Herbert B. Rosenstock

Measurement of Very Low Absorption Coefficients by Laser Calorimetry

Laser calorimetric or thermal rise techniques are useful for the determination of very low absorption coefficients in solids. A number of improvements in this technique are described of which the most important is a means of separating surface and bulk absorption. These techniques have been applied to study alkali halides in the ir but are applicable where laser sources of sufficient power are available.

Analysis of laser calorimetric data

Adiabatic laser calorimetry, which is the most widely used method for studying the absorption coefficients of low-loss materials, can be adapted to study both the bulk and surface absorption by using a long rod sample geometry. In the limiting case of small heat losses, calculations of the thermal rise curves obtained in laser calorimetry indicate that two regions of constant slope can be expected. The first of these can be identified with the bulk absorption coefficient only and the second with the sum of the surface and bulk absorptions. Experimental data illustrating this two-slope behavior are presented.

Anomalous specific heat of glasses: Its temperature dependence

Abstract The anomalous low-temperature specific heat of disordered solids, previously attributed to low frequency localized vibrations of single atoms trapped in a cavity, is shown to be linear in the temperature, in agreement with recent observations, provided the distribution of size of cavities is of inverse-cube nature.

Anomalous specific heat of disordered solids

Abstract Part of the vibrational spectrum of any solid are the so-called “elastic” or “acoustic” waves. These have very long wavelength, i.e. all the atoms over a considerable region move (nearly) in phase. The properties of these waves can therefore be (nearly exactly) computed from the bulk properties of the solid alone (i.e. from the macroscopic elastic constants), without regard for the detailed atomic forces. Since the frequencies of these modes are low and since the modes of low frequency are the ones that make the dominant contributions to the thermodynamic properties at low temperatures, it is sometimes believed that the low-temperature thermodynamic behavior of a solid can be computed from bulk measurements alone. It is here argued (1) that the above reasoning contains a non sequitur , since the “elastic” vibrations need not be the only ones that have low frequency, and (2) that such non-elastic modes of low frequency should in fact be expected in disordered solids. The low-temperature specific heat of disordered solids should thus be higher than the conventional computation based on bulk (elastic) data would indicate. Experimental evidence for this is discussed.

On the Optical Properties of Solids

A consistent treatment of the usual linear theory of lattice vibrations in ionic crystals without the use of the symplifying cyclic boundary conditions is shown to lead to an electric moment associated with each normal frequency which, like the frequency itself, is a quasicontinuous function of the propagation vector. As a result, a broadening of the line spectrum of elementary theory and additional absorption edges of apparently observable magnitude are predicted.

Infrared bulk and surface absorption by nearly transparent crystals

We present an analysis of laser calorimetric data that deduces both the bulk and the surface absorption in a single run. The method involves use of long rod geometry combined with an analytical solution of the heat equation for the temperature distribution in a sample that is heated both internally and on the surfaces. Bulk and surface absorption coefficients, heat transfer coefficient, and thermal diffusivity appear as parameters; the last is treated as known, and the thermal rise curve is fitted to the three others. The solution obtained is valid at all points and times, and measurement of the temperature during and after laser heating at different points therefore narrows the possible fit considerably. Examples illustrating the method are presented for ZnSe, CaF(2) NaF:Li, NaCl, KBr, and KC1 at 2.7 microm, 3.8 microm, and 10.6 microm. Surface absorption is found to be dominant in all cases.

Absorption measurements by laser calorimetry

A solution to the heat equation is given which describes a cylindrical body uniformly heated along its axis. The application considered is the determination of bulk and surface absorption coefficients of the sample material from temperature‐vs‐time measurements when the heat source is a weakly absorbed narrow light beam. Under certain conditions, the full solution can be greatly simplified and the inference of absorption coefficients thus facilitated; these conditions are discussed and specified quantitatively. Equivalent results for rectangular samples are also given. The utility of the analysis is illustrated by several experimental examples.

Dynamics of the Graphite Lattice

The distribution of frequencies of normal vibrations in the graphite lattice has been obtained in closed form for low temperatures in the two‐dimensional approximation for the values (α, β, 0) and (α, β, α/2) of the force constants (α, β, γ) for nearest, second‐nearest, and third‐nearest neighbors. The frequencies run from 0 to a finite value ωmax, with two logarithmic peaks in their density. The specific heat has been calculated for two special sets of force constant ratios. Deviations from T2 dependence set in at temperatures much lower than predicted by Debye theory. Comparison with experiment leads to a numerical value for θ=ℏωmax/k, from which ωmax, and therefore also α and one of the macroscopic elastic constants, c44, may be calculated. θ and ωmax appear very sensitive to the assumed force constant ratios, c44 less so.

Lattice vibrations and infrared absorption of mixed linear chains

Abstract The vibration spectrum, atomic displacements, and infrared absorption for isotopically disordered mixed linear chains of the type AB 1- x C x have been calculated as a function of composition for chains forty atoms long in which nearest neighbor interactions are assumed. Qualitatively different types of behavior are obtained depending on whether mass A is heavier or lighter than masses B or C. This may be related to the ‘one mode’ and ‘two mode’ behavior observed in infrared absorption spectra of mixed crystals.

Lattice Infrared Absorption and Raman Scattering in Finite Crystals

The ir absorption and Raman scattering associated with the lattice vibrations of a solid have been calculated for a simple harmonic model in which the system is treated as a giant molecule. A number of differences occur in the optical properties of this finite system and one in which the system is regarded as infinite in extent. The main difference is the appearance of some first order absorption and scattering over the entire range of permitted lattice frequencies instead of only at a few specific frequencies predicted by the factor group selection rules of the infinite system. While such differences might be difficult to detect employing the usual ways of investigating the optical properties of solids, they might become observable by the study of small crystals. In addition to being of fundamental interest, such observations may also be of some value in revealing critical and surface mode frequencies.