Power-law Region Research Articles

Turbulent non-Newtonian boundary layers on a flat plate

A theoretical relation between drag coefficients and non-Newtonian Reynolds numbers is developed in a manner analogous to a Newtonian analysis by Prandtl, using a lorgarithmic velocity profile proposed by Clapp. Velocity, profiles for power-law fluids flowing past a flat plate were measured with a laser velocimeter, and were used in numerical integration of the momentum boundary layer equation to obtain drag coefficients. The Prandtl-type of analysis correlated these experimentally generated drag coefficients with an average deviation of ± 7.837% in a power-law Reynolds number region of 10 4–10 6. This work is believed to provide the first measurement of velocity profiles in turbulent non-Newtonian boundary lasers on a plate. Use of the laser velocimeter has not previously, been reported in sush studies. The design of the water tunnel has been proved here to be suitable for the determination of this type of data.

The influence of stoichiometry on compression creep of polycrystalline UO 2+ x

Compressive creep tests have been performed on polycrystalline hyperstoichiometric uranium dioxide, as a function of temperature, stress and deviation from stoichiometry. Under low stresses measured steady-state creep rates for UO 2+ x increase linearly with applied stress, σ, and with oxygen excess, x. Creep rates for UO 2+ x tested at high stresses follow a power-law stress dependence of the form ε ̇ ∝ σ n where 4< n<7, and increase with x m where 1.75< m< 2. The transition stress, σ t, between linear and power-law stress dependence behavior decreases with increasing O U ratio. For polycrystals tested at high stresses, the creep activation energy, Q c , decreases with increasing x in the same manner as found for uranium dioxide single crystals. Creep activation energies also decrease with increasing x in the linear stress-dependence region, but values for Q c are lower at a given x than are values obtained in the power-law stress region. It is suggested that different diffusion processes control the observed creep behavior in the two different stress regimes.

Prebreakdown Behavior of Long Gold-Doped Germanium n+pp+ Diodes

Current-voltage and spatial potential distribution measurements were made on long p-type Au-doped Ge double-injection diodes over the temperature range 65–300 °K. The existing theory for these devices which is based on extensive approximations for the Ohm's-law and power-law region is extended to include the transition region. It is shown that it can occupy several decades of current and hence dominate the prebreakdown injection mode. An excellent fit with experiment is obtained for devices which are provided with probes to permit measuring of the bulk characteristics exclusive of contact drops. Also, the region where the field dependence of mobility and electron lifetime cause the behavior to depart from the low-field theory is clearly manifested. The potential distribution between the contacts was also found to be consistent with the theory. The electron-capture coefficients for neutral and singly charged Au atoms were determined in the temperature range 65–200 °K and were shown to be only slightly temperature dependent.

Prediction of activation energies for creep and self-diffusion from hot hardness data

It is shown that the activation energy for creep or self-diffusion for pure metals can be determined from hot hardness data above 0.75Tm by means of the expressionH/E=G expQL/nRT· HereH is the hot hardness,E is the elastic modulus,G is a material constant,QL is the lattice self-diffusion activation energy,R is the gas constant,T is the absolute temperature, andn is the stress exponent for creep assumed equal to five. Hot hardness data above 0.5Tm plotted as logarithmH/E against reciprocal absolute temperature reveal two straight lines with a break observed at about 0.75Tm. It is shown that the break occurs at a value of strain rate, ∈, over lattice self-diffusivity,DL, of about 109, a value associated with power-law breakdown for creep. These observations suggest two conclusions regarding the rate-controlling process during hot indentation testing of pure metals. Between 0.75 and 1.0Tm, the deformation process is associated with lattice self-diffusion and creep flow in the power. law region. Between 0.5 and 0.75Tm the rate-determining process is associated with dislocation pipe diffusion and creep flow in the power-law breakdown region.

Current Filaments in Semiconductors

A current filament is a non-uniform radial distribution of current in the presence of a uniform electric field in a uniform sample. These filaments can have diameters in the 0.005 inch range. The current density at the center of the filament can be several orders of magnitude higher than the background current density in the rest of the sample. Filaments have been studied in devices exhibiting the current-controlled negative resistance associated with specific cases of two-carrier space-charge-limited current double injection. Electrons and holes are injected from opposite contacts into a semi-insulator in which the lifetime of carriers of one sign is much longer than the lifetime of carriers of the opposite sign. When forward biased this device exhibits a high-voltage, high-impedance (10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sup> ohms) pre-breakdown region and a low-voltage, low-impedance (1 to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ohms) post-breakdown region. In the post-breakdown region current increases at a nearly constant voltage followed by a high-current power-law region. Current filaments have been studied throughout the post-breakdown region by recording the recombination radiation observed through one of the injecting contacts. Experimental and analytical studies of current filaments in silicon at 77°K and GaAs at 300°K are reviewed.

Raman Spin-Lattice Relaxation of Shallow Donors in Silicon

This work reports both experimental measurements and calculations of two-phonon Raman spin-lattice relaxation times for shallow donors in silicon. Saturation, line broadening, and adiabatic fast passage techniques were used to measure ${T}_{s} (\ensuremath{\Delta}{M}_{s}=\ifmmode\pm\else\textpm\fi{}1,\ensuremath{\Delta}{M}_{I}=0)$ between 2 and 30\ifmmode^\circ\else\textdegree\fi{}K for P, As, Sb, and Bi at 3300 G. ${T}_{x} (\ensuremath{\Delta}{M}_{s}=\ifmmode\pm\else\textpm\fi{}1,\ensuremath{\Delta}{M}_{I}=\ensuremath{\mp}1)$ was measured in the liquid He range for As, Sb, and Bi at 3300 G. The calculations of the spin-lattice relaxation rates $\frac{1}{{T}_{s}}$ and $\frac{1}{{T}_{x}}$ for Raman processes were made using only the $1S$ doublet and triplet valley-orbit excited states. The calculations were made for both the power-law temperature-dependent region and the exponential temperature-dependent region.