Arnold H. Kahn

Eddy‐current losses due to a surface crack in conducting material

Calculations are reported for the spatial distribution of magnetic fields in the neighborhood of a long surface crack in a conductor, where a uniform ac magnetic field is applied parallel to the length of the crack. The problem is resolved into tractable parts consisting of the cases of eddy currents near a semi‐infinite crack with a sharp tip and eddy currents near a square corner. The semi‐infinite crack problem is solved exactly by a modification of Sommerfeld’s diffraction theory and the corner problem is treated by a Green’s function obtained by the method of images. The composite solution is valid for a crack of depth equal to four times the electromagnetic skin depth or greater. From the solution, the Poynting vector is calculated and its integral over the surface computed. The change in power dissipation relative to the ’’uncracked’’ surface is given in a simple form.

Sensing and modeling of the hot isostatic pressing of copper pressing

Abstract A detailed experimental evaluation of mathematical models for densification during hot isostatic pressing (HIP) has been conducted using high purity copper powder as a model system. Using a new eddy current sensor, the density of cylindrical compacts has been measured in situ and compared with model predictions for the HIP process. Pressure shielding by the can has been found to influence the densification, and a simple plastic analysis of a thin-walled pressure vessel was used to account for its effects in the models. The existence of a low temperature creep mechanism during consolidation has been found and a formulation to account for its contribution to densification has been developed and implemented in the models. Other effects, believed to be associated with transient creep and the temperature dependence of power law creep parameters, have also been observed in the experiments and suggest the need for further model refinement.

Disappearance of impurity levels in silicon and germanium due to screening

We have studied the disappearance of impurity levels in silicon and germanium due to free‐carrier screening of the Coulomb field of the impurity ions. The ground‐state eigenfunctions and eigenvalues have been calculated for electrons described by an ellipsoidal effective‐mass Hamiltonian. A two‐dimensional finite‐element analysis was used to obtain the solutions. Only moderate carrier densities (1019 cm−3 for silicon and 1018 cm−3 for germanium) are needed to cause the impurity levels to disappear into the conduction band, the result at high doping densities being simply a degenerate semiconductor.

Exchange Interactions between Pairs of Differing Magnetic Spins in Heteropoly Complexes

Coupled pairs of differing magnetic spins in tungsto‐heteropoly complexes have been investigated by studying the magnetic susceptibility over the temperature range 2–300°K. The two sites of the magnetic ions are surrounded by oxygen ions in octahedral and tetrahedral coordinations with one oxygen ion in common. The ions studied were Co2+, Co3+, and Fe3+ in a total of six combinations on the two sites, offering a unique set of symmetries and ions for examining super‐exchange effects. A closed form for the susceptibility has been obtained on assuming the spin Hamiltonian H=β (g1S1+g2S2)· H‐JS1· S2, allowing for the possibility of g1≠ g2, S1≠ S2. Fitted values of J/k range from −6 to −70°K depending on the combinations of ions. The experimental agreement with the spin Hamiltonian for all cases studied is satisfactory for this system.

Reconstructing Electrical Conductivity Profiles from Variable-Frequency Eddy Current Measurements

A method for reconstructing radially varying conductivity profiles in cylindrical conductors is described. Solenoidal driving and sensing coils surround the cylindrical sample and an AC magnetic field applied by the driving solenoid induces axisymmetric eddy currents in the sample. It is shown how a radially varying conductivity profile can be recovered from measurements of the complex impedance recorded as a function of frequency, where impedance here is defined as the ratio of the induced electromotive force (EMF) in the sensing coil to the current in the driving coil. An iterative nonlinear least-squares algorithm is employed to reconstruct the profiles. Demonstrations of the reconstruction method are presented based on both simulated and experimentally recorded impedance data.

Eddy currents in a conducting cylinder with a crack

We report calculations for the impedance of a long solenoid which surrounds a cylinder of conducting material containing a radial surface crack of constant depth. The calculation is accomplished by solving for the longitudinal ac magnetic field in the interior of the ’’cracked’’ cylinder in terms of an infinite series of cylindrical Bessel functions. All the coefficients in the series are determined in principle by boundary‐condtion requirements and the most significant terms are obtained numerically by truncation of the series. The resulting impedance is calculated for a wide range of values of the ratios of crack depth to radius and radius to skin depth. The results are tabulated in a form useful for nondestructive testing purposes.

Nuclear Magnetic Resonance in RbMnF3

A nuclear magnetic resonance study of 85Rb, 87Rb, and 19F in paramagnetic RbMnF3 is reported. The measured shifts of the rubidium nuclear resonances are the first reported for the case of an alkali nucleus in the paramagnetic XMF3 perovskite compounds (X = Na, K, Rb, Cs; M = Mn, Ni, Co). The shift for rubidium is in the opposite direction from that expected from a 5s contact hyperfine interaction. The isotropic hyperfine interaction of the fluorine indicates the presence of 0.51% unpaired 2s spins in the F— orbitals from each Mn+ + neighbor; this result is in good agreement with previous work for the F— resonances in these paramagnetic materials. The anisotropic shift of the F— resonance was examined in a powder sample and a 2p hyperfine coupling coefficient obtained.

Boundary integral equation methods for two-dimensional models of crack-field interactions

An introduction to the application of surface integral equation methods to the calculation of eddy current-flaw interactions is presented. Two two-dimensional problems are presented which are solved by the boundary integral equation method. Application of collocation methods reduces the problems to systems of linear algebraic equations. The first problem is that of a closed surface crack in a flat slab with an AC magnetic field parallel to the plane of the crack. The second is that of av-groove crack in the AC field of a pair of parallel wires placed parallel to the vertex of the crack. In both cases, maps of the current densities at the surface are displayed, as well as the impedance changes due to the cracks.

Resistivity of linear scratches in doped (100) n-type single-crystal silicon

Four‐point probe measurements have been made on (100) n‐type Czochralski silicon wafers of initial resistivities 0.016, 0.96, and 3.35 Ω cm. The probe tips straddled linear single scratches formed by a Vickers pyramid diamond. The diamond was dead‐loaded with 0.25 N, and the scratches were made in a laboratory air environment with a relative humidity of 50%, as the silicon wafer was held at various elevated temperatures. The measurements show that the relative change in resistivity increases with temperature up to an optimum temperature, after which the resistivity decreases. The temperature at which the maximum occurs and at which the relative change in resistivity occurs depends on the initial resistivity of the wafers; the temperature at which the maximum change in relative resistivity occurs is 200 °C for the 0.016‐ and 0.96‐Ω cm wafers and 250 °C for the 3.35‐Ω cm wafer. The relative change between the undamaged wafer resistivity and the resistivity including the scratches for these same samples was ...

Eddy Current Measurement of Density During Hot Isostatic Pressing

Hot isostatic pressing (HIPing) is an increasingly used process for consolidating and densifying metal and ceramic powders to near net shape. Powder is encapsulated in a thin walled cannister under vacuum and placed in a pressure vessel where it is subjected to a temperature/pressure cycle, Fig. 1. The cycle used is normally empirically determined and aims to achieve 100 percent theoretical density in the sample.