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By Michael Tenenbaum, T. L. Joseph

In a previous investigation1 the authors studied the effect of pressure on the reduction of iron ores by hydrogen. With hydrogen as a reducing agent, the rate of reduction was increased substantially by increasing the pressure from 1 to 2 atmospheres. The results with hydrogen prompted the present study of the effect of pressure on reduction with carbon monoxide and with mixtures of carbon monoxide and nitrogen. Features of Reduction Process The gas stream in the lower part of the blast furnace always contains sufficient concentrations of reducing gases to complete reduction provided sufficient time is allowed for the reaction to proceed. Reducing gases react immediately with the iron oxide on the surface of lumps of ore. However, as the unreduced surface recedes from the easily accessible exterior of the lump, the reaction proceeds by virtue of the diffusion of the gases into and out of individual pieces. The rate of diffusion of gases, which undoubtedly plays an important role in the reduction of iron ores, depends on several factors, most important of which are: (1) molecular weight or density, (2) pressure, (3) temperature, (4) concentration gradient. Thus, the rate of reduction of a lump of iron ore at any temperature will depend not only on the specific reaction rate but also upon: (1) available surface of unreduced iron oxide, (2) rate of diffusion of the reducing gas to the reacting surface, (3) rate of effusion of the gaseous products of the reaction from the reacting surface, (4) adsorption of the gases on the reacting surface. The various features of the reduction process were discussed in previous work and need not be reviewed. However, in order to explain

Jan 1, 1940

By Emil Gathmann

Ik presenting this paper I will attempt to answer certain questions proposed at this meeting and describe and illustrate methods of producing sound steel in an economical and hence commercial manner, which are adaptable to the production of practically all steel manufacturers, by readily effected rational changes in the methods of casting, cooling, and subsequent handling of the ingots. In some of the high-grade mills of America, where it is essential to obtain perfectly sound billets or blooms, it is the practice to discard from 35 to 40 per cent. of the crop- or pipe-end, and even with this excessive discard, secondary pipe or shrinkage-cavities are frequently discovered during subsequent working of the blooms and billets into their various manufactured products. The usual discard of from 10 to 20 per cent, from the crop-end of the ingot, which is made by the present generally employed methods of form and solidifying of the castings, certainly does not give the slightest assurance of the saleable product being physically sound or chemically homogeneous. I am aware that in the past there has been and at the present time there still is a decided difference of expert opinion as to what constitutes physically sound steel. Physically sound steel, as I would classify it, must be free from blow-holes as well as pipe. The line of demarcation between harmless and harmful blow-holes is exceedingly difficult to define. It is certainly the better and safer practice to eliminate blow-holes from the saleable portion of the ingots and to form a well-defined shrinkage-cavity or pipe at the upper crop-end of ingot. The higher grades of steel are all piping-steels. Is not their superior physical quality due to this fact as well as to their better chemical composition ? Such

Jan 1, 1914

By C. S. Lyons and. A. L. Johnson

A few years ago a leading American builder of centrifuges said, "No one uses a centrifuge if the job can be done any other way." This statement was essentially true at that time, not because the basic functional and economic principles involved did not frequently favor centrifugal methods, but rather because so many of the highly specialized features of the mechanical and functional peculiarities of continuous centrifuges had not been fully developed. The idea of using centrifuges in mineral dressing is definitely not new. There are literally hundreds of patents on centrifugal machines and processes for the mining industry. Many of them cover principles that are basic to the functioning of most centrifuges in operation today. In spite of this, until 1935, there were practically no successful applications of continuous centrifuges in the United States in the mineral industry, nor for that matter were there more than a mere handful of such machines in operation in North America in any industry. This was true despite the obvious desirability of machines that could furnish the advantages of high centrifugal settling forces in a continuous operation. The reasons for this are simple, even if not obvious: I. Finely divided solids, when thrown out of fluid suspension under high cen- trifugal forces, frequently exhibit physic a properties (particularly rheological or flow properties) that are markedly different from those they possess when settled out by gravity alone, and machines that are not designed in careful detail to cope with these peculiarities 'seldom function satisfactorily. 2. Most continuous centrifuges embody a solids-conveying element in the form of a very special screw conveyor. The rotation of this member under conditions of operation culls for drive designs that were not satisfactorily provided until the introduction of the Bird gear unit about 1934. These matters will be touched on later. Continuous centrifuges are now operating successfully in the mineral industry. Some units have singly handled more than 500,000 tons of solids during the past ten years. Generally their operation has been characterized by large unit capacities, complete elimination of labor, minimum supervision, moderate maintenance and power costs. Typical Centrifuge Applications Most materials classified by centrifuges are of subsieve particle size. Practically speaking, this means her than 100-mesh. A unit of measure other than screens is needed in order to consider these products properly. Such a unit is the micron, which is equal to one one-millionth of a meter; roughly1/25,000 of an inch. The opening in a standard 200-mesh screen is about 75 microns while a 325-mesh opening is roughly 43 microns.

Jan 1, 1948

By H. L. James

This paper presents the results and analysis of field trials of various magnetic instruments over anomalies ranging from 20 to 5000 gammas of vertical intensity. The following instruments were used: Askania vertical magnetometer, Wolfson vertical magnetometer (model M-I), Hotchkiss Superdips (used both parallel to and normal to the magnetic meridian, with several settings of the "sigma" angle), Lake Superior dip needle, and the dipping circle for measurements of inclination. The change in inclination over the measured anomalies ranged up to 4"; this caused pronounced changes in sensitivity of the Hotchkiss Superdip oriented parallel to the magnetic meridian. The variable sensitivity not only gives apparent displacement of crests of anomalies, particularly at high sensitivities, but also makes the data difficult or impossible to use in preparation of iso-anomaly maps. This weakness in field performance of the Superdip is shown to be eliminated by orienting the instrument normal to the magnetic meridian and measuring vertical intensity only, which in the latitude of upper Michigan is equal to 97 pct of the total intensity. The dip needle is seen to be relatively ineffectual for location of anomalies of less than 400 gammas. Introduction The U.S- Geological Survey, in cooperation with the Geological Survey Division of Michigan Department of Conservation, has for the past three years been engaged in a restudy of the Iron River-Crystal Falls iron mining district of upper Michigan. The bedrock in a large part of this area is covered with glacial deposits as much as 500-ft thick, and, inasmuch as some of the rocks have moderate to high magnetic permeability, extensive magnetic mapping has been done to assist in unraveling the complicated structure of the area. Several types of instruments have been used, and the major purpose of this paper is to present comparative data on the field performances of some of these instruments so as to aid others who face similar problems elsewhere to evaluate and choose the instruments best suited for the work. The paper is directed primarily to geologists and engineers rather than to geophysicists, although some familiarity with the instruments is presumed. The geology of the area consists of a complexly folded series of weakly metamorphosed sedimentary rocks, including the iron formation, which rests on older greenstones. Although the iron formation itself is only locally magnetic, some of the beds stratigraphically above the iron formation are rather strongly so. By tracing these hanging wall magnetic anomalies valuable information is obtained from which the structure and distribution of the iron formation can be inferred. Critical anomalies range from 25 to 6000 gammas of vertical intensity. Many anomalies can be traced in part with the common dip needle, but detection of others requires more sensitive instruments.

Jan 1, 1949

By R. J. Shaffer

Hydraulic fracturing in rock masses involves complex and coupled processes of fractures propagating in discontinuous media and of fluid flow in discrete channels. The Unconventional Gas Program at LLNL is actively developing numerical models to gain insight in the physics of these coupled processes. This paper describes the current status of the FEFFLAP code, which models fluid-driven discrete fracture propagation in jointed media. We also discuss the results of a preliminary series of physical tests in which hydrofractures were driven across slanted interfaces between dissimilar materials, in blocks loaded in biaxial compression.

Jan 1, 1984

By H. A. Keller

(Chicago Meeting, being part of the International Engineering Congress, August, 1803.) Among the important implements of most of our Western lead and copper smelting-works is the slag-cart or buggy, commonly called slag-pot. A large number of such slag-pots being in service, durability, as well as lightness of running, is an important requisite, since repairs, though trifling in each single instance, may amount to a considerable item of cost in the course of a year. They should therefore be seldom necessary and inexpensive when necessary. Light run-

Jan 1, 1894

By Edwin C. Barringer

IRON and steel scrap has again become page one news, as it was during the war. To many this is anomalous because the common concept is that the theaters of war are literally paved with scrap as the by-product of war damage and abandoned materiel. To an extent this is true, the bottleneck being the ferreting out and transportation of this scrap. While you as consumers of the electric-furnace grades of scrap-the premium grades-are concerned primarily in only one segment of the scrap market, I believe you ill be interested in a general discussion of the market with subsequent funneling down to your specialty.

Jan 1, 1947

By J. G. Davis, P. C. Thakur

Hazardous methane gas in coal mining is receiving increased attention due to the increased US demand for coal which has resulted in the exploitation of deeper seams and the utilization of more productive equipment. Problems posed by methane emission has the Mining Research Division of Continental Oil Co. (Conoco) accelerating efforts that began in the early 1950's with Consolidation Coal Co. (Consol).1 The program's focus is on finding new techniques for degasification of virgin areas as well as control of methane in gob areas.

Jan 10, 1977

By Raymond E. Riethmann, Beuford M. Bunnell

The spiral classifier was originally developed for closed circuit grinding It has since been applied very successfully to other classification duties where a two-product size split is required. Inherent operational qualities of this classifier make it ideally suited for sizing, washing, or dewatering materials such as ores, phosphate rock, sands, coal, oyster shells, solar and potash salts. Operating characteristics, flexible design and guidelines for proper application are presented.

Jan 1, 1978

Jan 6, 1953

By Walter Crafts

Structural steels containing chromium have become widely used in the last 20 years. In the earlier part of this period the major applications were in chromium-molybdenum aircraft tubing and similar special high-strength steels. During the past 10 years there has been a notable expansion in the use of chromium-bearing steel for structural purposes when welding was utilized for fabrication. The chromium-bearing steels introduced by Saklatwallal (chromium-copper), Kinzel2 (chromium-manganese-silicon), and Schultz3 (chromium-copper) are being extensively used at the present time. General Effects of Chromium Chromium is so widely known for its carbide-forming tendency that its capacity to stabilize oxygen, nitrogen, and phosphorus is often overlooked. In low-carbon steels of the structural type these so-called secondary characteristics become more prominent. For this reason also, chromium in structural steel is definitely a toughening agent. As the carbon content is increased, the more widely known hardening effect becomes more evident. In low-carbon steels chromium increases the notched-bar impact strength substantially. This property persists at subzero temperatures and is utilized for low-temperature service in chromium-copper steel.4 Chromium also reduces any tendency to strain-aging embrittlement. In addition to improving the toughness of steels with the usual impurities, chromium has the specific property of counteracting the brittleness induced by high phosphorus.5,6 In steels low in carbon and alloys, chromium has an almost negligible effect on tensile strength, and a hardening influence is noticeable only in the stronger steels. The ductility of welds adjacent to the base plate is also improved by chromium, both in the range of foolproof welding steels having strengths of less than 80,000 lb. per sq. in. as well as in the higher strength steels.

Jan 1, 1939

By D. P. Morton

Since 1923, which closed the speculative era in the bituminous coal fields of the United States, there have been wide annual fluctuations in the national production of bituminous coal. These changes in annual output have been variously attributed to: (1) increased competition from petroleum products, natural gas and hydroelectric power; (2) lower unit consumption of coal; and (3) fluctuations in the general business level. The purpose of this paper is to measure, from a practical standpoint, the net effect upon the annual trend of bituminous coal production, and to give those who are interested a basis for estimating in advance the probable output of bituminous coal. It can readily be shown that changes in the level of general business affect the national production of bituminous coal more than does any other factor. Therefore it is necessary to use some standard measure of the relative business level for purposes of comparison. The Federal Reserve Board Index of Industrial Production offers the basis for such a measure.l This Index, a weighted composite of 81 different series, rests upon the averages of the years 1935 to 1939 as 100, and is presented graphically in Fig. I. Even a cursory examination of the chart will indicate a definite uptrend for industrial production over a period of years. This uptrend is due to at least two factors: (I) an actual increase in national population, and (2) a probable increase in the per capita consumption of goods. This means that there is no such thing as a fixed Normal, rather Normal is a variable, tending to increase from year to year. In order to measure the amount of annual increase in normal, the Index of Industrial Production must be studied in relation to its major components, Durable Goods and Nondurable Goods, Durable Goods are those made from the lasting materials such as iron, steel, other metals, lumber, stone, cement, clay, glass. Nondurable Goods are those for early consumption, such as foods, textiles, tobacco, chemicals, paper, gasoline, and goods made of leather and rubber. The purchase of Durable Goods may be postponed, but Nondurable Goods must be purchased currently unless the standard of living is lowered. The Federal Reserve Indexes of durable and nondurable goods are shown graphically, 1920 to 1939, on Fig. a (pp. 764-765 of ref. I). It is apparent that fluctuations in the production of nondurable goods are not nearly so wide as in the production of durable goods, and that the curve of Industrial Production (Fig. I) would fall between the two curves on Fig. 2. It would, however, seem logical that both curves should follow the same long-term trend, or that over a period of two to three decades the relative proportion of durable and nondurable goods, in periods of normal production, should be the same. It is neces-

Jan 1, 1942

By L. C. Uren, E. J. Bradshaw

This paper presents the results of a group effort by a number of University of California students and faculty members, and the authors attach their names primarily in the capacity of editors and interpreters of the data thus assembled. In addition to the writers, the following individuals have made substantial contributions in time and effort in the conduct of this research: Dr. A. J. Carlson, Associate Professor of Petroleum Engineering; J. E. Gosline, University Research Assistant; C. F. Bedford, G. W. Mikulasek and H. S. Conder, senior and graduate petroleum engineering students; H. Bachman, G. Spencer and G. W. Gard, mechanicians in the Department of Mining and Metallurgy. Acknowledgment is also due the Research Board of the University, the Department of Mining and Metallurgy, and Prof. F. H. Probert, Dean of the College of Mining, for continued cooperation in securing mechanical assistance and funds for the purchase and assembly of apparatus. Significance of the Pressure Gradient The expulsion of petroleum from its reservoir sand doubtless is due to expanding natural gas intimately associated with the oil, to the hydrostatic pressure of encroaching edge waters, and to gravitational influences. These forces may operate independently or collectively. In any case they subject the fluids stored within the reservoir sands to elevated pressures, thus causing movement of oil and gas through the productive formations toward the lower pressure of the well outlets. This movement is opposed by pore friction, capillarity and adhesion: resisting influences brought to bear by the reservoir sand on the moving fluids. The magnitude of the resisting force is influenced directly by the viscosity, surface tension and density of the oil, as well as by the properties of the gas. The more rapid the rate of flow, the greater will be the resistance offered, and the greater will be the energy consumed.

Jan 1, 1932

By D. P. Morton

Since 1923, which closed the speculative era in the bituminous coal fields of the United States, there have been wide annual fluctuations in the national production of bituminous coal. These changes in annual output have been variously attributed to: (1) increased competition from petroleum products, natural gas and hydroelectric power; (2) lower unit consumption of coal; and (3) fluctuations in the general business level. The purpose of this paper is to measure, from a practical standpoint, the net effect upon the annual trend of bituminous coal production, and to give those who are interested a basis for estimating in advance the probable output of bituminous coal. It can readily be shown that changes in the level of general business affect the national production of bituminous coal more than does any other factor. Therefore it is necessary to use some standard measure of the relative business level for purposes of comparison. The Federal Reserve Board Index of Industrial Production offers the basis for such a measure.l This Index, a weighted composite of 81 different series, rests upon the averages of the years 1935 to 1939 as 100, and is presented graphically in Fig. I. Even a cursory examination of the chart will indicate a definite uptrend for industrial production over a period of years. This uptrend is due to at least two factors: (I) an actual increase in national population, and (2) a probable increase in the per capita consumption of goods. This means that there is no such thing as a fixed Normal, rather Normal is a variable, tending to increase from year to year. In order to measure the amount of annual increase in normal, the Index of Industrial Production must be studied in relation to its major components, Durable Goods and Nondurable Goods, Durable Goods are those made from the lasting materials such as iron, steel, other metals, lumber, stone, cement, clay, glass. Nondurable Goods are those for early consumption, such as foods, textiles, tobacco, chemicals, paper, gasoline, and goods made of leather and rubber. The purchase of Durable Goods may be postponed, but Nondurable Goods must be purchased currently unless the standard of living is lowered. The Federal Reserve Indexes of durable and nondurable goods are shown graphically, 1920 to 1939, on Fig. a (pp. 764-765 of ref. I). It is apparent that fluctuations in the production of nondurable goods are not nearly so wide as in the production of durable goods, and that the curve of Industrial Production (Fig. I) would fall between the two curves on Fig. 2. It would, however, seem logical that both curves should follow the same long-term trend, or that over a period of two to three decades the relative proportion of durable and nondurable goods, in periods of normal production, should be the same. It is neces-

Jan 1, 1942

By J. S. Kirkaldy, W. V. Youdelis

THE occurrence of concentration distributions in rapidly cooled castings with gradients of opposite sign to those expected on the basis of the constitution diagram and diffusion controlled kinetics, has long interested metallurgists. The work on inverse segregation to 1937 has been adequately reviewed by Vaughan, and to 1949 by ell-walpole. The general conclusion for unidirectional solidification, that the enrichment of the initially solidifying regions with lower melting point compositions is due to the flow-back along interdendritic channels of normally segregated residual liquid, has a very sound experimental basis. Perhaps the best experimental work and the most complete qualitative description of the process has been given by Adams.3 The authors accordingly assume the reader's understanding of the content of this paper. It appears that one of the principal deterrents to the complete understanding of the process has been the lack of an analytical description. Although a number of workers including Masing,4-6 Sauerwald,7 and Adams3 have attempted quantitative predictions,

Jan 1, 1959

By A. G. Weber, R. L. Ledbetter, A. L. Hicks

A procedure which makes use of both analog and digital computers has been developed for predicting the pressure-production behavior. of water-drive reservoirs. The electric analyzer is used for matching the past pressure and production history of the reservoir and inferring the physical characteristies of the aquifer. When the history has been matched, a .set of base curves called influence functionce" are derived and the future behavior of the reservoir is calculated from these curves. INTRODUCTION Electric analog methods are particularly well-suited for complex water-drive problems. Like all other methods of analyzing water-drive reservoirs, however, analog methods are subject to certain limitations. One of the more obvious and serious of these results from inaccurate or insufficient knowledge about physical characteristics of the reservoir and aquifer. However, it is not insurmountable because the unknown characteristics can usually be inferred from the reservoir's previous behavior. Simons and Spain have shown that even with scant reservoir data and limited production history, electric analyzer studies can provide useful and reliable results. Aside from this limitation on analyzer predictions, the main disadvantage has been lack of a technique for keeping predictions abreast of latest production forecasts. Pressure behavior of a reservoir depends on the rate at which fluid is withdrawn; it is therefore necessary to specify the future withdrawal schedule before the future pressure behavior can be calculated. Conventionally, the electric analyzer predicts pressure behavior for a specific production schedule. If this schedule is abandoned in favor of some new one, as is frequently the case, either the study must be rerun or results adjusted in some manner. The usual procedure is to predict pressures for several different forecasts covering a wide range of production rates. Pressures for specific rates other than those studied can then be approximated by interpolating between the analyzer predicted curves. However, reliability of this type of prediction is doubtful. This paper describes a technique for predicting future behavior of water-drive reservoirs that retains all advantages of electric analyzer analysis and eliminates the main disadvantage. That is, the analyzer is used conventionally to infer unknown reservoir parameters from the pressure history, but not to predict the future behavior directly. Instead, a derived set of base curves, called influence l'unctions, can be used to calculate future behavior for any production schedule.

By J. H. Lightfoot, Stuart E. Buckley

DEEP drilling has led to the development of numerous pools which yield products consisting predominantly of natural gas accompanied by high-gravity water-white or slightly straw-colored liquid. Yields of this "condensate" or "distillate," as it is commonly called, vary from traces to over a hundred barrels per million cubic feet of gas. The fact that this liquid exists in the reservoir as an integral part of the gas phase and is formed by condensation attending simultaneous reduction of pressure and temperature after its entry into the well was apparently first recognized about 1932.1 The nature of the physical phenomena involved in this condensation was clarified for the petroleum industry in 1933 by a report by Sage, Schaafsma, and Lacey2 of the results of an experimental investigation of the behavior of mixtures of methane and propane. Search of the literature has revealed that the condensation of liquid from gaseous mixtures by isothermal pressure reduction is not a new discovery. Kuenen was led by theoretical considerations to expect such a phenomenon, and in 1892 reported3 the results of experimental verification of his deductions. This was followed by a considerable amount of work on the phase relations of mixtures by Kuenen4,5,6 and by others,7,8 mostly in European universities. Since 1930 investigators in this country have reported experimental data on the properties and behavior of a number of hydrocarbon systems.9-17 It is now generally known that in the presence of natural gas the solubility in the gas phase of the heavier and normally liquid hydrocarbons increases rapidly with increasing pressure above 500 to 1000 lb. per sq. in. Thus, at pressures of 2500 lb. per sq. in. or higher a gas may contain appreciable quantities of hydrocarbons with normal boiling points as high as 600°F., which in turn may be condensed from the gas phase by the reduction of their solubility therein attending pressure reduction. The combined effects of pressure and temperature on condensation and vaporization of mixtures are most readily visualized by the study of phase diagrams. Since the construction, application, and interpretation of such diagrams have been described fully in readily available literature, 18-20 this paper will not review the theoretical aspects of this subject. While the behavior of gas-distillate systems is now clearly understood, at least in a qualitative way, most of the published work deals with the results of laboratory studies of binary systems or of synthetic mixtures of hydrocarbons, and although several systematic investigations of the effects of separator pressure and temperature on the yields of liquid product from gas-distillate wells have been made21.22 it appears that in all cases the limitations have precluded the construction of even approximately complete phase diagrams for naturally occurring systems. There has

Jan 1, 1941

By Stewart Murray, Philip Klapwijk

INTRODUCTION Forecasting commodity markets is like predicting winners in a horse race: to get the answers right, one needs both luck and judgement. Commodity analysts bear some resemblance to racing tipsters as they try to convince interested parties that they have an inside track on which metal is going to win the great minerals race of the 1990s. Commodity analysts share some features with the gentlemen of the turf: • They influence other people in how to spend risk capital, • They don't put their own money at risk, and • If their tips consistently fail to deliver, then they end up looking elsewhere for employment. In order to find winners we need to know about the kind of race we are in and the strengths and weaknesses of all the runners. Miners are not interested in a five furlong sprint: their race is a long distance affair -- after all, the lead-times between discovery and start-up generally approach a decade for mines that will provide the staying power which leaders require in this industry. We need to look at the environment in which our commodities will be competing: in racing parlance, the going. Our equivalent is the economic background: just as some horses are at a relative advantage when the going is soft, so some commodities will do better than others if economic growth is sluggish. If we are going to pick the winners for the late 1990s, and as an industry, make the right investment decisions, nothing is more important than being able to forecast (with at least a semblance of accuracy) how and where the world's economy is going to develop in the next decade. In addressing the question of whether minerals are going to be leaders in the 1990s, this paper considers the idea that it will increasingly be the world outside the industrialised OECD that will provide the incremental growth in demand for mineral products. Economic growth in the Developing World is fundamentally different from that in the OECD, and the pattern of demand for materials in relation to economic output is much more favourable than in the OECD. If we are to forecast the future, we need to be able to understand the past, both in the boom times of the so called Golden Sixties and in the lean years that followed them. This should help us to decide whether the future is going to be like one or other of these extremes or, on the other hand, a return to normality. Having forecast the going, we can look at individual competitors. • Which are best placed to take advantage of the economic, social and industrial trends that we can now dimly foresee? • Which can resist the continued onslaught of the new materials and technologies? • Which of them will best weather the economic storms (assuming that recessions have not yet been abolished)? If we can provide answers to these questions, we will be well on our way to picking winners, i.e., the metals and minerals that will reward their owners with growing demand, steady (and high) prices leading to profits beyond the dreams of avarice.

Jan 1, 1990

By Walter Crafts

Structural steels containing chromium have become widely used in the last 20 years. In the earlier part of this period the major applications were in chromium-molybdenum aircraft tubing and similar special high-strength steels. During the past 10 years there has been a notable expansion in the use of chromium-bearing steel for structural purposes when welding was utilized for fabrication. The chromium-bearing steels introduced by Saklatwallal (chromium-copper), Kinzel2 (chromium-manganese-silicon), and Schultz3 (chromium-copper) are being extensively used at the present time. General Effects of Chromium Chromium is so widely known for its carbide-forming tendency that its capacity to stabilize oxygen, nitrogen, and phosphorus is often overlooked. In low-carbon steels of the structural type these so-called secondary characteristics become more prominent. For this reason also, chromium in structural steel is definitely a toughening agent. As the carbon content is increased, the more widely known hardening effect becomes more evident. In low-carbon steels chromium increases the notched-bar impact strength substantially. This property persists at subzero temperatures and is utilized for low-temperature service in chromium-copper steel.4 Chromium also reduces any tendency to strain-aging embrittlement. In addition to improving the toughness of steels with the usual impurities, chromium has the specific property of counteracting the brittleness induced by high phosphorus.5,6 In steels low in carbon and alloys, chromium has an almost negligible effect on tensile strength, and a hardening influence is noticeable only in the stronger steels. The ductility of welds adjacent to the base plate is also improved by chromium, both in the range of foolproof welding steels having strengths of less than 80,000 lb. per sq. in. as well as in the higher strength steels.

Jan 1, 1939

By R. L. Fullman

Relationships are derived between average dimensions measured on a polished cross section and the spatial dimensions of particles dispersed as uniform cylinders. The equations are applicable to the measurement of rods or plates without the stipulation that they be extremely thin. QUANTITATIVE analysis of the elements of mi-crostructures has been limited by a lack of knowledge concerning the relationships between observations on plane surfaces and the spatial nature of the structure. This paper is an extension of previous efforts to establish equations suitable for the quantitative investigation of microstructures. The equations derived fill two gaps in the range of particle shapes for which measurements may be required, namely those shapes lying between extremely thin plates and equiaxed particles (approximately spherical), and those intermediate between equiaxed particles and extremely thin rods or needles. In a previous paper' equations were developed relating dimensions measured on a polished cross section to the average spatial dimensions of particles in the form of spheres, extremely thin plates, and extremely thin rods. For extremely thin rods the dimensions measured on a polished cross section were found to depend on the radius only, so that no information concerning the rod lengths or number of rods per unit volume could be obtained from observations on a cross section. In this paper equations are derived relating dimensions measured on a polished cross section to the spatial dimensions of particles in the form of identical cylinders. These equations may be used to evaluate the dimensions of rods, as well as the dimensions of plates, without the stipulation that the plates or rods be extremely thin. The impossibility of evaluating the length of extremely thin rods from planar measurements appears as an increase in the amount of data required for a given precision, as the length-radius ratio increases. Consider a sample containing particles of a phase in the form of cylinders of uniform radius T and height t. If the cylinders are randomly oriented, as in a sufficiently large sample of a fine grained poly-crystalline material, area and lineal analysis may be carried out with parallel cross-sectional planes and lineal traverses. If the cylinders are not randomly oriented, it is necessary to randomize the orientations of the cross-sectional planes and traverse lines. Let a unit cube be cut from the sample, and a cross-section plane be passed through the cube parallel to one of the cube faces. The number of particles N, cut by the cross-sectional plane per unit area is equal to the number of particles N, per unit volume times the probability p1 of a plane intersecting a single randomly positioned and randomly oriented cylinder in the cube. Let J be the maximum cylinder dimension in the direction normal to the cross-section planes, as shown in Fig. 1. Since, of the various possible positions for the cross-sectional plane over the unit length from top to bottom of the cube, only those positions existing over the length J

Jan 1, 1954