5(-), and experimental evidence for the instability of N5(+)N3(-).

Ab initio molecular orbital theory has been used to calculate accurate enthalpies of formation and adiabatic electron affinities or ionization potentials for N3, N3-, N5+, and N5- from total atomization energies. The calculated heats of formation of the gas-phase molecules/ions at 0 K are DeltaHf(N3(2Pi)) = 109.2, DeltaHf(N3-(1sigma+)) = 47.4, DeltaHf(N5-(1A1')) = 62.3, and DeltaHf(N5+(1A1)) = 353.3 kcal/mol with an estimated error bar of +/-1 kcal/mol. For comparison purposes, the error in the calculated bond energy for N2 is 0.72 kcal/mol. Born-Haber cycle calculations, using estimated lattice energies and the adiabatic ionization potentials of the anions and electron affinities of the cations, enable reliable stability predictions for the hypothetical N5(+)N3(-) and N5(+)N5(-) salts. The calculations show that neither salt can be stabilized and that both should decompose spontaneously into N3 radicals and N2. This conclusion was experimentally confirmed for the N5(+)N3(-) salt by low-temperature metathetical reactions between N5SbF6 and alkali metal azides in different solvents, resulting in violent reactions with spontaneous nitrogen evolution. It is emphasized that one needs to use adiabatic ionization potentials and electron affinities instead of vertical potentials and affinities for salt stability predictions when the formed radicals are not vibrationally stable. This is the case for the N5 radicals where the energy difference between vertical and adiabatic potentials amounts to about 100 kcal/mol per N5.

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PubMed2003

Standard absolute entropy, S degrees 298 values from volume or density. 1. Inorganic materials.

Standard absolute entropies of many inorganic materials are unknown; this precludes a full understanding of their thermodynamic stabilities. It is shown here that formula unit volume, V(m)(), can be employed for the general estimation of standard entropy, S degrees 298 values for inorganic materials of varying stoichiometry (including minerals), through a simple linear correlation between entropy and molar volume. V(m)() can be obtained from a number of possible sources, or alternatively density, rho, may be used as the source of data. The approach can also be extended to estimate entropies for hypothesized materials. The regression lines pass close to the origin, with the following formulas: For inorganic ionic salts, S degrees 298 /J K(-)(1) mol(-)(1) = 1360 (V(m)()/nm(3) formula unit(-)(1)) + 15 or = 2.258 [M/(rho/g cm(-)(3))] + 15. For ionic hydrates, S degrees 298 /J K(-)(1) mol(-)(1) = 1579 (V(m)()/nm(3) formula unit(-)(1)) + 6 or = 2.621 [M/(rho/g cm(-)(3))] + 6. For minerals, S degrees 298 /J K(-)(1) mol(-)(1) = 1262 (V(m)()/nm(3) formula unit(-)(1)) + 13 or = 2.095 [M/(rho/g cm(-)(3))] + 13. Coupled with our published procedures, which relate volume to other thermodynamic properties via lattice energy, the correlation reported here complements our development of a predictive approach to thermodynamics and ultimately permits the estimation of Gibbs energy data. Our procedures are simple, robust, and reliable and can be used by specialists and nonspecialists alike.

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PubMed2003

Quantitative measure for the "nakedness" of fluoride ion sources.

A quantitative measure for the donor strength or "nakedness" of fluoride ion donors is presented. It is based on the free energy change associated with the transfer of a fluoride ion from the donor to a given acceptor molecule. Born-Haber cycle calculations were used to calculate both the free energy and the enthalpy change for this process. The enthalpy change is given by the sum of the fluoride ion affinity of the acceptor (as defined in strict thermodynamic convention) and the lattice energy difference (DeltaU(POT)) between the fluoride ion donor and the salt formed with the acceptor. Because, for a given acceptor, the fluoride affinity has a constant value, the relative enthalpy (and also the corresponding free energy) changes are governed exclusively by the lattice energy differences. In this study, BF(3), PF(5), AsF(5), and SbF(5) were used as the acceptors, and the following seven fluoride ion donors were evaluated: CsF, N(CH(3))(4)F (TMAF), N-methylurotropinium fluoride (MUF), hexamethylguanidinium fluoride (HMGF), hexamethylpiperidinium fluoride (HMPF), N,N,N-trimethyl-1-adamantylammonium fluoride (TMAAF), and hexakis(dimethylamino)phosphazenium fluoride (HDMAPF). Smooth relationships between the enthalpy changes and the molar volumes of the donor cations were found which asymptotically approach constant values for infinitely large cations. Whereas CsF is a relatively poor F(-) donor [(U(POT)(CsF) - U(POT)(CsSbF(6))) = 213 kJ mol(-)(1)], when compared to N(CH(3))(4)F [(U(POT)(TMAF) - U(POT)(TMASbF(6))) = 69 kJ mol(-)(1)], a 4 times larger cation (phosphazenium salt) and an infinitely large cation are required to decrease DeltaU(POT) to 17 and 0 kJ mol(-)(1), respectively. These results clearly demonstrate that very little is gained by increasing the cation size past a certain level and that secondary factors, such as chemical and physical properties, become overriding considerations.

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PubMed2003

Estimation of enthalpy data for reactions involving gas phase ions utilizing lattice potential energies: fluoride ion affinities (FIA) and pF- values of mSbF5(l) and mSbF5(g) (m = 1, 2, 3), AsF5(g), AsF5.SO2(c). Standard enthalpies of formation: Delta(f)H degrees (SbmF5m+1)(-),g) (m = 1, 2, 3), Delta(f)H degrees (AsF6(-),g), and Delta(f)H degrees (NF4+,g).

Fluoride ion affinity (FIA) values (and the associated pF(-) values) are difficult to establish experimentally for pentafluorides of arsenic and antimony. Our approach, utilizing estimated lattice potential energies, provides a further opportunity to establish this data for liquid (and gaseous) SbF(5) and gaseous AsF(5) which compliments values obtained using ab initio routes for monomeric gas phase molecules and adds to results based on rigorous methods. A strategy is developed whereby construction of (multiple) Born-Fajans-Haber cycles centered around the (target) FIA reaction of interest yield a plethora of estimates for the enthalpy change of interest. This general approach is illustrated here by specific estimation of some experimentally based FIA values of SbF(5) and AsF(5). FIA values/kJ mol(-1) and pF- values estimated in this paper are FIA(SbF(5),l) approximately equal to -475 (+/-63), pF-(SbF(5),l) = 11.4 (+/-1.5); FIA(SbF(5),g) approximately equal to -506 (+/-63), pF-(SbF(5),g) = 12.4 (+/-1.5); FIA(2SbF(5),l) approximately equal to -609 (+/-63), pF- (2SbF(5),l) = 14.6 (+/-1.5); FIA (2SbF(5),g) approximately equal to -671 (+/-63), pF- (2SbF(5),g) = 16.0 (+/-1.5); FIA (3SbF(5),l) approximately -635 (+/-39), pF(-) (3SbF(5),l) = 15.2 (+/-0.9); FIA(3SbF(5),g) approximately -728 (+/-39), pF(-) (3SbF(5),g) = 17.4 (+/-0.9); FIA(AsF(5),g) approximately equal to -421 (+/-22), pF(-) (AsF(5),g) = 10.1 (+/- 0.5); and FIA (AsF(5).SO(2),s) approximately equal to -390 (+/-22), pF(-) (AsF(5).SO(2),s) = 9.3 (+/-0.5). Related standard enthalpies of formation (in kJ mol(-1)) are also assigned: Delta(f)H degrees (SbF(6)(-),g) approximately equal to -2075 (+/-52); Delta(f)H degrees (Sb(2)F(11)(-),g) approximately equal to -3520 (+/-63); Delta(f)H degrees (Sb(3)F(16)(-),g) approximately equal to -4874 (+/-39); Delta(f)H degrees (NF(4)(+),g) approximately equal to 903 (+/-32); Delta(f)H degrees (AsF(6)(-),g) approximately equal to -1907 (+/-22).

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PubMed2002

Ionic hydrates, M(p)X(q).nH(2)O: lattice energy and standard enthalpy of formation estimation.

This paper is one of a series (see: Inorg. Chem. 1999, 38, 3609; J. Am. Chem. Soc. 2000, 122, 632; Inorg. Chem. 2002, 41, 2364) exploring simple approaches for the estimation of lattice energies of ionic materials, avoiding elaborate computation. Knowledge of lattice energy can lead, via thermochemical cycles, to the evaluation of the underlying thermodynamics involving the preparation and subsequent reactions of inorganic materials. A simple and easy to use equation for the estimation of the lattice energy of hydrate salts, U(POT)(M(p)X(q).nH(2)O) (and therefore for solvated salts, M(p)X(q).nS, in general), using either the density or volume of the hydrate, or of another hydrate, or of the parent anhydrous salt or the volumes of the individual ions, is derived from first principles. The equation effectively determines the hydrate lattice energy, U(POT)(M(p)X(q).nH(2)O), from a knowledge of the (estimated) lattice energy, U(POT)(M(p)X(q)), of the parent salt by the addition of ntheta(U) where theta(U)(H(2)O)/kJ mol(-1) = 54.3 and n is the number of water molecules. The average volume of the water molecule of hydration, V(m)(H(2)O)/nm(3) = 0.0245, has been determined from data on a large series of hydrates by plotting hydrate/parent salt volume differences against n. The enthalpy of incorporation of a gaseous water molecule into the structure of an ionic hydrate, [Delta(f)H degrees (M(p)X(q).nH(2)O,s) - Delta(f)H degrees (M(p)X(q),s) - nDelta(f)H degrees (H(2)O,g)], is shown to be a constant, -56.8 kJ (mol of H(2)O)(-1). The physical implications with regard to incorporation of the water into various types of solid-state structures are considered. Examples are given of the use of the derived hydrate lattice energy equation. Standard enthalpies of formation of a number of hydrates are thereby predicted.

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PubMed2002

Lattice potential energy estimation for complex ionic salts from density measurements.

This paper is one of a series exploring simple approaches for the estimation of lattice energy of ionic materials, avoiding elaborate computation. The readily accessible, frequently reported, and easily measurable (requiring only small quantities of inorganic material) property of density, rho(m), is related, as a rectilinear function of the form (rho(m)/M(m))(1/3), to the lattice energy U(POT) of ionic materials, where M(m) is the chemical formula mass. Dependence on the cube root is particularly advantageous because this considerably lowers the effects of any experimental errors in the density measurement used. The relationship that is developed arises from the dependence (previously reported in Jenkins, H. D. B.; Roobottom, H. K.; Passmore, J.; Glasser, L. Inorg. Chem. 1999, 38, 3609) of lattice energy on the inverse cube root of the molar volume. These latest equations have the form U(POT)/kJ mol(-1) = gamma(rho(m)/M(m))(1/3) + delta, where for the simpler salts (i.e., U(POT)/kJ mol(-1) < 5000 kJ mol(-1)), gamma and delta are coefficients dependent upon the stoichiometry of the inorganic material, and for materials for which U(POT)/kJ mol(-1) > 5000, gamma/kJ mol(-1) cm = 10(-7) AI(2IN(A))(1/3) and delta/kJ mol(-1) = 0 where A is the general electrostatic conversion factor (A = 121.4 kJ mol(-1)), I is the ionic strength = 1/2 the sum of n(i)z(i)(2), and N(A) is Avogadro's constant.

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