Search Documents

By R. J. Cowan

IN the art of cementation a controversy has been going on for years as to whether solid or gaseous carbon is the active agent in carburizing steel. More recently opinion has crystallized into a compromise to the effect that carburizing is a gaseous cementation of steel in the presence of solid carbon. The importance of this theory has a particular bearing upon the work to be described. In the art of carburizing, use is commonly made of such words as "catalytic," "atomic," "nascent" and "activated;" in an attempt to describe the process. These words are used indiscriminately. For, instance, the gas is said to be "catalytic" and carbon to be "nascent," or vice versa. In using these expressions, investigators are confirming the acceptance in their minds of the active conditions of both gas and carbon in the cementation process.

Jan 1, 1931

Abadilla, Quirico A. Catanawan, Tayabas, P I '20 Abbey, Robert Graham, District Mgr., The W. W. Sly Mfg. Co, 50 Church St, New York, N. Y. '21 Abbott,-A. N., Mines Supt, Mazapil Copper Co., Ltd .. Concepcion del Oro, Zac., Mexico. '23 Abbott, Clarence E., Mgr, Mines & Quarries, Tenn. Coal, Iron & R R Co. 1242 Brown Marx Bldg, Birmingham, Ala. '04 Abbott, Louis Benjamin, Chief Engr, Consolidation Coal Co, Elkhorn Div . Jenkins, Ky. '15 Abeel, George H., Jr., Cons Min Engr... . Box 427, Santa Monica, Cal. '18 Abel, Albert E., Asst. to Pres., Valley Mould & Iron Corp Hubbard, Ohio. '19 Abel, Raymond L., Asst. Prof., Dept. of Pet. Refin , Univ. of Pittsburgh Pittsburgh, Pa. '28 Abernathy, George Elmer, Prof. of Geol. & Min., Kansas State Teachers College. Pittsburg, Kans '20 ||Abernethy, D. Carl, Jr. Min. Engr., Hudson Coal Co . Scranton, Pa '27 Abey, Hiroshi, Min. & Met. Engr., Min. & Met. Dept, The Higher Technical School, Osaka, Japan. '17 Aborn, Robert H., Instructor in Met, Harvard University Cambridge, Mass. '19 Abozeid, Mahmood, Pet. Production Engr., Marland Oil Co Ponca City, Okla. '20 Abraham, Arthur W., Geol, Richfield Oil Co. Box 788, Bakeisfield, Cal. '20 Abraham, W. E. V., Member, Geol Staff of Burmah Oil Co, Ltd Nyaunghla. Upper Burma, India. '23

Jan 1, 1923

By Stanley D. Michaelson, Norman Weiss

This was a year of realization. Some years are for planning and development, some for designing and building, others for fulfillment. With greater hopes and plans for the future than ever before, the year 1954, nevertheless, will be remembered principally because of project completion. Among copper mines, for example, there were Silver Bell, Copper Cities, Bisbee, Yerington, and White Pine. In iron, there were the Humboldt, Coleraine, Cerro Bolivar, and Eagle Mountain. In asbestos, Johns-Manville's new mill at Asbestos, Que. In uranium, completion of the ninth mill on the Colorado Plateau-Kerr-McGee's at Shiprock, N. M. In research, 1954 marked the completion of Kennecott's Research Center in Salt Lake City, one of the historic forward strides in the science of minerals beneficiation. The year was fruitful in other directions as well. Investigations of a fundamental nature were on the upswing, and pilot plant projects have also increased in size and number. Progress in new reagents and equipment was greater than normal. It can already be conservatively predicted-from the technological point of view-that 1955 and 1956 will be tremendous years.

Jan 3, 1955

By Donald Barton

THE theory of gravitation is based on Newton's law that any two bodies exert a mutual attraction which is proportional to the product of their masses and inversely proportional to the square of the distance between them; i. e., A =KRM/R2 (1) where K is a constant, M and m are the respective masses of the two bodies, and R the distance between them. In the earth's gravitational system, the earth is one of the bodies; the other may be any body within or without the earth. In theoretical dis¬cussions and calculations in regard to gravity, that other body usually is taken as a unit of mass: in the C. G. S. system, a body of one gram in mass. GRAVITY AND LEVEL SURFACES Gravity is defined in geophysics as the force of attraction exerted by the earth, towards itself, on a body of unit mass. The intensity of gravity is usually expressed in dynes of force or in centimeters of acceleration. In geophysical work in America, most commonly it is expressed in dynes (per gram) with the "per gram" understood and not directly expressed. In geophysical work in Europe, most commonly it is expressed in centimeters per second per second (cm./sec.2) and less commonly merely as centimeter-gram-second units (C. G. S.). At sea level, the intensity of gravity amounts very nearly to 980 dynes. The vertical is the direction along which the attraction of gravity is exerted at any point. . In most cases, it is very nearly, but not quite, per¬pendicular to the earth's surface. The path that would be taken by a body falling freely through space toward the earth is vertical at each point and may be spoken of also as "the vertical," or as the line of the vertical, or as a line of force of gravity. At the earth's surface it com¬monly is very nearly, but not quite, a straight line.

Jan 1, 1928

By Wing L. Lew

LEAD, silver, and zinc, in quantities of economic importance are found in the Aguilar ore. The lead occurs as galena and the zinc as sphalerite and marmatite. The silver occurrence is more complex. Pyrargyrite and proustite have been identified only occasionally. Galena is silver-bearing and so are the various other sulphides, though to a lesser degree. The principal nonsulphide gangue minerals include calcite, quartz, wollastonite, rhodonite, and various calcium, aluminum, and iron silicates. A typical analysis of, the ore is: Pb, 11.2; Zn, 12.3; Fe, 4.4; Mn, 2.2; Cu, 0.15; S, 11.2; CaO. 7.6; "Insoluble," 50.1 percent; and Ag 263 g per ton. Crushing is done in three stages. The primary crusher at the mine is set to deliver about a 5-in. product. The crushed ore is then transported to the secondary crushing plant by a 3-km cableway where the general practice is to hold the product of the first Symons to about 1 in., and of the second Symons to about 1/2 in. When the ore is soft and rich the product of the first Symons is by-passed directly to the ball-mill bins. Dust control in the secondary crushing plant is effected by enclosing the dust-emanating sources and exhausting the enclosures with a Clarage No. 18 fan driven at 1300 rpm by a 20-hp motor. Use is also made of spray water at one or two critical places. Every effort is made to keep the air free from visible dust. Dust counts taken at the working places show dust concentrations of less than six million particles ner cu ft. The composition

Jan 1, 1947

By H. W. Gillett

MAINTENANCE of membership by the technical so¬cieties and the activity of these societies in spite of the adverse business situation have been noteworthy. This forcibly brings home the fact that industry recognizes that sound technical guidance is well worth its cost. The numerous difficulties and losses due to defects of various kinds arising from gas-metal reactions are now generally recognized and interest in these problems is widespread. The forthcoming A. I. M. E. round-table discussion of gas-metal problems will do much to clarify the situation and will permit us to assay our present knowledge and to suggest the proper direction for profitable future research. "The Age Hardening of Metal" was the title of the annual I. M. D. lecture delivered by Dr. Paul D. Merica. A critical review of the known facts relating to age-hardening phenomena was first given, followed by the presentation of a theory correlating the detailed observations which have been made regarding the mechanism of the hardening.

Jan 1, 1933

Jan 1, 1888

By A. G. Metcalfe, A. Siede

The hardening of annealed copper during fatigue testing appears to be independent of the applied stress and to occur largely within the first 4000 cycles. Copper hardened by fatigue is more resistant to annealing than copper hardened by static means, and softens by a multistage process. Creep studies at 300°C show that copper hardened by fatigue also has greater resistance to creep than statically hardened copper. Some theoretical explanations are discussed. RECENT interest in the behavior of metals subjected to fatigue stems from observations of phenomena which could not be explained by current theories of the structure of metals. In 1953 Bullen et al.l showed that the hardening caused by fatigue at low stresses did not cause severe bending of the lattice as did hardening by static methods. This was later confirmed by Wood, 'and Broom and Ham.3 Clarebrough et al4 showed that as the stress level used in fatigue hardening was increased, bending of the lattice was introduced, eventually approaching that of metals deformed by conventional cold-working methods. The type of hardening introduced by fatigue has other interesting characteristics. Kemsley5 showed that copper fractured by fatigue at low stresses resisted annealing as compared to copper hardened an equal amount by static means. The work of Clarebrough etal, shows that the manner of energy release during annealing differs for fatigue-hardened and statically hardened metal in both magnitude and temperature range of release. In addition to hardening of the lattice, fatigue has been shown to cause softening in materials previously hardened by static methods,5 and also in age-hardened alloys.7 The superposition of a small fatigue stress on the static loading of high-temperature alloys has been shown to increase their resistance to creep.' The present work was an attempt to determine the relationship between fatigue hardening, resistance to annealing, and the creep properties of pure copper. EXPERIMENTAL PROGRAM The program described here was designed to answer three questions: 1) Can stress-cycle combinations well below the failure values give significant increases in hardness? 2) Does hardening, under different stress-cycle combinations, give increase resistance to annealing? And if so— 3) Does superior resistance to annealing confer superior creep properties over statically hardened material? Three-quarter hard OFHC copper was annealed in vacuo at 550°C for 1 hr to produce a strain-free material having a fine grain size and uniform hardness. (The standard deviation of the mean hardness of the annealed samples was less than + 1.9 Dpn). Annealing was performed after machining the fatigue specimens so as to avoid work-hardened surfaces. Jigs were used to avoid distortion. The fatigue properties of the annealed copper were determined using an accurately aligned Baldwin-Sonntag SF1-U machine operating at 1800 cycles per min. This limited the minimum number of cycles which could be examined to about 4000 stress reversals. Since failure resulted in specimen damage, hardness increase with number of cycles was measured by testing specimens fatigued to different fractions of the failure values. The results are shown in Fig. 1, and are superimposed on the S-N curve of the copper in Fig. 2. The resistance to annealing of fatigue-hardened material was compared to that of material hardened by uniaxial tensile straining. Specimens hardened to equal values by both methods were progressively annealed for 1 hr at temperature in vacuo. After each annealing treatment the hardness was measured using a Leitz Durimet hardness tester with a 500-g load. At least five tests were made for each hardness determination. The standard deviation for individual specimens varied from 0.26 to 1.48 hardness points. The results are shown in Figs. 3 to 5. The discontinuous nature of the annealing process has been brought out by drawing idealized curves through the data points. This can be justified by the consistency of the results as well as by general agreement with results of Kemsley.5 The creep resistance of fatigue-hardened and

Jan 1, 1960

CORPORAL SHEPPARD B. GORDY Sheppard B. Gordy, a brief biography of whom was printed inn the January Bulletin, entered the employ of the Braden Copper Co. immediately on his graduation from the Sheffield Scientific School in 1912. He remained with this company four years, working up through the various grades to assistant foreman and foreman to one of the individual mines. The last year he was in its employ, he acted as general mine foreman. He was for a short time with the Chile Exploration Co. and then went with the Andes Exploration Co. (Anaconda) and remained with CORPORAL SHEPPARD B. GORDY. the latter, doing mine exploration and development work, until he sailed for home in June, 1918, to give a more personal and active service to his country in her need. He declined a tender of induction into an officers' training camp, at the urgent request of Professor McClelland supplemented by Mr. Potter, because they demonstrated to his satisfaction that he could give more valuable service to his country in helping out with the aircraft production. Being within the draft age, in order to carry out this plan, it was necessary for him to be called by his Local Board and sent to camp. This call came Aug. 26. Two weeks before that time lie had gone to Dayton, Ohio; to begin the study of aircraft production, and was sent by the Dayton Board to Camp Sherman, Chillicothe, Ohio, where he died of pneumonia on Oct. 9.

Jan 3, 1919

By E. DeGolyer

WAR has wrought sharp and sudden changes in the pattern of the oil industry. The most obvious and most striking of such changes have been in the fields of transportation and refining. A third of the world's total oil production formerly started to market, tanker-borne, over the waters of the Gulf and Caribbean. Most of this oil went to our North Atlantic ports, supply points for the world's greatest consuming center. This tremendous traffic, disrupted by the loss of tankers as a result of requisition for military purposes and by the activity of enemy submarines, has had to be substituted largely by such lines of supply as could be improvised without loss of too much time. No single solution for this gigantic problem has been found nor is it likely to be entirely solved for some time to come. It has been solved in part, however, by rearrangement, reversals, and patching up of existing pipe-line systems; by overland transport of crude and products in tank cars on a scale never before attempted; by barging over inland waterways; and through the construction at long last of the "big-inch" line, the first leg of which is just being put into operation as far as Norris City, III. The tank-car traffic alone, reaching a peak of deliveries of 856,710 barrels per day into District 1 during the week ending Sept. 19, 1942, and accomplished at an expense of millions of dollars in extraordinary transportation costs, defrayed by the Defense Supply Corp. and by the mobilization of tank cars from all over the nation, is a story worth the telling but by some of those who directed it.

Jan 1, 1943

By Leon Borgman, Michael P. Lipkewich

Orebodies at or near the surface are generally amenable to open pit mining. The development of a mining program involves designing an ultimate pit and a production schedule. This pit maximizes total profit while the production schedule maximize6 the present value of the property. Optimum pit limits can be approximated by two-and three-dimensional numerical techniques. These techniques presuppose that the mineralized area has been sufficiently sampled to allow a reasonably accurate prediction of grade at any spatial location.

Jan 1, 1969

By W. F. Flanagan, K. R. Evans

The strong temperature dependence of the flow stress of bcc metals has prompted considerable interest and controversy concerning the rate-controlling influence of the Peierls' mechanism upon deformation in metals.18"21 Dorn and Rajnak" recently offered a criterion for Peierls' deformation utilizing a line-energy model of a dislocation to estimate the saddle-point activation energy, for the nucleation of a pair of kinks as a function of applied stress and the height and shape of the peierls9- barrier. It was found that Un/2Uk, where 2Uk is the excess energy of a kink pair, was a unique function of where is the effective stress and 7p is the Peierls' stress as defined in Fig. 20. The relationship found by Dorn and Rajnak between is given by the solid line of Fig. 21. may be expressed in terms of the temperature of test, T, and the athermal temperature, T,, defined in Fig. 20. Considering the strain-rate, 9, of deformation for a thermally activated process to be given by where fo is nearly a constant, it is seen that and the theoretical relationship of Fig. 21 may be examined with readily obtainable experimental parameters. Dorn and Coworkers analyzed a large amount of experimental data in this manner for materials sus-

Jan 1, 1967

By R. V. Whetsel, Valentin R. Garfias

Mexican petroleum production for 1928 was approximately 50,000,-000 bbl., the lowest in 12 years, showing a decrease from 1927 of over 14,000,000 bbl. The steady downward trend for the past 7 years has allowed Russia to outrank Mexico by a wide margin for third position and if the expected decline continues during 1929 it should place Persia ahead of Mexico as fourth in rank. The year 1928 was characterized by a continuation of the reentrench-ment previously begun by the oil industry in Mexico in an attempt to adjust itself to the adverse conditions caused by the steady depletion of the fields, the rapidly increasing competition from Venezuela and the United States and the as yet unsettled petroleum legislation and taxation situation. With the exception of the Isthmus of Tehuantepee, drilling in proved fields was considerably curtailed and although the number of wildcats completed exceeded those of the previous year, no extensive drilling programs were undertaken. Practically without exception, the major companies reduced personnel and operations to a point where they could meet existing conditions and mark time while awaiting a more stable basis for the future testing of unexploited regions. Many terminal and transportation facilities were abandoned during the year. Development Only 371 wells were completed during 1928, as against 583 in the previous year and 808 during 1926, and although the percentage of producers in 1928 was 34 per cent., compared to 26 per cent. in 1927, the initial production of -wells was considerably lower than during the previous year, a great number of the wells showing salt water and becoming "strippers" from the time they started to flow. Development is summarized in Table 1. Drilling in the Northern fields did not prove any new pools of importance, the most successful wells being located in the old producing areas of Cacalilao, Panuco and Topila. (Fig. 1 Very few of the producers made more than 1000 bbl. daily, and a great many less than 300 bbl. a day.

Jan 1, 1929

By Chas. A. Ashburner

The occurrence of oil- and gas-springs in the State of New York has been a fact of historical record since 1627, when the existence of the Cuba oil-spring was first recorded. The utilization of natural gas at Fredonia in 1821 attracted the attention of the public to the possibility of obtaining an illuminating gas by digging and drilling into the rocks. No active search was made, however, for oil or gas by the drilling of wells until after the discovery of commercial oil in Pennsylvania in 1859. In 1862 a well was drilled at Bradford, McKean County, Pennsylvania, but a few miles south of the New York state line, to the depth of 200 feet, in search of the oil-sand which had been found at Titusville, Oil City, and at other points in Western Pennsylvania. Immediately subsequent to this, other wells were drilled in search

Jan 1, 1888

By H. H. Rachford, W. P. Schultz

The use of computing machines to solve physical problems has made it imperative to represent physical data in a form computing machines can use. Although curve-fitting is an old and well-practiced art, there still seems to be some interest in questions regarding what methods can be used and why. Even though there are many good references on this subject, it may be of some value to discuss a particular method which has been found to be useful, and to make available the associated tables for its use in the hope that there can be saved a few of the tedious hours necessary to reduce many of the suggested methods to practice. Although a very brief discussion of the mathematical background of the tables is included immediately below, those interested only in their use can skip directly to the section on Use of the Tables. Direct Fit of a Set of Points A frequently encountered problem is: Given data which can be represented by a smooth curve +(x), to find an easy-to-evaluate function F(x), with only a few coefficients, which is a good approximation of +(x) on the interval 0 5 x 5 x,,. Consider F(x) as a linear combination of m + 1 arbitrary, single-valued, continuous, linearly independent functions, f,(x), Ff.r) = a,f,,(x) + a,f,(x) + . . . -+ aifi(x) + If the value of Q(x) is known or can be read from the curve at the points xj: +(x,), +(x,), . . . +(xj) . . . +(x.), and if n = m, then all the coefficients of F(x) can be determined, and F(x,) — +(x,) = 0 for j =. 0, 1, . . . n. This follows from the solution of the set of linear simultaneous equations. +(x<.) = aofu(x,) + aJI(x0) + . . . + a,,f,,(x,) =a, = f,,(x,) + a,f,(x,) + . . . + a,f,,(x,) +(x,,) = a,,f,(x,,) + a,f,(x,) + ... + a,,f.,(x,,) ...........(2) for the coefficients ai. Although the set a, from the solutions of the set of Equations 2 yields an fix) which gives an exact value of $(x,) for the n + 1 points, there is no restraint on ~(xj in the interval xi < x < xj+,. Indeed, if the points +(x,) are not sufficiently smooth, very serious differences may arise between F(x) in the interval and the smooth curve +(x). Least-Squares Fit It has been suggested&apos; that if n is made to exceed m, and the set a, is found to minimize the function the function F(x) is much less sensitive to small errors in +(xi), and usually provides a much better fit to the smooth function +(x). This is known as the best fit in the sense of the least-squares error. To minimize $, set £ = 0,i = 0,1,... iTi,.....(3) The m + 1 equations from Equation 3 are k—n k=n a.^p /,,(a) f,(xt) + a, X A: = 0 k=O k = n k = n k=0 k=0 +(x.) f,(x,),............(4) one equation being obtained for each i = 0, 1, . . . m. Inasmuch as the arbitrary functions f(x) may be evaluated for x,, k = 0, 1, . . . n, and the +(x,) are known values of the curve to be fitted, the simultaneous Equations 4 may be solved for the set a,. Particular Functions Given the functions fi(x) and the set +(xj), the solutions for require evaluating a number of sums of products as well as the solution of an m + 1 order set

Jan 1, 1956

By Walter Miller

DURING the second year of America&apos;s active participation in the war the main objectives of the petroleum refining industry were again to provide the four most important product needs for war: 100-octane aviation gasoline, toluene for TNT production, high-quality lubricating oils for the needs of aviation and the armed forces, and petroleum chemicals for synthetic rubber manufacture. All other materials supplied by the petroleum industry took an inferior priority ranking, depending on the degree of essentiality. To accomplish the above objectives the industry initiated and carried on a building program during 1942 and 1943 which will put those two years down in petroleum refining history as the greatest construction years of all time, a record which will hold for decades to come. Led by an estimated total of $900,000,000 going into 100octane and contributory plant investment, it is easy to picture a total of two billion dollars and more going into additional refining-industry plant investment during 1942 and 1943, most of it privately paid for, but a substantial part covered by R.F.C. Government money financing.

Jan 1, 1944

By AIME AIME

MODERN metallurgy is an art and a science. The art is process metallurgy-extracting metals from their ores, refining them, and alloying them with one another and with certain nonmetals to produce thereby a variety of metallic materials which, owing to a wide range of useful properties, are for many purposes more valuable to man than the individual metals themselves; process metallurgy also includes shaping or otherwise treating metals and alloys to form objects useful to a complex industrial world. The science is physical metallurgy-organized knowledge of the constitution and internal structure of metals and alloys, of the relation of their composition and structure to properties, and of the laws, theories, and hypotheses that purport to explain this relation.

Jan 1, 1942

By Ralph Hultgren, Bernard York, David W. Mitchell

It is a well-known fact that magnesium-alloy castings are apt to be coarse grained if the melt is not superheated several hundred degrees above the melting point before casting. (The casting temperature varies according to the shape of the mold. A typical casting temperature is perhaps 1400°F.) British practice is to heat to 900°C. (1650°°F.) for 15 min., cool rapidly to casting temperature, and cast.1 In Germany superheating is carried out at 850° to 900°C. (1560° to 1650°F.) depending on the amount of scrap used. It is stated that further refinement will be obtained by prolonging the period of superheating or by increasing the superheat temperature to 950°C. (1740°F.).2 In the United States superheating is carried out at i600° to 1700°F. (871° to 927°C.), perhaps even higher in some places. It is stated that superheating effects are found as low as 1500°F. (816°C.), but several hours are required.3 These commercial treatments lead to grain sizes in sand castings that may vary from 4 to 8 grains per sq. mm.§ in heavy sections and from 60 to l00 in 3-in sections to perhaps 380 in thin sections. It is also generally known that the refining effect of superheating is lost if the melt is held for some time at lower temperatures before casting. Aside from these very qualitative statements, there is little to be found in the literature as to the effect of temperature and time of superheat on the final grain size. Because of the uncertainty of these factors, the Office of Production Research and Development of the War Production Board placed a research contract with the University of California, supervised by the War Metallurgy Committee. This research, which was done under the "Restricted" Project NRC-550, is the basis of this paper, which has been released for publication by the O.P.R.D. The material studied was an alloy prepared from carbothermic magnesium. The temperatures required for grain refinement proved to be widely different from those used in practice, as described in the statements in the first paragraph. This difference is attributed to the fact that the magnesium in the specimens was of carbothermic origin instead of the electrolytic magnesium in common use. MATERIALS AND METHODS The magnesium alloy studied was one of the most popular sand-casting alloys, with a nominal composition of 9 per cent aluminum, 2 per cent zinc, and 0.r per cent (minimum) manganese and the balance magnesium. This is designated

Jan 1, 1945

||Abad, Leopoldo F., Min Engr, Div of Mines, Bureau of Science Manila, P I &apos;23 Abadilla, Quirico A, Geol, Lago Pet Corp Box 172, Maracaibo, Venezuela &apos;20 ||Abbey, Robert Graham, The W W Sly Mfg Co Train Ave, Cleveland, Ohio &apos;21 Abbott, A. N., Mines Supt, Mazapil Copper Co, Ltd Concepcion del Oro, Mexico &apos;23 Abbott, Clarence E., Mgr, Mines & Quarries, Tenn Coal, Iron & R R Co, 1242 Brown Marx Bldg, Birmingham, Ala. &apos;04 Abbott, Louis Benjamin, Chief Engr , Consolidation Coal Co , Elkhorn Div Jenkins, Ky. &apos;16 Abbott, Robert R., Met Engr , Peerless Motor Car Co Cleveland, Ohio &apos;12 ||Abbott, Wells Osborn, Ray Consolidated Copper Co Hayden, Ariz. &apos;23 Abeel, George H, Jr., Cons Min Engr 4612 West 17th St , Los Angeles, Cal &apos;18 Abel, Albert E., Asst to Pres, Valley Mould & Iron Corp Sharpsville, Pa. &apos;19 Abernathy, George Elmer, Prof of Geol & Min , Kansas State Teachers College, Pittsburg, Kans. &apos;20 Abey, Hiroshi, Min & Met Engr, Min & Met Dept, The Higher Technical School, Osaka, Japan. &apos;17 ||d&apos;Ablaing, Philip R, Chem , Anaconda Copper Min Co Great Falls, Mont &apos;25 Aborn, Robert H , Research Assoc., Mass Inst of Tech Cambridge, Mass &apos;19 Abouchar, Sylvain Sley, Min. Engi & Geol , care of S H Sekaly, 13 Rue El Nimr, Cairo, Egypt &apos;17

Jan 1, 1923

By N. A. Gjostein

The formal descnption of the decay of an isolated scratch can be written in terms of an appropriate Fourier integral. With the application of certain approximations, this description leads to the second-moment analysis developed by King and Mullins. It is shown that the second-moment analysis does not adequately describe the behavior of a decaying, isolated scratch, and that it is difficult to obtain internally consistent values of the surface self-diffusion coefficient, D,,from this analysis. This inconsistency arises from contributions of higher-order moments to the decay process. Two new analytical methods, based on the Fourier integval representation of a scratch profile, have been developed for determining values of D, from the decay kinetics of isolated scratches. In the profile-matching method, a given initial profile is resolved into its Fourier components, the components are allowed to decay exponentially over an annealing time interval, At, and finally they are synthesized to form a decayed profile. The predicted profile is adjusted to fit the experimental profile by varying only the parameter, D,At; the contribution from volume diffusion is directly taken into account and the integrals involved in the Fourier analysis are evaluated by numerical integration on an electronic computer. In the kinetic method, the widths, W, of a series of predicted profiles are determined for various volume-diffusion contributions, and the results are plotted in the form W vs DSAt. For a fixed ratio of surface to volume diffusivities, R, these plots are linear; the slope of the lines increases as R decreases. A simi-lar analysis can be performed on the depths of the predicted profiles. In this case, plots of (l/df3 vs D,At are found to be nonlinear. The proper value of Ds is found by superimposing the data for the experimental widths and depths on Plots of this kind and adjusting Ds until a fit is obtained with the line having the appropriate value oj R. An analysis of the slopes of these plots for R —= (surface diffusion only) reveals that they do not give the correct value, 2276, for width tf second-moment standard profile. This finding allows one to modify the second-moment analysis in such a way as to obtain internally consistent values of Ds. ThERE are several processes, involving a flow of matter along a surface, due to gradients in curvature of the surface, that may be used to determine the surface self-diffusion coefficient, Ds. These processes are commonly known as 1) thermal grooving, 2) single and 3) multiple scratch decay, 4) blunting of field-emitter tips, and 5) sintering. In this series of papers, the first three of these processes are examined in detail in an attempt to subject the phenomenological theories governing these processes to a critical test and, furthermore, to make a critical comparison of the values of D, obtained from these techniques. Although the thermal grooving technique has been established&apos;&apos; as a reliable method for determining D, , this has not been the case for the process of scratch flattening. Mullins and coworkers374 have proposed phenomenological laws governing the growth of the width and the decay of the amplitude of an isolated scratch, but only in one study5 has the width-growth law been supported by experimental evidence. In paper I of this series detailed experimental evidence is presented that points up the deficiencies of the second-moment analysis; the origins of these deficiencies are also discussed. Following this development, some new analytical procedures, based on representing the scratch profile by Fourier integrals, are presented as a means of obtaining reliable values of D, from the kinetics of the scratch-flattening process. Further applications of the Fourier integral approach are reported in papers 11&apos; and 111,~ where the method has been useful in interpreting the anisotropy of flattening rates of isolated scratches (paper 11) and in describing the multiple scratch decay process (paper 111). THEORY OF SCRATCH DECAY Following ~ullins" approach we consider an arbitrarily shaped scratch profile, Fig. 6, at some time, t. The profile is designated by a function z(x,t) which can be expressed in terms of a Fourier integral as follows:

Jan 1, 1967