A scaling theory of solids under hydrostatic pressure

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Abstract
A scaling theory is proposed for solids under hydrostatic pressures which do not undergo structural phase transitions or symmetry distortions or for which distortions may be neglected. The theory is tested with two adjustable parameters by computing the linear frequency shifts (dν/dP) for the optical transitions 4A2(F) →2E, 2T2, 4T2(F), 4T1(F), 2T1 of Cr3+ ions in Al2O3. These results are further applied to Al2O3:Ti3+, V3+ with no additional parameter adjustments. Good agreement is found with all the data, including occurrences of both red and blue shifts. A general discussion of impurity ions isoelectronic to Cr3+ in Al2O3 is given. The evolution of the scaling theory into an effective potential representation of the externally applied pressure is also indicated.