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By K. H. Hiller

A rotational viscometer has been designed which perrnits the measurement of the rheological properties of drilling muds and other non-Newtonian fluids under conditions equivalent to those in a deep borehole (350F, 10,000 psi). The important mechanical features of this instrument are described, and its design criteria are discussed. The flow equations for the novel configuration of the viscometer are derived and the calibration procedures are described. The data and their interpretation, resulting from measurement of the flow properties and static gel strengths of homoionic montmorillonite suspensiom at high temperatures and pressures, are presented. Data are also presented for the flow behavier of typical drilling fluids at high temperatures and pressures. The pressure losses in the drill pipe and the annulus depend critically upon the flow parameters of the drilling fluid. This work demonstrates the need to measure these parameters under bottom-hole conditions in order to obtain a reliable estimate of the pressure losses in the mud system. INTRODUCTION The rheological properties of drilling fluids are affected by temperature and pressure, but the extent of these effects on the dynamic flow properties is not well known. Measurements of changes of the flow properties of clay-water drilling muds with temperature have been reported by Srini-Vasan and Gatlin.1 The temperatures reported did not exceed 200F, a limitation imposed by the apparatus used by these authors. The rheological properties of clay suspensions were measured at temperatures up to 100C by Gurdzhinian.' Neither the nature of the exchange ions in the clay suspensions nor the degree of purity were defined in his work, nor were the measurements extended to currently used drilling fluids. The lack of systematic measurements of dynamic flow properties at high temperatures and pressures seems the more surprising since during the last decade the importance of the control of the hydraulic properties of drilling fluids has come to be widely recognized. Very good mathematical treatments of the friction losses in drill pipe and annulus have been developed.3 4 These treatments are based on the assumption that drilling fluids behave as Bingham plastic fluids. Quite often this assumption is justified, while in other cases a power law equation pro- duces better fit than the Bingham model does. For convenience in applying viscometer data to pressure-drop calculations, the Bingham plastic flow equation is preferable and, therefore, has been applied to the data reported in this paper, although other equations may fit these data more accurately. In a Bingham plastic fluid the relationship between the shearing stress 7 and the rate of shear D is given by the following equation: where is the plastic viscosity and 4 the yield point. If 4 = 0, the equation for simple Newtonian flow, 7 = pD, is obtained. Two empirical constants are required for the description of laminar flow of a Bingham plastic fluid, and calculations of the flow behavior at high temperatures and pressures cannot be better than is permitted by the accuracy with which these constants are known. For this reason a high-pressure, high-temperature rhe-ometer has been designed to measure the plastic viscosity the yield point +, and the static gel strength S, at pressures up to 10,000 psi and temperatures up to 350F. The important features of its design will be described. The results of measurements on homoionic clay slurries will be discussed insofar as they are relevant to an understanding of the general flow behavior of clay-water drilling fluids. The results of measurements on some typical drilling fluids will be presented also, and their practical implications will be briefly discussed. DESCRIPTION OF EQUIPMENT MECHANICAL FEATURES A viscometer designed to measure the plastic viscosity, yield point and gel strength of non-Newtonian fluids must permit the measurement of the shearing stress t at any given rate of shear D. This is possible only if t and D are approximately uniform throughout the entire sheared sample. A Couette apparatus is the most convenient method of realizing this condition, as has been pointed out by Grodde." The "high-pressure, high-temperature rheometer" described in this paper is basically a rotational Couette viscometer that is immersed in a cell in which pressure and temperature can be controlled over the range of interest. Fig. 1 shows schematically the important features of the pressure cell and associated equipment. The heart of the instrument is the rotating cup. It is shown more clearly in Fie. 2. which revresents the lower one-third of the pressure cell (below the input drive shaft shown in Fig. 1), and it is shown in detail in Fig. 3. For measurements of dynamic flow properties, the rotating cup is driven by a 1/2-hp electric motor, which operates through a Vickers

By C. R. Wohrman

A MELT of pure electrolytic iron with about 0.4 per cent. sulfur and 7 per cent. manganese was prepared in connection with a study of inclusions in iron. The alloy darkened rapidly when etched with a 10 per cent. alcoholic solution of nitric acid, and microscopic examination revealed the presence of a semimartensitic, semi-Widmanstättian structure (Figs. 1 and 2) closely resembling the structures found by Benedicks in his artificially prepared "meteoric iron." 1 The structures found by Benedicks were readily explained by the presence in his alloy of the two well known iron-nickel solid solutions, taenite and kamacite, and of their eutectoid (?) aggregate, plessite. By analogy, one would infer the existence of similar phases in the iron-manganese alloy just described, such as inference being strengthened by the similarity displayed in many ways by nickel and manganese in their effects on iron. IRON-MANGANESE ALLOTS ARE REGARDED AS HOMOGENEOUS Heterogeneity of iron-manganese alloys has not been recognized heretofore, judging from the data of standard metallographic books and those of original papers. In fact, iron and manganese are quite generally regarded as completely miscible in the solid state. Dr. Rosenhain,2 for example, writes: Alloys of group (a), of which those of gold-silver, iron-manganese, and copper-nickel are examples, when allowed to crystallize sufficiently slowly to attain their condition of final equilibrium, present a microstructure exactly similar to that of a pure metal-the homogeneous character of the molten solution is in that case so completely maintained that the microscope cannot detect the presence of any second constituent.

Jan 1, 1927

THE first session of this meeting was held Tuesday evening, in the chamber of the Common Council, the President, Mr. David Thomas, in the chair. Mayor Carroll, of Troy, gave a cordial welcome to the Institute, which was responded to, on behalf of the Institute, by the first Vice-President, Mr. R. W. Raymond. The Council reported the names proposed for membership with recommendation for election. The following named gentlemen were duly elected: Anthony, J., . .Williamstown, Pa. Babcock, George, . . .Troy, N. Y. Blake, Theo. A., . . . . . . Sa n Francisco, Cal. Blossom, T. M., . . . . . . New Pork. Boalt, James A., . . .San Francisco, Cal. Bowman, Amos, . . . . San Francisco, Cal. Chester, Prof. A. H., . .Clinton, N. Y. Dewey, C., . Pittsfield, Mass. Dock, Gilliard, . Shamokin, Pa. Emerson, O. D., . .New York. Endres, John J., . .Pittsburgh, Pa. Firmstone, Frank, . Easton, Pa. Fowle, W. B., . Philadelphia, Pa. Frazier, Prof. B. W., . . .Bethlehem, Pa. Gardner, George A., . New Pork. Goodyear, Watson A., . .6an Francisco, C al. Griswold, Chester, . Troy, N. P. Griswold, J. A.,* . . .Troy, N. Y. Hague, J. D., . . .San Francisco, Cal. Hahn, 0. H., . .Eureka, Nev. Harkness, T. C., . . . . . . Wilkes-Barre, Pa Harris, Samuel, . . .Hudson, N . Y. Henry, &. T., . Oxford, N. J. Holley, A. L., . .Brooklyn, N. Y. Howe, H. W., . . .Troy, N. Y. Hunt, Dr. T. Sterry, . Boston, Mass. Jannet, J., . Troy, N. Y. Knapp, John A., . .New Pork. Laughlin, Henry A., . . .Pittsburgh, Pa.

1938 ABERNATHY, G E Feb 6, 1948 Min & Met Apr 1948 1937 ADAMS, ARMY Aug 20, 1949 Min Eng Dec 1949 1946 ADDY, GEORGE E Sept 24, 1950 Min Eng July 1951 1920 ALDERSON, WILTON P Feb 1951 Min Eng Sept 1952 1896 ALDRICH, T H , JR May 24, 1950 Min Eng Aug 1950 1942 ALDRIDGE, LEONARD June 8, 1952Jrn Met Sept 1952 1919 ALLEN, ROLLAND C July 18, 1948 Min &Met Sept 1948 1950 ANDERSON, C P Unknown Min Eng Feb 1951 1937 ANDERSON, JOHN H May 10, 1950 Min Eng Aug 1950 1914 ANDERSON, L DOUGLASS Unknown Min Eng Nov 1951 1948 ANDRAU, E W K Oct 20, 1951 1936 ANDREWS, CHARLES B Apr 19, 1950 Min Eng June 1950 1918 ARMITAGE, PAUL June 28, 1949 Min Eng Oct 1949 1924 ARMSTRONG, PERCY A E Jan 23, 1949 Min Eng May 1949 1906 ARNOLD, CHARLES LE NEVE Aug 7, 1949 Min Eng Oct 1949 1945 ARNOLD, HAROLD S Aug 7, 1950 Min Eng Oct 1950 1936 ASH, JAMES E Dec 17. 1949 Min Eng Apr 1950

Jan 1, 1952

By Richard Akerman, Frederick Prime Jr

[THE attention now being paid both in this country and Europe the greatest economy in the working of the blast furnace, and the eagerness with which all thoughtful men in the iron business look for any new information which will tend to throw light on this subject, is a quite sufficient excuse for presenting this paper to the American Institute of Mining Engineers.] I. It must be borne in mind that when two bodies unite to form a chemical compound, heat is almost always evolved. In order to

By AIME

AS with Phil Kraft, referred to on this page last month, travel has always held a great fascination for Raymond Frank Baker and for that reason he determined to become a geologist. He had heard that geologists travel and that was what he wanted to do. Now as chief geologist for The Texas Co. his early wish has been fulfilled-he spends almost one third of his time journeying' from one oil field to another. Mr. Baker was born in New Haven, Conn., on Jan. 11, 1892, and went through the public schools in New Britain. A stalwart New Englander, he attended Yale and in 1912 received a degree in civil engineering. For a year following this he worked as a civil engineer for the New York Central Railroad, but his early urge to travel widely could not be satisfied here. So in 1913 he re-entered Yale and until 1916 studied mining and economic geology. He had a little taste of field work, which later became so enjoyable to him, in the summer of 1915 when he worked with the U. S. Geological Survey as a geologic aid. In 1916 he made his first contact with The Texas Co. when he entered their Tulsa office as a geologist. This early career was interrupted by service in the

Jan 1, 1947

By Henry Louis

The object of the present paper is to call attention briefly to a novel method of analyzing the action of the ordinary gravity stamp, which has not only thrown much light upon the exact motion of the stamp-head, but promises also to be of value in determining the efficiency of a new mill before setting it to its work of crushing, and in this respect should be of service to constructors of mining machinery as well as to mining engineers. The method was devised by Mr. D. B. Morison, and developed in connection with his experiments on the comparative crushing-effects of his patent high-speed stamp and the ordinary cam-stamp, which were carried out at the works of Messrs. L. Richardson & Sons, Engineers, Hartlepool, and on which he read a paper at Newcastle in 1897.* Mr. Morison's experiments were of a very exhaustive nature; and having been consulted by him during his investigations, I had frequent opportunities of examining the methods employed and the results obtained. Experiments were first made with an apparatus resembling the indicntor of a steam-engine, inasniuch as the drum revolved alternately backwards and forwards, thus producing a closed diagram. This form was not found satisfactory, and it was therefore altered so as to cause the drum to revolve continuously in one direction, thus giving a continuous or open diagram. The arrangement is shown in plan in Fig. 1; a collar, A, surrounds the stamp-stem loosely and works between the guides B, B, which constrain it to move in a vertical line only. Immediately above it and below it, a couple of collars are clamped to the stamp-stem, so that the latter, while free to revolve,

Jan 1, 1899

By Richard Akerman

(Translated by FREDERICK PRIME, JR., Professor of Metallurgy in Lafayette College, Easton, Pa.) [THE attention now being paid both in this country and Europe to the greatest economy in the working of the blast furnace, and the eagerness with which all thoughtful men in the iron business look for any new information which will tend to throw light on this sub¬ject, is a quite sufficient excuse for presenting this paper to the Amer¬ican Institute of Mining Engineers.] I. It must be borne in mind that when two bodies unite to form a chemical compound, heat is almost always evolved. In order to

Jan 1, 1873

By Reinhardt Schuhmann JR

Metallurgical Engineering Volume I, by Reinhardt Schuhmann, Jr. Addison-Wesley Press. $7.50, 390 pp., 1952. -This first volume, engineering principles, of a two volume work, is intended by the author to meet a need for reorganization of instruction in extractive metallurgy. Its three main objectives are to organize the subject matter according to basic principles and unit processes; to integrate the underlying science of physical chemistry with metallurgical engineering; and to put greater emphasis on analysis and quantitative solution of engineering problems. Vol. I deals with unit processes, stoichiometry, thermodynamics, fuels, fluid flow, heat transfer, pyrometallurgical systems and refractories. Vol. II will take up the individual unit processes. Initiation and Growth of Explosion in Liquids and Solids, by F. P. Bowden and A. D. Yoffe. Cambridge University Press. $4.50, 104 pp., 1952.-The book is a study of decomposition by impact and by friction of explosive substances and deals mainly with the work of the authors and their collaborators. Research is still in progress but results thus far indicate that the mechanism of initiation is relatively simple. Findings are thoroughly discussed, and the latter part of the monograph describes the way in which a small nucleus of decomposition can grow into a large scale explosion.

Jan 1, 1952

Jan 1, 1966

By Shrikant Lele

INTRINSIC and extrinsic stacking faults may be formed in fcc structures by similar processes with bounding S-and D-Shockley partial dislocations respectively.' The only difference between these two dislocations is that the side on which the fault lies is reversed. The number of nearest and next nearest neighbors of atoms is identical for the two faults, but that of next next nearest neighbors is different. Thus, the energies associated with intrinsic and extrinsic faults may be expected to be different but of the same order of magnitude. An extrinsic fault can be constructed from two intrinsic faults on adjacent close-packed planes. This suggests that the extrinsic fault energy is higher than the intrinsic fault energy. It is, therefore, surprising that extrinsic faults have not been detected in X-ray studies2 of deformed alloys of low stacking fault energy. These have, however, been observed in cerium3 by X-ray diffractometry and in Au-4.8 at. pct Sn4 and Cu-16.6 at. pct A15 alloys by transmission electron microscopy.

Jan 1, 1968

By R. W. Raymond

IX the death of William H. Scranton, which occurred at Oxford, N. J., June 19, 1889, the Institute has been called once more to mourn the loss of a name from the fast diminishing list of those who constituted its membership in the first year of its existence. But it loses more than a name—a friendly presence and an intellectual force have departed ; a fruitful life has been cut short. Mr. Scranton was born in Belvidere, N. J., on the 13th of January, 1840. He was the eldest son of Colonel George W. Scranton, the

Jan 1, 1890

By H. W. Rogers

The first steam shovels used in this country were built by the Otis Company, of Boston, about 50 years ago, but as they were of very crude construction and rather unsuccessful only a few were built. For possibly 10 years prior to 1884 successful steam shovels were made and used on certain classes of work, but it was not until that time that they were manufactured in quantities and began to play an important part in all classes of excavation. From that time up to the present day there have been gradual but continuous improvements on the original shovel, not only in the mechanical construction, but also in the design of boilers and engines which are best adapted to this class of service. In proposing a change from steam to electric operation we have to deal with a steam equipment which has not only proved its worth but has probably reached its highest stage of development and efficiency. That the electric shovel is a possibility cannot be denied, as at present from 12 to 18 shovels are in operation in this country. These shovels may be divided into three classes: the friction electric, which is operated by a single constant-speed motor with friction clutches; the three or four motor direct-current equipment, and the three or four motor alternating-current equipment. It is the second and third classes that I wish to deal with, as the first class does not compare favorably with the steam shovel so far as speed is concerned, although it may be operated as cheaply. There is probably no other class of machinery that presents a duty cycle as severe as that of the shovel, which is very short, varying from 7 to 12 sec. on the hoist, from 7 to 12 sec. on the thrust, and from 10 to 18 sec. on the swing, making a complete cycle in from 17 to 30 sec., and the motor to meet these requirements must have a sufficiently low armature inertia to permit of rapid acceleration and quick reversals under small power. It should also be a motor of rugged design, as it must be subjected to severe overloads and shocks and frequent reversals. This is especially true of the hoist motors and, to a lesser degree, of the swing motor; the thrust motor being practically stalled during the digging operation, although it may revolve or overhaul, according to conditions, and is operated at full speed only after the hoisting operation is completed.

Jan 1, 1915

By Phillip B. Bucky, Fred D. Wright

The present known petroleum reserves are limited, and unless important new fields are discovered the Nation will be dependent, in the not too distant future, upon imports or upon synthetic liquid fuels to supplement domestic petroleum supplies. As a national defense measure, it would appear desirable to develop a substitute source of liquid fuels within the borders of the country if new discoveries of petroleum should Prove disappointing. Congress undoubtedly had this in mind when it passed the Synthetic Liquid Fuels Act (78th Congress, approved April 5, 1944). The act directed the Bureau of Mines to construct and operate demonstration plants for producing synthetic liquid fuels from coal and oil shale, and from forestry and agricultural products. As a part of this program, the Bureau of Mines has built a demonstration plant at Anvil Points, near Rifle, Colo., for retorting the oil shale, and has developed a mine to supply the plant with oil shale. At the beginning of mining operations, the physical qualities of the oil shale, which would have a bearing upon the selection of mining methods and practices for exploiting the deposits, were largely unknown. A comprehensive mining-research program has been set up to determine the best methods and practices to follow to obtain the lowest overall practicable mining cost for producing the oil shale on a large scale. Unusually low mining costs will be necessary for shale oil to be produced commercially. Consideration now is being given to exploiting a series of flat-lying beds 70 ft thick by a room-and-pillar method of three benches with the advance heading at the top. This report is one of a series giving the results obtained in research on mining problems, The structure and physical qualities of the oil shale indicate that the 70-ft interval of the oil-shale measure can be safely mined in open stopes; studies indicate that this method would be the most economical one to use.' As labor will be a major item of expense, the largest equipment that could be operated efficiently in the workings would be required to obtain the lowest practicable mining Cost. It Was therefore desirable to know the maximum safe span of unsupported rooms and the size of pillars necessary to support the overburden. This paper describes the work done at the Columbia School of Mines Barodynamic Laboratory in determining the maximum safe unsupported roof spans and the minimum safe pillar dimensions for the oil-shale mine at Rifle, Colo.

Jan 1, 1949

By R. W. Raymond

Samson Jordan was born at Geneva, Switzerland, June 23, 1831. At the age of 20 years he entered the Ecole Centrale des Arts et Manufactures, at Paris, from which he was graduated with high honors in 1854. After some months of service with the Compagnie du Chemin de Fer du Nord, he was employed (upon the recommendation of his former instructor, Prof. Burat, who had recognized his remarkable ability) at the mines of Portes, belonging to the Société de l'Elairage au Gaz et des Hauts Fourneaux, etc., of Marseilles, and subsequently to construct the St. Louis iron blast-furnaces of that Co. After finishing this work, he remained at Marseilles as a member of the directory of the Co., particularly connected with the development of its mines. In 1862 he became the general advisory engineer of the Co., and still later (1873) its general manager (Administratet~r), a position which he retained until his death, February 24, 1900. He became subsequently Administrateur of other important French industrial enterprises, including those of the Compagnie des Naut Fourneaux, Forges et Aciéries de Denain et Anzin, and the Compagnie Banco-Belge des Mines de Somorrostro ; and he was also, at various times, President of the Société technique du Gaz, Vice-President of the Comité des Forges de France, mepber of the Council of the Société d'Encouragement pour l'Industrie nationale. In all these positions, it is the unanimous testimony of his colleagues that he was no mere ornamental figurehead, but a profoundly wise, practical and industrious laborer and adviser, both patient and keen in the mastery of details, yet at the same time competent to apprehend the wider bear-

Jan 1, 1902

Discussion of the paper of THEODORE P. HOLT, presented at the Salt Lake meeting August, 1914, and printed in Bulletin No. 91, July, 1914, pp. 1699 to 1708. F. S. SCHMIDT, Salt Lake City, Utah.-Any furnace that can make a chloridizing roast to yield an extraction of 92 to 93 per cent. and do this at a cost of less than 24c. per ton in a 10-ton unit opens great possibilities for the treatment of certain classes of ores. This cost does not include the salt and will be reduced to about 16 1/2c. per ton in the 35-ton furnace which are now being designed. On a trial run the roaster treated 9.6 ton: of Ontario stope fillings crushed to pass a ¼ -in. opening. The ore is well adapted to chlorination with the exception of insufficient sulphur and occasional days of high lime, but is not adapted to any other process The following is an analysis of the crude ore: Ag, 9.52; Au, 0.029 oz. Pb, 0.71; Cu, 0.11; SiO, 79.4; Zn, 0.57; S, 1.00; Fe, 7.9; Mn, 0.89 CaO, 1.20 per cent. The composition of the mix was: Per Cent. Dry crude ore : 83.4 Moisture 4.4 Salt 8.3 Coal dust 2.3 Pyrite, 70 per cent. pure 1.6

Jan 11, 1914

By AIME AIME

A FALL meeting that should have repercussions both in the "Transactions" and MINING AND METALLURGY was that of the Industrial Minerals Division (Nonmetallics) at Wilmington, Oct. 21-23; headquarters, Du Pont Hotel. The sixteen technical papers and two addresses were substantial and interesting. Moreover, in every instance but one, the author made the presentation, and the one exception must have been next of kin because the ensuing discussion indicated his command of the subject. The meeting schedule clicked at every turn, thanks to Dr. Gillson, chairman of the local committee, and even the four field trips adhered to the time table. The program pre-empted morning, noon, afternoon and night two general luncheons, two dinners, and an evening technical session reminding one of the Annual Meeting. Only the registration was disappointing - about 80.

Jan 1, 1943

By T. A. Rickard

T HE life and career of Daniel Cowan Jackling constitute a distinctive part of a passing era, marked by the intensive exploration and exploitation of the mineral resources of the western regions of the United States. In the development of his abilities and in the use of his opportunities, he typifies the initiative, the energy, and the skill of a modern captain .of industry. Daniel C. Jackling was born at Hudson, Mo., on Aug. 1.4, 1869. He was the only child of Daniel Jackling, born in England of English parents, and Lydia Jane (Dunn) Jackling, born in the United States, but of Scottish ancestry. His father died a few months after he was born, and he lost his mother less than two years later. The orphan boy was adopted by his aunt. He went to school as soon as he was old enough to walk the two miles, and back, alone. As opportunity offered, he went

Jan 1, 1937

By Henry D. Hibbard

Henry D. HibbaRd, Pittsburgh, Pa,: This is a most interesting and instructive paper, some of whose lessons should find immediate application. It points out how fuel-consumption is to be decreased in open-hearth practice, by changes in the plan of the furnace. To look first at the greatest item of loss, radiation, it is seen that thicker brick-work is advisable to lessen this. Especially is this true of the roof, made at present, almost universally, only 9 inches thick to prevent cutting. Now that high roofs, well above the course of the flame, are becoming general, and the average melter is better able to judge the temperature of his furnace, that reason has less force; and we may build roofs 18 inches thick, or perhaps better cover the usual 9 inches with an equivalent layer of sand, which has the advantage of following the arch as it rises and falls with the different degrees of heat. The side-walls of the hearth, usually 131/2 inches thick, may also he thickened up to 18 inches, and the door-linings to 7 inches; and the heat thereby saved will be valuable, while its absence from the working-platform will be much appreciated by the workmen.

Jan 1, 1892

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