Double Extrapolation Research Articles

The strain dependence of the flow stress-grain size relation for 70:30 brass

The grain size dependence of the stress-strain behavior of annealed 70:30 brass was evaluated using room temperature tensile tests. The resulting data, which covered × 10-5 to 4 × 10-1, were analyzed in terms of the conventional Hall-Petch stress-grain size equation, σ∈ = σO∈ +k∈l-1/2, and, also, in terms of the extended Hall-Petch equation previously proposed for 70:30 brass, σє = σ0y+ A Єp + β(єp/l1/2 +kl−1/2 The lattice friction stress, σ0∈, increased linearly with plastic strain over nearly the full strain range. The lattice friction stress for the initiation of plastic flow, σ0y, was evaluated using two alternative double extrapolation procedures. Both extrapolation techniques, which involved the macrostrain behavior, gave the same σ0y value of 3.4 kg/mm2, which agreed with the σ0∈ value determined directly in the microstrain region (∈ <-10-3). Large grain size specimens, which yielded homogeneously, exhibited a kx2208; value of only 0.2 kg/mm3/2 at a plastic strain of 1 × 10-5; however this small kx2208; increased rapidly with increasing microstrain. For the small grain size specimens, which yielded via a Luders extension,ke was essentially constant at 0.8 kg/mm3/2 for all microstrains; however, kx03B5; did increase in the macrostrain region to a maximum value of 1.6 kg/mm3/2. When consideration was given to a grain size dependent increase in dislocation density, an intrinsic grain boundary resistance to plastic flow of approximately 0.7 kg/mm3/2 was obtained.

Double-extrapolation method for m.o.s.t. threshold-voltage measurements

The measurement of the m.o.s.-transistor threshold voltage under current-saturation conditions by double extrapolation to VD=0 and ID=0 is described. For comparison, it is shown that corresponding values obtained on thin- and thick-oxide devices conventionally, by single extrapolation to ID=0, may depend critically on the drain voltage and misrepresent the voltage at which the channel becomes inverted.

Theoretical Studies of the Use of the Double Extrapolation Method to Determine the Forward Scattering of Light by Spherical Colloidal Particles

Abstract An application of the double extrapolation method (the Zimm-plot method) for the reduced intensity of light scattered by colloidal dispersions, instead of polymer solutions, is discussed theoretically on the basis of the Mie theory. The correction factor, F, required to recalculate the experimental value of the molecular weight, MR, to the true value, M (M=FMR), is equal to unity in the case of the Rayleigh scattering (α→0) and the Rayleigh-Gans-Debye (R-G-D) scattering (|m–1|→0, where m is the relative refractive index of the sphere to the medium). Usually, however, the value of F is not equal to unity, but is found to be given by an empirical equation F=1–0.155Q+bQ1.5, where Q is a quantity proportional to the reduced specific scattering intensity at θ→0. For the determination of the radius of gyration from the “initial slope,” the R-G-D equation is applicable even in cases where |m–1| is not small. In order to determine the true molecular weight from the molecular weight, Mτ, obtained from the specific turbidity at the infinite dilution, the factor Φ is needed (M=ΦMτ). The factor Φ is considered to be a product; that is, Φ=F\varphi, where the factor \varphi seems to be independent of the m value. The empirical equation obtained was \varphi=1+0.537α2.08

The Effect of Pressure on pH and Dissociation Constants from Measurements with Buffered and Unbuffered Glass Electrode Cells: Acetic, Formic, Phosphoric, Carbonic Acids Adenosinetriphosphate and Phosphorylcreatine

is used to measure the effect of pressure on the ionization constant K of weak acids (HR) in the presence or not of the corresponding Na or K salt (MR). Double extrapolation, to zero weak electrolyte concentration and zero KCl concentration, yields log Kp/K1 values at and the molal volume change on ionization for the reaction is computed at 1 atm for acetic acid, formic acid, carbonic acid (buffered and unbuffered solutions), phosphoric acid (2d step), adenosinetriphosphate and phosphorylcreatine.

Loss of Electrons from Collecting Electrode in High-Energy Photon Beams Investigated with a Double Extrapolation Chamber

In the course of taking readings on surface dose (1) with the high-energy photons of cobalt and betatron radiations, it was found that the measurement with positive saturation potential on a parallel-plate ionization chamber was considerably greater than that with negative. A similar effect has been reported (2) for cobalt. Failla (3), in 1937, called attention to the problem. In the present case, the difference between the two measurements becomes less as the thickness of the upper electrode is increased, vanishing at the equilibrium thickness for cobalt. With the betatron there is a slight reversal at this point, the reading with negative potential on the upper electrode becoming slightly greater than with positive. A double extrapolation chamber was designed in which the lower plate was made of a conducting plastic which could be increased in thickness, while the upper plate was increased in the usual way. For a thin upper electrode, the difference between positive and negative readings became greater ...