Pressure and temperature of crystallization from elastic effects around solid inclusions in minerals?

Abstract

Earth processes commonly result in the transfer of a mineral grain from the pressure-temperature (P,T) condition of its origin to considerably different pressure-temperature conditions. If a mineral grain (h) includes a grain of another mineral (i), transfer to new P-T conditions commonly will cause anisotropic elastic strain effects around the inclusion owing to different coefficients of thermal expansion (alpha ) and compressibility (beta ) for the 2 minerals. To the extent that these elastic effects remain reversible over geologic time intervals, they represent stored information concerning the pressure and temperature of origin. The differential equation for the pressure-temperature curve representing absence of anisotropic stress around an inclusion of one isometric crystal (also a homogeneous fluid) inside of another isometric crystal is given. Experimental determination of 2 such P-T curves (conditions: P i =P h ; T i =T h ) for a given host containing 2 different kinds of inclusions, known to have been included contemporaneously, would result in an intersection representing the pressure and temperature of origin (P o ,T o ). Among suggested techniques for determination of P-T curves is one using a window pressure-temperature bomb for observation of specimens between crossed polarizing filters to obtain the pressure-temperature coordinates for points of null piezobirefringence around inclusions. An auxiliary method, based on conventional P-T equipment, involves an electrical null technique using either a symmetrical combination of 2 slide-wire piezometers (Bridgman) or a related device and a Wheatstone bridge. The 2 slide-wires comprise 2 resistances of the bridge in the first device. In the second device the bridge is unbalanced by severance of one of its arms. The few noted natural examples of stress effects around inclusions in diamond and associated pyrope are consistent with extrapolations based on known values of alpha and beta and inferred pressure-temperature conditions within the earth. Examination of these minerals, having a probable origin in the mantle but now included in the kimberlites, should allow determination of specific temperatures at specific pressures equivalent to depths within the mantle of the order of 100 mi. or more, using available experimental equipment.