Straight-line Plots Research Articles

Ionization Yield of Protons in Nitrogen and Argon

The total ionization yield of protons in nitrogen and argon gases was studied for energies in the range of a few to 250 kev. A large cylindrical ionization chamber was used for this study. The chamber was alternately operated as a proportional counter and an ionization chamber to measure the rate with which the protons entered the chamber and the total ionization produced by them, respectively. The results indicated a straight-line relation between the ionization yield and proton energy for energies above 75 kev in nitrogen and above 25 kev in argon. Straight-line plots of the data had slopes corresponding to 36.6\ifmmode\pm\else\textpm\fi{}0.7 ev per ion pair for nitrogen and 26.5\ifmmode\pm\else\textpm\fi{}0.5 ev per ion pair for argon. For argon the straight-line plot intercepted the energy axis at 1.4\ifmmode\pm\else\textpm\fi{}0.9 kev, indicating a slight ionization defect.

Spectral Absorption Method for Determining Population “Temperatures” in Hot Gases*†

A spectroscopic method, useful for strongly absorbed lines, has been investigated for measuring temperatures of hot gases. The minimum transmission of discrete spectral lines in gases at equilibrium has a simple dependence upon the absolute temperature and this relation is used to measure temperature from a straight line plot. An experimental study has been made of the absorption due to the rotational lines of OH (2∑←2Π) between 3067 and 3090 A in an oxygen-acetylene flame. It is shown that temperatures measured by this method are less affected than the conventional one by lack of sufficient resolving power, flame thickness, and various light sources (either continuous or line).

Effect of Temperature on Azeotrope Compositions

Graphical methods for predicting pressure-temperature relations of binary azeotropes have been suggested in the past. Starting with the observation that the logarithum of the azeotropic pressure versus 1/(t+230) yields a straight line plot for binary systems, thermodynamical equation have been developed which relate:(1) the azeotropic pressure and temperature to the heat of vaporization of one of the com-onents and its liquid phase activity coefficient, and(2) the liquid phase activity coefficients and compositions of the binary azeotrope to its azeo-tropic temperatures.As suggested by the thermodynamic derivations the liquid phase activity coefficients of the azeotrope plots as a straight line function when plotted versus 1/T. A method is described for predicting the compositions of the azeotrope at various temperatures from two experimental azeotropic compositions. Tables and figures are presented to illustrate the application of this thermodynamic nalysis.

The Mechanical Properties of the Cell Surface

ABSTRACT A new instrument for measuring the mechanical properties of the cell surface is described. It consists of a micropipette connected to a moveable reservoir of water. The tip of the pipette is brought up to a cell and a bulge sucked out of the surface by lowering the reservoir. A plot of deformation (i.e. degree of bulging) against negative hydrostatic pressure gives a straight line for the sea-urchin egg at all stages. We have called the slope of this line the ‘stiffness ‘of the cell membrane ; it varies with the stage of the egg, the size of the pipette and the speed at which readings are taken. A comparison of the straight-line plots actually obtained with the curves to be expected from pure surface tension or from a thin-walled elastic sphere, leaves no doubt that the cell membrane is not behaving like either of these systems. It is concluded that the membrane is sufficiently thick to resist deformation by virtue of its own rigidity, resembling therefore a tennis ball rather than a rubber balloon or a fluid drop. An analysis of the problem in terms of a thick membrane is mathematically intractable, and is only possible by means of models. Experiments, using a large-scale pipette to suck bulges out of rubber balls, show that over a considerable range of wall thicknesses, the pressure-deformation curves are in fact linear. It is shown that the slope of the pressure-deformation curve or ‘stiffness’ depends on Young’s modulus and the internal pressure. It is not possible to separate these two variables by direct means. A dimensional analysis shows that it is permissible to scale down from model experiments to arrive at Young’s modulus and the internal pressure of the cell. For any given value of ‘stiffness’ there is a series of solutions, with values for the modulus decreasing from a certain figure, and values for the internal pressure increasing from nil. A limit can, however, be set to this series by other measurements.

A “sub-regular” solution model and its application to some binary alloy systems

The thermodynamic properties have been examined for binary solutions whose excess free energy of solution is given by ΔF = A 1x 2y + A 2xy 2 + RT (x ln x + y ln y) where x and y are the atomic fractions; the model may be termed a “sub-regular” solution. The equations for the terminal solubility curves of elements with the same lattice structure can be arranged as (x 1 + x 2) RT ln x 1 x 2 + (y 1 + y 2) RT ln y 1 y 2 = (A 1 − A 2)(x 1 − x 1) 3 where the subscripts to x and y indicate the compositions in equilibrium. A straight line is obtained when the left-hand side is plotted against ( x, − x 2) 3 as long as ( A 1 − A 2) is independent of temperature. The systems silver-copper, silver-platinum, aluminium-zinc and gold-platinum, and the high temperature part of the sodium chloride-potassium chloride solubility curve give nearly straight lines and approximate to sub-regular solutions. The gold-iron, gold-cobalt and gold-nickel solubility curves show appreciable deviations from a straight-line plot. These systems together with potassium chloride-sodium chloride show a temperature dependence of A 1 and A 2 which introduces an entropy term of similar magnitude to the positional entropy.

The Mechanism of Field Dependent Secondary Emission

In recent experimental investigations, it was found that secondary emission ratios as high as 10,000 to 1 could be attained utilizing field dependent secondary emission from magnesium oxide. Early tests showed the mechanism causing the high gains to be fundamentally different from the more standard secondary emission phenomenon.The hypothesis was made that the mechanism of field dependent secondary emission was a process similar to that of the "Townsend avalanche" occurring in gas discharges. As the surface of the dielectric film was bombarded with primary electrons, the high resistivity of the material in combination with the secondary emission current caused the surface to charge to the potential of the collector grid, producing a high field within the dielectric. Electrons released within the material could then gain enough energy to liberate additional electrons, and an avalanche type process resulted.Experiments were conducted to test this hypothesis and each proved to be consistent with the above theory. The main content of these experiments can be summarized in the following statements:(1) The high yields appeared to be independent of the base material. This indicated that the surface or volume effects were most important, implying that a Fowler type field emission from the base metal was not a significant factor.(2) In studying the secondary current as a function of field, the gas discharge equations were found to be correct. These equations predicted a straight line plot of the $\mathrm{ln}\mathrm{ln}\ensuremath{\delta} \mathrm{vs} \frac{1}{E}$, and in addition, gave a close estimate of the magnitude of the secondary emission ratio.(3) By means of retarding potential measurements, the energies and mean free paths of the emitted secondary electrons were determined. These data were in good agreement with the results in item (2).(4) The rise time for surface charging was determined by using square wave variations of bombarding currents, and was found to be consistent with the original hypothesis.

A Note on the Interrelationship Between Wetting and Nonwetting Phase Relative Permeability

In a recent publication wetting phase relative permeability was expressedas: (Equation 1) and it was stated that a similar expression applied, mutatis mutandis, tonon-wetting phase relative permeability; i.e., (Equation 2) In Equations (1) and (2), Sw and So are respectively the wetting andnon-wetting phase saturations as a fraction of the pore volume; Pc is thecapillary pressure; I, the wetting phase electrical resistivity index; IN, theanalogous non-wetting phase electrical resistivity index and Krw and Krnw, thewetting and non-wetting phase relative permeabilities. Equation (3) is interesting because it expresses the nonwetting phaserelative permeability of a porous medium at any saturation as a function of thewetting phase relative permeability at that saturation, the saturation itselfand parameters which bear directly on the distribution within the pores of thenon-wetting and wetting phase fluid networks. It is thus inherentlyplausible. Equation (3) is not readily checked against experimental data since fewreliable relative permeability figures have appeared in the literature; also nopublished information exists on the probable relationship between IN and So.However, if the Krw and Krnw figures of Leverett for unconsolidated sands areused in conjunction with the relationship I = Sw-2 for sands of this type, itis possible for Equation (3) to compute IN as a function of So. The results areshown in the accompanying figure and it will be seen that IN = So-1.72. Asynthetic sandstone for which Muskat quotes relative permeability data, alsogives a straight line plot between IN and So if I = Sw-1.8 is assumed. (Aresistivity index exponent of 1.8 appears to be the best average forconsolidated porous media.) T.N. 93

Surface energy and structure of crystal boundaries in metals

The variation of boundary energy y R in lead with the difference of orientation θ was determined using the methods previously described for tin. It was found that the energy decreases progressively as the difference of orientation decreases below about 16°. The curve relating energy with difference of orientation extrapolates to zero energy at zero angle. These results agree qualitatively with those of tin and offer further strong support for the ‘ transitional lattice ’ theory of the crystal boundary. Straight-line plots of log θ against γ R / θ were obtained for lead and tin. These results are closely consistent with Shockley and Read’s theoretical predictions based on a dislocation model of the transition boundary.

Neutron Cross Sections at 120 and 345 Ev

Total neutron cross sections of 19 elements have been measured at 120 and 345 ev by employing the neutron resonance scattering properties of cobalt and manganese. Thin foils of cobalt and manganese were used as neutron detectors at 120 and 345 ev, respectively. A semilogarithmic plot of neutron counts versus thickness of sample was made for each element for each of the two energies. An initial curvature in the plot indicated that the detector resonance overlapped a resonance in the element under study. The cross section determined from either a straight-line plot or the asymptotic part of a transmission curve was identified as either the potential scattering cross section, the off-resonance scattering cross section, or as the minimum cross section in the neighborhood of a resonance.