Abstract
An empirical relation H=K(1−2/3α4) has been derived between the hardness H of A m B n-like crystals, as obtained by smoothing the Mohs hardness scale, and the bond-ionicity α, where K is a constant determined by the number of the rows to which the atoms A and B belong in the periodic classification of elements. The applicability of the above relation is extended to crystals in which B is a polyatomic anion. Electron charges in some crystals have also been calculated with help of the proposed relation.
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Barinsky, R.L., Kulikova, I.M.: Metamict transformations in some niobates and zircons according to X-ray adsorption spectra. Phys. Chem. Minerals 1, 325–333 (1977)
Chelikowsky, J.R., Schlüter, M.: Electron states in α-quartz. A self-consistent pseudopotential calculation. Phys. Rev., B 15, 4020–4029 (1977)
Collins, G.A.D., Cruickshank, D.W.J., Breeze, A.: Ab initio calculations of the silicate ion, orthosilicic acid and their L2,3 X-ray spectra. J. Chem. Soc. Faraday Trans. II 68, 1189–1195 (1972)
Coulson, C.A., Rédei, L.B., Stocker, D.: The electronic properties of tetrahedral intermetallic compounds. I. Charge distribution. Proc. Roy. Soc. (London), Ser. A 270, 357–372 (1962)
Dana's Texbook of Mineralogy, Ford, W.E. (ed.). New-York: John Wiley and Sons, 4th ed., 1958
Grimley, T.B.: Homopolar effects in crystal having the sodium chloride type of lattice. Proc. Roy. Soc. (London), Ser. A70, 123–133 (1957)
Handbook of Chemistry and Physics, Cleveland: The Chemical Rubber Co, 48th ed, 1967
Hardy, J.R.: Effective ionic charge in relation to lattice vibrations. Phil. Mag. 6, 27–35 (1961)
Harrison, W.A.: Bond-orbital model and the properties of tetrahedrally coordinated solids. Phys. Rev., B 8, 4487–4498 (1973)
Jørgensen, Ch.K., Berthon, H., Bakenc, L.: Photo-electron spectra of fluorides and the influence of the Madelung potential. J. Fluor. Chem. 1, 327–336 (1971)
Julg, A.: Chimie Théorique, Paris: Dunod, 1964
Julg, A., Julg, O.: Exercices de Chimie Quantique, Paris: Dunod, 1967
Julg, A., Marinelli, F.: Halogénures alcalins: Un modèle incluant une délocalisation à courte distance. Application à la stabilité relative des divers arrangements cristallins. Int. J. Quant. Chem. X, 1037–1047 (1976)
Julg, A., Marinelli, F., Pellégatti, A.: Determination of the polarity in nonmetallic crystals. I. Theory and application to tetrahedrally coordinated solids. Int. J. Quant. Chem. (1978) (accepted for publication)
Löwdin, P.O.: Quantum mechanics and molecular physics of solids. In: Aspects de la chimie quantique contemporaine. 208–223, Paris: Centre National de la Recherche Scientifique, 1971
Picus, G., Burnstein, E., Henvis, B.W., Haas, M.: Infrared lattice vibration studies of polar character in compound semiconductors. J. Phys. Chem. Solids 8, 282–285 (1959)
Roothaan, C.C.J.: New developments in molecular orbitals theory. Rev. Mod. Phys. 23, 69–89 (1951)
Szigeti, B.: Polarisability and dielectric constant of ionic crystals. Trans. Faraday Soc. 45, 155–166 (1949)
Vleck, J.H. Van, Shermann, A.: The quantum theory of valence. Rev. Mod. Phys. 7, 168–227 (1935)
Yip, K.L., Fowler, W.B.: Electron Structure of SiO2. II. Calculations and results. Phys. Rev. B 10, 1400–1408 (1974)
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Julg, A. An empirical relation between hardness and bond-ionicity in a crystal. Phys. Chem. Minerals 3, 45–53 (1978). https://doi.org/10.1007/BF00357446
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DOI: https://doi.org/10.1007/BF00357446