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By Craig S. Hartley

An approximate expression is obtained for the energy of a closed dislocation loop in equi1ibriu)n with a constant net stress. The result obtained is valid for loops in isotropic or anisotropzc materials provided that they are suJficiently large that the energy per unit length of a segment of the loop can be approximated by that of an infinite straight dislocation tangent to the loop. It is shown that this approximation leads to very close agreement with a more rigorous calculation of the elastic energy of a circular glide loop. The Gibbs-Wulff Form, GWF, of a dislocation is the closed planar loop which has the smallest elastic self-energy of all possible loops having the same Burgers vector and enclosing a fixed area, A.' The energy of such a loop is related to the net resolved shear stress* required to expand the loop and to the stress required to activate a Frank-Read source.223 In the following sectiorls the problem of determining the form of the GWF is discussed and an approximate method for calculating its elastic self-energy is presented. It is demonstrated that the approximations employed lead to no serious errors when applied to a calculation of the elastic energy of a circular glide loop. This method is then used to obtain a closed form expression for the energy of GWFs in isotropic and anisotropic materials. THEORY Burton, Frank, and cabrera4 have proved that the relationship of the equilibrium shape of a two-dimensional array of atoms under the influence of the Gibbs free energy associated with unit length of its boundary, G(O), is that the polar plot of G(0) vs 0 is proportional to the pedal of the GWF.* The angle 0 is measured "The pedal of the polar graph ofG(0) vs0 is the envelope of tangents to the eraph.relative to some crystallographic reference direction. The difficulty in applying this result to a closed dislocation loop arises from the self-interaction of the loop. For a dislocation the energy analogous to G(0) is a function of the total configurati~n.~ Consequently the relation which determines the GWF is an integro-differential equation rather than the simple differen- tial equation which results when G(8) is a function of 0 alone. Mitchell and smialek3 and Brown~ have used the self-stress concept introduced by ~rown' to calculate the shapes of dislocations in equilibrium with an applied stress. In this approach the glide force on an element of the dislocation loop due to the interaction of the element with the rest of the loop is equated to the glide force exerted by the local applied stress. The shape of the loop is then adjusted so that the two forces above are equal at all points on the loop. It is possible to calculate the energies of such loops by noting that, for equilibrium with an applied stress, the energy is equal to pijbiAj (summation convention) where bi is the Burgers vector, p.. is the local net stress tensor, and Ai is a vector directed perpendicular to the plane of thd loop with magnitude equal to the area of the loop. Also Brown' has calculated the energy of a hypothetical polygonal GWF using the above technique and anisotropic elasticity. However, his indicated solution for the energy in the general case of an arbitrary GWF is only slightly less involved than an iterative solution of the integrodifferential equation referred to earlier. In the present work the approximation employed by DeWit and Koehler' is used to calculate the energy of a closed loop in equilibrium with an applied stress. That is, the energy of a loop segment, ds, is approximated by the product of ds and the energy per unit length of an infinite, straight dislocation in a cylinder coaxial with the tangent to the loop at the angular position of the segment. This is known as the "line tension" approximation. The inner cutoff radius of the elastic solution defines the core radius, while the outer cutoff radius is determined by some characteristic dimension of the loop. Actually, both of these radii vary with the edge-screw character of the segment. The effective core radius changes because of the orientation dependence of the Peierls width of a dislocation,8 and the outer radius should be the radial distance from the circumference of the loop to the center of symmetry of the area enclosed by the loop.g However, since the energy varies logarithmically with the ratio of these radii while depending directly on the effective elastic constants, only the effect of the latter is considered. This approximation also neglects the self-interaction of the loop segments. For small loops this will doubtless be extremely important, but for large glide loops produced by plastic deformation the self-interaction is not nearly so important in determining the energy of the loop. This point is illustrated by the following calculation of the energy of a circular loop. Consider a circular loop of radius R which lies in the XI - x, plane of an infinite isotropic continuum and whose Burgers vector makes an angle $ with xs. The first-order solution for the elastic self-energy is:'

Jan 1, 1970

By Franklin D. Cooper

Three model dwelling units were redesigned to achieve specific levels of noise reduction above that provided by conventional construction. Using 1968 prices, the added costs of materials and installation were found to range from $500 to $5,000 depending upon the size of the dwelling unit and the degree of insulation. The potential aggregate expenditures for sound insulation materials are projected to reach $617 million in 1975, including about $408 mil- lion for the mineral-based materials, in 1968 constant dollars. The report includes a brief review of the mechanics and effects of sound.

Jan 1, 1970

By A. W. Effinger

The Bureau of Mines used regression analysis and applied statistical methods in an effort to rationalize the results of an experiment examining the effects of certain variables on carbon deposition in a reservoir for thermal recovery of petroleum. Although none of the 15 trials of the original experiment resulted in the response of weight-percent of carbon regarded by the experimenter as adequate, values calculated using canonical analysis in two trials yielded responses 33 and 54 percent higher than the minimum acceptable figure. The actual responses differed by less than 3 and 6 percent, respectively, from the predicted responses. Methods are described for defining a path of increasing response based on the minimum point and the response surfaces and for defining a set of values for the parameters in question, which result in increased response, A detailed explanation of the mathematical process used in this analysis is presented in the appendix for ease in computer programing the technique.

Jan 1, 1970

By C. Ortuglio

The effect of cracking by increasing the free space above the charge on the composition and yields of the volatile products from carbonization of Pittsburgh-bed coal and one industrially used blend from Eastern United States and one from Western United States was investigated with the BM-AGA carbonization apparatus. Increasing the free space above the charge from 1 inch to 3 inches, to 6 inches, and to 9 inches resulted in lower tar yields and increased gas and light oil yields. Anthracene and naphthalene yields were increased; quinoline and benzene insoluble fractions of both the tar and pitch increased considerably with increased free space, although the carbon content of the tars and pitches increased only slightly. Increased cracking, occasioned by the increase in free space, resulted in a decrease in the yields of tar acids, tar bases, neutral oils, olefins, aromatics, and paraffins and naphthenes. Gas composition was relatively constant; hydrogen and methane tended to increase and ethane decrease. Results of the investigation are being used to design a unit to upgrade the volatile products of carbonization by cracking the hot products as they leave the carbonization chamber.

Jan 1, 1970

By F. O. Shuck, F. E. Butler

A diaphragm diffusion cell suitable for use with liquid metals was designed and tested by measuring the diffusion coefficients for a Hg-10 pct In alloy at 25°C. The binary diffusion coefficient and the coefficients for In and Hg tracers were measured at this composition. The measured coefficients for both tracers were less than the binary diffusion coefficient. When these coefficients were combined with the activity correction term of Darken, the predicted binary coefficient was somewhat higher than the experimental value. In recent years a number of investigators have been studying diffusion of liquid metals in order to gain a better understanding of the liquid state and to examine possible applications to liquid metal processing. The bulk of this work has involved either self-diffusion or diffusion of low concentrations of solute metals in an essentially pure solvent metal. The most common experimental technique employed has been the capillary-reservoir method of Anderson and saddington1 since it is well-suited to measurements involving low concentrations of solutes. As an expansion of previous studies, an investigation of the variation of diffusion coefficient over large composition ranges has been undertaken in this laboratory. Although it is possible to modify the capillary-reservoir method for such measurements, the technique loses its principal advantage of requiring only small quantities of solutes. Therefore, it was felt desirable to investigate other possible experimental techniques applicable to measurements over large composition ranges. A technique which has been used widely in measurements of other liquid systems and seemed potentially applicable to studies of liquid metals was the diaphragm cell. This method has been found to combine relative simplicity of operation with accurate and reproducible results. In use with normal liquids, the tyiical diaphragm cell utilizes a porous glass disk. However, because of the high surface tension, it is not possible to use a diaphragm of such fine pore structure with liquid metals. Furthermore. projected use at high temperatures makes the use of glass undesirable. Consequently, the first problem was the search for an appropriate cell design. EXPERLMENTAL Diaphragm Cell. A number of possible cell designs were examined. Prototypes of several were constructed and tested. The final design is shown in an exploded view in Fig. 1. The cell consists of two identical chambers, one on either side of a 0.20-in.-thick partition. The chambers are 0.15 in. deep and have a volume of 3.45 cu cm. Each chamber is provided with two small threaded holes for filling and emptying. The filling holes may be sealed with stainless-steel screws. Drilled lengthwise through the center partition is a 0.250-in.-diam hole. Inserted into this hole is a rod having seven 0.059-in.-diam holes drilled radially through it. The total "hole" volume is 0.078 cu cm. When the rod is properly aligned, the holes in it constitute the "diaphragm" through which diffusion occurs. The center section was of Teflon and the rod and face plates were of Plexiglas. Four such cells were constructed and used in this study. Subsequent to this investigation, a similar cell constructed entirely of iron was fabricated and tested at higher temperatures. Several considerations led to this final design. It is desirable to minimize the volume of the cell chambers to decrease the time required for a measurement. However, the total volume of metal in the diaphragm must be small in comparison with that in the chambers. To facilitate filling and emptying it is desirable to have a diaphragm which may be closed.

Jan 1, 1970

By T. E. Seidel, A. U. MacRae

The dependence of the electrical and crystalline properties of silicon containing ion implanted boron atoms have been studied as a function of the incident dose, substrate temperature, and annealing tempera-ture. Hall effect studies show that the compensation due to defects is negligible after annealing at and above 500°C for a dose of 1013 ions per sq cm. Steps occur in the isochronal annealing curve for the sheet resistance at 300°C and 800°C and the mechanisms responsible for these steps are discussed. The range of the ions at 150 kev is 3500 * 5001. Electron diffraction studies on samples implanted with 150 ker ions show the existence of damaged (polycrystalline) silicon closer to the surface than the range of the ions. Etching and subsequent annealing of etched and unetched specimens suggest that the poly crystalline silicon is closer to the surface than the bulk of the distribution of ions. THE purpose of this study is to investigate some electrical and crystalline properties of ion implanted boron in silicon. Sheet resistance, Hall measurement, depth distribution by chemical staining, thermal probe and electron diffraction have been used to study the properties of samples implanted in a random direction with ions having energy up to 150 kev. The boron-silicon system has been the subject of considerable study'-7 due to its possible application in the fabrication of electronic devices. The implanted ions produce considerable crystalline damage to the substrate crystal before they lose most of their primary energy and come to rest. Fortunately, most, if not all, of this damage can be removed by subsequent annealing or by holding the substrate at an elevated temperature during the implantation process. Sheet resistivity measurements of the p-type layers produced by boron implantation into room-temperature silicon, reveal that the annealing occurs in a two-step process: the first occurring at -300°C and the second at -800°C.' Electron-microscope and low-angle electron diffraction studies of this damaged material indicate that the bombarding ions produce an amorphous silicon region about the trajectory of each ion.' At high doses, these damaged regions overlap and an amorphous surface layer results. Furthermore, the 800°C annealing step, appears to be associated with the elimination of this gross damage. The depth distribution of the as-implanted and also the annealed samples have been studied by an angle lap and staining technique as well as by Hall measurements.3-7 We find the experimentally determined ranges of the boron are less than those calculated by the Lindhard-Scharff-Schiott theorys (hereafter referred to as the LSS theory). Our results are in essential agreement with pre- vious results. In addition, we have made Hall measurements on samples bombarded with a low dose (2 x 1013 ions per sq cm) to minimize impurity banding effects, and find that deep ionized levels influence the carrier concentration and room-temperature hole mobility until the sample is annealed at temperatures above 500°C. Above this temperature, the data corresponds to that obtained when silicon is doped with boron by conventional techniques. We have also made a depth distribution determination of the crystalline damage due to the implanted boron by using glancing angle electron diffraction techniques. It was found that the gross damage depth distribution of heavily implanted samples is closer to the surface than the depth distribution of the electrically active boron. By removing this gross damage, without affecting the distribution of the implanted boron, we have determined that the 800°C annealing stage is not exclusively due to the improvement in the crystalline perfection of the amorphous material but also appears to be associated with the annealing of some point defects. These results and their relation to previous results are discussed in the following sections. IMPLANTATIONS Boron ions were implanted into silicon samples using an accelerator capable of operating from 10 to 150

Jan 1, 1970

By Fathi Habashi

METALS COMMONLY leached may come from one of the following sources: 1) Occurring in nature in the native state, e.g., gold, silver, platinum metals, copper. 2) Produced as by-product of a metallurgical process, e.g., gold, silver, platinum metals, selenium. 3) Produced by reduction of an oxide ore, e.g., copper, nickel. GOLD AND SILVER Cyanidation According to Mellor (1923) the alchemists of the eighteenth century knew that gold was soluble in aqueous solution of potassium cyanide, and the early jewelers probably utilized this fact in gilding. He also mentions that Scheele in 1783 and later Bagration in 1843 noted the solvent action of aqueous solutions of alkali cyanides on gold. Yet it was not until 1887 that the value of this observation was recognized, when MacArthur and Forrest (1887) made use of it in leaching gold from its ores. Since then, the process has spread to every gold and silver mining district in the world.

Jan 1, 1970

By J. B. Mitchell

The intelligent selection of comminution systems for industrial minerals requires a broad background of comminution experience. At the same time a thorough knowledge of the specific mineral occurrence, the applicable process and the product end use is required. To illustrate the different ways to process potash ores three flow sheets have been selected for presentation.

Jan 1, 1970

By T. E. Green

The Bureau of Mines Heavy Metals Program emphasizes the need for improved analytical methods for gold determination. A commercially available ion exchange resin with high selectivity for gold was investigated as a potential method to collect gold from solution. The resin was found to quantitatively collect gold from acid solutions over a wide range of acid concentrations. Common metals were not collected by the resin nor did they seriously interfere with the collection of gold. X-ray spectrographic and neutron activation methods based on the use of papers containing this resin are proposed.

Jan 1, 1970

By John F. Abel

AIME is closing the books on its first 100 years. In the next year the meetings and many papers will doubtless be filled with statistics on the growth of AIME, and, incidentally, on the mining industry. Let's try to keep our cool and avoid breaking our arms patting ourselves on the back. AIME, nationally and locally, runs on the drive and dynamism of a rather small number of its members. If you look at the annual SME Blue Book of national officers and committee members, you will be struck by the repetition of the same names throughout. Trend for a few men to shoulder the burdens and responsibilities can be seen on the local level, too.

Jan 1, 1970

By J. A. Reeves

The unit-train for moving mineral raw materials is considered by many railroad men as the most significant contribution toward reducing rail freight costs since the introduction of the diesel locomotive. The idea, which involves assigning railroad equipment to only one haul and keeping the equipment rolling, results in the maximum utilization of equipment. For example, before the unit train was placed in service on coal hauled to one of Mid-Continent Coal and Coke Company's customers, about 900 cars and 9 locomotives were needed to move its coal requirements, compared with 250 cars and 6 locomotives currently used. If unit-train economics are to be achieved, coal companies cannot use railroad cars as small storage bins on wheels to accumulate their coal in train-load shipments, instead, these companies must build large bins which incorporate facilities for the rapid loading of railroad cars in a minimum length of time.

Jan 1, 1970

By W. T. Malone, J. R. Williams, R. L. Tiner, J. M. Tinsley

Hydraulic fracturing methods for production stimulation have become a common procedure in the oil and gas industry. Fracturing treatments are performed on wells of various potentials to help increase the production rate. In addition to the desire for increased production is the need to predict what increase might be expected. This knowledge is useful in economical treatment planning to accomplish the desired production goals for the well. Theoretical production increases due to horizontal radial fractures may be calculated using equations developed from mathematical analyses and electrical models.1,2,6 It also is possible to predict theoretical production increases due to vertical fractures using curves developed from electrical3 and mathematical models.8 However, these studies assumed that the vertical fracture height and the formation height were equal, which may not be true." In addition, the final fracture height through which fluid is produced may not be equal to the created height. The development of vertical fracture proppant transport relationships has made unrealistic the assumption that propped fracture height is equal to created fracture height. Through the use of published proppant transport equations,4'12 it is possible to calculate the height of a bed of propping agent deposited in a fracture of a given height. Assuming that the fluid flowing in the fracture moves through only the propped portion of that fracture (i.e., that the un-propped part of the fracture heals) it becomes essential to know how production increase varies with the ratio of propped fracture height to formation height. It should be recognized that future investigation may determine that the fracture does not heal completely and that a highly permeable channel exists over the deposited bed of proppant. The effect of this channel was not considered for the present study. The following analysis of experimental data allowed development of curves to determine theoretical production increases considering fracture height as a variable. Discussion In designing a fracturing stimulation treatment a number of variables must be considered. The size of the treatment, type of proppant used, proppant concentration, treatment fluid properties and well conditions are all factors affecting the dimensions and permeability of the fracture. Production increase due to a vertical fracture is affected by propped length, height, width and permeability of the fracture for a given set of formation conditions. Production increase may be defined as the ratio of production rate after fracturing to the production rate before fracturing at the same pressure differential, pe — pw. The producing rate in an

Jan 1, 1970

By G. G. Campbell

Bureau of Mines research to develop an in situ retorting recovery method for oil shale has involved field testing of fracturing techniques for creating fluid-flow paths in impermeable oil shale. Electrolinking, hydraulic fracturing without and with sand propping, and explosive fracturing with a liquid explosive were tested in a 25-ft-square, five-spot pattern. These wells were drilled into oil shale at 50-to 88-ft depths near Rock Springs, Wyo. Results of the fracturing tests were evaluated by injecting air into a test well and measuring flow rates and flow profiles in adjacent test wells before and after each test. To identify points of air entry (location of fractures) in wells, flow profiles were determined by use of inflatable packers and by continuous logging with an airflow probe developed during the fracturing program. Electrolinking and hydraulic fracturing without sand propping were relatively ineffective; hydraulic fracturing with sand propping created horizontal fractures with desirable flow capacity; and fracture flow capacity was significantly increased by detonation of nitro-glycerin displaced in the natural and hydraulically induced fracture systems.

Jan 1, 1970

By O. D. Maurice

"This paper will essentially update the information that is already known and published on the limestones of the Province of Quebec. The excellent report by M. F. Goudge (1935)m is difficult to improve upon and the areas of limestone quarrying are generally the same as they were at the time of Goudge's report. Our knowledge of the limestones of Quebec has been improved considerably in recent years by the publications of T. H. Clark, 2 who, since 1938, has been mapping and reporting on these lime-stones and has discussed their stratigraphy, their structural features, their history and their economic value. One economic aspect is the presence of natural gas in these formations and the possible occurrence of oil. A total of 150 test holes had been drilled to a depth of more than 500 feet by the end of 1967 and, in addition, at least 256 more shallow holes had been put down in the St. Lawrence Lowlands. The information from these test holes has greatly improved our knowledge of the thickness and extent. of the various formations of Paleozoic limestone and shale in Quebec.This paper will then review briefly the limestone occurrences in Quebec, using the old as well as the more recent reports as principal references"

Jan 1, 1970

By G. W. Weems

The specific objective of this investigation was to determine the compressibility factors for helium and carbon dioxide mixtures at -10° and -20° C and pressures to 1,000 psia. A Burnett apparatus was used. Data from the experiments were treated by the method of Barieau and Dalton. Tables of compressibility factors and approximations of the virial coefficients are presented for 10 binary mixtures as well as for helium and carbon dioxide. The results follow the same trend as data previously reported.

Jan 1, 1970

By R. L. Christie

"THE ISLANDS lying north of the Canadian mainland, and the large Boothia and Melville peninsulas, form one of the great archipelagos of the world; this sparsely vegetated and nearly unpeopled region extends about 1,500 miles east to west and 1,200 miles from the mainland to the northern tip of the northern-most island. Sea access to most of the islands is restricted by ice to the summer season, and the 'polar pack' ice of the Arctic Ocean presses the year round against the northwest margin of the archipelago. Although the region is remote, the accessibility has greatly increased through a network of weather stations, airfields and air routes connecting with southern centres.The area considered in this paper is that part of the island region underlain mainly by sedimentary rocks. In broad terms, this includes the land and sea areas of the archipelago and the adjacent continental shelf, but excludes the dominantly 'Shield' terrain of Baffin Island, and of Melville and Boothia peninsulas. An impression of the size and potential of this sedimentary region may be gained by comparing some areas: the land area of islands underlain mainly by sedimentary rocks is over 300,000 square miles or about 50,000 square miles greater than the area of Alberta. The total area of the region, including the continental shelf and the inter-island areas, may be double this figure, and may approximate one-seventh of the land area of Canada."

Jan 1, 1970

By W. V. Youdelis, W. H. Bear, G. Cochrane

HERETOFORE, there has been very little study of the effects of various metallurgical factors on the behavior of thermoelectric materials, the need for which is evident if optimum processing and design of thermoelectric devices is to be realized. Accordingly, we have undertaken such an investigation on the thermoelectric materials bismuth and Bi-Sb alloy and in this paper present some preliminary results which merit consideration, in particular the relatively high thermoelectric power and figure of merit values obtained for the Bi-12Sb (at. pct) alloy powder compacts. The thermoelectric parameters for ingot and powder compact specimens are determined and the results are compared with published data for single crystals. Preparation of Materials. The bismuth and antimony used in this investigation are six nines pure. Melting and casting of the ingots was carried out in air for expediency, since most oxidation unavoidably occurs during the preparation of the powder by filing of the ingots. Chill cast ingots of pure bismuth were prepared by pouring the melt into split copper chill molds, and unidirectionally solidified ingots of bismuth and Bi-Sb alloy were obtained by slow directional cooling in pyrex tubes. All melts remained bright during melting and casting, indicating minimum oxidation. Powder for the powder compact samples was obtained by filing the ingots with a fine and coarse file to give a variation in the particle size of the compacts. The particles in the fine powder compacts varied in size from approximately 28 pct less than

Jan 1, 1970

By S. E. Khalafalla

The extremely sluggish oxidation of steel scrap was appreciably accelerated when the charge was pretreated in aqueous solutions of sodium metavanadate or sodium molybdate. The degree of oxidation acceleration was inversely correlated with the melting point of the promoter oxide possessing the highest valency. The magnitude of oxidation enhancement exhibited a systematic inverse dependence on the duration of pickling processes; mere dipping of the oxidizable charge in the vanadate bath was most effective. In general, the rate of steel scrap oxidation increased with increasing concentration of the pickling reagent. The results are explained on the basis of the hydrolytic decomposition of the pickling agent with subsequent slow interaction with the metal surface, coupled with the tendency of vanadium to form polyanions in alkaline media. The data not only served to elucidate the mechanism by which catastrophic oxidation takes place, but also showed that the accelerating species need not be alloyed with the oxidizable metal; surface impregnation by minute amounts of the accelerating species can still produce catastrophic effects.

Jan 1, 1970

By Richard J. Robbins

This paper is presented with particular reference to the findings of the OECD Advisory Conference on tunneling held last July in Washington D. C. A great deal has been said about the Conference in the past few months, but it may be appropriate to review briefly the background and objectives of the Conference to better understand how the mining community can relate its underground excavation problems to the results of the Conference. OBJECTIVES OF THE OECD CONFERENCE The world demand for tunneling (the term tunneling is used here loosely to include almost all forms of underground excavation) is expected to grow at an in- creasing rate. During the decade of the ?70's, the demand is expected to at least double by comparison with the previous decade. Much of this increase in demand will be due to the rapid growth of urbanization around the world. As urban populations grow larger and denser, the conservation of surface land and the quality of the environment become more important. This aspect of the increasing demand poses a difficult challenge to those who must plan and implement urban development.

Jan 1, 1970

By W. F. Chiao

With the application of dislocation damping theory an attempt was made to determine whether the generation and extension of dislocations is inherently more difficult in a brittle steel than in a ductile steel. A ductile steel was compared with a brittle stee1 by simultaneously measuring the ultrasonic attenuation and velocity during tensile test, and the density of free dislocations and their mean loop length were then calculated as a function of strain. The results showed that in the ductile steel there was always a large generation of dislocations and great extension of loop length occurring at some stage within the early plastic region. In contrast, the brittle steel showed very little or no such sudden changes in dislocation dynamic states after the onset of plastic deformation. Furthermore, a strong temperature dependence of dislocation dynamic states was also observed in the ductile steel and a hypothesis was suggested that a thermally activated process of dislocation rearrangement could occur at higher deformation temperatures. The activation energy of dislocation rearrangement at room temperature was estimated as about 2030 cal per mole.C. DUCTILITY is an indispensible property in the application of engineering materials, especially steel. During the past two decades the theoretical and experimental approach to the understanding of flow and fracture of metals has been constantly undergoing changes and progress." while the fracture behavior of metals can be influenced by many factors such as chemical Composition,3 second-phase particle mor-phology,4 and dislocation arrangement,5 it is now a general belief that the fundamental understanding of the ductile-brittle fracture phenomena of solid materials must stem from the study of dislocation dv-namics developed under stress conditions.6,7 Most of the traditional ductility tests, such as Charpy impact test, slow bend test, and tensile fracture test, cannot by themselves reveal directly the mechanisms of ductile to brittle transition of materials. In the experimental investigation of tensile ductility it would be ideal to be able to study directly the dynamics of dis-locations in a bulk specimen during the process of deformation. Since the ultrasonic pulse technique is the only satisfactory method for studying dislocations and the fine details of deformation characteristics in metals in the course of a tensile test, it would appear that a comparative study of ultrasonic attenuation changes during tensile tests of metallic materials exhibiting different ductility might be very informative. So far no work comparable to this study has appeared in the literature. Recent progress in both theory and experiment has indicated the feasibility of studying the dislocation mechanisms of ductility behaviors by ultrasonic measurements during tensile test. Granato and Lucke8 have developed a quantitative theory that enables the calculation of dislocation density and their average loop length from the measurements of ultrasonic attenuation and velocity, and several investigators, including Chiao and Gordon,9'10 have shown that simultaneous ultrasonic measurements can be successfully made during a tensile test. Furthermore, many investigators11-13 have repeatedly proposed in the past several decades that deformation and fracture are mutually self-exclusive, and that the ability or inability of a material to deform plastically, i.e., to generate dislocations, is a major factor in determining whether the material will be ductile or brittle. Thus, in the present work an attempt was made to determine whether the generation and extension of dislocations is inherently more difficult in a brittle steel than in a ductile steel. This article is principally concerned with the study of the relation between the propagation of ultrasonic waves and tensile deformation in a steel series which displays quite different toughness at room tempera-turk. changes in attenuation and velocity of ultrasonic waves have been measured as a function of strain during the deformation process. The results have been interpreted in terms of the vibrating string model for dislocation damping as developed by Granato and Lucke, and it has been found that some of the more subtle predications of the model are in good agreement with the experiments. This would be especially meaningful because most of the previous experiments in testfying the model were carried out with single crystals of high-purity materials and little work has been done with polycrystalline steel alloys. EXPERIMENTAL PROCEDURES AND RESULTS Specimen Materials. The tensile specimens used throughout this experiment were of two compositions selected from a series of Fe-Mo-0.77 pct Mn-0.22 pct C steels prepared for a ductile-brittle fracture transition study. One steel contains 0.21 pct Mo and the other 1.03 pct Mo. These two compositions were chosen for the present study because they possess quite different toughness properties at room temperature. The 0.21 pct Mo steel is quite ductile while the 1.03 pct Mo steel is rather brittle, as measured by the standard Charpy impact test. The alloys had been prepared by vacuum induction melting and chill casting in steel molds. The ingots were hammer-forged into 1/2-in.-sq bars from which tensile specimen blanks were cut. These blanks were first normalized under argon atmosphere at 1700°F and then reaus-tenitized and isothermally transformed at 1050°F to a bainitic microstructure. The chemical compositions, heat treatments, hardness measurements, and Charpy transition temperatures of the two steels are listed in Table I.

Jan 1, 1970