Energy associated with dislocations: A calorimetric study using synthetic quartz

High temperature oxide melt solution calorimetry was used to study the energy associated with dislocations in quartz by comparing undeformed and deformed single crystals of synthetic quartz. Samples were deformed at 698 K, 1000-1500 MPa at a strain rate of 10^-5 sec^-1. Two sets of calorimetric measurements were made: (i) using a Pt capsule as a container for powdered sample, and (ii) using pellets made from sample powder without any container. For the first set of measurements, the undeformed sample with a dislocation density of enthalpy is sum of heat content H₉₇₃-H₂₉₅ and enthalpy of solution in molten lead borate at 973 K of 39.22 ± 1.00 kJ mol^-1, while the sample deformed in the dislocation creep regime with a dislocation density of 6 × 10¹⁰ to 1 × 10¹¹ cm^-2 gave an enthalpy of 38.59 ± 0.78 kJ mol^-1. For the second set of measurements the measured enthalpy of the undeformed sample was 38.87 ± 0.31 kJ mol^-1, and that of a deformed sample with a dislocation density of 3 × 10¹⁰ to 1 × 10¹¹ cm^-2 was 38.24 ± 0.58 kJ mol^-1. The present study and previous theoretical calculations and estimates are consistent and suggest that the energy associated with dislocations in quartz is ∼ 0.6 ± 0.6 kJ mol^-1 for a dislocation density of ∼ 10¹¹ cm^-2; a precise value is difficult to determine because of the overlapping errors. These results indicate that for geologically realistic dislocation densities, the maximum excess energy due to dislocations would be ∼ 0.5 kJ mol^-1 for most minerals; the exact value would depend on the Burgers vector as well as the shear modulus.