R. W. Hopper

Mechanism of Inclusion Damage in Laser Glass

The mechanism of inclusion damage in laser glass is associated with the temperature rise of particles, or surface regions of particles, relative to the surrounding glass. The particles of greatest concern are metallic, although at very high‐power levels ceramic inclusions containing large concentrations of highly absorbing ions can likewise result in failure. Solutions to the heat‐flow problems of a perfectly conducting sphere in a medium of finite conductivity and of the infinite composite solid indicate that temperatures of metal particles subject to a 20‐J/cm−2, 30‐nsec laser pulse can exceed 10 000°K for a range of particle sizes. These high temperatures produce stresses in the glass adjacent to the particles which can exceed the theoretical strength of the glass, and result in failure. The effects on the breakdown condition of flux level and pulse time, as well as the size, shape, thermal expansivity, and spectral emissivity of the particle, and the heat capacity and thermal conductivity of particle ...

Crystallization statistics, thermal history and glass formation

Abstract The formal theory of transformation kinetics describes the volume fraction of a phase transformed in a given time at a given temperature. The basic concepts are extended for isotropic crystal growth in a material having a known thermal history T ( r , t ). A crystal distribution function ψ ( r , t , R ) is defined such that the number of crystallites in a volume d υ at r having radii between R and R + d R at time t is ψ ( r , t , R ) d υ d R . The function ψ contains essentially complete statistical information about the state of crystallinity of a material. Formal expressions for ψ are obtained. Applications are discussed, including predictions of crystallinity when T ( r , t ) is known; predictions of glass-forming tendencies; experimental determination of nucleation rates; and the determination of the thermal history of a sample from post mortem crystallinity measurements. As an example, ψ ( r , t , R ) is calculated for a lunar glass composition subjected to a typical laboratory heat treatment.

Solute redistribution during crystallization at constant velocity and constant temperature

Abstract An analysis is presented for the time-dependent solute redistribution which occurs during crystallization at constant velocity and constant temperature. The analysis is suggested to be applicable to many studies of crystallization in glass-forming systems, where solidification takes place at temperatures well above the solidus and where the solubility in the crystalline phase is quite limited. Appropriate for these situations, the usual condition of Cs = kCL is replaced by the approximate condition of Cs = Csolidus. The results indicate a concentration of the liquid at the interface which is limited only by the liquidus composition, and not by a steady-state composition of CO/k. Limitations of the present analysis for cases where the growth rate becomes concentration-dependent are discussed.

Temperature distributions during crystallization at constant velocity

Abstract The temperature distribution in a crystal-melt system solidifying with a planar interface is examined. The case of an infinite system, initially at a uniform temperature, solidifying at a constant (interface controlled) velocity is solved explicity. The limiting interface heating is found to be the latent heat divided by the specific heat, which can be quite large. Estimates of the effect of finite sample size are given. Interface attachment kinetics and heat flow control mechanisms are discussed. The results of the analysis are compared with experiments on three representative materials: sodium disilicate (an oxide glass-former), α-phenol o-cresol (an organic glass-former) and tin (a metal).

Spinodal decomposition without diffuse interface theory-I. Theory

Abstract It has been shown that when higher derivative tenns of the diffuse interface expansion are included in the theory of spinodal decomposition, exceptional results are obtained. Within a mean field pair interaction (MFPI) interpretation, the coefficients of terms ▽ 2 n c in the extended diffuse interface expansion eventually become infinite in magnitude. These anomalies are discussed and circumvented in a new analysis of spinodal decomposition. Within the MFPI interpretation a Fourier analysis of the composition is made at an earlier stage in the analysis. The result is a diffusion equation which can be related to the usual diffusion equation of spinodal decomposition. In the early stages, the only change encountered is that the factor κβ 2 in the amplification factor is replaced by a function K ( β ). When κ is defined, K ( β ) approaches κβ 2 in the limit of small β. When, because of long-range intermolecular potentials, the standard definition of κ does not converge, K ( β ) remains well defined but no longer increases as β 2 in the small β limit. This can result in amplification factors which are qualitatively different from those predicted by the standard theory.

Higher Derivatives in the Thermodynamics of Nonuniform Solutions. I. Basic Interface Theory

The thermodynamics of nonuniform solutions usually employs a gradient energy term in the expression for the local free energy. This arises from retaining the first nonvanishing terms of a MacLaurin expansion of the free energy in the composition and its derivatives. The nature of this expansion is discussed, and the formulation is extended to include derivatives higher than the second. General, a priori arguments suggest that a reasonable next approximation is f*=f(c) + κ1 ∇2c+κ2 (∇ c)2 + κ3∇4c+κ4(∇2c)2 + κ5∇ c · ∇3c + κ6(∇ c)2∇2c+ κ7(∇ c)4, for an isotropic solution. The results for a cubic system are also presented. The significance of the coefficients are discussed using a simple mean field pair interaction analysis. This interpretation provides physical insight into the nature of the terms and suggests that in the absence of specific knowledge about a particular situation, the derivative terms may be ordered in the following sequence of decreasing importance: κ1 ∇2c, κ3∇4c, [κ2(∇ c)2, κ5∇ c · ∇3c], [κ...

Spinodal decomposition without diffuse interface theory, II: K(β) and comparisons

A recent mean field pair interaction (MFPI) formulation of the theory of spinodal decomposition is extended with quantitative calculations based on representative pair potentials. These include a nearneighbor potential, a screened impurity potential, and various inverse power law potentials. For the nearneighbor potential, as well as for power law potentials with exponents n ≥ 5, results in accord with the standard theory are obtained. For power law exponents n < 5 (for systems in which long-range intermolecular potentials are important), the amplification factor, R(β), is expected to decrease less rapidly with increasing wavenumber at large β than predicted by the standard theory, and R(β) should not be quadratic in β for small β. The predictions of the MFPI formulation are compared with experimental data on the kinetics of phase separation. A qualitative preference for the MFPI formulation seems indicated: but in quantitative detail, the agreement between theory and experiment still leaves much to be desired. The needs for further extensions of the theory, and most importantly for reliable experimental data on initially homogeneous specimens, are emphasized.

Higher derivative terms in spinodal decomposition

Abstract The effects of higher order terms on the kinetics of spinodal decomposition are evaluated. The terms considered are the higher derivative terms in the diffuse interface free energy expansion. It is shown that the next approximation to the local free energy results in a kinetic amplification factor of the form: R(β) = N v −1 M (−ƒ″β 2 − 2κβ 4 + 2μβ 6 ) , where μ can be related to coefficients in the free energy expansio Problems associated with a continuation of the expansion to evaluate further effects on spinodal decomposition kinetics are noted.

Sintering, crystallization, and breccia formation

The process of breccia formation by viscous sintering in the absence of pressure, advanced forcefully by Simonds (1973), is examined in detail. The limitations on the standard model for such sintering are considered. The competing process of crystallization is analyzed kinetically in terms of time-temperature-transformation curves corresponding to various degrees of crystallinity. The analysis is applied to Lunar Composition 15418 to illustrate the approach. The results indicate that close constraints can be placed on the thermal histories of lunar breccias, particularly breccias with modest degrees of crystallinity, from microstructural observations and kinetic measurements.

On diffusive creep and viscous flow

Abstract The relation between viscous and diffusive deformations is discussed, and their nonequivalence is emphasized. Molecular theories relating self diffusivity to viscosity, as well as the macroscopic behavior of materials deforming by diffusive creep and by viscous flow, are reviewed. It is concluded that while molecular theories can properly relate viscosity to diffusivity, viscous flow and diffusive creep are not macroscopically equivalent. A “viscosity” obtained by equating a diffusive creep flow to a viscous flow will in general depend upon the state of stress and will therefore not be a material property. The differences between the flow types are illustrated with two examples, the spheroidization of a nearly spherical particle, and the effective viscosity of a suspension of particles in viscous liquid.