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E. E. THUM,* Salt Lake City, Utah (written discussion?).-While the present paper is confined exclusively to the microstructure of fusion welds, it may be of interest to draw attention to certain appearances existing in resistance welds such as spot or butt-welded joints produced by the Thomson process. For instance, a butt weld between two pieces of carbon tool steel (carbon about 0.90 per cent.) will show concentric ellipsoids of the various materials from pearlite to martensite. The surfaces of demarcation are quite well defined, the center of the ellipsoid being at the intersection of the axis of the piece and the plane of the weld. Often these unannealed welds show a troostitic center; evidently this core was not quenched as rapidly as the surrounding shell. Such specimens are beautiful samples for instruction purposes. An annealed butt weld of this kind will show a very well defined central ellipsoid of decarburized, materials. It is interesting to consider the reason why this change takes place. It must be understood that the heat is on the metal for a very short time, possibly 30 sec. It is therefore evident that the decarburization, or migration, of the carbon takes place with extreme rapidity. Since no blowholes are evident in a well-made butt weld, the deoxidizing air and the products of combustion must migrate with the highest speed; second, the carbon might migrate back into the stock; or, last, a large proportion of the pearlite may be extruded with the hot metal, which forms a fin at the plane of weld. Examining these possibilities in detail, it is not probable that such deep-seated decarburization, extending with maximum effect to the very center of a 2-in. round bar, is done by reaction with the oxygen of the air. This would postulate entrance of oxygen and egress of carbon oxides in large quantity without leaving behind traces in the form of oxides or

Jan 5, 1919

By John V. Beall

BROMO Seltzer blue has gone to war. The blue of the Bromo Seltzer bottle is a product of cobalt, the Nation's No. 1 strategic metal. When the National Production Authority, on Nov. 21, 1950, ordered a 70 pct cutback in domestic use of cobalt, a stab of pain was felt in the hearts of the glass, porcelain enamel, steel, paint, pottery, and electrical and electronic equipment industries. The reason: A full-scale wartime economy with astronomical requirements for jet engines, high velocity projectiles, armor plate, electronic equipment, and the many products needed to win a war. There is little potential comfort for cobalt users in nonessential manufacturing, and the military will be pinched for optimum supplies of the metal. However, if proper measures are taken immediately and current plans are completed, in two years there will be far more cobalt available than ever before. When normal times return, cobalt supplies should be sufficient to meet peacetime military requirements, and greatly expanded domestic requirements that will result from new technological development for wartime but adaptable to peacetime products. The pres-

Jan 1, 1951

By E. P. Bayer

MESABI RANGE ore is mined largely by the open-pit method. This involves having available at all times sufficient working places which in combination will produce ore of guaranteed analysis. Fast- loading power shovels turn out under favorable conditions 1000 tons per hour from each unit. Each unit loads ore differing materially in analysis from that loaded by the others, One may load high grade, another low grade, and another may be in a mixed bank with the lead ore so placed that the product must be mixed at the shovel before it is loaded into cars. In such cases the bank is combed with the bucket, the door being left open to permit the material to fall through.

Jan 1, 1937

By P. H. Wendland

Calculations are presented for the design of a silicon photodiode in which the incident light beam makes multiple passes between the detector surfaces. Total internal reflection is used for this "light-trapping" effect. By this means, the optical path length can be extended to several millimeters, while the electrode separation remains less than 102 cm, as required for nanosecond response time. Data are presented for a Schottky barrier photodiode constructed on a multiply reflecting silicon base wafer. It is shown that the long-wavelength response is considerably extended in such structures without a corresponding sacrifice in high-speed response. The development of efficient and powerful lasers at 1.06 p has stimulated interest in detectors which operate at this wavelength. In typical silicon photodiodes, for detecting 1.06 p radiation, the requirements for high speed and high sensitivity are mutually exclusive. Since the absorption coefficient is only 25 cm-', a lo-'-cm path length is required to absorb 92 pct of the incident 1.06 p radiation. If the electrode separation is greater than 10 cm, however, the carrier transit time will be greater than 1 nsec. This problem can be solved by allowing the incident light beam to make multiple passes between the electrodes. The optical path length can then be extended to several millimeters, as required for complete absorption, while the electrode separation remains less than 10' cm, as required for nanosecond response time. In a typical photodiode geometry, one ohmic contact and one rectifying contact are formed on the two opposite surfaces of a base wafer, and the wafer thickness determines the electrode separation. The objective of the multiple reflection design is to allow all 1.06 p radiation to enter the detector front surface and to form the back detector surface so that no 1.06 radiation can exit. Total internal reflection at the back detector surface is well-suited for light trapping of 1.06 p radiation because the relatively large dielectric constant of silicon leads to a critical angle of 16.5 deg for total internal reflection. LIGHT TRAPPING It is well-known that, as light passes from one medium such as air into another medium such as glass or silicon, the angle of refraction is always less than the angle of incidence. In the limiting case, where the incident rays approach an angle of 90 deg with the normal, the refracted rays approach a fixed angle +, beyond which no refraction is possible: this is called the critical angle. It follows from Snell's law that where = critical angle, n - index of refraction of air, n' - index of refraction of the medium. Applying the principle of reversibility of light rays, all internal angles of incidence greater than +, will produce total internal reflection and "light trapping". The index of refraction of silicon at 1.06 p is 3.5,' and the critical angle is thus 16.5 deg. Fig. 1 shows these relationships for silicon. This very small critical angle in silicon is significant because all incident angles between 16.5 and 90 deg will produce total internal reflection and "light trapping". This effect can be implemented with a "prismlike" geometry, so that incident light can be introduced into the sample without loss and "trapped". PHOTOSIGNALS A precise knowledge of the absorption coefficient at 1.06 in silicon is of critical importance to the design of fast and efficient silicon photodiodes for 1.06 radiation. Dash and newman2 show a value of 25 cm-l, and our measurements have corroborated this value. Assuming that the collection of photoinduced minority carriers is perfect, the quantum efficiency of a photodiode is dependent only on the absorption coefficient. It then follows from Lambert's law that where QE is the quantum efficiency in pct, a is the absorption coefficient, d is the optical path length, and the reflectivity at the surface is assumed to be completely suppressed by an optical interference layer. Fig. 2 gives the maximum quantum efficiency for 1.06p radiation of a silicon photodiode with optical path length d, using Eq. [2]. The ultimate response time of a fully depleted photodiode to an incident light pulse can be considered to be the arrival times of all photoinduced carriers at the contacts, i.e., the minority carriers at the junction interface and the majority carriers at the oppo-

Jan 1, 1968

[L. W. KEMPF, Chairman E. E. SCHUMACHER, Past-Chairman E. A. ANDERSON, Senior Vice-Chairman A. A. SMITH, JR., Vice-Chairman 11. A. MALONEY, Treasurer ERNEST KIRKENDALL, Secretary 29 West 39th Street, New York 18, N. Y. Executive Committee 1947 C. Y. CLAYTON A. B. GRENINGER CURTIS PIGOTT 1948 WALTER BONSACK W. A. DEAN LOUIS JORDAN 1949 J. D. HANAWALT W. A. JOHNSON E. W. PALMER]

Jan 1, 1946

By N. Arbiter, C. C. Harris

In 1961, a research program started at Columbia into the mechanical aspects of flotation,* and certain ends are now in view. The purpose of this note is to explain these tentative conclusions in the hope of stimulating discussion and eliciting new data, especially industrial data, with which to test the views expressed. The variables presently under consideration are impeller rotational speed, N, volumetric air rate, Q, and impeller diameter, D, the latter being the parameter chosen to designate cell size. The most favorable *The latest work 1 references all previous publications. chemical environment is not under discussion since the procedures for establishing it are better understood than those for optimizing N and Q by virtue of a longer history of more intensive investigation. THE GRADE AND RECOVERY SURFACES With a given ore, chemical treatment, and flotation machine, both grade, G, and recovery, R, are functions of N and Q. The GNQ and RNQ relationships are best viewed in terms of three-dimensional surfaces (Fig. 1) which are experimentally determinate.2 TO maintain grade at an acceptably high level, it is necessary for N and Q to lie within certain limits, and similarly with recovery. However, the ranges of N and Q for grade on the one hand and recovery on the other are rarely the same. Selecting the single N

Jan 1, 1970

By Wayne Loel

THE application of aerial photographs to all phases of geologic mapping is set forth, indicating the advantages to be gained in different types of country and under varying climatic conditions, Methods of field and office procedure are given from a geological point of view, as well as suggestions regarding the best methods of aerial mapping for different uses and under varying field conditions, including the study of submarine geology. Aerial photographs with accompanying geologic maps are shown to illus-trate the appearance from the air of different geologic features under varying climatic and topographic conditions.

Jan 1, 1938

By J. M. Clark

(Wilkes-Barre Meeting, June, 1911.) For some years past, those interested in the development of the increasingly important mining industry of Canada, have urged the adoption by the Dominion Parliament of a federal mining-law, which would have the force and stability of statutory enactment. At present, placer-mining in the Yukon Territory, is governed by the Yukon Placer Mining Act. All other mining under federal jurisdiction is governed by 'Orders in Council and Ministerial Regulations. In the earlier stages of development, it is perhaps a matter of necessity that these important matters should be so dealt with; but it is now felt that the time has come when mining-rights in the extensive regions under federal control should be put on a permanent basis, -and that any changes required from time to time should be made only after full and open discussion in Parliament. A short sketch will suffice to indicate how vast and varied the interests affected really are. When the Dominion of Canada was constituted by the Imperial Statute known as the British North America Act of 1867 (which came into force by proclamation on July 1 of that year), it comprised only the present Provinces of Ontario, Quebec, Nova Scotia, and New Brunswick; but provision was made for the inclusion of Newfoundland, Prince Edward Island, British Columbia, Rupert's Land, and the North West Territories. Subsequently Rupert's Land and the North West Territories were acquired, the 'Crown Colonies of British Columbia and * SECRETARY'S NOTE.-Mr. Clark, an eminent Canadian lawyer, and joint author of the treatise on "The Law of Mines in Canada," has been requested by the Do¬minion Government to prepare a Federal mining-law, and presents this paper, by invitation of the Council, in order to obtain, if possible, useful suggestions from members of the Institute.-R. W. R.

Apr 1, 1911

By Charles Will Wright

FRANCE will be given a large portion of the Marshall Plan funds for relief, reconstruction, and industrial development in France and in her colonial possessions. At present that country is not in position to export any large tonnages of the mineral products needed in the United States. However, if, through Marshall Plan aid and private capital investment, production of these products can be largely increased, agreement should be made by which the United States is to get a substantial portion of such increased output in part payment for the material and technical aid they receive. France issued a decree, published in the "Official Gazette" on Feb. 3, 1948, which permits conversion into dollars of dividends derived from dollar investment in Government-approved projects and will agree to a scale of capital amortization to be determined in each individual case. This decree is to encourage private capital to cooperate with local capital in industrial undertakings. The French Colonial Ministry has prepared an extensive program for aid to the mining industries in overseas possessions to be undertaken by

Jan 1, 1948

By J. W. Hickman, E. A. Gulbransen

In a previous paper' the authors have investigated the structure of the oxide films formed on most of the metals that make up the alloys of this study. The metals were studied in order to provide basic information on the structures, both physical and chemical, of the oxide films and to determine how these structures are effected by the temperature, time of oxidation, and surface preparation. It was felt that an understanding of the physical and chemical structure as well as the stability of the oxide film might furnish clues as to the nature of the reaction process and the protective quality of the film. The oxidation of the metals was studied over the temperature range 300' to 7o0°C. except for copper, wherc the range selected was 100' to 500°C. The results of these studies were presented in graphical form as existence diagrams of the oxides on a time-temperature scale. For some of the metals the existence diagrams were simple and showed few chemical transitions, but there were numerous cases where the physical state of the oxide surface was a function of time and temperature. In general the physical state of the oxide surface changed with increasing temperature so as to increase the sharpness of the diffraction patterns and to cause orientation effects to be more pronounced. Deviatiois in lattice Darameters from X-ray values were noted. In general these deviations were of positive nature and may be due to solid solution of the metal in the oxide lattice. This effect might be expected in thin oxide films. In a study of the oxidation of alloys containing two or more metals, there may arise the complicating factor of identification of the oxides formed. A thorough understanding of the oxides formed on the pure metals, therefore, was, essential before investigation of the oxidation of alloys. In this paper it is our purpose to present a study of the following problems: 1. The existence diagrams of various alloys. 2. The effect of the structure of the alloying metal on the existence diagram of iron. 3. The effect of the percentage of chromium on the oxides formed on Fe-Cr alloys. 4. The relationships, if any, between the oxides formed and the protective quality of the oxides. The following alloys are included in this study: alloys of iron with body-centered cubic, face-centered cubic and other metals, 13 Cr-Fe, 18-8 stainless steel, K4²B, Nichrome V, Hipernik, Inconel, Stellite "²I," Refractaloy, Kovar, mild steel, a series of Cr-Fe alloys and a series of Co-Fe alloys. Since many of the commercial alloys in this list contain more than two metals, various complicating factors in the identification of the oxides formed may arise.

Jan 1, 1947

By E. A. Gulbransen, J. W. Hickman

In a previous paper' the authors have investigated the structure of the oxide films formed on most of the metals that make up the alloys of this study. The metals were studied in order to provide basic information on the structures, both physical and chemical, of the oxide films and to determine how these structures are effected by the temperature, time of oxidation, and surface preparation. It was felt that an understanding of the physical and chemical structure as well as the stability of the oxide film might furnish clues as to the nature of the reaction process and the protective quality of the film. The oxidation of the metals was studied over the temperature range 300' to 7o0°C. except for copper, wherc the range selected was 100' to 500°C. The results of these studies were presented in graphical form as existence diagrams of the oxides on a time-temperature scale. For some of the metals the existence diagrams were simple and showed few chemical transitions, but there were numerous cases where the physical state of the oxide surface was a function of time and temperature. In general the physical state of the oxide surface changed with increasing temperature so as to increase the sharpness of the diffraction patterns and to cause orientation effects to be more pronounced. Deviatiois in lattice Darameters from X-ray values were noted. In general these deviations were of positive nature and may be due to solid solution of the metal in the oxide lattice. This effect might be expected in thin oxide films. In a study of the oxidation of alloys containing two or more metals, there may arise the complicating factor of identification of the oxides formed. A thorough understanding of the oxides formed on the pure metals, therefore, was, essential before investigation of the oxidation of alloys. In this paper it is our purpose to present a study of the following problems: 1. The existence diagrams of various alloys. 2. The effect of the structure of the alloying metal on the existence diagram of iron. 3. The effect of the percentage of chromium on the oxides formed on Fe-Cr alloys. 4. The relationships, if any, between the oxides formed and the protective quality of the oxides. The following alloys are included in this study: alloys of iron with body-centered cubic, face-centered cubic and other metals, 13 Cr-Fe, 18-8 stainless steel, K4²B, Nichrome V, Hipernik, Inconel, Stellite "²I," Refractaloy, Kovar, mild steel, a series of Cr-Fe alloys and a series of Co-Fe alloys. Since many of the commercial alloys in this list contain more than two metals, various complicating factors in the identification of the oxides formed may arise.

Jan 1, 1947

By Arthur Philips

THE purpose of this paper is to present certain data and observations resulting from a series of experiments dealing with the heat treatment and microstructure of commercial white cast iron and its derivative, malleable iron. In planning the experimental work, particular pains were taken to secure for the tests white cast iron of "normal" composition; i.e., within the composition limits commonly prescribed by manufacturers of malleable castings. A review of the literature leads us to believe that much data of a fragmentary character treating of the graphitization of white cast iron have been of little value, mainly because of the diversity in chemical composition of the materials employed in the tests. Moreover, when feasible, annealing periods at least comparable to those of current practice have been adopted. We wish to acknowledge our indebtedness to the members of the research department of the Eastern Malleable Iron Co. for the white cast iron used in the tests and, particularly, for their active cooperation during the experimental stage of the work. In this paper the following subjects will be discussed in the order indicated: Data on the thermal critical points of white cast iron and malleable iron. Changes produced in tensile properties and microstructure of white cast iron by annealing at different temperatures within the range, 760 to 1100° C. Relation of thickness of wall section of hard iron to microstructure and tensile properties of malleable iron obtained under normal annealing conditions. Notes on mechanics of graphitization of normal white cast iron as observed in specimens quenched after various periods of anneal at approximately 800° C.

Jan 1, 1922

By E. G. Dahlgren, Dan O. Howard

THE West Edmond oil field, which covers parts of Oklahoma, Canadian, Kingfisher, and Logan Counties in the State of Oklahoma, is in geographical extent the largest single oil field found in the state. At the present time, its area of 26,800 acres is almost twice as large as the Oklahoma City field, which hitherto was the state's largest field. Many authorities believe that the West Edmond field is the most important oil pool found in the United States since Pearl Harbor. The discovery of the field without the help of geological, geophysical, or other recognized technical information, the fact that the oil and gas accumulated in a stratigraphic or wedge-type trap, and the rapid development of the productive area under wartime conditions are some of the interesting features of the field. The West Edmond field lies west of the Oklahoma City, Britton, and Edmond fields. The field is in an area that has been considered on the west flank of the Granite Ridge line of folding, on which a number of Central Oklahoma's most important oil fields are located. Over a period of years, especially since the discovery of the new pools such as Oklahoma City, Edmond, Britton, and Crescent, the general area of the West Edmond field has been explored intensively by geological and geophysical methods. This led at times to the drilling of a few dry Wilcox sand tests.

Jan 1, 1945

By S. E. Maddigan

MANY experimental and theoretical investigations have been made on the processes involved in annealing and recrystallization of metals. Most of these, however, have treated the time element as constant and heat-treatments used have been for relatively short times. Aside from the early work by Carpenter and Elam,1 the few that have investigated the effect of time on the processes have usually done so for fairly short time periods. During recent years the growing interest in long-time creep properties of metals and alloys under stress has made increasingly important a better knowledge of the recrystallization during prolonged heating. The recrystallization temperature of 70-30 brass given by Clark and White2 in 1932 was somewhat above 400°F. (204°C.) but under 500° (260°C.), whereas in our laboratory recrystallization has been observed in creep specimens at 204°C, the lowest temperature of Clark and White's range. Since the creep properties are quite different above and below the recrystallization temperature, erroneous conclusions can readily be drawn by the application of short-time recrystallization data to creep problems. It was thus considered of both practical and theoretical value to make long-time annealing studies near the minimum recrystallization temperature. In this way useful additions could be made to data on recrystallization temperatures and, since the reactions in this range are relatively slow, additional insight could be obtained into the factors involved in annealing. Several comprehensive reviews of recrystallization processes have been written,3-5 therefore only a brief review of the generally accepted facts will be given here.

Jan 1, 1940

By E. C. Wright

FOR many years the cost of making pig iron and steel in the Birmingham district has been about the lowest in the United States. The close proximity of the important raw materials such as coal, iron ore, limestone, and the large available scrap supply made it possible to assemble all of the important ingredients necessary for steel- making with only nominal costs for transportation. Both iron ore and coal were being mined in this district at one time for about $1 per ton from underground operations. At that time mining wages were low everywhere and the labor rate in the South was considerably below that of other mining districts. This situation persisted until the emergence of labor unions as an economic and political force, emigation of southern labor to northern plants, and continued growth of industry in the South in the years following the depression of 1932. Since that time union organizing of miners and steel workers throughout the nation has increased labor costs in mining and steelmaking. This influence has been felt particularly in underground mining operations since the proportion of labor cost to total cost is still high. The previous advantage in basic labor rate in the South has been almost entirely eliminated by the equalization of labor rates in basic industries by national unions. Since 1945 these influences have been especially noticeable in increasing the cost of mining coal and iron ore in the South. The northern steel districts are still being largely supplied with iron ore from the Minnesota open-pit mines and the cost of this ore has not increased nearly as much as the cost of ore obtained from underground mines in Birmingham. A similar situation exists in coal mining; the thinner seams in Alabama are not so amenable to mechanization as the northern mines and, as a result, the output per man-day in southern mines is only about three tons of coal as compared to five or six tons per man-day in the large captive mines of West Vir-

Jan 1, 1950

THREE regional meetings are planned for this summer and fall following the spring meeting held under the auspices of the Iron and Steel Committee and the Ohio Section at Cleveland in April and in lieu of a general fall meeting of the Institute. Plans for all of them are maturing rapidly. Excellent programs and. interesting visits to points of local tech¬nical interest are already assured. THE SALT LAKE CITY MEETING This meeting will be under the auspices of the Milling Committee and the Utah Section. It will be one of the features of the joint convention held the week of August 22 to 26 with the Western Division of the American Mining Congress. The Congress will be responsible for the general arrangements and for the program on the first day. The following general committees have been appointed:

Jan 7, 1927

By Lord Marley

ACTIVE participation by the United States in the war acted as a stimulant on the Annual Institute Meeting in New York rather than a retardant as feared. Attendance was about 10 per cent under the all-time high reached last year, but considering the number of men who could not possibly come because of active military service and the additional number who are devoting their whole time and effort to turning out vital war materials, the registration was really greater than might have been expected. But all in all the Institute put on a show that taxed the capacity of the Engineering Societies Building as well as the capacity of the visitors to find time to attend everything that promised to be of interest.

Jan 1, 1942

By A. W. Gauger

Coal as mined contains varying quantities of inorganic components (mineral matter) which, on combustion, produce the residue known as ash. It has long been realized that the weight of this residue does not equal the weight of the mineral matter originally in the coal, because of the chemical changes that take place during the ashing process. Moreover, the ordinary ash analysis presents the ash as a mixture of oxides with little or no clue to the identity of the mineral species originally present in the coal. It is only for pyritic sulfur that an attempt is made to determine a mineral component. So far as the authors are aware, there are practically no experimental data in the literature as to the percentages of the different mineral species present in coal. The oft-quoted table of Marson and Cobb1 cannot rightly be considered as data, since the authors merely state that the table "shows the probable forms in which these ash constituents exist in coal." In view of the attempts to calculate analyses and determinations of the calorific equivalent of coal to the mineral-matter-free basis, as well as the importance of the mineral species in clinkering, combustion and coking, it seems strange that so few data are available on this phase of coal technology. For example, numerous empirical corrections for use in the scientific classification of coal have been suggested to compensate for the losses from the mineral matter during ignition of the coal to ash. These include multiplication of the ash percentage by various factors such as l 1/10 and 156, the use of the Parr unit coal formula (1.08 A + 22/40 S, where S = total sulfur) as well as certain modifications of the Parr formula that attempt to correct for the organic sulfur present in the coal. Although many experiments have been made to determine the loss on ignition of the clays associated with the coal measures and correction

Jan 1, 1934

By W. M. Robertson

The formation of grain boundary grooves on surfaces of poly crystalline samples of cobalt and iron immersed in liquid lead has been studied. The grooves form by volume diffusion of the solutes cobalt and iron in the liquid. The diffusion coefficients of the solutes in liquid lead are derived from the measured rate of grooving. The diffusion coefficients are described by the relation D = Do exp (-Q/RT), with, for cobalt, Do = 4.6 x 10-4 sq cm per sec and Q = 5300 ± 800 cal per mole, and for iron, DO = 4.9 x 10-3 sq cm per sec and Q = 10,500 ± 1500 cal per mole. LIQUID metal-solid metal interactions occur at solid-liquid interfaces. Interfacial energy provides a driving force to change the morphology of the interface. Mullins1,2 has derived expressions for the kinetics of interface morphology changes driven by capillarity. These expressions can be applied to an isothermal system of a solid in equilibrium with a liquid saturated with the solid. Surface profile changes can occur by volume diffusion of the solute in the liquid, by volume self-diffusion in the solid, and by interfacial diffusion at the liquid-solid interface. A groove will form at the intersection of a grain boundary with a solid-liquid interface, reducing the total interfacial free energy of the system. The solid-liquid interfacial energy ? must be greater than half the grain boundary energy of the solid ?6 for Mullins' calculations to apply. If ? is less than ?b/2, then the liquid penetrates the boundaries, separating the grains rather than forming grooves. Boundary penetration did not occur in the work described here. where CO is the equilibrium volume concentration of the solid in the liquid, Dv the volume diffusion coefficient of the solid in the liquid, ? the interfacial free energy of the solid-liquid interface, O the atomic volume of the solid crystal, k Boltzmann's constant and T the absolute temperature. Eqs. [1] and [2 ] also apply to grooving by volume self-diffusion in the solid,1 with CoODv = D Self, where DSelf is the volume self-diffusion coefficient of the solid. For a grooving mechanism of interfacial diffusion at the solid-liquid interface, the groove width is given by2 where CS is the interfacial concentration of the diffusing species, and DS is the interfacial diffusion coefficient. Eqs. [1] and [3] can be used to determine the mechanism of groove growth. A t1/3 dependence of the growth indicates volume diffusion and t1/4 indicates interfacial diffusion. In some cases, volume diffusion and interfacial diffusion both can contribute substantially to the grooving process, causing the time dependence to be intermediate between t 1/3 and t1/4.3 For these cases, the relative contributions of the two processes can be separated.4 However, in many cases, one process will be dominant, and the data can be analyzed on the basis of Eq. [1] or Eq. [3] alone. The time dependences for volume diffusion in a liquid and volume self-diffusion in a solid are the same. However, the self-diffusion contribution of the solid is usually negligible compared to volume diffusion in the liquid. After the grooving mechanism has been determined, Eq. [1] or Eq. [3 ] yields the kinetic parameter A or B. The kinetic parameter can be used to calculate values for the unknown quantities in the product CD?. Usually C is known or can be estimated. If ? is known, then D can be calculated. In a measurement of grain boundary grooving of copper in liquid lead,' the time dependence indicated volume diffusion in the liquid. The quantities Co, Dv, and ? were obtained from the literature, giving excellent agreement between the observed values of A and the values calculated from Eq. [2 ].5 In a study of the grooving of several refractory metals in liquid tin and liquid silver, A1len6 educed that grooves formed by volume diffusion in the liquid. In a study of nickel in a nickel sulfide melt, Steidel, Li, and spencer7 found volume diffusion grooving kinetics. Both Dv and ? were unknown, so they could not obtain either one separately, though they did obtain a reasonable value for the temperature dependence of the product Dv ?. Several methods have been used to obtain surface profiles. It can be done by sectioning through the interface7 or by chemically removing the liquid from the solid surface after solidification of the liquid.6 However, if the liquid dewets the solid on removing the solid from the melt, then the interface can be observed directly. This method was used previously' and was utilized also in the present study. EXPERIMENTAL PROCEDURE Lead of 99.999 pct purity was obtained from American Smelting and Refining Co. Cobalt sheet was obtained from Sherritt-Gordon Mines, Ltd., with a nominal purity of 99.9 pct, the principal impurities being nickel, iron, copper, carbon, and sulfur. The sheet was

Jan 1, 1969

By E. Lifshin, R. E. Hanneman

QUANTITATIVE applications of the electron micro-beam probe frequently involve the evaluation of complex mathematical expressions and/or the analysis of large amounts of experimental data. The purpose of this communication is to describe briefly a versatile and useful computer program system that is applicable to analyze rapidly a wide variety of practical microprobe problems. This system consists of a group of ten FORTRAN programs that can be stored on tape, cards, or in the memory disc of the computer. These programs, or links, can be run individually or in any prespecified sequence without interrupting the operation of the computer or without destroying information which is being transfered from one link to another. For the program system described here a GE-235 computer with disc storage was used, so that the DCHAIN method of program linking was employed. Included in the library are programs to: 1) initiate analysis of a new set of data and transfer control between all other programs in any predetermined manner; 2) generate theoretical calibration curves of composition vs relative intensity; 3) generate empirical deviation parameters from least-square fits of experimental calibration data from standards of known composition; 4) convert raw X-ray data to corrected composition; 5) determine inter diffusion coefficients by Matano analysis of con centrat ion -distance data on a uniaxial diffusion couple; 6) determine activation energies and frequency factors of temperature-activated processes such as diffusion; and 7) generate calibration curves for determination of the thickness of thin films using microanalysis. A detailed description of these computer programs and their underlying principles is available on request from the authors."' The first program to generate theoretical calibration curves of corrected relative intensities vs composition uses the Poole and Thomas atomic number correction' and the Philibert absorption factor' with a voltage-dependent mass absorption coefficient for electrons in the alloy. A modified Castaing fluores- cence correction is also used which includes the effects of both Ka and KO radiation and over voltage.' Once the theoretical curves have been calculated in 1 wt pct intervals, these results are least-squares fit to obtain Ziebold deviation parameters' which are stored in COMMON in the computer memory. The net discrepancies between the original theoretical calibration curve and the regenerated curve using the Ziebold parameter are computed. Although this link is explicitly written for K-K fluorescent interactions, it can be applied to K-L, L-K, and L-L interactions as previously disc~ssed."~ Similar programs have also been written to utilize the Wittry fluorescence correction, Birks combined corrections, and various other corrections.' These modified programs have proved to be quite useful for quantitative comparisons of the results of the various theories. The program for conversion of raw X-ray data to corrected composition includes corrections for drift, backround, and instrumental dead time. The corrected intensities are converted to composition by use of the Ziebold equation"2 and parameter obtained from the program system. The results can be obtained for either atom or weight fractions. In addition to accurately computing interdiffusion coefficients the Matano analysis program calculates least-square smoothed values of concentration, concentration gradient, and curvature for each point on the raw input concentration profile. In order to obtain high accuracies a unique method of performing a least-square polynomial fit to incrementally advancing profile segments which overlap is used.' This program has been successfully modified for use in ternary diffusion problems3 and can readily be modified to handle analysis of diffusion profiles which include phase boundary discontinuities. This link is generally applicable to analysis of interdiffusion data obtained by other techniques as well as by the microprobe. The primary function of the next program is to least-squares fit experimental diffusion data to the normal Arrhenius function: D = Doexp(-Q/RT), to obtain values of Do and Q. In addition the probable error and one, two, and three u statistical confidence limits of DO, Q, and log D are evaluated. This program is also directly useful for analysis of any other simple temperature-activated processes including conductivity, and certain deformation and chemical processes. The program to generate calibration curves for film-thickness determination using the microprobe is based on a numerical integration of the equation derived by Cockett and ~avis.' Values of film thickness obtained by this program for copper on various substrates are in good agreement with measurements made by other techniques. Versions of the above program system have been prepared for use with or without a remote teletype connection to the computer for processing on either a real-time or time-share basis. The instrumentation coupling a microprobe to a teletype for automatic data collection and analysis by the presently described program system has been reported elsewhere by the authors.' If teletype equipment is not used to communicate with the computer, standard methods of card reading and tape reading can be used. In either

Jan 1, 1967