Higher order elastic constants of rare earth metals: gadolinium,dysprosium and erbium

The expressions for the second and third order elastic constants of the rare earth metals, gadolinium dysprosium and erbium have been worked out and their values have been determined. The present theoretical values are compared with the experimentally observed results. It is also suggested that the third order elastic constants of these metals may be measured using ultrasonic technique under high pressures.