The following report is the final technical report on a series of reports under contract AT(11-1)-515, titled "Niobium Phase Diagrams", covering the period from April 15, 1957 to April 16, 1960.

Abstract: "The accuracies which can be achieved in analog recording systems are for the most part tape limited. While reasonable variations in tape speed do not directly affect the accuracy, such variations result in improper tape tensioning, which in turn results in poor head-to-tape contact. The quality of the tape transport mechanism should be such that the error introduced by improper head- to tape contact is less than tape errors. Some additional equipment is necessary in setting up a tape recorder for a given experiment. The amplitude of the input pulse spectura to the recorder should be adjusted for optimum value and, if possible, the counting rate should be adjusted to obtain good tape utilization. An oscilloscope is probably adequate to satisfy both conditions."

Scope. This specification covers ingots of zirconium alloy designated as Zircaloy-2, and intended for the production of reactor components.

Scope. This specification covers Zircaloy-2 wire material for reactor use where high integrity and satisfactory corrosion resistance at elevated temperatures are required.

Scope. This specification covers Zircaloy-2 tubing, both seamless and welded, for reactor fuel rod sheathing where high integrity, and satisfactory corrosion resistance at elevated temperatures ae required.

Scope. This specification covers Zircalogy-2 sheet and strip material for reactor use where high integrity and satisfactory corrosion resistance at elevated temperatures are quired.

From preface: This report satisfies the quarterly progress report requirements for PL-1 and PL-2 plant design work for the period ending September 30, 1960 At present time a SL-1 Core 2 is under construction. This is a replacement core for SL-1 (ALPR) and will be identical to a PL-2 core; a PL condenser is under test at the SL-1 facility; final construction plans for PL components and modules which are not site sensitive will be completed in March 1961.

The purpose of Project Cowboy was to investigate the seismic signals generated by chemical explosions in underground cavities, with particular emphasis on the possibility of decoupling of these signals from the surrounding media. The project site was the Carey Salt Company salt mine, located approximately five miles west of Winnfield, Louisiana. The tests were run during fiscal year 1960. This report presents the results of tests performed on specimens from the samples of salt taken in the area.

"We compute the equilibrium configuration of a collision-free plasma contained in an axially symmetric magnetic field. The plasma is characterized by a non-scalar pressure tensor which is obtained from a microscopic distribution function in a form suggested b the guiding center approximation. The solution is calculated in the limit where the ratio of the width to the length of the plasma region and the ratio of the gas to the magnetic pressure are both small. Boundary values at the midplane as well as the shape of the plasma appear as arbitrary parameters in the solution. We give the solution to a corresponding scalar pressure problem for comparison."

One of the problems involved in the design of NPR is the method to be used for decontamination, Considerable effort has been made in both laboratories and pilot plants in developing and evaluating decontamination processes under ideal conditions. Promising processes must be tested under prototypical conditions of velocity, water quality, manner of make-up, type and degree of contamination, addition of decontaminating solutions, and so on.

Work on the preparation of graphite spheres containing thorium oxide for use as breeder elements in the Pebble Bed Reactor-Steam Power Plant is described. Graphite spheres of varying density were infiltrated with thorium nitrate solutions, followed by denitration to thorium oxide.

The objective of the study which is being carried out under contract AT(30-1)-2477 is the exploration of all aspects of research in water resources and supply to determine the potential for using radioisotope technology in this research. Problem areas in the application of tracers in this research are being investigated through the evaluation of past experimentation with radioisotopic techniques and through discussions with those who are active in this work. A series of suggestions relating to these techniques will de drawn up to indicate which techniques should be developed further in order that more extensive applications may be found for them.

"This is the first quarterly report on Task II of the subject Utilization of Radioactive Isotopes in Coal Process Research. There were two separate projects on Tank I; I. methods Development for Tritium Labeling of Coal Product Hydro-carbons, and II. Applications of Radio-Tracer Techniques to the Study of Fluidized Particle Mechanics. The following extended work on Task II concerns only Methods Development of Radio-Tracing With Tritium."

"With careful attention to details, tritium assays of satisfactory accuracy have been achieved on low activity standard samples by dry combustion and liquid scintillations counting of the product water.This method is faster, more accurate and dependable than the zinc fusion-ion chamber method fro low level tritium assays. At 380 degrees C, tritium loses from hydrocarbon tracers by isotopic exchange is significant and must be corrected for in tracer measurements at this elevated temperature."

Scope. This specification covers ingots of zirconium alloy designated as Zircaloy-4, and intended for the production of reactor components.

Scope. This specification covers Zircaloy-4 wire material for reactor use where high integrity and satisfactory corrosion resistance at elevated temperatures are required.

Scope. This specification covers Zircaloy-4 sheet and strip material for reactor use where high integrity and satisfactory corrosion resistance at elevated temperatures are required.

Absolute (p,n) cross sections have been measured for Ti47, V51, Cr52, Co59, and Cu63 at energies between 4 and 6.5 Mov. These data plus earlier measurements of the cross section for inelastic proton scattering have been used to estimate total proton absorption cross sections for V51 and Co59. An optical model calculation using parameters giving a good fit to elastic scattering measurements predicts an absorption cross section in good agreement with the measurements for Co59. For V51, some sets of parameters gave good agreement with the measured absorption cross section, but the fit to the elastic scattering data was only fair.

"A finite difference approximation to a non-linear set of parabolic differential equations arising in shallow water theory is given. These difference equations were used to determine the shape and rate of propagation of a hum of fluid down a channel of constant depth. The hump of fluid was found to spread instead of steepen, as is the case in the usual shallow water theory."

"The loss of particles through a cusp of a particular containment geometry utilizing cusped magnetic field lies is considered. A velocity space loss criterion analogous to the loss cone in the mirror machine is derived. The effect of a uniform longitudinal magnetic field perpendicular to the containing field is considered and a loss criterion is derived. The effect of the longitudinal field is to decrease cusp losses.

The fabrication processes applied to nuclear fuels are subject to severe limitations because of the conditions imposed by the reactor environment. The combined problems of neutrons fluxes, high heat fluxes, corrosion by the coolant , and embrittlement by hydriding or similar reactions may be minimized through establishing rigorous materials and fabrication specifications for fuel and cladding.

The result of a leak in a PRTR process tube between the flow monitor and the heated section would be to increase the flow through the monitor, but to decrease the flow through the heated section. The concern for the case of small leaks is whether the increase in flow through the flow monitor is sufficient to cause a high flow tip and a reactor scram for the condition where the flow through the heated section is reduced to the point to cause excessive fuel element temperatures.

"The problems of sequencing jobs through machines are discussed in a linear graph framework. The construction of feasible schedules from given technological orderings is related to the construction of transitive graphs from given component graphs. Methods of constructing transitive graphs are given and bounds on the number of different transitive graphs constructed from given components are determined. A recursive convex function defined on the transitive graphs-the job operation completion time and schedule time-is studied. Bounds on the number of different values that the schedule time can attain is obtained. Examples of multiprogramming, flow shop and machine shop scheduling are studied."

"An algorithm for the generation of feasible schedules and the computation of the completion times of the job operations of feasible schedule is presented. Using this algorithm, the distribution of schedule times over the set of feasible schedule—or a subset of feasible schedules—was determined for technological orderings that could occur in a general machine shop. These distributions are found to be approximately normal. Biasing techniques corresponding to “first come first serve,” random choice of jobs ready at each machine and combinations of these two extremes were used to compute distributions of schedule times."