Dislocations, Relaxations, and Anelasticity of Crystal Quartz

By careful grinding and etching, contouring and mounting in a vacuum, very small internal friction coefficients Q^-1 are found in AT shear vibrating crystals. Various tests show that the internal friction corresponds to that of the quartz itself. The internal friction at room temperature increases proportionally to the frequency up to 100 Mc/sec indicating the presence of relaxations. These have been investigated by measuring the internal friction at very low temperatures down to 1.5^∘{}K and two relaxations were found. One having a time constant of 10^-13 second appears to be connected with a distorted lattice due to impurities while the other having a time constant of 7.7×{}10^-10 second is thought to be connected with dislocation loops. Using equations developed previously for metals the indicated number of dislocations is N̄≈10³/cm², the average loop length about 1.8×{}10^-3 cm and the ratio of Peierls force to shear modulus about 5×{}10^-8. Confirmation of these values is given by the time constant 7.7×{}10^-10 second and the change in frequency as a function of amplitude. A long-time aging effect is thought to be due to closer pinning of dislocations by impurity atoms. It is suggested that an improved frequency standard, free from aging, can be obtained by holding the temperature of the crystal at liquid helium temperature.