On the energy gap for Fe-poor oxide and silicate minerals

Abstract

A relationship between the energy gap (E _G) and the density (ρ) over mean atomic weight (〈A〉) ratio for Fe-poor oxide and silicate minerals is derived from simple properties of their free atom-components. Theoretical considerations are based on the Lorentz electron theory of solids. The eigenfrequency ν ₀ of elementary electron oscillators, in energy units h ν ₀, is identified with the energy gap of a solid. The numerical relation is of the form

$$(\langle U_0 \rangle ^2 - E_G^2 )\frac{{\langle A\rangle }}{\rho } = \frac{4}{3}\pi \hbar ^2 \frac{{e^2 }}{m}N = 276.79 eV^2 cm^3 /mol$$

where 〈U ₀〉 is the average first ionization potential (per free atom), ħ is crossed Planck's constant, e is the electron charge, m is the electron rest mass, and N is Avogadro's number. For several geophysically interesting oxide and silicate minerals which are in general composed of four different elements (O, Si, Mg and Al), we obtain from laboratory data that the mean value of

$$\left\langle {[\langle U_0 \rangle ^2 - (E_G^{lab} )^2 ]\frac{{\langle A\rangle }}{\rho }} \right\rangle \approx 248.2 \pm 20.9eV^2 cm^3 /mol.$$

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