Search Documents

By Strathmore R. B. Cooke, Thomas E. Ban

MUCH experimental work has been performed on the mechanism of agglomeration and pelletizing of moist ore and concentrates and on the process of firing agglomerates, but except for the work of Tigerschiöld and Ilmoni1 much of the published information is empirical, and the literature contains no information concerning the structure of fired pellets. Results of a preliminary study of the microstructures occurring in pellets produced both in the laboratory and on a pilot-plant scale are presented in this paper. Most of the results were obtained from pellets prepared from Mesabi magnetic taconite, but through the courtesy of the staffs of the Minnesota Mines Experiment Station and the Bethlehem Steel Co., fired pellets produced from limonite and hematite ores and from Lebanon magnetite have also been examined. The work has been restricted almost entirely to pellets produced without additives, the exceptions being those in which coal was. added to the filter cake before rolling. Schwartz has described the microstructures occurring in ore sinters produced under reducing conditions.2 Many of the structures and constituents he describes are common to fired pellets, but the constituents normally occur in markedly different proportions. His statement that "in all satisfactory sinter the amount of hematite is small, perhaps not over 2 or 3 per cent" is inapplicable to pellets produced by pilot plant operation or by any process in which air is not deliberately excluded. Pilot plant pellets contain over 90 pct by weight of hematite, and those produced in the smaller furnaces of the Minnesota Mines Experiment Station contain more than 80 pct of that constituent. Preparation of Specimens It is difficult to examine unfired pellets microscopically because of their insufficient coherency to withstand sectioning and polishing. Fired pellets sometimes lack coherency and frequently contain holes which are troublesome during polishing. Impregnation of both air-dried and fired pellets is readily accomplished by the use of methyl methacrylate monomer.3 The dry pellets are covered in a test tube with excess monomer, to which a small amount of accelerator has been added. When the test tube is placed in a cooling bath and evacuated with an aspirator, most of the entrapped air is removed, and disruption of weak pellets by boiling of the monomer is reduced to a minimum. Polymerization is then effected by immersion of the test tube in a water-bath at about 45°C, this temperature being held for 4 or 5 days. The test tube may then be broken away from the solidified mass and the pellets sectioned by a carborundum wheel or a diamond saw. Where time is important, impregnation is carried out at a higher temperature by Meyer's method.4 Air-dried pellets must be impregnated with especial care; otherwise swelling occurs and the solids are displaced. It is more important to be certain that the monomer forms a reasonably complete network throughout the specimen than that all entrained air is removed, and for this reason the vacuum technique may be omitted. Impregnated agglomerated products and pellets are extremely coherent, section well, and may be polished either by hand or by machine. Hand polishing is not satisfactory for the examination of conditions existing at the boundaries of grains, and for this machine polishing must be used. The Graton-Vanderwilt machine gives excellent results, provided that pressure on the specimen is considerably in excess of that recommended by the manufacturer. Mineralogy of Fired Pellets Only two opaque iron minerals, magnetite and hematite, have been recognized in pellets. The complete identity of these artificial minerals with their corresponding natural counterparts is shown by their mineralographic characteristics and their X-ray structures. Wüstite has not been found. Slag is the most common transparent constituent of fired pellets. Occasionally conditions have been appropriate for the crystallization of fayalite from the slag, and at other times another crystalline sil-

Jan 1, 1952

By H. B. Huntington

Some of the basic problems in understanding elec-tromigration in metals are discussed, along with the attempts that are being made to handle them. One such problem is the effect of the electrostatic forces. It is now acknowledged that the momentum exchange with charge carriers plays generally a dominant role in the driving force but the question remains to what extent the electrostatic force may still be effective. The electromigration of interstitial impurities is also an area which presents some intriguing questions. For the substitutional impurity, moving by the vacancy mechanism under the influence of an electric field, the correlation considerations are somewhat more complex than have been previously recognized. Another problem of basic importance in the calculution from first principles is the strength of the "electron friction" force, say for a simple one-band metal. A related problem growing out of the preceding is the prediction of the direction of the "electron wind" force for metals with band structure involving both holes and electrons. THE term electromigration has come to be used to describe the flow of matter in condensed phases carrying high electronic currents such as metals and alloys, whereas one usually reserves the term electrolysis for situations where the current is largely ionic, particularly in the liquid state such as molten salts. It follows that the mass transport number in electromigration is always very small, of the order of 10-7. Studies of electromigration date back some 30 years but the modern period would appear to date from the work of Seith and Wever1 who in the mid 1950's first incorporated markers to display mass motion relative to the lattice and first suggested that the direction of the mass flow was primarily determined by the sign of the charge carriers. Since that time interest in the field has grown steadily and more rapidly recently as certain technological applications became apparent. Chief of these is certainly the deleterious effects that electromigration can cause, even at relatively low temperature, to current-carrying elements in integrated circuitry.2 These phenomena have been the subject of intense study and considerable ingenuity. On the constructive side electromigration has proved a useful tool in the purification of certain metals.3 The interest of this paper is, however, centered more on the basic aspects of the subject than on its technological applications. That high electric currents should give rise to mass flow in metals and that the driving force should be more directly associated with momentum exchange with the charge carriers than with the electrostatic field are ideas that no longer cause surprise or particular interest. The field has matured to the point where the general concepts are widely accepted and continued progress in basic understanding rests on more detailed and quantitative exploration. It is the purpose of this paper to point out what are some of the current problems. As a result, we expect to raise more questions than we answer. The first of these will be the role of electrostatic forces, if any, in electromigration. A second section will deal with the electromigration of interstitials. A third and final section treats with electromigration of substitutional impurities or of the matrix atoms themselves. ELECTROSTATIC DRIVING FORCE In the conceptual treatments of electromigration it has been customary to write the driving force in terms of an effective charge number Z* and to divide it into two terms F = e£Z* = e£[Zel- z(pd/Nd)(N/p)(m*\m*\)] [1] The first of these represents the electrostatic force under immediate consideration in this section and the second and usually dominating term for metals arises from momentum exchange with charge carriers, commonly called the "electron drag" term. As can be seen it is set proportional to the electrons per atom, z, and the ratio of the specific resistivity of the moving entity to the corresponding resistivity per matrix atom. The (m*/Im*I) factor takes into account the fact that the sign of the charge carrier determines the sign of the driving force. The specific resistivity of the moving entity is averaged over its path. In the case of motion of the matrix atoms by vacancies this gives rise to approximately one-half the resistivity at the saddle point since the scattering power of the atom at its equilibrium position bordering the vacancy differs only slightly from that of a normal matrix atom. Although the formulation of the "electron drag" term in Eq. [I] is based on a highly simplified model for electron defect scattering, the essential features implicit in the expression are common to all the theoretical approaches that have so far appeared in the literature.4-6 As for Zel, most treatments of electromigration have included the quantity as the parameter which measures the direct interaction of the electrostatic field with the ion and equated it to the nominal valence of the latter. However, there has been considerable discussion whether this interaction may not be 0 in many cases.6 If the moving ion is always enveloped by the same distribution of shielding charge, then clearly its motion will not involve any work done by the electric field and one can expect there will be no electrostatic force exerted on such a neutral composite. From this point of view the shielding charge around the ion would be said to be complete and hence the entity within the Debye shielding sphere would be unaffected by the electrostatic field per se. There is, however, the prospect that, as the moving ion progresses, new charge comes in to participate in the shielding action

Jan 1, 1970

By E. Buehler, J. E. Kunzler

High-pu.1-ity molybdenum has been heat treated, melted, and zone refined and the physical and chemical changes that are produced by these processes have been studied by making resistance ratio measurements. Pronounced effects are observed that are associated with recrystalliza-tion at about 1200°C and with melting. Melting alone is found to result in a substantial purification by the evaporation of impurities such as iron. Zone refining is found to be reasonably effective with four passes producing a three-fold decrease in resistance ratio and a minimum ratio of 0.0003. With the aid of low temperature measurenzents, it has been shown that the build-up of a deposit of the material being zone refined on the radio frequency coil used for heating can lead to contamination of the sample. CONSIDERABLE interest in high-purity refractory metals for the study of mechanical properties has developed during recent years. Also the need for highly pure metals in certain fundamental studies, such as electronic band structure, has become quite widely appreciated. Molybdenum can now be produced with sufficiently high purity to make it attractive for such investigations. The most suitable measure of chemical purity of metals used for many of these studies is its resistance ratio, R,.,o,/Ro, During the purification of molybdenum by zone refining and its subsequent evaluation by this technique, a number of informative observations were made. These observations concern the effectiveness of zone refining, the volatilization of impurities at the melting point, and the recrystallization of molybdenum and appear to be pertinent to other refractory metals. Also, the usefulness of low-temperature resistance measurements as an analytical tool for evaluating the presence of chemical impurities and physical defects in metals is again illustrated. Samples of high-purity molybdenum of known mechanical history were heated to various temperatures between 800°c and their melting point. Resistance ratios of the samples were measured after they had been given a specified treatment. The data were used, along with mass spectrographic analysis, as an aid in interpreting the nature of the processes that occurred in conjunction with each treatment. Changes in the concentrations of chemical impurities and physical defects are typical of things that effect the low-temperature resistivity. SAMPLES The starting material was obtained from Westing-house Corp., Bloomfield, N.J. It was in the form of molybdenum rods, usually 1/8 or 3/16 in. in diameter. These had been previously processed from bars, 5/8 in, in diameter, originally reduced from 4 in. diam arc-cast ingots, by hot swaging at about 1300°c. In the final step, the temperature was lowered to about l lOO°C which resulted in the production of elongated grains. Typical grains were about 0.03 mm thick and 0.6 mm long. The molybdenum was quite pure as is indicated by the results of mass spectro-scopic analysis1 given in Column 2 of Table I. Other nongaseous elements not listed in the table were not detected. ZONE REFINING AND THERMAL TREATMENT OF SAMPLES Several sample rods, 8 to 10 in. long, were zone refined or were heat treated at several temperatures. Both types of operations were performed using 3 me-

Jan 1, 1962

By J. E. Pavlick, A. G. Guy

The total creep of tin alloys containing antimony in solid solution was observed to decrease with increase in antimony content. However, near the solubility limit an anomalous maximum in deformation was. found, in agreement with similiar observations by Bochvar. IT has long been recognized that alloys may deform more rapidly under stress if there is a tendency for a phase change or other structural change to occur simultaneously. However, the phenomena involved are complex and in some instances the opposite effect, strengthening, may result.' This area of research has not attracted much interest in the western world, and although Russian investigators have studied it for the past 15 years their work has not received due attention here. Recently diametrically opposing views on one aspect of this problem have been espoused by two Russian investigators, Kornilov and Bochvar. The question is this: in certain binary alloys tested in creep at the temperature where the solute is at the limit of solid solubility, does the incipient formation of the second phase strengthen or weaken the alloy? Korni-lov's arguments in favor of strengthening were presented at the 1954 Symposium at the National Physical Laboratory, =Creep and Fracture of Metals at High Temperatures.The most recent statement of Boch-var's theory of weakening is in Oding's new book on creep and rupture.3 Although Bochvar agrees that strengthening occurs in some alloy systems, he argues that in certain alloys an anomalous weakening is observed. However, the extensive work of Korni-lov's group on creep properties of alloy systems has not revealed any anomaly of this type, but instead has tended to refute Bochvar's theory. This clear-cut controversy offered a good opportunity for a simple experiment to resolve the problem. The experiment and its results supporting Bochvar are the subject of this paper. However, it will be helpful first to sketch the present status of the larger question of the effect of a phase change or other structural change on plastic deformation. PREVIOUS WORK One of the first researches in this area was by Pfei1,37 who investigated the creep resistance of an 80 Ni-20 Cr alloy containing varying amounts of titanium. He found that the resistance to creep increased rapidly as the solid solubility limit in the alloy at 775'c was approached and slightly exceeded. With further addition of titanium the creep resistance decreased, presumably because of precipitation effects. Bochvar's first work in this field was a study in 1945 of "superplasticity" in zinc alloys containing 15 to 25 pct Al.4 He found that alloys quenched from about 400 had anomalously low hardness when tested below this temperature. The following year, in a paper on the dependence of mechanical properties on the composition and structure of alloys,5 he extended some observations of Kurnakov to predict that at high temperatures of testing the hardness values for solid-solution alloys might be lower than those for the component metals. He also pointed out the influence of changes in solidus temperature in affecting curves of hardness vs composition, and he

Jan 1, 1962

By B. M. Larsen, T. E. Brower

Introduction and Summary By "thermochemical factors" we refer to those variables which affect the net heat which must be put into the bath in order to make a heat of steel from any given set of charge materials. This is admittedly only one phase of the production rate problem. The whole problem includes also consideration of rate of charging, flame radiation intensity, rate of optimum fuel input obtainable without undue damage to the furnace structure and any variations in conditions such as stirring, slag volume or viscosity which affect the rate at which heat can flow down and away from those exposed surfaces where the heat is first received from the flame. Because a given type of charge in a shop is often considered as being nearly constant in both physical and chemical characteristics from one heat to another, and because such a state of affairs may be thought of as resulting in a reasonably constant net heat requirement, this requirement is usually neglected as an invariable, inevitable matter, about which nothing can be done. With normally variable charge, and variable percentages of limestone and cold pig, however, the net heat requirement can be subject to very appreciable change; it may also be affected by such things as the currently popular procedure of blowing oxygen into the bath. To bring the general problem of production rate into better perspective, therefore, it seems worthwhile to try to evaluate the net bath heat requirement and the amount by which it may change through variation in different factors. Because our calculated values of net heat are admittedly uncertain, we have tried to check them in part by statistical data on actual production rates over rather large groups of commercial heats. The results of calculation of net heat requirements in a wide range of actual commercial practices may first be summarized briefly. We find a wide range between the extremes of different practices, as would be expected, with duplex practice (essentially blown metal plus hot metal) having essentially a zero net heat requirement, an all-cold charge practice somewhat over I million Btu per ton of steel and a high hot metal practice about 0.75 million Btu per ton. Over the commercial range of scrap plus hot metal practice, increasing the percentage of hot metal from 40 to 78 pct, with other factors nearly constant, decreased the net heat by only some 5-10 pct. The net heat is increased by about 1.2 pct for each I pct of the metallic charge present as cold pig. Calculated values of oxygen supplied by air varied from about 25 up to 60 lb per ton of steel, and in a 60 pct hot metal practice, an increase from 32 to 52 Ib oxygen from air decreased the calculated net heat from 0.88 to 0.74 million Btu per ton. Use of pure cold oxygen to substitute for about one half of the total charge ore (about 28 Ib oxygen replacing 145 Ib ore per ton of steel) decreased the

Jan 1, 1949

By B. M. Larsen, T. E. Brower

Introduction and Summary By "thermochemical factors" we refer to those variables which affect the net heat which must be put into the bath in order to make a heat of steel from any given set of charge materials. This is admittedly only one phase of the production rate problem. The whole problem includes also consideration of rate of charging, flame radiation intensity, rate of optimum fuel input obtainable without undue damage to the furnace structure and any variations in conditions such as stirring, slag volume or viscosity which affect the rate at which heat can flow down and away from those exposed surfaces where the heat is first received from the flame. Because a given type of charge in a shop is often considered as being nearly constant in both physical and chemical characteristics from one heat to another, and because such a state of affairs may be thought of as resulting in a reasonably constant net heat requirement, this requirement is usually neglected as an invariable, inevitable matter, about which nothing can be done. With normally variable charge, and variable percentages of limestone and cold pig, however, the net heat requirement can be subject to very appreciable change; it may also be affected by such things as the currently popular procedure of blowing oxygen into the bath. To bring the general problem of production rate into better perspective, therefore, it seems worthwhile to try to evaluate the net bath heat requirement and the amount by which it may change through variation in different factors. Because our calculated values of net heat are admittedly uncertain, we have tried to check them in part by statistical data on actual production rates over rather large groups of commercial heats. The results of calculation of net heat requirements in a wide range of actual commercial practices may first be summarized briefly. We find a wide range between the extremes of different practices, as would be expected, with duplex practice (essentially blown metal plus hot metal) having essentially a zero net heat requirement, an all-cold charge practice somewhat over I million Btu per ton of steel and a high hot metal practice about 0.75 million Btu per ton. Over the commercial range of scrap plus hot metal practice, increasing the percentage of hot metal from 40 to 78 pct, with other factors nearly constant, decreased the net heat by only some 5-10 pct. The net heat is increased by about 1.2 pct for each I pct of the metallic charge present as cold pig. Calculated values of oxygen supplied by air varied from about 25 up to 60 lb per ton of steel, and in a 60 pct hot metal practice, an increase from 32 to 52 Ib oxygen from air decreased the calculated net heat from 0.88 to 0.74 million Btu per ton. Use of pure cold oxygen to substitute for about one half of the total charge ore (about 28 Ib oxygen replacing 145 Ib ore per ton of steel) decreased the

Jan 1, 1949

By E. J. Schmitz

The mining of the Triassic coals of the Richmond basin has been carried on, upon a larger or smaller scale, for more than a hundred years. Notwithstanding the close proximity of the field to a large city and to tide-water, assuring both a good home-market and cheap transportation, and notwithstanding the good quality of the fuel and the great thickness of the principal bed developed and worked, operations in this field have been conducted with but limited success. The basin comprises about 189 square miles, being from 24 to 31½ miles in length by 5½ to 10 miles in width. Not much more than one-tenth of this area has been explored in a practical and efficient way, and not over 1200 acres have been worked near and along the outcrops or edges of the coal. The practical mistakes which have been committed undoubtedly in a number of the mine-operations of the past, do not alone explain the unsatisfactory success and progress of the industry of this field ; nor can it be ascribed to the lack of local enterprise. Other reasons have to be looked for; and, as a principal one, the irregularity and the faulted conditions of the coal deposits must be pointed out. As a second cause, the indifference of the State government, which leaves the development of the field entirely to private enterprise, instead of aiding it by systematical and practical geological investigations, deserves to be mentioned. Nothing has been done by the State since the excellent work done more than fifty years ago by Professor Rogers, who could not at that time enter into the details of such

Jan 1, 1895

• One effect of the British devaluation of the Pound Sterling, with its resultant lowering of the pay limit, was the addition of considerable tonnages of previously marginal ore in gold mining. Crown Mines, Ltd., reported that 1,245,000 tons of such ore had been added to available reserves. But for devaluation, a steady decline in ore reserves had been a feature of operations during the previous ten years, and would have continued. •Loree Colliery of the Hudson Coal Co. is using a Humphrey spiral cleaning plant to meet requirements of the state in the matter of stream pollution. However, the process is producing a salable product. •Noranda is considering plans for constructing a commercial sized unit designed to produce elemental sulphuric acid and sintered iron oxide from pyrite. Test plant results have indicated the No. 5 ore zone can be treated by the new process economically. •A magnetic fluid clutch, and magnetic amplifiers for motor and generator control, have been developed under Navy contract by Vickers' Electric Division, in St. Louis, Mo. This constitutes the first commercial production of the clutch recently developed by the Bureau of Standards. •Fuel experts estimate coal production will run up to 500 million tons this year based on the expectation that business conditions will continue to be good. They also expect that in the future the use of coal will increase by 50 pct over today's level. These expectations are based on the fact that it provides the bulk of the heat, light, and power for making steel, for manufacturing, and for generating electricity as well as the development of the coal burning gas turbine and processes for making gas, gasoline, and oil from coal. •Entombed miners may benefit from a two-way communication system which utilizes the earth's strata as a network for electric signals. The use of FM radio waves makes this possible. The invention includes a portable transmitter-receiver unit kept near the face, and a more powerful portable equipment of the same sort above ground. In use, two probes on wires from the apparatus are driven into the earth. • The Union of South Africa has launched a uranium production project which government leaders think will help the West maintain world atomic supremacy. Experiments under way in the pilot plants are expected to lead to the establishment of a chain of processing factories along the Witwatersrand in which uranium will be reclaimed from gold tailing. •Recent developments in mechanized mining at the Bureau of Mines oil-shale mine near Rifle, Colo., have lowered mining costs to 29 cents per ton of shale. The cost of producing crude shale oil from 30-gal-per-ton-shale, using the new mining and processing techniques, would be about $1.50 per barrel. This is 500 lower than any previously stated price. • COMINCO is planning to open the old Bluebell lead-zinc mine near Nelson, B. C., on a 500-ton-per-day basis. The old workings will be pumped and a 970-ft incline sunk. A mill will be constructed at the property.

Jan 7, 1950

By Irving Cadoff, Richard Nolder

An analysis oj a series of samples of single -crystal silicon grown on sapphire shows that ,four distinct orientation relations exist. There are at least thirteen crystallographic planes which serve as substrates ,for epitaxial growth The model which assumes that silicon substitutes for aluminium and bonds with the oxygen atoms of the sapphire to form the first later for subsequent growth can account for the epitaxial geometry in all four cases. Multiplici-ties 01 specific orientations are found which are explained by the symmetry of both the sapphire and silicon crystal structures. It was reported in the previous paper' that single-crystal silicon films can be deposited on single-crystal a A1,03 (sapphire) with a wide variety of orientations. The silicon films, however, were found to deposit in only four different orientation relationships with respect to the sapphire substrate. The X-ray data have been analyzed to determine the plane and direction of atomic fit and an atomic model to account for the epitaxial relationships at the silicon-sapphire interface has been developed. These results are described in the present paper. EXPERIMENTAL The Laue X-ray data described in the previous paper were reduced to stereographic projections in a standard manner. These data were supplemented with X-ray reflection data obtained with -& E and A Full-Circle Goniometer (Electronics and Alloys, Inc.) mounted on a Phillips diffractometer unit. The silicon films were thin enough to result in characteristic reflections from the substrate as well as the silicon. The superimposed stereographic projections were analyzed to determine the orientation relationships. Ambiguities were resolved by referring to constructed models of various lattice planes for both silicon and sapphire. These lattice models were also used to develop the model for atom fit at the interface. DATA AND ANALYSIS 1) Crystal Structures. The crystallography of silico-n, which is of the diamond cubic class with a. = 5.4~, is straightforward. The sapphire structure is more complex and generally difficult to represent in pictorial form. It is of the rhombohedra1 class but usually referred to hexagonal axes. The transformation of indices between these two systems can lead to ambiguities which will have bearing on the analysis presented herein. Therefore, the basis used in this paper is described in the appendix. Referred to the hexagonal system, the parameters of sapphire are co = 12.95.&, a, = 4.75~, c/a = 2.73. All parameters are for room temperature. Figs. 1 and 2 illustrate schematically the hexagonal unit cell model of sapphire used for this analysis. The oxygen atoms are assumed to occupy positions in an idealized hexagonal array on basal planes. Their actual positions are in a slightly distorted hexagonal array. The aluminum-atom positions are scaled to their actual positions in the lattice with respect to the basal layers of oxygen atoms. It was found that an idealized model where the aluminum atoms are assumed to lie exactly at the octahedral interstices of the oxygen lattice, similar to that used by ~ronberg,' was not adequate for this study.

Jan 1, 1965

By B. M. Larsen, T. E. Brower

INTRODUCTION AND SUMMARY BY "thermochemical factors" we refer to those variables which affect the net heat which must be put into the bath in order to make a heat of steel from any given set of charge materials. This is admittedly only one phase of the production rate problem. The whole problem includes also consideration of rate of charging, flame radiation intensity, rate of optimum fuel input obtainable without undue damage to the furnace structure and any variations in conditions such as stirring, slag volume or viscosity which affect the rate at which heat can flow down and away from those exposed surfaces where the heat is first received from the flame. Because a given type of charge in a shop is often considered as being nearly constant in both physical and chemical characteristics from one heat to another, and because such a state of affairs may be thought of as resulting in a reasonably constant net heat requirement, this requirement is usually neglected as an invariable, inevitable matter, about which nothing can be done. With normally variable charge, and variable percentages of limestone and cold pig, however, the net heat requirement can be subject to very appreciable change; it may also be affected by such things as the currently popular procedure of blowing oxygen into the bath, To bring the general problem of production rate into better perspective, therefore, it seems worthwhile to try to evaluate the net bath heat requirement and the amount by which it may change through variation in different factors. Because our calculated values of net heat are admittedly uncertain, we have tried to check them in part by statistical data on actual production rates over rather large groups of commercial heats. The results of calculation of net heat requirements in a wide range of actual commercial practices may first be summarized briefly. We find a wide range between the extremes of different practices, as would be expected, with duplex practice (essentially blown metal plus hot metal) having essentially a zero net heat requirement, an all-cold charge practice somewhat over 1 million Btu per ton of steel and a high hot metal practice about 0.75 million Btu per ton. Over the commercial range of scrap plus hot metal practice, increasing the percentage of hot metal from 40 to 78 pct, with other factors nearly constant, decreased the net heat by only some 5-10 pct, The net heat is increased by about 1.2 pct for each I pct of the metallic charge present as cold pig. Calculated values of oxygen supplied by air varied from about 25 up to 60 lb per ton of steel, and in a 60 pct hot metal practice, an increase from 32 to 52 lb oxygen from air decreased the calculated net heat from 0.88 to 0.74 million Btu per ton. Use of pure cold oxygen to substitute for about one half of the total charge ore (about 28 lb oxygen replacing 145 lb ore per ton of steel) decreased the

Jan 1, 1948

ASIDE from the John Fritz Medal, in which the Institute participates through its representation on the John Fritz Medal Board; the Institute itself has three awards to make annually, as follows: the Robert W.' Hunt Medal and Prize, the J. E. Johnson, Jr. Award, and the James Douglas Medal. ROBERT W. HUNT MEDAL AND PRIZE The partners of Robert W. Hunt established a fund which was presented to the Institute at a fitting ceremony on May 27, 1920, to establish an annual medal and a sum of money to be awarded under the following rules: 1. The award shall consist of two prizes; first of a. gold medal, second of a sum of money; a certificate to accompany each prize. The money prize shall not be awarded to a member over 40 years of age, but under unusual circumstances, both prizes may be allotted to one person provided that he is not over 40 years of age. In general it will be understood that the Committee shall award the money prize to the younger men, rather than the medal. 2. The awards shall be made not oftener than once a year to that person or persons contributing to the Institute the best original paper or Papers on iron and steel. The scope of the term "iron and steel" shall be determined by the sub-committee considering the awards. In general, papers dealing with the practical side of. the subject have preference over those dealing with the theoretical, side in recognition of the fact that Captain Hunt's main contributions to the industry have been in the improvement of production and quality of material. 3. A sub-committee of three to five, including the Chairman of the Iron and Steel Committee, shall be appointed by the Iron and Steel Committee annually to adjudge the. award subject to approval. 4. The awarding committee shall submit its report to the Iron and Steel Committee at its October Meeting, and the award shall be certified to the Secretary of the Institute in time to permit the presentation to be made at the Annual Meeting of the Institute. 5. The recipient of the award shall be designated "The Hunt Medallist." This prize is administered. by the iron and Steel Committee. J. E. JOHNSON, JR., AWARD This award is made from the income of a fund of $30000 donated by Mrs. Margaret Hilles. Johnson in memory of her husband, J. E. Johnson, Jr., who was a prominent engineer, author of two valuable volumes on iron blast-furnace construction and practise, vice-chairman of the Institute's Iron. and Steel Committee, and a frequent contributor of papers to the Institute's TRANSACTIONS. This prize is administered by the Iron and Steel Committee. The intent of the donor is to encourage young men in creative work in branches of the metallurgy or manufacture of pig iron with which the professional activities of Mr. Johnson were chiefly concerned. The control off the fund and distribution of the awards having been vested in the Board of Directors of the Institute, this Board has made the following regulations concerning it:

Jan 1, 1925

ASIDE from the John Fritz Medal, in which the Institute participates through its representation on the John Fritz Medal Board, the Institute itself has five major awards to make annually for excellence in technical papers, as follows: The Robert W. Hunt Medal and Prize, The J. E: Johnson, Jr. Award, The Lewisohn Platinum Prize to senior members, and the James Douglas Medal. ROBERT W. HUNT MEDAL AND PRIZE The partners of Robert W. Hunt established a fund which was presented to the Institute at a fitting ceremony on May 27, 1920, to' establish an annual medal and a sum of money to be awarded under the following rules: 1. The award shall consist of two prizes; first of a gold medal, second of a sum of money; a certificate to accompany each prize. The money prize shall not be awarded to a member over 40 years of age, but under unusual circumstances, both prizes may be allotted to one person provided that he is not over 40 years of age. In general it will be understood that the Committee shall award the money prize to the younger men, rather than the medal. 2. The awards shall be made not oftener than once a year to that person or persons contributing to the Institute the best original paper or papers on iron and steel. The scope of the term" iron and steel" shall be determined by the sub-committee considering the awards. In general, papers dealing with the practical side of the subject have preference over those dealing with the theoretical side in recognition. of the fact that Captain Hunt's main contributions to the industry have been in the improvement of production and quality of material. 3. A sub-committee of three to five, including the Chairman of the Iron and Steel Committee, shall be appointed by the Iron and Steel Committee annually to adjudge the award subject to approval. 4. The awarding committee shall submit its report to the Iron and Steel Committee at its October Meeting, and the award be certified to the Secretary of the Institute in time to permit the presentation to be made at the Annual Meeting of the Institute. 5. The recipient of the award shall be ,designated "The Hunt Medallist." This prize is administered by the Iron and Steel Committee. J. E. JOHNSON, JR. AWARD This award is made from the income of a fund of $3000 donated by Mrs. Margaret Hilles Johnson in memory of her husband, J. E. Johnson, Jr., who was a prominent engineer, author of two valuable volumes on iron blast-furnace construction and practise, vice-chairman of the Institute's Iron and Steel Committee, and a frequent contributor of papers to the Institute's Transactions. This prize is administered by the Iron and Steel Committee. The intent of the donor is to encourage young men in creative work in branches of the metallurgy or manufacture of pig iron with which the professional activities of Mr. Johnson were chiefly concerned. The control of the fund and distribution of the awards having been vested in the Board of Directors of the Institute, this Board has made 'the following regulations concerning it:

Jan 1, 1925

By E. B. Swanson

Crude oil production in Iraq during 1932 was maintained at slightly higher levels than in 1931, but the output continued to be restricted to the requirements of local consumers. The Iraq Petroleum Co., representing British, American and French interests, which has been operating within its concession east of the Tigris River since 1926, began drilling operations on Apr. 5, 1927, and completed its first well at Baba Gurgur on Oct. 14, 1927, to which area the company has since confined its drilling activities. Relatively small quantities of oil have been produced annually, but the products have been utilized in company operations and have not been offered on the Iraq market. The Khanaqin Oil Co., which has its field of operation at Naft Khana in the so-called Transferred Territories, has been supplying the Iraq market with petroleum products from Iraq wells since March 12, 1927. The output of the Khanaqin Oil Co. refinery, at Alwand, during the past three fiscal years ending March 31, has been as follows: (In Barrels of 42 Gallons Each) 1930 1931 11931 Gasoline................................. 102,940 104,571 118,012 Kerosene................................ 104,010 108,112 111,624 Fuel oil...........................1 286,9001 332,142 354,244 503,850 544,825 583,880 The Iraq Petroleum Co. has a small topping plant, with a capacity of about 150 bbl. a day, used in the manufacture of petroleum products for the company's own needs. During the 1932 fiscal year, the production was 3918 bbl. of gasoline and 2235 bbl. of kerosene, as compared with 8157 bbl. of gasoline and 6308 bbl. of kerosene during the preceding fiscal year.

Jan 1, 1933

By V. Patarini, M. Salkind

BECAUSE of its high strength and stiffness coupled with low density, continuous boron filament is showing great promise as a potential reinforcement for both metals and nonmetals. Of primary consideration for structural applications is the fatigue behavior of boron fiber composites. Composite fatigue behavior is dependent upon three factors: 1) fiber fatigue behavior, 2) matrix fatigue behavior, and 3) the effect of the interface and fiber ends. The purpose of this note is to describe the behavior of boron filament in rotating beam fatigue. The filament, described by Talley' and Galasso, Salkind, Kuehl, and Patarini,' was made by the hydrogen reduction of boron trichloride on a hot tungsten filament. Testing was performed using a commercial rotating beam wire fatigue tester* described by Votta.~ One end of the test sample is held in a chuck in a synchronous motor. The sample is bent around in a "U" shape, and the other end inserted into a carbide bushing. The maximum strain occurs at the bottom of the "U" where the radius of curvature is a minimum. The strain is adjusted by adjusting the length of the specimen and the location of the bushing. Samples were rotated at 3600 rpm and an automatic shutoff device used to determine the number of cycles to failure. The measurements were accurate to the nearest 360 cycles. The fatigue behavior is summarized in Fig. 1 for fifty-one samples of 4.8 x 10"3 in. diam fibers and ten samples of 3.2 X 10"3 in. diam fiber. The two sample groups represent two different filament production runs and two different nominal size groups. Both groups exhibited nominal tensile strengths of 400,000 psi. No significant difference in the fatigue behavior of the two sample groups is apparent. The scatter in the data is not unexpected for a brittle filament which exhibits a tensile strength distribution with a standard deviation of 10 to 15 pct. Because the test procedure provides a known outer fiber strain in the sample, the maximum stress was calculated assuming a Young's modulus of 58 x 10' psi. This value was selected as being representative of several nominal fiber sizes.2 All of the samples which failed exhibited sudden, catastrophic fracture, and no permanent deformation. One sample was stopped after 1.66 x lo8 cycles at *200,000 psi. The fiber exhibited no apparent damage or deformation. It is apparent that the fatigue resistance of boron filament is quite good. It can therefore be speculated that the fatigue behavior of boron fiber composites would be controlled by the "weaker links", namely matrix fatigue resistance and interface behavior. In fact, preliminary investigations have revealed that this is true for boron-reinforced aluminum? It should be noted that the data presented herein may not necessarily reflect the tensile fatigue behavior of boron filament. It is well-known that boron filament has a radial residual stress pattern with the outer surface in ~om~ression.~ Because of this fact, tensile failure is normally nucleated in the interior of the filament.5 Since the data presented herein is for a rotating beam test in which only the outer surface of the fiber is stressed to the maximum value, it would be incorrect to assume that the failure mechanism and fatigue behavior would be the same if the fiber were tested in tensile fatigue. The fact that many of the data are well above the nominal 400,000 psi tensile strength would tend to support this argument. The authors would like to express their appreciation to the United Aircraft Research Laboratories for supporting this investigation and for permission to publish the results. A portion of this effort was supported by the Air Force Materials Laboratory under contract AF33(615)-2125.

Jan 1, 1968

By H. G. Doll

A new electrical logging method called Laterolog is described which provides for better recording of formation resistivity. In this method a current, preferably of constant intensity, is forced into the formation perpendicularly to the wall of the hole as a sheet of predetermined thickness by means of a special electrode arrangement and of an autonlatic control system. The essential advantages of the Laterolog over the regular resistivity logs are explained. With the Laterolog, the mud column has much less influence than with conventional methods. The Laterolog is, therefore. particularly useful in wells drilled with highly conductive mud. Moreover. when the electrode system is located opposite a bed of moderate or small thickness, the disturbing effect of the adjacent formations becomes practically eliminated, provided the bed is thicker than the sheet of current. which itself is usually a few inches to a few feet thick. The sequences of beds are. therefore, much more sharply differentiated, and, in many cases, it is possible to read directly from the logs values close to the true resistivities of the formations without further corrections. Field examples are shown to illustrate the results of the method in various types of formations. INTRODUCTION As soon as it was introduced into the petroleum industry, electrical logging roved to be a powerful instrument for the delineation of the strata traversed by bore holes and for correlation of such strata." Research and engineering efforts were mostly devoted at this early time to the design of the techniqurs which could provide the best data for these purpoes. Later, attention was directed toward the quantitative analy5i.s of electrical logs, in order to obtain information on. reservoir characteristics, and, in particular, on oil and water saturation.3,4 Efforts have been made, accordingly, with a view to improving the already existing methods, or to finding new methods which could satisfy these new requirements." Quantitative analysis implies a determination as accurate as possible of the true resistivity of the formations. In fact, however; the "apparent resistivity" recorded in front of a given bed by a conventional electrical logging method is frequently quite different from the true resistivity of this bed. This is due to the combined influence of the mud column, of the adjacent formations both above and below the bed, and of the invaded zone, in which the original fluid has been more or less replaced by mud filtrate. When the beds are thick enough, and, as is frequently the case in sand and shale formations, when their resistivity is not much greater than that of the mud, it is generally possible to obtain their true resistivity directly on the electric log, or at least to obtain an approximate value which can be corrected without undue difficulty by means of recently published charts known as "departure curves."" When the beds are thin, and particularly when, in addition. their resistivity is substantially greater than that of the mud column, the apparent resistivities recorded on conventional logs are seriously affected, and it is generally very difficult, if at all possible, to estimate their true resistivity with a good enough accuracy. In the most severe cases, such as are encountered in holes drilled through hard formations with muds of high salinity, the conventional logs are so distorted and rounded that they do not even show clearly the houndaries of the different beds. In order to overcome the effect of the mud column and of the adjacent formations, it is possible to make use of appro. priate systems whereby the measurements involve a comp3ratjvelv thin slice of space at the level of the measuring device. A mention is due, in this respect, to a measuring system. called the "guarded electrode;" invented by C. Schlumberger over 20 years ago. The system, schematically represented in

Jan 1, 1951

By H. G. Doll

A new electrical logging method called Laterolog is described which provides for better recording of formation resistivity. In this method a current, preferably of constant intensity, is forced into the formation perpendicularly to the wall of the hole as a sheet of predetermined thickness by means of a special electrode arrangement and of an autonlatic control system. The essential advantages of the Laterolog over the regular resistivity logs are explained. With the Laterolog, the mud column has much less influence than with conventional methods. The Laterolog is, therefore. particularly useful in wells drilled with highly conductive mud. Moreover. when the electrode system is located opposite a bed of moderate or small thickness, the disturbing effect of the adjacent formations becomes practically eliminated, provided the bed is thicker than the sheet of current. which itself is usually a few inches to a few feet thick. The sequences of beds are. therefore, much more sharply differentiated, and, in many cases, it is possible to read directly from the logs values close to the true resistivities of the formations without further corrections. Field examples are shown to illustrate the results of the method in various types of formations. INTRODUCTION As soon as it was introduced into the petroleum industry, electrical logging roved to be a powerful instrument for the delineation of the strata traversed by bore holes and for correlation of such strata." Research and engineering efforts were mostly devoted at this early time to the design of the techniqurs which could provide the best data for these purpoes. Later, attention was directed toward the quantitative analy5i.s of electrical logs, in order to obtain information on. reservoir characteristics, and, in particular, on oil and water saturation.3,4 Efforts have been made, accordingly, with a view to improving the already existing methods, or to finding new methods which could satisfy these new requirements." Quantitative analysis implies a determination as accurate as possible of the true resistivity of the formations. In fact, however; the "apparent resistivity" recorded in front of a given bed by a conventional electrical logging method is frequently quite different from the true resistivity of this bed. This is due to the combined influence of the mud column, of the adjacent formations both above and below the bed, and of the invaded zone, in which the original fluid has been more or less replaced by mud filtrate. When the beds are thick enough, and, as is frequently the case in sand and shale formations, when their resistivity is not much greater than that of the mud, it is generally possible to obtain their true resistivity directly on the electric log, or at least to obtain an approximate value which can be corrected without undue difficulty by means of recently published charts known as "departure curves."" When the beds are thin, and particularly when, in addition. their resistivity is substantially greater than that of the mud column, the apparent resistivities recorded on conventional logs are seriously affected, and it is generally very difficult, if at all possible, to estimate their true resistivity with a good enough accuracy. In the most severe cases, such as are encountered in holes drilled through hard formations with muds of high salinity, the conventional logs are so distorted and rounded that they do not even show clearly the houndaries of the different beds. In order to overcome the effect of the mud column and of the adjacent formations, it is possible to make use of appro. priate systems whereby the measurements involve a comp3ratjvelv thin slice of space at the level of the measuring device. A mention is due, in this respect, to a measuring system. called the "guarded electrode;" invented by C. Schlumberger over 20 years ago. The system, schematically represented in

Jan 1, 1951

By Frederic L. Kadey

Perlite, as a volcanic glass, has been recognized since the Third Century, B.C. (Langford, 1978). The precise details of discovery often become lost in antiquity, and the variations among the stories pertaining to the more recent discovery of perlite as a material of commerce are no exception. Credit in the United States is given to a dentist who, while experimenting with tooth enamels about 1941, discovered that perlite-the rock-intumesced when subjected to heat. At about the same time it is reported that the chief geologist of Silver and Barytes Ores Mining Co. attempted to put out a picnic bonfire on the shores of Milos Island, Greece by throwing beach sand on it. The ensuing pyrotechnic display immediately conjured up in that man's mind the possibility of a new use for the volcanic rock that constituted most of the island. Very little was done with this discovery either here or abroad until after World War II. Today the name perlite is applied to both the hydrated volcanic glass, generally of rhyolitic composition, and to the lightweight aggregate that is produced from the expansion of the glass after it has been crushed and sized. Petrologically, it is defined as a glassy rhyolite that has a pearly luster and concentric, onionskin parting. Occurrences of perlite are restricted to several Tertiary to Quaternary age rhyolitic belts that trend in a generally north-south direction around the world. Commercially suitable deposits generally occur as domes of several hundred feet in height, although glassy zones in welded ash-flow tuffs and others associated with dikes and sills also have been reported. Mining is by ripping and blasting from open pits. Because of weight considerations, perlite usually is shipped to the local market area for subsequent expanding. In the United States, New Mexico leads in production with Arizona, California, Nevada, Idaho, and Colorado following in approximately that order. The principal use for expanded perlite is as a lightweight insulating aggregate in cryogenics, in plaster, concrete, and in loose fill insulation. Expanded perlite is also used in horticultural applications, and after subsequent milling and classification, as a filter aid. The United States is the world's largest producer and consumer of perlite. Table 1 shows the world production of perlite and Table 2 shows the perlite mined, processed, expanded, and sold or used by producers in the United States. Geology Composition and Morphology Any discussion of perlite must take into consideration its dual nomenclature, for it is known by the same name as both the naturally occurring rock and, after processing and expansion, as the lightweight aggregate of commercial significance. In its naturally occurring form, perlite is a rhyolitic glass that contains from 2 to 5% combined water. While perlite also can occur as andesitic or dacitic glass, these latter types are of negligible commercial significance. Table 3 lists the chemical composition of a few typical perlites (Anderson, et al., 1956; Langford, 1979). What sets perlite of commercial significance apart from other volcanic glasses is the fact that under the proper conditions of preparation-crushing and sizing-it will, when rapidly introduced into a flame of sufficient temperature, expand or "pop." All of the elements of composition contribute to the expansibility of the rock. The role of the combined water, however, is the most significant because it is believed not only to produce a fluxing effect in the softening of the highly siliceous glass prior to expansion, but it is also responsible for the explosive force of expansion through volatilization during heating. The current theory of the origin of the water in perlite is now less con-

Jan 1, 1983

By B. D. Cullity, O. P. Puri

The magnetostrictia of nickel after increasing amounts of plastic elongation was measured at field strengths up to 1500 oe. In addition, the residual stress was measured by means of X-ray line shifts. The observed decrease in magnetostriction following plastic strain is shown to be associated with residual compressive stress. If a metal bar, whose longitudinal axis is taken as the x direction, is plastically elongated in the x direction and then unloaded, X-ray diffraction measurements will indicate the presence of a residual compressive macrostress 0%. However, stress measurement by means of mechanical relaxation does not reveal any macrostress. In a previous paper1 the fictitious macrostress indicated by X-rays was ascribed to a particular distribution of micro-stress, namely, one in which the bulk of the material was stressed more or less uniformly in compression and a very small portion in tension. It was shown that this distribution would account for Neurath's measurements2 of magnetic losses in silicon steel, because of the effect of residual stress on magnetostriction. The present paper is concerned directly with magnetostriction, in nickel, and with the effect on magnetostriction of the residual stress created by plastic elongation. The residual stress was determined by measurements of X-ray line shifts. MATERIAL AND METHODS Commercially pure "A" nickel was investigated. Its nominal composition, in weight percent, is 99.4 Ni + Co, 0.2 Mn, 0.15 Fe, 0.1 Cu, 0.1 C, 0.05 Si, and 0.005 S. Magnetostriction was measured by means of SR-4 electrical-resistance strain gages mounted on specimens 1/4 in. sq and 8 in. long. Magnetic fields up to about 1500 ce were provided by a multilayer, non-cooled solenoid. A considerable amount of heat was developed at the higher field strengths, and, to avoid errors due to changes in the specimen temperature, the following procedure was adopted. Each measurement of the magnetostriction X at a particular field strength H was preceded by demagnetization and an adjustment of the strain indicator to zero; the field H was then quickly switched on and the strain read immediately. Curves of ? vs H were flat for field strengths above about 750 oe for all specimens, and this constant value of X was accordingly taken as the saturation magnetostriction ?s The X-ray measurements of residual stress were made with a Norelco diffractometer on specimens cut from flat bars 1 1/4 in. wide, 1/8 in. thick, and 12 in. long. These measurements were confined to lattice planes parallel to the surface of the specimen. Two reflections were studied: the 311 CrKß line at 28 = 157 deg, and the 420 CuKal line at 28 = 155 deg. The line centers were determined by fitting a parabola to the peak of the line, as suggested by Ogilvie3 and as modified by Koistinen and Marburger.4 The CuKa doublet from the plastically elongated specimens was first resolved by the Rachinger method5. All X-ray measurements were made by counting at fixed angular positions. RESULTS The results of the magnetostriction measurements are shown in Fig. 1 and Table 1. The magnitude of

Jan 1, 1963

By Dwight K. Smith

A new pozzolanic composition has been developed for cementing oil wells where moderate to high temperatures prevail. This material is an entirely different concept to other oil well cementing materials, such as portland cements, cements containing additives, or liquid resins. Its characteristics are such that it is not, at present, recommended for use at temperatures less than 140º F. It can he either accelerated or retarded across a wide range of well conditions. This new cement is composed of a pozzolanic material, hydrated lime, and a chemical activator to give it early initial strength. This material can be used in wells from 6,000 to 18,000 or more feet where temperature conditions are similar to those along the Gulf Coast. This cement, when set, has no soluble portion subject to leaching or any compounds that should be attacked by sulfate waters or brines. For this reason, it should be permanent when placed adjacent to formations carrying any type of fluid. The compressive strengths in 24 hours are more than adequate for wells where temperatures are 140°F and higher. These values ore in excess of many other types of cementing composition presently in use in the field. This pozzolanic composition does not retrogress in strength at high temperatures as do some other types of cementing materials. The slurry weights of this material will vary slightly according to the specific gravity and water requirements of the pozzolnn itself. The materials covered herein will mix from 13.5 to 14.3 lb/gal, and will have a waiting-on-cement time comparable to other materials used under the same conditions. Economically speaking, this composition is less expensive than either portland cements or retarded cements presently being used under deep well conditions. INTRODUCTION Pozzolans are siliceous material which, though not cementitious in themselves, contain constituents which at ordinary temperatures will combine with lime in the presence of water to form compounds which have a low solubility and possess cementing properties. The use of pozzolanic materials dates back many hundreds of years and both the ancient Greeks and Romans were aware that certain volcanic deposits, if finely ground and mixed with lime and sand, yielded a mortar which possessed special properties. Generally, the early strengths of such materials were rather weak and were considered insufficient for modern commercial usages. Pozzolanic materials have been used extensively with portland cement in mass concrete to obtain special properties. In recent years, large quantities of certain pozzolanic materials have been used successfully admixed into portland cements for oil well cementing. Pozzolans, being reactive silicates, will combine with the free lime that is an inherent component of set portland cements and thereby. becomes cementitious themselves. POZZOLANS FOR OIL WELL CEMENTING There are many types of pozzolans, some of which are more reactive than others. The quality of the pozzoIan depends on the degree of reactivity, chemical composition, fineness, and other less well understood factors. Some of the more widely accepted pozzolans are those classified as fly ashes, while others are certain materials of volcanic origin. pozzolans which require large vol-

Jan 1, 1957

By M. C. Flemings, A. A. Tzavaras

Analytical and experimental procedures are descrihed for quantitative determination of volume-fraction microporosity in metals by mimorarlio-graphg. The analysis assumes spherical pores but allows for the observed fact that pores or portions of pores smaller than a given thickness do not project an image on the film. Volume-fraction microporosity was measuured in cast low-alloy steel and shown to vary from 0.6 x 10-4 to 10 x 10 depending on mode of solidification and on whether the material was air- or vacuum-cast. The aim of work described herein was to develop a method of quantitative measurement of the volume fraction of microporosity in cast metals. Microporosity, present in nearly all castings and ingots, is always interdendritic in nature and may be large enough to be seen on a polished surface with the naked eye. More generally, it is smaller in size, and its detection more difficult. Three techniques might be considered for measurement of microporosity: 1) lineal analysis of a polished metallographic surface, 2) density measurement, or 3) quantitative microradiography. As will be shown later, volume fractions of porosity in directionally solidified castings may be the order of 10-4 to 10-3; such small amounts of porosity are difficult to identify and measure on a polished surface. Density measurement is also not a suitable technique (for alloys) when the volume fraction of porosity is low. This is because the density of the base metal is often not known within the necessary accuracy, due to microsegregation or partial phase transformations. In general, it is not possible to completely eliminate microsegregation without also altering the porosity. Because of the limitations of the foregoing techniques, quantitative microradiography was employed to determine amount of porosity. In recent work, microradiography has been found to be useful for qualitative measurement of porosity, including determination of size and shape of individual pores;&apos;)&apos; however, quantitative determination of amount of porosity has not been attempted. I) CALCULATION OF VOLUME-FRACTION POROSITY The following analysis employs procedures similar to those of Cahn and Nutting3 and Hilliard.4 Major simplifications are that pores are assumed to be spherical and to be present in sufficiently small quantities that no overlapping occurs. A basic difference from the previous treatments is that the limited "sensitivity" of microradiography is considered. Assume first 1) cavities are spherical and of uniform diameter, 2) cavities are randomly distributed, 3) volume-fraction porosity and specimen thickness to pore radius ratio are sufficiently small that overlapping of the projected images of cavities is negligible, 4) sensitivity is limited (i.e., holes or portions of holes of less than a given thickness do not project an image on the film). The sensitivity, is defined as: where 5 = minimum thickness of void from which an image will be projected on the film and t = specimen thickness. Now, from Fig. 1, it is possible to distinguish between two different types of holes. These are 1) holes whose centers lie within the region t/2 > X > 6/2, where X is distance from one surface of the specimen (positive into the specimen), and 2) holes whose centers lie within the region (6 — r) < X < 6/2, Holes whose centers lie outside X = (6 -r) project no image on the film. These two types of pores are considered separately below. Type 1 Pores. When 6 is greater than 0, the image of a spherical cavity of radius r appears on the film as a circle of radius a which is smaller than r. From geometry, Fig. 1: a2=r2-52/4 [2] where a = radius of image of pore on film and r = radius of pore. Since the pores are randomly distributed and spherical V =4/3pr2Nv [3] where V = volume fraction of voids and Nv = number of pores per unit volume and the number of images of Type 1 pores per unit area of film, N&apos;A, is

Jan 1, 1965