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By K. M. Busen, J. Lindmayer

A heterojunction model is suggested for descrihzng the electronic conditions at oxide -semiconductor interfaces. Detailed study of the silicon oxide-silicon interface shows that the heterojunction model explains many experimental facts; however, it is necessary to assume that a transition layer exists at the interface. It will he demonstrated that ionic contrbution way also he present. Extended low-temperature heating stabilizes the oxide to a charge carrier density in the order of 10' cln-: determined by the heterojuncton model. OXIDIZED semiconductor surfaces are widely used, since they offer technological advantages and "passivate" the surfaces of semiconductor devices. However, it has been recognized that there are always n-type inversion layers formed in the silicon oxide-silicon system, which must be regarded as a definite disadvantage. An added complication is the "instability" of these inversion layers;' the inversion layer appears to vary with the processing and they change at temperatures as low as 100" to 200°C This paper will point out that the inversion layer is a result of the dissimilarity of the contacting materials and therefore must always be present. The dissimilarity is the essence of the heterojunction or electronic model and involves directly the structure of the materials involved. In addition, one finds the contribution from ions; this disturbance, however. can be eliminated for the case of silicon oxide-silicon interface. The strength of the inversion layer or channel will be expressed in terms of the density of elementary charges per square centimeter, N*, maintaining the channel. The next section contains the formulation of the heterojunction model by assuming a contact between two homogeneous materials. This calculation should not imply that silicon oxide is homogeneous; it serves only to point out the general properties of the electronic model. Following the electronic model, the practical case of the silicon oxide-silicon interface will be discussed. I) THE HETEROJUNCTION MODEL Contacting an oxide with a semiconductor, a work-function difference must be accommodated. Fig. 1 represents the oxide and the semiconductor before and after contact. When the contact has been made, one finds that qVi + qV, = A@; i.e., the work-function difference is distributed between the oxide and the semiconductor. Normally, the work-function difference appears on the wide-bandgap material, but in the present case the oxide is thin and far from being a single crystal. Accordingly, a significant fraction of the work-function difference must appear on the semiconductor. The work function of silicon2 is about 4.8 ev, but we shall not assign any particular work function for the oxide as it may vary. However, oxides usually have lower work functions and therefore the potentials must build up in the manner shown in Fig. 1. Such an argument predicts that the inversion layer must be n type, as opposed to the clean surface which is p type. Another important factor to be considered is that the oxide is disorderly and therefore contains many trapping levels. As a result, the charges in the oxide arise primarily from the change in trap occupation, while on the semiconductor side the space charge is composed of mobile free electrons. The consequence of this fact is that a change to another thermal equilibrium will require some time, dictated by the traps in the oxide. The conditions can easily be calculated on the semiconductor side. Assuming an intrinsic semiconductor, Poisson's equation is

Jan 1, 1965

HENRY M. HOWE, Bedford Hills, N. T. (communication to the Secretary?).-The authors valuable results as to the effects of the air-hardening temperature on high-speed steel may be summed up thus: Influence of Rising Air-Hardening Temperature on. High-Speed Steel Air-hardening microstructure Cutting Properties temperature S Austenite Grain Free Carbide Grains Boundaries Too low Small or Narrow Maximum Too soft undeveloped Intermediate, Well-developed Intermediate Little or even Best correct none Too high Coarse hide, even with Minimum . Weak, brittle, three-rayed crumbling stars Here the suggestion is that as the air-hardening temperature rises it causes two prominent effects, one helpful and the other harmful, the increase of the former exceeding that; of the latter up to a certain point, at which the steel is most useful, and then in turn being outrun by it. The first is the progressive dissolving of the free carbide in the austenite, increasing the stability of the red-hard state. The second is the progressive coarsening of the grains, and thickening of the intergranular cement, developing at last into spandril-like three-rayed stars of the 1,288° specimen. (2,350° F.) of Plate D, thus giving clear proof of incipient fusion, that is of crossing the solidus. This causes intergranular weakness. The individual grains may have great red-hardness, but they do not cohere. They approach the condition of a bag of emery grains.

Jan 6, 1917

By L. K. Borrett ond C. S. Yusi

The authors have made extensive use of a modern field of mathematics, topology, to give a new approach to the study of sintering. They present a topological model for the sinter body and the void space, and establish a relationship between them. However, in an interdisciplinary paper of this nature it is important that the material be presented, insofar as possible, in

Jan 1, 1967

By B. M. Larsen

Jan 1, 1965

By Dennis A. Clark, Brent Larsson

Tunnelling today is a lot more than drilling and blasting. The developments in drilling and blasting technique have made it pos¬sible to save costs both by increasing the advance per round and optimizing the demands on the final contour. Increasing the hole depth by using longer feeds and bigger dril¬ling rigs make the drilling time shorter compared to the set up time. It is important that the deeper holes are followed up by using a suitable cut. The most common cut in Sweden today is a parallel hole cut with one or more large holes; with a diameter corresponding to the hole depth and wanted advance per round. It is often specified that smooth blasting is to be carried out with a specific drill hole spacing. It is extremely rare, however, for specifications to be issued concerning the alignment of the raw of holes closest to the contour holes. It is very easy to ruin the effect of smooth blasting altogether by firing the rest of the round carelessly with an excessively high charge distribution. The drilling and blasting of the contour holes and the line of holes closest to the contour holes is therefore an extremely important part of any underground work. Accuracy and care in connection with the drilling of contour holes is also extremely important since it is possible to reduce the amount of overbreak, the result being more rapid mucking out, smoother and more durable surfaces and also less consumption of concrete for lining purposes.

Jan 1, 1983

By Dwight E. Woodbridge

DuriNg April, Max, and June, 1910, I was in charge of an examination of the greater part of the Moa iron-ore area in Oriente Province, Cuba, on the north coast, near the east end of the island. My instructions, on arrival at the properties, were to check former estimates of tonnages and grades, and to re-examine the ore comprised in claims covering 44,727 acres. This work included the running of lines dividing the properties into co-ordinate planes, the boring of many thousand feet of holes spaced at the intersections of these co-ordinates, the taking of samples of the ore penetrated, the analysis of these samples for their various constituent minerals, and the determination of the results as to tonnages, depths, and grades, both for individual properties and for the entire group. Each section of every one of the thousand holes drilled was to be compensated for depth and grade with every other, a series of simple arithmetical calculations of no slight magnitude, the mere mechanical labor of which consumed much time, but finally resulted in giving a complete average of all the essential facts for the entire area of 18,000 hectares, Had it not been for the more than willing, active, and able co-operation of the officers of the Spanish-American Iron Co., from Charles F. Rand, President, and Jennings S. Cox, General .Manager, down to the most humble water-carrier, the work would have consumed far more time than it did. The lands thus systematically explored by me were comprised in the following denouncements: Punta Gorda, Yaminiguey, Baracoa secunda, Sagua, Moa, Yajrumaje, Lirio, and Cabanas, all of which were massed as the Moa group, so called, and cover an area of 13,832 hectares, or 34,179 acres. Some 10,000 acres additional to this was included in neighboring properties, lying between Moa and the east end of the island, the Buena Vista,

Jan 1, 1912

By H. Y. Yancey, B. M. Bird

During the past four years the experimental work in coal washing carried on by the U. S. Bureau of Mines and the University of Washington has been devoted mainly to the development of special methods for the tabling of fine sizes of coals that are difficult to wash. One important outgrowth of this investigation has been the application of hindered-settling classification to coal tabling. Although used for many years in ore dressing, the term "classification" as used here may be new to many readers. It may be defined as the separation obtained when a bed of particles is held in a uniform state of suspension in an upward current of water, either continuous or pulsating, just sufficiently strong to keep the bed in a mobile condition. A common example of this type of separation is a jig in which there is no suction stroke. When the hindered-settling classifier is used with the coal-washing table, the fine-size raw coal, instead of being fed direct to tables, as is the prevailing practice, is first fed to the classifier and grouped, according to the rate of settling against the upward current of water, into perhaps six separate products. After dewatering, each of these except the sixth, a refuse product, is elevated to a seperate feed bin arid washed on a separate table. This paper gives a brief discussion of the basis for the use of hindered-settling classification of a table feed; a description of the experimental work; a comparison of the results obtained with and without classification; and a discussion of the application of the classifier in commercial coal washing. Basis for Use oF Hindered-settling Classification of Table Feed Although theoretical reasoning might be used to justify treating a table feed by hindered-settling classification,l the simplest method of demonstrating the need of such a step before tabling is to show the

Jan 1, 1930

By P. R. PaeIay, A. Slibar

Using three-dimensional, stress-deformation rate equations for a Bingham plastic, an approximate solution for the laminar flow of drilling mud between the drill pipe and casing is given for the case when the velocity gradients due to axial flow are large compared to velocity gradients due to rotation. INTRODUCTION The fact that drilling mud can be treated, to a first approximation, as a Bingham plastic has been established by several investigators12,3,4,5. A Bingham plastic is a material that is rigid until a certain combination of stresses exceeds a critical value. When the stresses are sufficiently high to initiate flow, the reduced stresses have a constant ratio to the corresponding deformation rates at each point. Prediction of pressure and torque requirements to produce the desired flow of the material have been made by analytical solutions due to Bingham6, Reiner7, and Buckingham8. One part of the present means of calculation that requires clarification is the flow between the drill pipe and casing. Present methods treat the flow resulting from the rotation of the drill pipe separate from the flow produced by the axial pressure gradient. Since the non-linear behavior of a Bingham plastic implies that solutions cannot be superposed, the present analytical investigation was undertaken to obtain a solution to the problem of combined axial and tangential flow. Equations have been proposed for the three-dimensional flow of a Bingham plastic9,10,11 and it has been shown that the proposed equations lead to the usual solutions from the one-dimensional theory". Applying these equations to the flow between two concentric cylinders the problem of axial flow only13 and tangential flow only12 have been solved. In addition to the separate problems of axial and tangential flow between concentric cylinders, the authors have determined the relationship between external torque on the inside cylinder and axial pressure gradient necessary to initiate flow". The solution given in Ref. 14 points out the complexity of the present problem. The problem considered here is the case of simultaneous axial and tangential flow. The axial flow, necessary to keep the drill bit free of removed material, results from the axial pressure gradient. Tangential flow is present since the drill pipe rotates in the hole. The solution given here is valid when the shear stresses in the drilling mud due to rotation are small compared to the shear stresses resulting from the axial flow. This case for laminar flow can be encountered in oilfield drilling. STRESS-DEFORMATION RATE EQUATIONS A detailed derivation of the equations governing the behavior of a Bingham plastic is given in Ref. 10. This section briefly outlines the physical reasoning leading to this three-dimensional formulation of the stress-deforma-tion rate law. Experiments on a certain class of materials have demonstrated the following properties: (1) when a certain combination of the stresses is below a critical value no deformation of the material occurs, (2) to a first approximation this combination of stresses is independent of the hydrostatic pressure (negative average normal stress), (3) if flow occurs the ratio of the reduced stress to the corresponding deformation rate is constant at each point of the flowing material, and (4) incom-pressibility. For the one dimensional case of shear deformation, Bingham6 formulated the governing equation as dxx, = 0 for sxx < to and µdxx = s xx = to for sxx to , . where dxx is the shear deformation rate, sxx the shear stress, to the critical shear stress, and p the slope of the sxx vs dxx curve for dxx > 0. Fig. 1 shows the behavior for pure shear between two parallel plates. Taking into account the physical properties given above and assuming the critical combination of stresses to be measured by the octahedral shear stress, the fol-lowing three-dimensional equations have been proposed.

Jan 1, 1958

THE metal iron has physical and chemical properties which are somewhat different from those of steels, but a knowledge of the pure metal is a useful starting point in studying the behavior of steels. Solid iron exists in two different crystalline forms, called alpha (a) and gamma (?) iron, the former being the ordinary form at room temperature. When heated above the "A2 point," 1400°F. (760°C.), the metal becomes non-magnetic, and at the "As point," 1670°F. (910°C.), it undergoes a change in crystalline form to become gamma iron. In the range 1400 to 1670°F., it is sometimes called beta (0) iron to distinguish it from the magnetic alpha, but the two are identical in crystal structure. When gamma iron is further heated to 2550°F. (1400°C.), it changes into delta (d) iron, which is identical with beta or non-magnetic alpha iron. Pure iron melts (in a hydrogen atmosphere) at 2795°F. (1535°C.); the melting point is generally lowered by alloys or impurities. PROPERTIES OF IRON AT HIGH TEMPERATURES Many of the properties of iron undergo abrupt changes at the transition temperatures. (1) For example, in heating through the As point a sudden shrinkage in volume occurs. Similarly, melting is attended by sharp physical changes such as an increase in volume. Table 27 contains a summary of the measured physical properties of pure iron at several temperatures. Usually the properties change smoothly within the range of stability of a given form, but this is not always the case. For example, the specific heat reaches a sharp maximum at the A2 point although no transformation occurs. Solvent Powers of Liquid Iron. Liquid iron is capable of dissolving most of the other metals and many nonmetallic elements as well. Of the metals which are liquid at the melting point of iron only lead, silver, and bismuth refuse to dissolve to an appreciable extent. The non-metals presumably dissolve by virtue of the formation of an iron compound; for example, sulphur is thought to dissolve as the compound FeS. However, there is no satisfactory method of proving that this

Jan 1, 1944

By E. W. Davis

THIS nation has been depending upon the Lake Superior iron ranges for most of its iron ore requirements for over half a century. Furthermore, it can continue to draw the major portion of its ore requirements from the same source for another century or more, but to accomplish this, great changes must take place in the present ore mining industry. Preliminary preparations for these changes are now underway and in the next few years decisions of far-reaching importance must be made. But to understand the situation, it is first necessary to know something of the nature and occurrence of the Lake Superior iron formation. So far as is known, the merchantable grades of iron ore remaining in the various Lake Superior ranges are as shown in Table 1, which shows that

Jan 1, 1947

By Paul M. Tyler

YEAR after year, the kaolin industry of the United States has been setting new production records and making better products. High-grade paper, pottery, and rubber clays are produced in this country mostly in the South. Georgia alone contributes over 70 pct and South Carolina almost 20 pct of the total domestic output. Residual kaolin is mined in North Carolina, highly plastic but naturally sandy Tertiary (Eocene) potting clays are worked in north central Florida, and good white clays are produced in several other states, but the main sources of kaolin or china clay have been numerous deposits in the Tuscaloosa (Upper Cretaceous) formation. This formation of generally sandy sediments is called the Middendorf member in older geologic reports and corresponds in age with some of the New Jersey clays. As shown in fig. 1, it crops out almost continuously in a generally southwesterly direction across South Carolina and Georgia and into Alabama. Clay is mined from this formation in all three states but the principal producing centers lie within about 10 miles of a straight line drawn between Aiken, S. C., and a point about 10 miles south of Macon, Ga. The white kaolins of the South were recognized and used prior to the Civil War but suitable treatment processes were not introduced until World War I when imports, chiefly from England, were curtailed. Although imports of high-grade clays were resumed after 1918, the domestic industry managed to treble its prewar production record during the early 1920&apos;s and has continued to grow. Whereas the 1909 to 1913 average total production in the United States was only 132,104 short tons valued at $705,352 f.O.b. mines, the output in 1948 was 1,-568,848 tons worth $19,756,738. Paradoxically, it seems in retrospect that the early failure of the American industry to meet foreign competition was due to the superior quality of our sedimentary clays in their natural state. Kaolin, of course, is the principal decomposition product of feldspars which originate in acidic igneous rocks such as granite, aplite, alaskite, granodiorite, quartz porphyry, etc. English china clays occur in residual deposits and before they can be marketed they have to be treated to remove accompanying quartz, mica, and other impurities. Notwithstanding the relatively crude methods employed, the final product is a beneficiated clay which is subject to a certain amount of technical control as to quality and uniformity. Although the naturally concentrated deposits in Georgia and South Carolina contain some of the finest crude white kaolin in the world, even it can be made better by suitable treatment. In recent years well over half of the high-grade china clay produced in the United States has been used in making paper. Some qualities of paper clays are still produced by the dry process, or air flotation, but the paper industry&apos;s specifications have grown so exacting that wet processing was adopted and more refined methods had to be perfected. Notwithstanding notable advances in clay-preparation technology during the past decade, or possibly because these advances have implemented and encouraged technologic changes in consuming industries, demand has grown for products of higher uniform quality than can be obtained from even the best natural deposits without rigidly controlled fractionation. Largely as a result of the wide adoption of machine coating for paper, the clay industry has been obliged not merely to eliminate virtually all mineral impurities but also to segregate the clay substance itself into narrow particle-size ranges. By extraordinary coordination of sales effort and production technology, several Georgia companies manage to market a wide variety of specialized joint products but the commercial success of many producers depends upon their mining only the best parts of their deposits and then skimming the cream of this almost pure clay in order to obtain a maximum yield of kaolinite finer than about 2 microns in maximum particle size and possessing low viscosity as well as the more familiar attributes of suitable color and brightness, or reflectance. To the casual visitor from another mineral industry, the kaolin mines and plants may appear to be

Jan 1, 1951

By Paul M. Tyler

YEAR after year, the kaolin industry of the United States has been setting new production records and making better products. High-grade paper, pottery, and rubber clays are produced in this country mostly in the South. Georgia alone contributes over 70 pct and South Carolina almost 20 pct of the total domestic output. Residual kaolin is mined in North Carolina, highly plastic but naturally sandy Tertiary (Eocene) potting clays are worked in north central Florida, and good white clays are produced in several other states, but the main sources of kaolin or china clay have been numerous deposits in the Tuscaloosa (Upper Cretaceous) formation. This formation of generally sandy sediments is called the Middendorf member in older geologic reports and corresponds in age with some of the New Jersey clays. As shown in fig. 1, it crops out almost continuously in a generally southwesterly direction across South Carolina and Georgia and into Alabama. Clay is mined from this formation in all three states but the principal producing centers lie within about 10 miles of a straight line drawn between Aiken, S. C., and a point about 10 miles south of Macon, Ga. The white kaolins of the South were recognized and used prior to the Civil War but suitable treatment processes were not introduced until World War I when imports, chiefly from England, were curtailed. Although imports of high-grade clays were resumed after 1918, the domestic industry managed to treble its prewar production record during the early 1920&apos;s and has continued to grow. Whereas the 1909 to 1913 average total production in the United States was only 132,104 short tons valued at $705,352 f.O.b. mines, the output in 1948 was 1,-568,848 tons worth $19,756,738. Paradoxically, it seems in retrospect that the early failure of the American industry to meet foreign competition was due to the superior quality of our sedimentary clays in their natural state. Kaolin, of course, is the principal decomposition product of feldspars which originate in acidic igneous rocks such as granite, aplite, alaskite, granodiorite, quartz porphyry, etc. English china clays occur in residual deposits and before they can be marketed they have to be treated to remove accompanying quartz, mica, and other impurities. Notwithstanding the relatively crude methods employed, the final product is a beneficiated clay which is subject to a certain amount of technical control as to quality and uniformity. Although the naturally concentrated deposits in Georgia and South Carolina contain some of the finest crude white kaolin in the world, even it can be made better by suitable treatment. In recent years well over half of the high-grade china clay produced in the United States has been used in making paper. Some qualities of paper clays are still produced by the dry process, or air flotation, but the paper industry&apos;s specifications have grown so exacting that wet processing was adopted and more refined methods had to be perfected. Notwithstanding notable advances in clay-preparation technology during the past decade, or possibly because these advances have implemented and encouraged technologic changes in consuming industries, demand has grown for products of higher uniform quality than can be obtained from even the best natural deposits without rigidly controlled fractionation. Largely as a result of the wide adoption of machine coating for paper, the clay industry has been obliged not merely to eliminate virtually all mineral impurities but also to segregate the clay substance itself into narrow particle-size ranges. By extraordinary coordination of sales effort and production technology, several Georgia companies manage to market a wide variety of specialized joint products but the commercial success of many producers depends upon their mining only the best parts of their deposits and then skimming the cream of this almost pure clay in order to obtain a maximum yield of kaolinite finer than about 2 microns in maximum particle size and possessing low viscosity as well as the more familiar attributes of suitable color and brightness, or reflectance. To the casual visitor from another mineral industry, the kaolin mines and plants may appear to be

Jan 1, 1951

By A. Tanaka, K. G. Carroll

The existence of local room-temperature plastic flow in germanium, which has been a subject of controversy for nearly two decades, has recently received renewed attention, albeit no more agreement than hitherto. Phenomenologically one major facet of the problem has been reduced to the question whether or not indentation can be effected in germanium without the introduction of cracks. That plastic flow can be induced at room temperature by fracture appears to have been rather convincingly demonstrated recently by Suzuki and Kamada and by Noble and Henisch.1 The literature contains both direct and incidental references to Vickers and Knoop indentations showing no cracks, within resolution of optical microscopy. Recently, however, following a controversy on the subject,2,3 johnson4 made a study of indentations produced by spherical indenters and concluded that these are accompanied by cracking. This study in-

Jan 1, 1969

By Norman P. Goss

The Chairman.—Thank YOU, Mr. Goss Gentlemen, I believe we have heard one of the finest papers, especially since Mr. Goss has been very generous in his frank discussion of continuous casting. One point he has brought out which 1 think some of us have not thought through to the same extent that he has—that the continuous casting process offers the small producer an opportunity to compete with the larger, more conventional and presumably better established industries. The meeting is now open for discussion. Are there any questions concerning the first two papers? J. A. Malone.*—I should like to ask Mr. Goss whether there is any special problem involved in the first part, the upper part of the mold before he gets to the first graphite lubricant area. N. P. Goss.—You mean in the forming chamber where chilling first takes place? J. A. Malone.—Yes. N. P. Goss.—So far I have not had any trouble in this part of the setup. My only

Jan 1, 1945

As a result of Engineering Council&apos;s request to the Director of the Census, the National Service Committee has been successful in effecting a reclassification of engineers so that all technical men will be listed as such and they will be separate and distinct from the non-technical engi-neers. Thus, the next census will bring an enumeration of all technical engineers together as one unit under the main headings of civil, mech-anical, electrical and raining; architects also will be enumerated separately. This will enable the engineering profession, the Government or any other interested organization to know exactly how many technical men there are in the United States and in each state. The enumeration will also include non-technical engineers, except that there will be no such heading and in order to get the totals of non-technical men all of the various grades of this classification would have to be sorted out and added.

Jan 12, 1919

By Graham MacFarlane

The largest area of high-grade cannel coals known in America is doubtless found in eastern Kentucky. Notwithstanding the popular belief to the contrary, there is no reason to doubt that these eastern Kentucky cannel-fields, following the general rule, will be uncertain and treacherous. But, taken in the aggregate, their extent is very great. The principal service to which cannel coal can be put is enriching illuminating-gas. The electric light has, to a certain extent, created a demand for better gas, and has increased the market for gas-enrichers. Before the discovery of rock-oil, coal-oil was distilled from cannel coal and cannel shale. This business was getting fairly started when the cheaper rock-oil, or petroleum, overcame it, and the great distilleries went into disuse and ruin. Now, again, the chief competitor with cannel coal is oil, namely, the cheap oil of Lima, Ohio. Under proper treatment the vile odor of this oil can be removed.

Jan 1, 1890

A completely automated primary crusher is now in operation at Kaiser Steel Corp.&apos;s Eagle Mountain, Calif., iron mine. The word "completely" is italicized to underscore its literal meaning- automation so thorough that even the control room for the crusher does not require a man to watch the flickering dials and lights. The automation of the unit is such that its operation, including starting and stopping, are controlled from the secondary crusher station. The crusher-a Symons 60-in. gyratory which can handle 3600 tph-features built-in safety devices that will turn the crusher off if oil pressure drops, if oil overheats, if bearing temperatures exceed permissible limits, or if parts of its electronic brain fail. According to reports, the worst that can now happen is a plugging of the crusher.

Jan 6, 1963

By Norman D. Fitz Gerald

THE growth of domestic requirements for motor fuel has been phe-nomenal, rising year after year in a fashion almost unique among com-modities, resisting depressions and forging rapidly ahead in times of prosperity. Consumption advanced from 226 millions of barrels in 1925 to 522 millions of barrels in 1938; or 130 per cent. The economic influ-ences generating and sustaining this demand are of vital concern to the petroleum industry. The general factors affecting utilization of motor fuel are well known but it is the purpose of this paper to employ the recently developed technique of economic dynamics to describe them mathematically. Such problems in economic analysis are complicated by the freedom of all the variables to fluctuate, their mutual interdependence, changing incidence upon one another, and the nonquantitative character of some of them. Economic quantities and relationships, unlike those of the physical world, are continuously changing and this dynamic characteristic is both a distinguishing and confusing feature in economic research. The com-plexities of the problems require application of the analytical devices of mathematical statistics to uncover the probable relationships between factors. The procedure employed is to formulate a logical relationship linking the dependent to the independent variables, and then simul-taneously, rather than sequentially, determine their separate effects by multiple correlation. This transformation of common knowledge to quantitative terms makes it possible to measure the probable effects of changing conditions upon requirements, assisting in the sound interpreta-tion of economic policies. The utility of the results of such dynamic analysis is in sharp contrast to the sterility of the trends and other simple empiricisms of descriptive statistics. It is not intended in this study to throw light on the reasons why any motor fuel at all is consumed; but to discover relationships explaining why more was consumed at one time than at another. Specifically the prob-lem is confined to the measurement of the influences of statistically

Jan 1, 1940

By C. Atkinson

A method is described for the numerical solution of the diffusion equation with a composition-dependent diffusion coefficient and applied to the radial growth of a cylinder; the radial growth of a sphere, and the symmetric growth of an ellipsoid. Sample applications of the method are made to the growth of particles of proeutectoid ferrite into austenite. RECENTLY&apos; we described a method for numerical solution of the diffusion equation with a composition-dependent diffusion coefficient for the case of the growth of a planar interface. In this paper we extend this method to describe the radial growth of a cylinder, the radial growth of a sphere, and the symmetric growth of an ellipsoid. In the latter case, limiting values of the axial ratios of the ellipsoid reduces the problem to one of a cylinder, a sphere, or a plane depending on the axial ratio. A check on these limiting values is made in the results section. In all of these cases we consider growth from zero size. A natural consequence of this assumption as applied to the sphere, for example, is that the radius of the sphere is proportional to the square root of the time. This is consistent with the condition that the radius is zero initially, i.e., grows from zero size. It may be argued that it is more realistic to consider particles which grow from a nucleus of finite initial size; even in this case the analysis of this paper is likely to be applicable. This can be seen if a comparison is made of the work of Cable and Evans,2 who consider a sphere of initially finite size growing by diffusion in a matrix with a constant diffusion coefficient, with the results of Scriven3 for growth from zero size. This comparison shows that the rates of growth in each case differ trivially by the time the particle has grown to about five times its initial size." This investigation is a generalization of those of Zener,4 Ham,5 and Horvay and cahn6 to the situation often encountered experimentally, in which the diffusion coefficient varies with concentration. First let us consider each of the cases separately. I) GROWTH OF SPHERICAL PARTICLES FROM ZERO SIZE In this case the differential equation in the matrix depends only on R, the radius in spherical coordinates, and can be written: ? 1 <^\ ^13D . , dt U\dRz + R 3Rj + dR dR [ J where C is the composition, t is the time, and D is the diffusion coefficient which depends on c. The boundary conditions will be: c = c, at the moving interface in the matrix, c = c, at infinity in the matrix (and at t = 0, everywhere in the matrix), c = X, is the composition in the spherical particle. Each of the above compositions is assumed constant. In addition there is the flu condition at the moving interface which can be written: , dR0 ~/3c dt \dR/H =Ra where R,, which is a function of t, is the position of the moving interface. We make the substitution q = RI~ in [I] reducing this equation to: & - m - *ws) »i where we have written D = D,F(c) or simply D,F, and Do = D(c,). Thus F[c(q0)] = 1 where q, = ~,/a is the value of the dimensionless parameter q evaluated at the interface. Multiplying Eq. [2] by dq/dc and integrating, we find: where the lower limit of the integral has been chosen so that dc/dq — 0 as c — c,, thereby satisfying the boundary condition at infinity. We require, then, to solve Eq. [3] subject to the condition c = c, when q = q, (this follows from putting R = R, at the interface) together with the flux condition which can be rewritten in terms of q as: Eqs. [3] and [4] together with the condition c = c, at q = q0 enable us to find 77, and the concentration profile c = c(q). Numerical Method. We treat Eq. [3] in the same way as we did the corresponding equation for the planar interface problem&apos; i.e., by dividing the interval c, to c, into n equal steps so that: cr = ca -rbc [5] where r takes the values 0, 1, ... n and we call no,, q1, ... nn the values of n corresponding to the compositions c,, c,, ... c,.

Jan 1, 1970

By ROBERT E. CROCKETT

MAGNETITE mining and milling in New York, New Jersey and Pennsylvania continued to remain comparatively inactive during 1933, owing to the low rate of output of the steel industry and also to unrestricted importation of foreign ores. However, some improvement over conditions existing in 1932 was noticeable, particularly in New Jersey, where one plant, that of the Washington mine of the Alan Wood Mining Co., at Oxford, went on full production in August. At Lyon Mountain, N. Y., the Chateaugay Ore and Iron Co. resumed mining and milling operations in October, on a reduced scale, principally to provide employment during the winter months. The Chateaugay company produces a special low-phosphorus pig iron. During the year they obtained a contract to supply their product for use in the manufacture of the suspension cables of the New. Golden Gate Bridge.

Jan 1, 1934