Temperature dependence of Frenkel-defect formation energy deduced from diffusion of sodium in silver chloride

Batra, A. P.; Slifkin, Lawrence

doi:10.1103/physrevb.12.3473

Cited by 52 publications

(15 citation statements)

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“…We also calculated the diffusion coefficient of Naf in AgCl using our calculated formation energies, the calculated value for the migration energy of Na+ in AgCl, AuNa+(T), and the constant value of sF (4.72 k) that fits the conductivity. As shown in figure 4 the results agree excellently with Batra and Slifkin's experimental values [44]. I should ,perhaps comment on the constancy of s, with T. At first one might expect that if u, depends on T, so much s, through the thermodynamical relation to the dilemma appears to be that the temperaturedependent defect formation energy calculated from the HADES program in the quasiharmonic approximation is not a thermodynamical enthalpy, since it results from a minimization of the potential energy of the crystal rather than its free energy.…”

Section: Determination Of Diffusion Coefficients By Nmrsupporting

confidence: 80%

PLENARY SESSIONMatter transport in ionic crystals

Jacobs

1980

J. Phys. Colloques

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RCsumC. -L'analyse des mesures de transport sur les cristaux ioniques en termes de mod&les des di.fauts est s~mplifiee si quelques paramktres des defauts peuvent Ctre connus par d'autres experiences, comme les mesures NMR, ou par des calculs theoriques. Ce papier demontre que le calcul des parametres des dtfauts ponctuels est trks utile pour la resolution de plusieurs probltmes de transport dans les halogenures alcalins et d'argent. La croissante concurrence entre les rksultats des analyses fondires sur les mesures macroscopiques (conductiviti. ionique) et microscopiques (NMR) est montree en se refkrant aux resultats sur les cristaux qui ont la structure de la fluorite.Abstract. -The analysis of transport measurements on ionic crystals in terms of defect models is facilitated if some of the defect parameters can be determined from separate experiments, such as NMR measurements, or from theoretical calculations. This paper shows how the calculation of point defect parameters has proved useful in resolving a number of transport problems in the alkali and silver halides. The growing measure of concurrence between the results of analyses based on macroscopic (ionic conductivity) and microscopic (NMR) measurements is illustrated by reference to results for crystals with the fluorite structure. are inconsistent with those determined from diffusion measurements [7]. The reason for this is not hard to see. Alkali halide crystals generally contain an excess of divalent cation impurities like Ca2+ so that the conductivity in the extrinsic temperature range is dominated by the motion of cation vacancies. The cation migration and association parameters are therefore determined very precisely. An analysis of the whole conductivity curve using an imperfect model thus forces the parameters for the minority carriers -the anion vacancies -to assume incorrect values. If these are constrained to values consistent with diffusion measurements, then the Schottky defect formation parameters assume unrealistically high values. One of the principal difficulties about the non-linear least squares analysis of conductivity data is the high correlation that exists between some parameters. The use of more elaborate defect models inevitably means the introduction of more parameters with the result that the whole procedure tends to become rather intractable. There are two main ways out of this dilemma. One is to exploit selective doping that will accentuate one or more transport mechanisms at the expense of others, so that the precise value of the defect parameters corresponding to the latter have little effect and they may be held constant during the leastsquares analysis. The other is to make full use of other methods of determining some of the transport parameters, that is by theoretical calculation or by one of the microscopic methods of measuring defect parameters. There is one microscopic technique which provides direct information about the diffusional motion of defects and that is nuclear magnetic reso-'Article published online by EDP ...

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Section: Determination Of Diffusion Coefficients By Nmrsupporting

confidence: 80%

PLENARY SESSIONMatter transport in ionic crystals

Jacobs

1980

J. Phys. Colloques

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“…We also demonstrate that by using this calculated temperature-dependent Frenkel defect energy together with the mobility parameters determined experimentally by Friauf and Aboagye (1975) and the association parameters peculiar to a particular crystal (Corish and Jacobs 1972) we can account very nicely for the entire experimental conductivity curve. In 0 4 we calculate the activation energy for the diffusion of a sodium ion impurity through silver chloride by the vacancy mechanism and show that values calculated for the sodium ion diffusion coefficient using this mobility and our theoretical vacancy concentrations agree very well with the values obtained by Batra and Slifkin (1975) over the entire temperature range in which their measurements were made. The defect mobility parameters calculated for the transport of the silver ion are, on the other hand, uniformly too high and we speculate that this may be due to ion deformation, as suggested by Kleppmann and Bilz (1976).…”

Section: Introductionsupporting

confidence: 62%

“…Further evidence for the anomalous behaviour in silver chloride (on the basis of conventional models) at least in the last 150 K below the melting point, comes from the data on the diffusion of Na' impurity in the crystal obtained by Batra and Slifkin (1975). They found a non-linear Arrhenius plot for the diffusion process which had been shown earlier (Siiptitz 1965) to occur by a vacancy mechanism.…”

Section: Introductionmentioning

confidence: 89%

Fibreoptic methods of cross-polarisation optical coherence tomography for endoscopic studies

Gelikonov¹,

Gelikonov²

2008

Quantum Electron.

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A theoretical study has been made of the defect structure of silver chloride. An interionic potential based on the quasiharmonic model is developed and temperaturedependent Frenkel defect formation energies are calculated using the HADES program. These defect formation energies, when used in conjunction with experimentally determined defect migration and interaction energies, are shown to reproduce the relevant conductivity data from room temperature to the melting point. The activation energy for the migration of Na* ion impurity in silver chloride has also been calculated and used, together with the theoretical defect concentrations, to calculate diffusion coefficients for the sodium ion. These theoretical diffusion rates are in excellent agreement with the experimental data over the complete temperature range in which the measurements have been made.

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“…These include rapid increases in dielectric constants, 8 large decreases in the elastic moduli, [9][10][11] large increases in thermal expansion [12][13][14] and ionic conductivity, [15][16][17][18][19] a strong dependence of the long wavelength absorption edge on temperature, 20,21 and continuous curvature in the Arrhenius plots of the diffusion coefficient of Na and K in AgBr and AgCl. 22,23 These anomalous changes are associated with a rapid increase in the concentration of Frenkel defects that are formed at high temperatures because of a temperaturedependent decrease in the Gibbs free energy for defect formation. 15,20,25 The Frenkel defect concentration at the melting point has been estimated to be between 0.2 and 0.7 % in AgCl, 15,24 and between 1.5 and 4 % ͑probably an overestimate͒ in AgBr.…”

Section: Introductionmentioning

confidence: 99%

Second-order elastic constants of AgCl from 20 to 430°C

Hughes

Cain

1996

Phys. Rev. B

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The three independent adiabatic second-order elastic constants of AgCl have been measured from 20 to 430°C using the McSkimin pulse-superposition technique. Two single crystals with ͑110͒ and ͑001͒ axes were used in the measurements. Measurements on the ͑110͒ crystal gave the complete set of constants and showed that the longitudinal elastic constant C 11 Ј ϭ(C 11 ϩC 12 ϩ2C 44 )/2 decreased by 37%, the shear constant C 44 decreased by 15%, and the shear constant CЈϭ(C 11 ϪC 12 )/2 decreased by 65% over this temperature range. The longitudinal elastic constant C 11 decreased by 45%, the elastic constant C 12 decreased by 31% and the bulk modulus B s ϭ(C 11 ϩ2C 12 )/3 decreased by 37%. The ͑001͒ crystal was used as a check on the consistency of the measurements. The decreases in the elastic constants are linear, as expected, until approximately 320°C, whereupon C 11 Ј , C 44 , C 11 , C 12 , and B s begin to decrease more rapidly than linearly and are 6.8, 0.8, 6.0, 9.2, and 8.0 %, respectively, below the expected linearity at 430°C. By contrast, the shear constant CЈ decreases linearly over the entire temperature range. The elastic constant behavior thus becomes anomalous near the melting point, just like many of the other physical properties of the silver halides. This anomalous behavior may be attributed to the unusually high defect concentration near the melting point. Similar changes in elastic constants are seen in superionic conductors near the transition into the superionic state: a large decrease in C 11 , but only small changes in C 44 . This may indicate that the silver halides are just starting the transition to the superionic state when the halide sublattice melts and the transition is frustrated.

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Temperature dependence of Frenkel-defect formation energy deduced from diffusion of sodium in silver chloride

Cited by 52 publications

References 13 publications

PLENARY SESSIONMatter transport in ionic crystals

PLENARY SESSIONMatter transport in ionic crystals

Fibreoptic methods of cross-polarisation optical coherence tomography for endoscopic studies

Second-order elastic constants of AgCl from 20 to 430°C

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