will treat the cases of platinum, antimony, and Al2O3 inclusions as representing the thermal, elastic, and optical properties of several possible inclusions in laser glass hosts. The theory will be valid, however, for other hosts which exhibit isotropic elastic properties and for other absorbing centers.

The several properties of the center-host system which determine the probability for internal cracking to occur may be divided into four groups. The first group consists of the bulk properties of both the inclusion and host and includes the respective thermal conductivities, heat capacities, thermal expansion coefficients, elastic properties, absorption coefficients for the incident radiation, and equations of state for the liquid and gas phases. The second group contains geometric properties of the inclusion which also influence its ability to cause fracture, such as the size, shape, and orientation to the incident radiation. The distribution and nature of initial microcracks and of optical imperfections form the third group of properties which determine the resistance of the host to internal cracking. Finally, the fourth group of properties describes the absorbing center-host interface; namely, the absorptance, emissivity, and initial thermal contact between the absorbing center and the host. The elastic properties, the thermal properties, and the optical properties of Pt, Sb, Al2O3, and two representative neodymium doped laser glasses are cited in tables 1, 2, 3, 4, and 5.

TABLE 1

Values of the elastic parameters. The quantities E, G, v, and x are respectively Young's modulus, shear modulus, Poisson ratio, and isothermal compressibility.

Values for the photoelastic coefficients, P1 and P12, the stress-optic coefficients, B|| and B. and the change of index of refraction with respect to temperature, (dn/dT).

The model formulated in this paper contains many physical assumptions which are necessary to render the problem solvable. The major assumptions are summarized here and are discussed in greater detail in the following sections.

(a) The inclusion is a sphere of radius ro and is always in good thermal contact with the host. The number of inclusions per unit volume is assumed to be sufficiently small so that they do not interact with one another. The effects of shape and orientation to the incident radiation also are neglected in the model.

(b) The host material is isotropic, continuous, and of infinite extent. It also is initially at an ambient temperature To and free from all stresses and strains. Because the energy content of the incident radiation is finite. the latter statement requires the temperature to be To at infinity and all stresses and strains to vanish at infinity. The distribution and nature of microcracks and optical imperfections are not treated in the model.