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By W. D. Johnston, T. P. Thayer

THE minerals that collectively are known as chromite form an isomorphous series of the general formula (Mg,Fe) 0. (Cr,Al,Fe) 203. So wide is the range in chemical composition in this group that chrome ore consisting entirely of the mineral chromite may range from less than 30 pct to more than 60 pct Cr203. The most comprehensive published data on the chemical com- position of chromite are by Stevens,62 who made complete analyses of 52 samples of chromite concentrate from many localities in North, Cen- [ ] tral, and South America. These samples were mechanically purified to remove associated silicates and might be regarded as the cleanest chromite that could be obtained by any mechanical milling process. Fig 1 shows the predominant zone of isomorphism, within the triangular prism of composition defined by the mineralogical end members of the series, wherein his analyzed samples fell.

Jan 1, 1949

By Prince Lazarovich, Hrebelianovich

I WAS asked by the chairman of one of the Sessions on Employment Problems to talk about the viewpoint of the foreign workingman. I am not a workingman. I have never done what a work-hand might call an honest day's labor; that is, I have never been in a factory or manufacturing plant or in a mine, though in truth, hard work and I are well acquainted. I was a soldier, am an engineer, have long been actively interested in the most important waterway construction in the near East, have served politics and diplomacy, written books and lectured at universities. My knowledge of the foreign workingman in this country comes from the fact that my own compatriots here at various times came to me and appealed for advice and help, and last year I was asked by the employment manager of a corporation to undertake a welfare job at one of their plants. I went out, saw the plant, talked with the superintendent and outlined certain of my ideas which he personally heartily approved, but which did not find favor with those higher up. I approach the subject of the foreign workman's point of view with the understanding that the industrial employer's effort is for the maximum of efficiency. I am conversant with labor conditions abroad both in industry and agriculture. What I have learned of industrial conditions in America as they affect the foreign immigrant has been chiefly gathered from the cases referred to of foreign workmen who from time to time have come to me with their troubles. In the course of those investigations, in order to give whatever help or advice was possible, I have been impressed with the fact that the great United States industries evidently had- pot yet sufficiently recognized the value of studying the conditions of the workingman in the lands of his origin across the seas. A careful study of that which could be called the moral element in connection with its foreign labor would give industry a knowledge of the man's reason for coming, what' grievances he brings with him, his hopes for a future, and the peculiar character of his capacities. The employer would thereby be enabled to meet the man, to be helpful to him, to aid him and at the same time promote industrial efficiency, inasmuch as a workman who believes that he is being dealt with humanly and squarely is contented and satisfied and will give willingly, and even with pride, the best that is in him; justice and a fair deal is all the man wants.

Jan 4, 1918

By Ballard H. Clemmons

THE future of the steelmaking industry of the Birmingham, Ala., district is closely related to and, in a large measure, dependent on the development of workable, economic processes of ore concentration. Operations thus far in the area have been possible only because of the fortuitous occurrence of iron ore, fluxing stone, and coking coal-all the primary iron-making materials- within a 25-mile radius of the blast furnaces. Commercial ore of the district consists mainly of a 10 to 20-ft hematite-calcite-silica bed locally known as the "Big Seam," a component of the Clinton formation of Silurian Age. At present mining rates, this ore will be available for a number of years. It is largely mined under 1000 to 2000 ft of cover and transported on 15 to 20" slopes that, in some instances, are as much as 10,000 ft long. Under these conditions, particularly with increasing distances from face to portal, mining costs are gradually becoming disproportionately high. Although not a major factor thus far, it should also be noted that the average annual ore output of the district is gradually be- coming more siliceous.

Jan 1, 1950

By William Campbell

FiRst I must express my deep appreciation for the honor of being privileged to give the Howe Memorial Lecture this year and at the same time my feeling of inadequacy to do justice to the subject. The first Howe lecturer was most fittingly, Professor Sauveur, his contemporary and friend, and the subject was beta iron. Last year the second Howe lecture was delivered by Dr. Mathews, one of his most distinguished pupils, who spoke on austenite. This year, the Howe Professor of Metallurgy was chosen to deliver the third annual lecture, and the subject ought to be martensite. No one but Professor Sauveur could have brought to life what was considered by many to have been dead and buried, and he so persuasively and convincingly proved to us by his experiments the existence of something that the followers of that new cult "X-Ray and Crystal Structure " would have us believe is simply alpha iron. And Dr. Mathews from his wide practical experience was so easily able to convince us that austenite was not only the most wonderful of the iron-carbon series, but that it was the wonder alloy of the future. If I were to follow in the footsteps of my distinguished predecessors, I would talk to you about martensite. But when I had planned this lecture, I found that I was writing about Professor Howe and his work and his influence on the science of metals of today, and that martensite had become the secondary theme. And when finally I was obliged to choose a title, I remembered that it was in 1901 I came from Roberts-Austen with a letter of introduction to his very dear friend, Henry Marion Howe, at the Columbia School of Mines, to continue my work at the next bench to Dr. Mathews. Since then a quarter of a century has gone by, and during that time all branches of science seem to have been remade, so great has been our advancement in knowledge and discovery. And now that Metallography has finally established its place as an important branch of science, with its own textbooks and literature, I would like to review what seem to me to be the most important advances we have made in the last 25 years. To do this, I would start with Howe's "Iron, Steel and Other Alloys," and end with Jeffries and Archer's " Science of Metals." In the preface of the former, Professor Howe wrote: My warmest thanks are due to the friends who have aided me with their counsel and knowledge. In particular, let me thank most sincerely Prof. Margaret E. Maltby

Jan 1, 1926

Discussion of the paper of R. J. COLONY, presented at the New York Meeting, February, 1921, and issued With MINING AND METALLURGY No. 169, January, 1921. R. J. COLONY (author's reply to discussion).-The work of Sosman and Merwin on the system lime-ferric oxide, mentioned by Mr. Rankin, was not overlooked. When studying portland cements and portland-cement clinkers petrographically, however, the lime-iron compound was difficult to correlate with the very definite dicalcium ferrite described by those investigators, which possesses such well-defined optical properties. In portland cements, the calcium ferrite (or ferrate?) is an indefinite, fuzzy, and generally amorphous, or apparently amorphous substance that is distributed interstitially with respect to the other grains, from which it was very difficult to derive any satisfactory results. For this reason, the writer, tentatively, chose to regard it as related to the aluminate, and assigned to it the composition 3CaO.Fe203, which may be incorrect, however, as Mr. Rankin suggests.

Jan 8, 1921

By R. S. Montgomery

Laboratory experiments simulating rock drilling were conducted on a number of commercial grades of tungsten carbide in order to determine their wear rates when they are used as inserts in percussive rock drill bits. The test rock was Barre granite and tests were made at conditions similar to those of the carbide buttons near the periphery of a large, down-hole, button bit. In addition, some wear rate measurements were made at a low blow energy. Wear rates of these carbide buttons were an extremely sensitive function of their cobalt contents and hardnesses and were proportional to e-°.57Hup to a hardness of about 91 RA. The point of minimum wear rate, which occurs at about 92 RA, corresponds to the point of maximum compressive strength. Modern percussive rock drill bits have inserts of cemented tungsten carbide on their wear faces. These inserts have drastically reduced bit wear in comparison to that of earlier all steel bits. The most common cemented carbide grade used in percussive rock drill bits contains about ten weight percent cobalt, although grades containing more or less cobalt are also used. Contrary to the case with carbide in metal-cutting tools, alloying materials are rarely used in mining grades. There are a number of designs of rock bits in current use. The most common form is an X bit which has four chisel-form radial wings. The button bit is another important design and one which has been recently developed. This design uses a flat steel face studded with relatively small hemispherically tipped carbide buttons. These types are illustrated in Fig. 1. Studies have been made of the sliding wear of cemented tungsten carbide on rock 1-4 and multiple-impact fracture', 5-6, b~t there has been comparatively little published on the percussive wear of this material although the wear of the impact face is the most important. There is some available data on the rate of dulling of rock bit inserts in actual drilling 7 but no laboratory studies. Sliding wear studies are useful for understanding the wear of coal and mineral cutting tools and gauge wear of percussive drill bits. but the

Jan 1, 1970

By Jack L. Taylor

As expected from similar crystal structures and favorable atomic size factors, titanium, vanadium, and molybdenum are completely soluble in one another above the transformation temperature of titanium. The fl phase parameters of the continuous solid solution are shown graphically. Limiting compositions for retained fl phase have been determined. VANADIUM and molybdenum both have body-centered-cubic structures at all temperatures and, from the atomic diameter comparison factor, 3.9 pct, would be expected to form a complete series of solid solutions. The existence of complete solubility has been confirmed by work' at the Jet Propulsion Laboratory. Furthermore, vanadium and molybdenum have favorable atomic size factors to form complete binary solid solutions with the B phase, high temperature form of titanium, which also has body-centered-cubic structure. Pietro-kowsky and Duwez' and Hansen et al." have established the existence of the complete series of solutions in these binary systems. It would be logical, therefore, to expect that p-titanium, vanadium, and molybdenum would be completely soluble in one

Jan 1, 1957

By L. H. Simons, H. H. Spain

I NT RODUCTION Theory indicates that linear water-floods should exhibit scaling and stabilization properties in both oil-wet and water-wet porous media'. Experimental verification of these proper-ties in oil-wet media was obtained some time ago', and more recently, Perkins', employing a high permeability unconsoli dated sand and a low oil-to-water viscosity ratio, has obtained flooding data in a water-wet medium which follow the pattern of scaling and stabilization. Also, Root and Calhoun3 have found similar trends in the displacement of gas by liquids from unconsolidated sands. In general, however, the experimen-tal evidence appears still somewhat conflicting since scaling and stabilization of water floods in water-wet media has not been observed in most of the studies to date'.".'. The purpose of this paper is to provide a more comprehensive picture of waterflood behavior in water-wet media and to corroborate the validity of the scaling and stabiliza-tion concepts. The need for differentiating between the intrinsic nature of water-oil displacements inside a porous medium and perturbating secondary end effects is discussed, pertinent experimental procedures are outlined and the results of flooding tests conducted at low and at high oil-to-water viscosity ratios on con- solidated, water-wet Alundum cores are analyzed. END EFFECTS IN WATER-WET MEDIA Outlet End Effects The peculiar feature of the outlet end effect in water-wet cores is that it not only results in an excessive wetting phase saturation at the outflow face,'.' but that it also retards the moment of water breakthrough: i.e., causes an undue delay in the appearance of water in the produced effluent. Conditions existing in a water-wet core when water first arrives at the outflow face are schematically shown in Fig. 1. At this flooding stage the saturation distribution, Fig. la, has not yet been distorted by the outlet end effect. A water-invaded pore at the outlet core face, opening into the oil-filled void space between the end of the core and the end plate of the flooding cell, is illustrated in Fig. lb. The curvature of the water-oil interface is concave toward the outlet, and the pressure on the water side of the interface is lower than on the oil side by an amount equal to a certain capillary pressure (Fig. lc). Before the water (of this particular pore) can be produced from the core, it is apparent that the pressure in the water phase must exceed that in the oil outside the core. Accordingly. when water first reaches the outlet face, it will not leave the core but will accumulate inside, and only oil will be produced. Eventually, as the water injection is continued. sufficient pressure is built up in the water to reverse the curvature of the interfaces in the outlet pores, and only then will water be produced from the core. This stage, illustrated in Fig. 2. corresponds to the conventional "water breakthrough" observed in flooding experiments. For purposes of discussion, it is convenient to distinguish between the flooding stage at which water first arrives at the outlet face of a core (Fig. 1) and the stage at which water is first produced from the core ( Fig. 2). The former will be referred to as "water arrival" and the latter water breakthrough. In oil-wet media

By Chester A. Fulton

SUPPLYING as it does a necessity for healthy animal and vegetable phosphate production is a most important industry. We human beings also are animal as this war so surely proves. Unlike many other elements no substitnite is available for phosphorus or its compounds. Marvelous as are modern plastics none can lake the place of phosphorus in making hone structures. As meassured in these times the phosphate industry is not a large industry. Output of phosphate rock, the original source of our agricultural and ,chemical phophates amounts to only some twelve million long tons per annum in the entire world. Phosphates are compounds of phosphorus, which is always found in nature combined with other elements. It never occurs in nature as such. The first choice of the element phosphorus is tie itself strongly to oxygen and then to water moisture - thus becomeing phosphlic acid. This phosphoric acid in turn hunts around for a base such as lime for instance and together they make phosphate of lime.

Jan 1, 1944

THE solid nonmetallic inclusions present to some extent in all commercial steels have been variously designated. In early references they were usually called slag inclusions, and this terminology is still retained to some extent. On the premise that all nonmetallic matter produced in a metallurgical process is slag, this can be justified. We have come to think of slag, how- ever, in a more restricted sense, and calling these particles slag inclusions is further objectionable because it fosters the erroneous concept that they are actually incorporated portions of furnace slag. Rarely is this true. The term sonims (coined from solid nonmetallic impurities) was proposed many years ago but never came into common use. In general, the term non- metallic inclusions seems to be satisfactory and adequate. NATURE AND CONSTITUTION OF NONMETALLIC INCLUSIONS From the standpoint of origin, inclusions fall naturally into two classes: (1) those occurring as a result of reactions taking place in the body of molten or solidifying metal and (2) those resulting from mechanical incorporation of refractories or other materials with which molten steel comes in contact. The former are by far the more numerous and have been called indigenous, natural, or native inclusions. The latter are by their very nature sporadic in occurrence and have been called exogenous, accidental, adventitious, or foreign inclusions. They are often referred to as the "slag-stringer" type, though here also the material is not likely to be furnace slag. Substances Found in Inclusions. Nonmetallic inclusions are composed principally of oxides and sulfides but carbides and nitrides sometimes play an important role. In the case of indigenous inclusions the reactions by which these particles are precipitated from molten or solidifying steel may be caused by: (1) oxidation such as may occur during refining or during tapping and teeming, (2) deoxidation by added alloys, (3) change

Jan 1, 1951

By A. W. Schlechten, R. P. Abendroth

Jan 1, 1960

By Eugene R. Rice

There are many methods for determining the meridian, but all of those in common use involve at least two separate observations, one for latitude and one for azimuth. Such observations made upon a south star at any hour are open to the objection of possible inaccuracy due to ignorance of the absolute refraction, and also to slow change in the altitude of the star when near the meridian. The method of observing a circum-polar star at elongation. besides requiring a separate observation for latitude, is open to the serious objection that clouds may obscure the star at the critical moment. Moreover, a tedious wait for the star to come to elongation is sometimes necessary. Many of us can recall 'long, cold, weary vigils, waiting for Polaris to reach elongation. For observing a circumpolar star at any hour, not only the latitude, but also the true time, must be known. This it is practically impossible to obtain, except in regions reached by the telegraph, and usually then one has to know the longitude also, in order to reduce " standard time" to " local time." The results obtained by this method, when the star is at culmination, are not very good, unless the true local time is absolutely known. The methods of obtaining the nleridian from the sun, by means of a solar attachment, or by direct observation, while good, are not absolute, by reason of refraction, change in declination of the sun, and small change in vertical angle, when the sun is near the meridian. For these two methods, latitude, time, and approximate longitude have to be known. In the method here described, only one observation is needed, and from it are computed azimuth, latitude, aud sidereal time. In other words, one call observe a circumpolar star—Polaris

Jan 1, 1911

By G. E. Frantti

UNDER the auspices of the Geophysical Committee of Michigan College of Mining and Technology, an investigation was made in Michigan's Upper Peninsula to obtain geophysical data" related to the regional subsurface geology in the area covered by Paleozoic sediments. The area surveyed includes that portion of the Upper Peninsula which lies between R18W to R26W and T41N and T49N, covering approximately 1300 square miles. On the index map, Fig. 1, it is represented by the cross-hatched zone west of Munising. Four of the five sites of detailed investigation are indicated by the letters A, B, C, and D. A detailed gravity and magnetic survey had previously been conducted by J. G. Wilsonz near Perkins, 8 miles north of Rapid River, on a local anomalous area. Results of his work, which showed a large positive magnetic anomaly associated with a gravity anomaly, aroused interest in the possible economic significance of the formations underlying the Paleozoic sediments in this part of the Upper Peninsula. Early in the 1900's the Michigan Geological Survey, as well as many private companies, had done a considerable amount of dip needle work near the southwest corner of the area discussed in this paper. Most of the information available to the writer was obtained from indicated magnetic anomalies on the geological map of the northern peninsula of Michigan. Results of the geophysical activities of mining companies in the vicinity of the Marquette range and Gwinn district were unavailable to the author. Physiography and Geography: The region under consideration has low to moderate relief. About half the area is comprised of swampy lowlands, and because of the swamps and forests much of the land is almost inaccessible. The major drainage system is dendritic, with streams flowing into Lake Michigan on the south and Lake Superior on the north. The general geology, shown in Fig. 2, indicates an overlay of Paleozoic sediments on pre-Cambrian formations along a line running approximately south from Marquette (not shown on the geological map). Actual contact between pre-Cambrian and Paleozoic sediments is not known because most of the area is covered with glacial till, and outcrops are very scarce. Exposures of the Paleozoic sediments show that these beds in the northern areas dip gently under Lake Superior and that in the southern areas they 'dip gently to the southeast. Outcroppings of the pre-Cambrian formations occur primarily to the west of the surveyed area except in the northwest corner where the Laurentian series outcrop as far east as the Gwinn district and also in T46N, R24W. Instrumentation: Gravity measurements were made with the Worden portable gravity meter. Since this was chiefly a reconnaissance regional survey, both the large and small dials were used. The instrument used had a constant of 0.0035 milligals per scale division, a working range of about 25 milligals.

Jan 1, 1957

Jan 1, 1962

By B. A. Wilcox

ThERE are several reports in the literature which indicate that both solid-solution hydrogen and hydride precipitates can promote low-temperature em-brittlement of tantalum.1-3 For example, Imgram et al.2 showed that hydrogen additions in the range of 140 to 580 ppm promoted a ductile-to-brittle transition at slightly above room temperature in both wrought and recrystallized tantalum. This contrasts with the observation that tantalum of norma1 purity is very ductile, even at liquid-nitrogen temperature. Imgram et al. also found that hydrogen additions caused a deterioration of notch tensile properties of tantalum. The purpose of this communication is to present some limited evidence that hydrogen can also cause fatigue embrittlement of tantalum. The material used in this investigation was wrought, stress-relieved (1000°C, 1 hr), are-melted tantalum rod (5/8-in. diameter) containing the following impurities in weight percent: 0.005 C, 0.007 02, 0.0005 H2, 0.003 N2, 0.08 Cb, 0.01 W, and 0.01 Fe. Hydrogen charging was done in an atmosphere of flowing dry hydrogen for 3 hr at 600°C, followed by an homogenizing anneal in purified argon for 15 min at 600°C, and cooling in an argon atmosphere. Typical micro-structures of the hydrogen-free and the hydrogen-charged materials are shown in Fig. 1(a) and Fig. 1(b), respectively. Fig. 1(b) shows the appearance of hydride precipitates which, in many cases, formed preferentially parallel to the rod axis. The hydride dispersion was uniform across the diameter of the specimen. The fact that the precipitate was a tantalum hydride was tentatively confirmed by X-ray diffraction on a metallographically prepared surface. After hydrogen charging, chemical analyses by vacuum fusion revealed the hydrogen content to be 0.0295 wt pct. In addition, the oxygen and nitrogen contents were slightly raised to 0.0095 O2 and 0.005 N2.

Jan 1, 1964

By E. H. Crabtree

IN an ideal mill, with perfect milling operations, the mineral extraction would be 100 per cent, the, concentrate would be 100 per cent mineral, the tailing would assay zer.0 mineral and the milling cost would be zero dollars. Such an operation can, of course, never be attained. We can only strive to approach it as nearly as possible and in doing so most recognize .the fact that the three primary factors in milling: assay of concentrate, assay of tailing, and cost of operation bear a definite economic relationship to each other. This relation will change from time to time and will be different for different mills, depending on milling equipment, character and quality of feed, market conditions, and other factors. It is granted that for a given operation there is an economic point, but the location of this point is difficult. It is for the purpose of making some of these economic points a little more tangible that this paper has been prepared.

Jan 1, 1930

By R. N. Zitter

PRESENT work was done in connection with a program for obtaining a low energy gap semiconductor suitable for photodetection. The inter-metallic compound InSb, which is now being in-

Jan 1, 1959

By NONE N

Jan 1, 1963

By C. H. Wayman, D. W. Fuerstenau

The effect of bubble size and concentration of certain reagents on the terminal velocity, shape, path, and drag coefficients of single air bubbles in distilled water has been investigated. Bubbles of a certain size range rise considerably faster than Reynolds number-drag coefficient relationships predict, whereas a small amount of frothing agent reduces their terminal velocity. The rapid velocity at which bubbles rise in distilled water appears to result from slip at the boundary and from circulation within the bubbles. Surface-active agents retard bubble motion through prevention of both circulation and slip at the boundary. A surface tension concentration gradient helps maintain bubble sphericity. HE gas phase is one of the indispensible in-gredients in flotation operations. Flotation depends on the collision of an air bubble and a mineral particle in a pulp and their ability to remain in contact long enough for adherence to take place. Before it is possible to understand the mechanics of air bubble-mineral particle encounter, it is necessary to learn more about the nature of bubbles themselves before collision with a mineral particle has taken place. To date, little work has been done on air bubbles in flotation systems. In 1945 Fahren-wald' presented a study of the role of frothers on air bubbles and on aeration in flotation, and recently Wark and Sutherland' discussed the work of Rosenberg- in relation to flotation. The research reported in this present article was undertaken to investigate systematically the effect of bubble size and the concentration of certain reagents on the terminal velocity, shape, path, and drag coefficient of single bubbles in distilled water. Most of the work is concerned with the effect of a-terpineol on bubble motion in water, but studies were made with potassium chloride, potassium hydroxide, potassium ethyl xanthate, and potassium amyl xanthate. Experimental Method and Materials: To obtain free bubble rise and reduce wall and surface effects, the investigators used a tank of 5½x5½x30-in. internal dimensions, filled with water to within 4 % in. of the top.' The tank was made of acrylic plastic so that the walls would have good optical properties. Distilled water, which was re-distilled in a block tin still and saturated with air before each test, was used in all the experiments. All solutions were made with reagent-grade chemicals. During each experiment the water was at room temperature, and during the course of an experiment the temperature did not fluctuate more than 0.5°C. Since the experiments were performed over a period of six months, the temperature varied between 25° and 27°C. The temperature at which each series of experiments was conducted is recorded with the data. The experimental apparatus is presented dia-grammatically in Fig. l. Individual air bubbles were generated from purified compressed air through a capillary of 0.003-cm internal diameter at a rate

Jan 1, 1959

By D. Turnbull, H. N. Treaftis

Precipitation of tin from Pb-Sn alloys (lead-rich) occurs by the nucleation and growth of hemispherical cells which consist of tin lomelloe interspersed in the depleted solid solution. Nucleation and growth of these cells and the tin interlamellar spacing at various compositions and temperatures have been investigated. The interlamellar spacing increases approximately as the reciprocal of the logarithm of the supersaturation ratio. For constant initial tin concentration the concentration of cell nuclei increases with decreasing temperature to a limiting temperature-independent value. The kinetic results support the view that the cell growth rote is governed by the diffusion of tin along the cell boundary. In the main, the results confirm the authors' earlier deductions, drawn from resistometric and calorimetric data, about the precipitation mechonism. IT has been shown1, 2 that tin (ß) precipitates from lead-rich (a) PbSn solutions by the nucleation and growth of cells (cellular or discontinuous precipitation). These cells consist of tin lamellae, with a spacing 1, interspersed in a depleted a solution. Reorientation of a also accompanies cell growth. The kinetics of cellular precipitation of tin from lead have been measured by resistometric2, 3 and ca1orimetric1, 3 techniques. The time-transformation isotherms (t equals time; x, volume fraction of specimen transformed) of the initial rapid precipitation, which drains about 60 pet of the tin from solution, have been described by a kinetic law having the form x = 1 —exp (—bt n) [I] where n usually has the value 3.0. It was shown" that this law and the other kinetic facts can be explained satisfactorily if it is assumed that the cells grow at a constant rate and that all the cells nucleate in a time negligible in comparison with the period of cell growth before impingement. Thus, for hemispherical cells b = (2/3)pNG3 [21 where G is the rate of cell growth in cm per sec, and N is the number of cell nuclei per unit volume. The rapid rate of cell growth at low temperatures can be accounted for"' if it is assumed that the dissolved tin drains to the lamellae edges by diffusion along the sweeping cell boundary rather than by diffusion through the a crystal (volume diffusion). For cell growth governed by cell boundary diffusion it was shown, approximately G=2(X° - X° / X° ) DBA / l2 where A equals the thickness of the cell boundary; D R, the coefficient of diffusion of tin atoms within the boundary; and X° and X, are the atom fractions of tin in the supersaturated and saturated solutions, respectively. Zener8 had already shown that, where

Jan 1, 1959