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Erwin S. SperRy, Bridgeport, Conn.: The analysis of refined copper is a subject of great importance, and has not received the attention it deserves. Copper metallurgists, therefore, will welcome the paper of Mr. Heath with satisfaction. The state of the art of the chemical analysis of copper has been such that consumers, if they could not afford to run any risk, have been obliged to buy copper from the smelter having the best reputation, and a specification for copper to meet certain requirements could not be drawn up by the mere giving of the chemical constituents. Mr. Heath has brought the analysis of the copper to such a state that when a specification calls for copper " equal to Lake copper " one will know immediately what percentage of the pure metal to expect. It seems to be a pretty well established fact that the copper of Lake Superior is practically free from antimony and bitmuth ; and, with the exception of arsenic, the other elements are easily separated from copper by electro-deposition in an acid solution. The authorities differ in regard to the question whether antimony is deposited with the copper in an acid solution. Classen* recommends the employment of a solution containing 10 per cent. of free nitric acid, sp.gr.1.21, and the strength of the current from 0.3 to 0.4 ampere, in order to prevent the other metals from being deposited with the copper; and for this reason, I presume, the method has been generally used. I, myself, have been accustomed to use such a solution for the analysis of copper-alloys, but have found that for such alloys only a small quantity of nitric acid is necessary, if sulphuric acid is present in sufficient amount to give the solution the required conductivity.

Jan 1, 1898

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

Jan 1, 1923

Jan 1, 1923

By M. F. Hawkes

Austenite grain size has long been recognized by metallurgists as an important property of steels because of its influence on toughness, hardenability, ma-chinability and creep strength. Much research has been carried out on wrought steels to develop methods for disclosing austenite grain size, and to, provide knowledge of the grain-size characteristics of steels produced and heat-treated in various ways. Much less work in these fields has been done on steel castings; partly because, owing to the variable and complex microstruc-tures of cast steels, it is frequently very difficult to obtain results that are not questionable. The object of this investigation, therefore, was to establish, for a wide variety of carbon and alloy cast steels, suitable methods for disclosing austenite grain size and some knowledge of the grain-size variations to be expected. The steel foundryman is interested in austenite grain size at two different stages in the manufacture of his products; one is just after the steel is cast, and the other is after any reheating operation carried out above the critical temperature range. In both, it must always be kept in mind that the grain size being sought is actually a previous austenite grain size, and that the austenite no longer exists once the steel has cooled to room temperature. The prob-lem of the investigator is always to use evidence obtained from the structure at room temperature to deduce this previous austenite grain size, which was established the last time the steel existed at a temperature above the critical range. Since most steel castings today are at least annealed or normalized, the measurement of austenite grain size established by heat-treatment will he considered first. More than 50 commercially produced cast steels rcpresenting a wide variety of compositions and melting practices were used in the study. For each steel, grain-size determinations were made after each of three widely varying heat-treating schedules namely, one hour at I550'F, one hour at I700°F, and six hours at 1700 F. The list of steels and results obtained on them will be found in the appendix. (See page 530.) A discussion of the knowledge gained on the applicability of various test methods and on grain-size characteristics of cast steels in general follows. MEASUREMENT OF AUSTENITE GRAIN SIZE ESTABLISHED BY HEAT TREATMENT Methods Suitable foR Determining Austenite Grain Size after Heat-treatment at Ordinary Temperatures and Times It was desired, as one of the results of this investigation, to be able to recommend to steel foundries a method, or methods, of disclosing grain size best suited to accurate

Jan 1, 1948

By M. F. Hawkes

Austenite grain size has long been recognized by metallurgists as an important property of steels because of its influence on toughness, hardenability, ma-chinability and creep strength. Much research has been carried out on wrought steels to develop methods for disclosing austenite grain size, and to, provide knowledge of the grain-size characteristics of steels produced and heat-treated in various ways. Much less work in these fields has been done on steel castings; partly because, owing to the variable and complex microstruc-tures of cast steels, it is frequently very difficult to obtain results that are not questionable. The object of this investigation, therefore, was to establish, for a wide variety of carbon and alloy cast steels, suitable methods for disclosing austenite grain size and some knowledge of the grain-size variations to be expected. The steel foundryman is interested in austenite grain size at two different stages in the manufacture of his products; one is just after the steel is cast, and the other is after any reheating operation carried out above the critical temperature range. In both, it must always be kept in mind that the grain size being sought is actually a previous austenite grain size, and that the austenite no longer exists once the steel has cooled to room temperature. The prob-lem of the investigator is always to use evidence obtained from the structure at room temperature to deduce this previous austenite grain size, which was established the last time the steel existed at a temperature above the critical range. Since most steel castings today are at least annealed or normalized, the measurement of austenite grain size established by heat-treatment will he considered first. More than 50 commercially produced cast steels rcpresenting a wide variety of compositions and melting practices were used in the study. For each steel, grain-size determinations were made after each of three widely varying heat-treating schedules namely, one hour at I550'F, one hour at I700°F, and six hours at 1700 F. The list of steels and results obtained on them will be found in the appendix. (See page 530.) A discussion of the knowledge gained on the applicability of various test methods and on grain-size characteristics of cast steels in general follows. MEASUREMENT OF AUSTENITE GRAIN SIZE ESTABLISHED BY HEAT TREATMENT Methods Suitable foR Determining Austenite Grain Size after Heat-treatment at Ordinary Temperatures and Times It was desired, as one of the results of this investigation, to be able to recommend to steel foundries a method, or methods, of disclosing grain size best suited to accurate

Jan 1, 1948

Coal - Surface Mining Coal Preparation Coal Utilization Research and Development Health and Safety

Jan 3, 1976

By R. B. G. Yeo

Pronounced isothermal martensite formation at room temperature was measured dilatometrically in a steel containing 0.01 pct C, 24.9 pct Ni, 0.26 pctAl, 2.58 pct Ti and 0.25 pct Cb. It is shown that martensite will form isothermally if stabilization of the austenite-martensite transformation is eliminated by removal of carbon. The decarburization of two iron-nickel alloys allows isothermal transformation to martensite to occur at temperatures above their athermal Ms temperatures. In an Fe-22.4 pct Ni alloy, at the 0.008 pct C level, the Ms temperature during air cooling is 85°F higher than that during- water quenching-. At the 0.15 pct C level this difference is reduced to only 5°F. The introduction of carbon causes stabilization during air cooling which lowers the Ms temperature virtually to the same level as determined during mate?. quenching. Thus in the 0.15 pct C alloy, the Ms temperature is almost independent of cooling rate. It is suggested that rival theories of martensite formation should be reexamined in alloys of sufficiently low carbon and nitrogen content to eliminate the complication of stabilization. The Ms temperature of a steel containing 0.01 pct C, 24.9 pct Ni, 0.26 pct Al, 1.58 pct Ti and 0.15 pct Cb, solution treated at 1500°F and air cooled as 1/8-in. diam specimens, was found to be 57 °F. 1 However, when held for several hours at room temperature the steel hardened slightly and became appreciably ferromagnetic. Isothermal transformation to martensite was first revealed by Kurdjumov and Maksimova2 in an iron-base alloy containing 0.6 pct C, 6.0 pct Mn and 2 pct Cu. Most of the other studies of isothermal martensite have also been confined to highly alloyed steels which transform at subzero temperatures; for instance, DasGupta and Lement, 3 Cech and Hollomon, 4 Machlin and Cohen,5 Shih, Averbach, and Cohen.6 Averbach and cohen7 noted a rapidly decaying volume increase at room temperature in a steel containing 1 pct C, 1.5 pct Cr and 0.2 pct V. cina8 and Marshall, Perry, and Harpster9 have described the isothermal transformation to martensite at room and subzero temperature in stainless steels. Kurdjumov10 has recently reviewed the subject, noting that the isothermal formation of martensite can be observed only in the temperature range somewhat below Ms or below -50°C. The isothermal formation of martensite may be characterized as follows: 1) It occurs in steels of widely different compositions, the main prerequisite being a low transformation temperature. 2) The transformation occurs by the formation of new plates and not by the growth of old ones. 3) The isothermal transformation is suppresed by stabilization during slow cooling or holding at temperatures near room temperature. However, the factors governing this mode of transformation are still not fully understood. The formation of martensite isothermally suggests an activated process. The early theories of martensite formation did, in fact, utilize classical nucleation concepts. Kurdjumov 11 first proposed the presence of thermally activated nuclei of different sizes and compositions which would grow if they reached critical size during cooling. This treatment was enlarged and developed quantitatively by Fisher, Holloman, and Turnbull12,13 and was later reviewed by the latter two authors.14 Fisher15 associates Ms with a nucleation rate of one per cc per sec. At slightly higher temperatures the nucleation rate is so low that isothermal formation of martensite is not observed in reasonable times. At slightly lower temperatures the nucleation rate is so high that it could not be suppressed by rapid cooling. By judicious use of parameters Fisher 16 was able to obtain good agreement between classical nucleation theory and the incubation times of martensite formation.4 However the application of these principles to martensite formation in iron-nickel alloys15 predicts that an alloy containing about 30 pct (31 at. pet) Ni would not transform. The presence of an Ms temperature at -223° C in an alloy containing 34.1 pct (33 at. pct) Ni led Kaufman and cohen17 to reject the hypothesis of homogeneous nucleation in favor of the reaction path theory originally proposed by Cohen, Machlin and Paranjpe.18 This theory conveniently explains the formation of martensite athermally but becomes labored when dealing with isothermal formation. Kaufman and cohen19 did explain the isothermal activation of embryos by assuming it to be a result of the expansion of their boundary dislocation loops but this treatment predicts an upper temperature limit of isothermal martensite formation.

Jan 1, 1962

By H. M. Chance

The iron-ore deposits of the Hartville district are located near the new town of Guernsey, about 100 miles north of Cheyenne. The writer has been familiar with them since 1887, having visited the district several times for different clients— his last examination having been made in November and December, 1897. The deposits extend in a general N.E.-S.W. direction from a point in Section 33, Range 65 W., Township 28 N., on the west side of Whalen cañon, through Sections 4, 5, 6, 7 and 8 of Township 27 N. in the same Range, and over into Sections 1 and 12 of Township 27 N., Range 66 W. General Characteristics. The ore is a remarkably pure red hematite, extremely low in phosphorus, and carrying a small percentage of silica, as shown by analyses given below, and similar in many respects

Jan 1, 1901

By Norman Weiss

THE need for more efficient utilization of labor in the metal-mining industry has been the subject of several recent editorials in the mining press, and one attractive possibility for such improvement lies in the designing of future milling plants particularly with economy of man-power in mind. We are accustomed to think of mill design as the selection and coordinated arrangement of process equipment, but if labor is to be efficiently utilized it must be given early consideration in planning the new mill. There are three good reasons for economizing in labor: (I) to reduce costs, not only in the form of wages but also in housing, hospital, welfare, and other obligations that a company accepts when a new man is added to the payroll; (2) to prepare for recurrent periods of manpower shortage, during which a well-designed plant can manage to get along with skeleton crews; (3) because a milling plant that must depend upon an inordinately large labor force for its operation and maintenance is certain to be inefficient in other respects, for many of the shortcomings in design that make necessary the excessive use of labor are generally not corrected merely by having too many men. A simple example of this is a poorly designed ore-feeding system: if this is inadequate to the extent that one man must be constantly unclogging feed chutes, it may help the situation to put two men or three at this task instead of one, but the feed rate will still be inconstant. First of the factors that affect labor saving is the location of the mill. This is often determined by transportation costs alone, and as a result the mill may be placed close to the mine regardless of the nature of the terrain. The designer must then adapt his layout to the conditions, favorable or not. This happens often at small properties, where capital investment may seem more important than operating expense. In most instances, however, a mill site carefully selected for the advantages it gives the designer in laying out the plant is the most economical in the long run, even if it involves a slight increase in cost of ore haulage. Given some freedom of choice, the design engineer may be able to find just the piece of ground that provides the proper gradient for the needs of the flowsheet, permits installation of essential yards and trackage, and perhaps supplies an excellent site for a tailing dam. Further justification for having placed the mill not too close to the mine sometimes emerges only years later as an opportunity to treat ores from other properties. When it is known from the beginning that the new mill will serve a number of scattered mines, a free choice of mill site is naturally stimulated. The most important single factor in limiting the labor requirements of a mill is its materials-handling system for bring-

Jan 1, 1946

By A. G. Allten

EXAMINATION by metallographic and X-ray diffraction means of an austenitic steel containing 0.06 pct C, 1.26 pct Mn, 0.38 pct Si, 21.15 pct Ni, 18.72 pct Cr, 3.07 pet W, and 9.14 pet Mo indicated that a - phase, which had not been reported in the literature, existed in this steel. Both the s and car-bides of the M6 C type were present in the as-forged steel. The carbides dissolved completely in the aus-tenite at approximately 2200°F (1205°C). The s, however, was present at all temperatures up to the solidus temperature of the steel at approximately 2375°F (1300°C). Ferrite was not found in any condition of the steel. The faintness of some of the s lines in X-ray patterns obtained from samples of the steel made it desirable to isolate the s prior to verification of its entire pattern. It was found that the s phase could be separated from samples of the steel which had been water quenched from 2250°F (1230°C) by dis-

Jan 1, 1955

By F. F. Hintze

Petroleum production in the Rocky Mountain district during 1929 registered a small decline from that of the previous year, conforming with a gradual decrease in the amount of oil produced during the last few years. A number of causes may be mentioned to account for this result, chiefly overproduction in other regions and the apparent desire of operators in this territory to conform to the policy of proration and retrenchment adopted by special agreement among operators in many of the fields. Unit operation has been adopted to control oil production from the Sundance sands in the Salt Creek field, Wyoming, in line with the general effort to stabilize this phase of the industry and prevent excessive drilling of new wells. Another factor which greatly retarded development in the Rocky Mountain region was the executive order of President Hoover issued in March refusing the award of new prospecting permits to future applicants and threatening cancellation of all existing permits upon which actual drilling had not been done as specified by law. Only four states in the Rocky Mountain region are important oil producers. In 1929 Wyoming led with an average daily output of 52,600 bbl., followed by Montana, with 10,730 bbl.; Colorado, with 6500 bbl., and New Mexico with 2700 bbl. daily average. These states bear the following percentage relation to total production in the Rocky Mountain district: Wyoming, 72; Montana, 15; Colorado, 9; New Mexico, 4., (Table 1.) The total average daily production was approximately 73,000 bbl. and the total production of all four states during the year was 26,534,606 bbl. This is 2.7 per cent. of the total oil production of the United States during this period. Colorado Although Colorado is not a large producer of oil and natural gas, its oil operations are widely distributed over the state. The Florence field is one of the oldest oil fields in the country, and there are good reasons for believing that the state will retain its place for many years to

Jan 1, 1930

By GILBERT C. DAVIS

ANY thought of Morenci naturally includes its sister town of Clifton, its gateway to the outside world. Clifton, the country seat of Greenlee County, is the terminus of a branch line of the Southern Pacific railroad from Lordsburg, N.M. Carload freight incident to the Morenci operation moves from Clifton over Phelps Dodge?s standard-gauge industrial railroad. Private freight must be hauled by truck. These two communities fell far short of supplying adequate housing for the personnel concerned with the new operations so a new townsite, Stargo, was developed adjacent to Morenci. Here 234 housing units with garages have been built and twenty similar units have been erected near the reduction works.

Jan 1, 1942

By AIME AIME

THE week, of April 5 will long be remembered by those that attended the Birmingham meetings of the Open-Hearth and Blast Furnace committees of the A.I.M.E. Iron and Steel Division. Birmingham iron and steel own received the 450 delegates with open arms; described and discussed their southern metallurgical practices and problems and compared experiences with their northern brother metallurgists in two days of technical sessions on Wednes-

Jan 1, 1937

By W. A. Wall, R. L. Kidd

IN present-day flotation practice, grinding of the flotation feed is carried to extremely fine sizes, 70 to 80 per cent minus 200 mesh being customary. The greatest flotation losses occur in the coarsest and finest sizes, but the losses in the very fine sizes are, of course, much the more important because of the large proportion of fines in the feed. These losses are particularly high in zinc ores so a study of the effect of size on the flotation of sphalerite has been made. The mineral used in these experi¬ments was a pure sphalerite, especially free from copper, from the Joplin district in Missouri. The sizes coarser than 200 mesh were separated by screening, the sized mineral then being deslimed on a Wilfley table. The sizes finer than 200 mesh were obtained by water elutriation as described by H. R. Bradford (M. S. Thesis, University of Utah, 1932) ; particles finer than 6.5 microns could not be obtained with the apparatus used.

Jan 1, 1933

By Frank W. Harris

The strength of hard drawn copper wire is a question of considerable importance to both manufacturer and consumer. Unlike steel and alloy wires, in which strength is governed by both chcniical and physical considerations, t,he high conductivity required for copper wire in the clcc-trical industry generally precludes the possibility of obt,aining tensile strength through the use of alloys. Consequently, this strenglh is largely a rnatter of the ~hysical structure, and all factors known to affect this structure, such as rolling temperature, die contours, lubricants, drawing speeds, etc., arc matters of prime importance. The experiments described here have becn carried out dl~ring the past year at the Baltimore plant of the American Smelting & Refining Co., in connection with a general investigat,ion of sorne of the questions mentioned above, with the object of studying thc physical ~t~ructure of hard drawn copper wire and the influence of ccrtain factors on t,hat st'ruct.ure. The work has been of an exploratory nature, rather than con~prehensivc., but it was thought that the result,s might prove of sr~fficient general interest tjo warrant their publicatlion. The bulk of the hard drawn coppcr wire used in places where strength is an important factor is rnanufacturcd to strict specification, based USU-ally in the United States on thab of t,he Arrlerican Society for Tcst'ing Materials (B-1-23). This specification calls for almost as high a, valuc of t,ensilc strength, consistent with elongation, as it is possible pract'icnlly to obtain, and only physically perfect mlaterial can be relied on to lliect such a specification. Obvious defects, such as laminat'ions protluc:etl through fins in bhe original rods or brittleness duo lo ovt~rdrawing, arc. usually recognized and need only passing refercncc. Laminatlions can be detected by twisting and untwisting the wircx several times; they will show up on the surface in the form of fins. Pig. 1 shows a very bad example of this defect. Thc wire may bc perfectly smooth before twisting hut, when such larrlinations arc3 prcstmt they will readily show up under this treatrncnt. This trouble is caliscd by sirriilar defects in the original rod produced by overfills in rolling. Fig. 2 shows the cross-section of the rod from which thc wire in Fig. 1 was drawn.

By G. R. Speich

The age-hardening of Fe-18 to 21 pct Ni marten-sites containing small amounts of titanium, aluminum, copper, or molybdenum has been studied by hardness measurements, transmission electron microscopy, extraction replicas, and X-ray and electron diffraction. Electyon-probe microanaly-sis of the extracted precipitates was also performed. The effects of temperature and composition on the aging kinetics have been studied in detail for Fe-20 pctNi-Ti martensites. All the martensites hardened on aging at 400" to 500 "C with a single aging peak. In the Fe-20 pct Ni-Ti martensites hardening was associated with the formation of a fine dispersion of NisTi. No precipitation was observed in an Fe-21 pct Ni-2.6 pct A1 alloy, although the hardness increased from 327 to 545 Dph during aging at 500°C. Copper was precgitated from an Fe-20 pct Ni-10.7pct Cu alloy, at least during the later stages of age-hardening. Hardening in an Fe-18 pctNi-5pct Mo alloy was associated with the precipitation of an intemzetallic compound tentatively identified as NisMo. The formation of austenite and the recovery of the defect structure of the martensite occur simultaneously with the normal precipitation processes &ring aging of these alloys. THE age-hardening of substitutional iron-base martensites is an important subject for study since age-hardening is one of the principal means of strengthening the substitutional iron-base martensites in precipitation-hardening stainless steels1 and maraging steels.a~4 In contrast to Fe-C martensites, these martensites are relatively soft and ductile in the as-quenched condition, due to the low solid-solution hardening effect of the substitutional elements as compared to carbon. Also, these martensites are hardened by aging at low temperatures in contrast to Fe-C martensites which generally soften on tempering. Titanium and aluminum, singly or in combination, as well as copper and molybdenum, have been the principal alloying additions to stainless steels to obtain an age-hardening reaction.' Ti-A1 or Co-Mo-Ti combinations have been used in the case of maraging steels.3"4 The present work has been confined to a study of the age-hardening characteristics of an Fe-18 to 21 pct Ni martensite to which small amounts of titanium, aluminum, copper, and molybdenum were added in order to study the effects of each alloying element separately. The age-hardening characteristics of these alloys were studied by hardness measurements, transmission electron microscopy, extraction replicas, and X-ray and electron diffraction. Electron-probe micro-analysis of the extracted precipitates was also performed. The types and dispersion of precipitates, the formation of austenite, and the recovery of the defect structure of the martensite all were studied. EXPERIMENTAL PROCEDURE Alloys. The compositions of the alloys studied are listed in Table I. The level of 18 to 21 pct Ni was chosen to assure complete transformation to martensite on quenching and is the same nickel level used in maraging steels. The concentrations of titanium, aluminum, copper, and molybdenum were chosen after a study of the and Fe-Ni-MO' ternary diagrams indicated how much of each alloying element could be dissolved in austenite. Alloys with 2 and 4 pct Cu were also studied, but these did not show precipitation hardening at the nickel levels studied and will not be discussed further. The alloys were prepared from electrolytic iron and high-purity* nickel, titanium, aluminum, copper, and molybdenum by vacuum melting of 20-lb heats. These were vacuum-cast into two 8-lb ingots. The ingots were hot-rolled at 1100°C to 1/2-in. plate and subsequently cut into 3/8-in. cubes. The cubes were sealed in evacuated quartz capsules and solution-treated for 16 hr at 1100°C, except for the Fe-20 pct Ni-10.7 pct Cu alloy and Fe-21 pct Ni-2.6 pct A1 alloys which were solution-treated for 16 hr at 1300" and at 1250"C, respectively. Metallographic examina-

Jan 1, 1963

By John V. Beall

Let's start at the beginning, Mr. Turner. Where and when were you born? In Lansing, Mich., on July 31, 1880. And what was your education? I went to the University of Michigan, where I got an A.B. degree in 1902; then to the Michigan College of Mines at Houghton, graduating from there in 1904 with a B.S. and an E.M. What was your first job in the mining industry, Mr. Turner, and what were you paid? In the summer of 1902, 1 was a field assistant for the U. S. Geological Survey in southwestern Idaho and southeastern Oregon, working under Israel C. Russell, professor of geology at the University of Michigan, who incidentally, had just returned from an expedition to study the effects of the eruption of Mt. Pelee, on Martinique. I was paid $60 a month and found; in addition to doing geologic and hydrographic work, I cooked many of the meals for a party of four, and wrangled four horses. I slept for four months under the stars, without a tent.

Jan 1, 1949

By L. S. Darken

IN the study of reactions occurring in liquid iron, alone or in contact with a liquid oxide or slag phase, it has been found that the experimental data over a limited range of concentration can in some cases be repre-sented satisfactorily by the simple equilibrium expression K - (p1)p1 (p2)p2 . (R1)r1(R2)r2 . where (P) denotes the concentration of a product and (R) the concentra-tion of a reactant in the reaction r1R1 + r2R2 + . . . Some of the reactions for which it holds are listed in Table 1. For others, however, the simple equation apparently does not hold. This has been attributed to an improper method of expressing concentration (for instance, weight per cent instead of mol fraction); or it has been supposed that the solutions are not ideal in the sense that the activity of a com-ponent is not proportional to its true mol fraction, But it may be that the problem has been oversimplified by neglecting some molecular species actually present; that is, by considering only the ostensible simple com-ponents and thus leaving out of account possible compound formation. It is the purpose of the present paper to point out how, in a group of related cases, a reasonable consistent assumption relative to the presence of a compound makes it possible to express the experimental data satis-factorily by the simple equilibrium expression when this compound is taken into account, and to bring into harmony data referring to different reactions in liquid iron. There are several a priori reasons for believing that solutions in liquid iron should not deviate far from ideality, provided that the concentration of solute is not too great and is expressed in proper terms. The factors that commonly lead to nonideality in systems at ordinary temperature as ionization or the occurrence of polar and nonpolar molecules-are presumably less effective in metal and in slag systems at high temperature. Again, the type of equation commonly used to express the value of

Jan 1, 1940

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'' 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' 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