Leon Trilling

The interaction of monatomic inert gas molecules with a continuous elastic solid

Abstract A calculation of the energy exchange between inert gases and a wide variety of alkaline and non-alkaline metals is presented under the assumption that the solid is a semi-infinite elastic continuuum. For choices of interaction well-depth consistent with those used in lattice calculations and in lobular scattering calculations, the agreement between this calculcation and experiment in the thermal range is excellent.

Scattering of Monoenergetic Argon Beams from Heated Platinum: Planar Time‐of‐Flight Measurements

Time‐of‐flight measurements were made in the plane of incidence with initially monoenergetic argon beams (speeds 5.4 × 104 and 9.55 × 104 cm/sec) before and after reflection from heated platinum. The time‐of‐flight data were used to compute low‐order moments of velocity distribution: relative number flux, momentum, and energy flux. Flux ratios yield mean speed, mean energy, and speed distribution as functions of angle of reflection. In all cases the mean speed and mean energy of the reflected stream show marked angular dependence, decreasing at a given incidence angle with increasing angle of reflection from the target normal. The mean tangential velocity of the reflected stream is close to that of the incident beam. Calculated incident beam speed distributions are near 0.1 whereas in the reflected streams values are closer to the Maxwellian limit 0.363.

The scattering of ions from a clean solid surface in the 1 to 10 eV range

Abstract We have proposed a surface model which consists of partially screened spherical caps oscillating in a direction normal to the undisturbed surface to correlate measurements of the trapping probability of sodium and potassium ions on clean (110) tungsten surfaces at energies of 1 to 15 eV and incidence of 10° to 70° from the normal to the surface. The trapping probability may be represented as a relatively simple function of angle, mass ratio, surface temperature and beam energy to ionization potential ratio, with good agreement with experimental data. The model depends on some assumptions about elevation and azimuthal screening of lattice sites which cannot fully be justified from first principles. Further analysis of the data, particularly with respect to scattered particle distribution and additional data for the scattering of lithium and cesium might help refine those assumptions.

The dependence of accommodation coefficient on surface temperature

Abstract The dependence of energy accommodation coefficients of inert gases on clean metal surfaces is analyzed in the framework of classical lattice theory. It is found that a Knudsen layer must exist next to the surface to adjust the gas molecular velocity distrivution to surface conditions. At energies below the well-depth, the accommodation coefficient slope is inversely proportional to the square root of the temperature; at energies above the welldepth, the accommodation coefficient is independent of surface temperature.

ASYMPTOTIC SOLUTION OF THE BOLTZMANN-KROOK EQUATION FOR THE RAYLEIGH SHEAR FLOW PROBLEM

An asymptotic solution of the Boltzmann‐Krook equation is constructed for the Rayleigh shear flow problem. The distribution function is expanded in powers of the square root of the inverse Knudsen number assumed small. If it is required to satisfy boundary conditions on the averaged flow parameters, the first term of the expansion yields a term identical with the solution of the Navier‐Stokes equation with no‐slip condition; subsequent terms yield slip and satisfy a sequence of linear equations whose coefficients are determined by the no‐slip Navier‐Stokes solution. If the boundary condition is specified on the distribution function, there is in addition a molecular sublayer whose thickness is of the order of the mean free path.

THEORY OF GAS-SURFACE COLLISIONS

Abstract : A theory of gas surface interaction should predict the distribution of molecules re-emitted from a surface in function of the properties of the incident flux and the physics of the surface. It depends on our uncertain knowledge of free-bound heterogeneous molecule interactions and our equally uncertain knowledge of atomic lattice dynamics. The paper critically summarizes and compares with experimental results an increasingly detailed lattice model which gives plausible energy exchange predictions and a geometrical (hard cube) model which shows promise as a correlator of data on scattering direction distribution. Both these models are based on classical interaction mechanisms; some potential generalizations to quantum models are suggested. (Author)

ON PLANE LINEAR MAGNETOHYDRODYNAMIC WAVES

The perturbation modes of the steady parallel flow of a compressible fluid of finite constant viscosity and electrical conductivity in a uniform, arbitrarily oriented magnetic field are examined. In particular, in addition to the classical fast and slow sound and Alfven modes, some waves are obtained whose amplitude is finite whenever the diffusive coefficients are finite and which resemble the diffusion of vorticity from stream surfaces in classical hydrodynamics. Upward-facing MHD waves and upstream wakes are re-interpreted.

Determination of near wake shear layer by shock expansion method for axisymmetric slender body

Abstract This paper shows how the shock expansion theory can be applied to determine the shear layer, which is part of the near wake of an axisymmetric slender body flying at hypersonic speed. Previous investigators have shown that this flow region can be described by neglecting transport properties and thus applying the method of characteristics. This paper shows that the same flow pattern can be computed, to a reasonable degree of accuracy, by further neglecting one family of characteristics. Hence the overall structure of the shear layer is due to an expansion around the corner followed by a recompression due to axisymmetric forces, where the entropy is constant along each streamline. Furthermore, the characteristics coalesce after the neck and form a trailing shock. Numerical computations using this method are straightforward and fast.

The Scattering of Gas Molecules from Metal Surfaces

The physical process of energy and momentum exchange between inert gas molecules and clean metal surfaces in the range between 0.05 eV and several eV is described and computed accommodation coefficient and scattering pattern shifts are compared to measurements. Several features of time of flight measurement techniques are described.

TIME OF FLIGHT MEASUREMENTS IN AN ARGON BEAM DEFLECTED BY A HEATED PLATINUM TARGET

Time of flight (TOF) measurements have been made in argon beams before and after reflection from heated platinum targets. Targets were prepared by chemical cleaning followed by extensive heating above 900°C in vacuum. Beams directed at these targets were reflected in directed lobes (see Refs. 20. 21 ) and the molecular TOF distributions in these lobes were investigated. Low order moments of the velocity distribution are obtained directly from the data by integrating the TOF curves after they are weighted by appropriate, derived functions. The derivation of these functions is explained. Relative number flux, momentum flux and energy flux are obtained and ratios of these fluxes yield mean speed and mean energy as a function of angle of reflection. These integrated results are presented for incident beam angles of 40° and 60° to the target normal and a target temperature of 1000°C. Other results are discussed for target temperature of 600°C and 800°C. In all cases reflected mean momentum and energy show a marked angular dependence, decreasing with increasing reflection angle from the target normal at a given angle of incidence.