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By Samuel S. Wyer

THE installation of the gas-producer power-plant in America has been so unusual that all engineers have viewed it with in¬terest; a large majority, however, regard it with a lack of con-fidence and many with positive distrust. Despite the fact that European engineers have usually been less inclined to take the initiative along experimental lines than are Americans, they have, nevertheless, developed the gas-producer plant to a very high state of efficiency to which they were forced by the neces¬sity of economy in fuel-consumption. The gas-producer power-plant is so common in Europe that engineers as well as the general public regard it with the same degree of confidence that is now universally placed in steam¬plants. Gas-engines, both small and large, are in general use there, and central stations, aggregating several thousand horse¬power, are quite numerous. The fact that gas-producer power-plants have received so little attention in America may be attributed to five conditions:-1', ignorance and prejudice; 2, newness of work; 3, in-

Mar 1, 1905

By D. F. Hewett

ALTHOUGH most persons will agree that an individual or a nation can profit from the experience of other individuals or nations, there is always room for debate over the degree of similarity of their past and present conditions and of their future problems. Noting the increasing interest that Americans are showing in our mineral problems, I have felt that we could profit from reviews of the experiences in mineral exploitation acquired by the industrial nations of Europe. Whether we can learn much from Europe's experience in exploiting such minerals as petroleum may be debatable, but certainly, with a record of metal production extending back nearly 3000 years, Europe should hold much of value for America. A trip to Europe in 1926 permitted me to visit 28 mining districts, of which about half are now or have been in times past outstanding sources of several metals. The districts range from England to Greece and from Spain to Poland. To summarize briefly my impressions of these mining districts, as well as such reactions to the thought and life of Europe as so short a visit permits, I shall only venture the opinion that Americans can review with great profit the ideas and actions of Europeans, with regard not only to the production of metals but to many expressions of life. I believe that America has made and is making new contributions to the art of living, as well as to the arts of mining and metallurgy, but in so far as Europe is and has been a laboratory of economic, social and political experiments, the results she has attained deserve the thoughtful attention of America. I have come to believe that many of the problems that harass Europe lie in our path not far ahead. I have therefore hoped that a review of metal production in Europe in the light of its geologic, economic and political background may serve to clear our vision with regard to our own metal production. One can not examine the literature of national metal production without being impressed that the countries of continental Europe, especially Germany and Austria, have shown greater interest and devoted more time to research into the record of metal production than Great

Jan 1, 1929

By RAY LYMAN WILBUR

SINCE boyhood I have had a keen interest in mining engineering. To see the prospector with his pack outfit and his pan, followed by the assayer and the trained engineer, has always had -something of the lure of romance for me. It is appropriate that the American Institute of Mining and Metallurgical Engineers should hold a general meeting in California, since this State has long been a home of mining engineering. Here, after the early open methods of mining, it has been necessary for the universities to train men in geology and mining, so that the earth could be penetrated and the rich ledges opened. In the eighty years in which the mines of California have been offering experience to the miners of the world, we have seen mining engineering evolve from a comparatively simple art, covered largely by rule of thumb, into a complex group of specialties, each utilizing the very latest discoveries in the various fields of physical sciences. Mining, too, has become a great business requiring large financial support and the most careful handling. Those mining engineers who have applied new processes in special fields have thus been able to give a wide-flung range to their activities in all parts of the world. The hand of nature in distributing minerals over the surface of the earth has compelled the mining engineer to become a modern pioneer, facing the heat of the tropics as well as the frozen regions of the north. There has been a marked cosmopolitan aspect to mining engineering, since the engineer had to go wherever the prospector discovered favorable leads. This has meant dealing with the harshest of conditions, the handling of labor of all sorts, the control of sanitary conditions, and relations to all forms of transportation. Naturally this has called on some of the very best minds in all countries to unlock the stores of hidden wealth. To make them available for civilization has been the job of the mining engineer.

Jan 1, 1929

By M. von Heimendahl, G. Thomas

The microstructure of TD-Ni has been examined by transmission electron microscopy in the extruded, annealed. and deformed states. The tensile properties hove been correlated with the observed microstructures and the results ore com-pared with those obtained from pure nickel. The important conclusions are that the thorin particles in TD-Ni act as strong burriers to dislocntion motion during both deformation (slip) and annealing (climb). During deformation. the dislocations tangle around the particles and a cell structure is devleloped after 10 pct or more strain. The cell size appears to be determined by the spacing of the largest particles and is about five times smaller than that in pure nickel for the same strain. The higher work-hardening rate in TD-Ni compared to nickel is probably due to the more rapid rate of dislocation multiplication in the alloy as a result of dislocation-particle interactions. The Th0,particles inhibit recrystallization and twin growh so that some strengthening may arise from the high density of small annealing twins. THE strengthening of materials due to the presence of a dispersed second phase has been the subject of considerable experimental and theoretical investigation in recent years. One of the newest dispersion-strengthened alloys to be developed is TD-Ni,1 a system of approximately 2 vol pct thoria (ThO2) dispersed in a matrix of commercially pure nickel. This material is fabricated by powder-metallurgical techniques and offers high-temperature stability and useful mechanical properties virtually to the melting point of the base metal. While the mechanical properties of this system have been investigated,2,3 there have been no reports in the literature concerning the microstruc-ture of TD-Ni and its correlation to mechanical properties. This paper describes a transmission electron microscopy investigation of the micro-structure of TD-Ni together with its mechanical properties. The results are compared with the structure and properties of pure nickel.

Jan 1, 1964

THE annual meeting of the Arizona Section was held at the Pioneer Hotel in Tucson on Dec. 10, 1951. Registration and ticket sales for the social functions started at 8:00 am and lasted throughout most of the day. There were 489 registrations, consisting of 216 members, 64 students, and 209 guests. Chairman Harrison Schmitt opened the Mining Geology Div. meeting and a short business session was held at which Dr. Charles Anderson of Prescott, Ariz. was elected chairman and Seton Williams of Tucson was elected secretary for 1952. Dr. B. S. Butler was program chairman with R. B. Mulchay as co-chairman at the technical program. Eldred Wilson spoke on Oxidation and Water Levels at Some Arizona Mines. George Kiersch spoke about Economic and Engineering Significance of Ground Water Localization in Limestones - Big Bend Country, Texas. Harrison Schmitt gave The Definition and Use of Terms in Mining Geology. These talks were followed by discussions. E. N. Pennebaker, A. D. Wandke, and H. Schmitt gave informal talks on foreign trips made during 1951, the meeting was then adjourned.

Jan 1, 1952

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 Samuel Taylor

IT is customary for the president of an engineering society, in his annual address, to describe either some engineering problem with which he has beer connected or to review the work of the society during his administration. My first thought, this being the sesquicentennial year of our nation, was to review the advance in coal mining for the past fifty years, during which period I have been more or less intimately con-nected with the bituminous coal industry, and have personally witnessed most of the great changes which have occurred in methods and machinery used in the production of coal, but preparation of the requisite address would take more time than could be spared to prepare it, and its presentation would consume so much time that it .would not be suitable. The new arrangement providing for giving the presi-dent's address at the business meeting makes it more .appropriate to review the work of the Institute during the past year, together with some suggestions which appeal to me as being of advantage to the future wel-fare of the Institute, which I will try to do briefly. The work of the business office has been reviewed in the Secretary's report and it will not be necessary for me to dwell on it. Suffice it to say, it seems to be going along very well. Additional work could be done which would be to the advantage of the Institute, if we had the money with which to defray the necessary ex-pense incident to it, but I will refer to this again later. I would be derelict if I did not refer to the splendid work of the Secretary and the Assistant Secretary. Keeping in touch with all the sections, which number now about 26, and affiliated student societies which number 40, besides special committees, and represent-ing the Institute on various boards, provides work enough to occupy the Secretary's time almost exclu-sively. In addition to this the Secretary and the As-sistant Secretary have the work of editing and publishing the TRANSACTIONS of the Institute; the issuing of the magazine, MINING AND METALLURGY, in the splendid manner in which it goes out to the mem-bership is no light task and I think they should receive the commendation of the membership for this work.

Jan 3, 1927

By M. C. Fuerstenau, R. B. Bhappu

The response of beryl to sulfonate flotation was examined. The dependence of flotation recovery on sulfonate concentration, pH, and the absence or presence of various ions is also demonstrated. The response of quartz and feldspar to sulfonate flotation at various values of pH is given to. show the conditions necessary for selective separation. Finally, beryl was successfully concentrated from a natural ore using a technique devised from experimental observations on systems of pure minerals. With the possible exception of quartz, the flotation characteristics of silicate minerals are rather poorly understood. This is due in part to the com- plexity of the mineral systems themselves and in part to an insufficient amount of flotation data. The complexity of the systems arises from the wide range of chemical composition that the silicate minerals can assume. This is reflected in the variability of such physical properties as hardness and cleavage. Although the chemical composition of silicate minerals can vary considerably, a general grouping can be accomplished conveniently on the basis of the assemblage of SiO4 tetrahedra in all the silicates. That is, it has been shown that six basic groups can be obtained, depending on the arrangement of oxygen sharing between adjacent silicon atoms (or substituted aluminum). When all four oxygen atoms are shared, a framework structure such as quartz or feldspar is obtained. When three oxygens are shared, infinite sheets are obtained as in the micas and clays. When two oxygen atoms of the tetrahedra are shared, infinite chains are obtained, such as those in

Jan 1, 1963

The Nominating Committee for Institute Officers in 1953, John R. Suman, chairman, completed its work at the Annual Meeting in February, and has made its report to the Board of Directors. The President-Elect in 1953 serves as President in 1954. The ticket follows: For President-Elect and Director, Leo F. Reinartz; for Vice-President and Director, A. B. Kinzel and Lloyd E. Elkins; for Director, Hjalmar W. Johnson, Philip Kraft, Gail Moulton, Edwin L. Oliver, Philip Wilson, and Elmer Isern. Mr. Reinartz is a vice-president of the Armco Steel Corp., Middletown, Ohio. As required by the bylaws, brief biographical sketches of the nominees will be published in the July issues of the journals.

Jan 1, 1952

By K. A. Pauly

(Wilkes-Barre Meeting, June, 1911.) COMPRESSED air has been and is still very extensively used in connection with mining-operations, but its application in the past has been almost entirely confined to supplying power to underground machinery. Its introduction was due to the difficulty of taking care of the steam which is exhausted underground, rather than to any advantage in efficiency to be gained by its use. The ease with which electric power may be carried to the remotest parts of the mine and the high efficiency of the electric motor have long been appreciated by mine-operators, and electric power is now extensively used underground in the more recent developments, while many of the compressed-air engines in the older workings are being rapidly replaced by electric motors. Recently, however, it has been suggested to use compressed air for driving the large shaft-hoists, the air for the engines being supplied by electrically-driven compressors, and an installation of this character is being erected at Butte; Mont. It is the object of this paper to compare the compressed-air system of hoisting with the various electrical systems, from the stand-points of first-cost and cost of operation. However, before entering into a discussion of the various systems, it will be well to consider briefly the conditions affecting the choice of a system of hoisting in which electricity is the ultimate source of power. The power required by a mine-hoist is extremely intermittent and fluctuates between very wide limits, the all-day average consumption of power not exceeding from 5 to 15 per cent. of the maximum demand during hoisting. The cost of supplying power for such a fluctuating load is necessarily higher than that for supplying an equal amount of

Dec 1, 1911

By Haydn H. Murray, Sam H. Patterson

The term "clay" is somewhat ambiguous un¬less specifically defined, because it is used in three ways: (1) as a diverse group of fine-¬grained minerals, (2) as a rock term, and (3) as a particle-size term. Actually, most persons using the term "clay" realize that it has several meanings, and in most instances they define it. As a rock term, clay is difficult to define be¬cause of the wide variety of materials that com¬pose it; therefore, the definition must be gen¬eral. Clay is a natural earthy, fine-grained ma¬terial composed largely of a group of crystalline minerals known as the clay minerals. These minerals are hydrous silicates composed mainly of silica, alumina, and water. Several of these minerals also contain appreciable quantities of iron, alkalies, and alkaline earths. Many defini¬tions state that a clay is plastic when wet. Most clay materials do have this property, but some clays are not plastic; for example, halloysite and flint clay. As a particle-size term, clay is used for the category that includes the smallest particles. The maximum-size particles in the clay-size grade are defined differently on various grade scales, Soil investigators and mineralogists gen¬erally use 2 micrometers as the maximum size, whereas the widely used scale by Wentworth (1922) defines clay as material finer than ap¬proximately 4 micrometers. Some authorities find it convenient to use the term "clay" for any fine-grained, natural, earthy, argillaceous material (Grim, 1968). When used this way, the term includes clay, shale, or ar¬gillite, and some argillaceous soils. Even though no standard definition of the term clay is accepted by geologists, agronomists, engineers, and others, the term is generally un¬derstood by those who use it. Clay is an abun¬dant natural raw material, and it has an amaz¬ing variety of uses and properties which will be discussed in this chapter. Clays rank among the leading industrial min¬erals in both tonnages produced and total value. Their importance is indicated in Table 1, which lists the 1970, 1971, and 1972 production and values according to the U.S. Bureau of Mines (Ampian, 1972). Adequate reliable statistical data on which to summarize world production of clay are un¬available; this paragraph outlines the world re¬quirements for clay only in a very general way. According to one estimate, the world bentonite production in 1972 was 3.5 million tons (Anon., 1973a), but in the authors' opinion it was prob¬ably at least 5 million tons. The total fuller's earth produced was at least 1.5 million tons and may have been as much as 2 million tons. The total world kaolin production in 1972 was more than 10 million tons. Approximately 7 million tons of this total was produced in only two regions-the Georgia-South Carolina kaolin belt in the United States and the Cornwall re¬gion, United Kingdom. The world's 1972 out¬put of ball clay, which is also produced pri¬marily in the United States and the United Kingdom, was approximately 1.5 million tons or perhaps a little more. The total world fire clay production in 1972 was probably about one and one-half to two times and the miscellaneous clay production three times the United States production. As industrial minerals, clays are a complex group that consists of several mineral commodi¬ties, each having somewhat different mineral¬ogy, geologic occurrence, technology, and uses. In this chapter these commodities are organized

Jan 1, 1975

Discovery of a deposit of magnetite ore estimated at 3 million tons and of quality sufficient to warrant mining has been located near Reading, Pa. by the Bethlehem Steel Corp. Last January; the company spent nearly $400,000 for about 1750 acres of farm land which had been valued at only about $50 per acre. It is expected that a pilot shaft 18 in. in diam will be sunk some time this spring. The ore body, delimited by diamond-drilling by Sprague Henwood, is said to measure roughly 2000 sq ft and 1000 ft thick, beginning 1500 ft below the earth's surface. In a continuing search for strategic minerals, the Atomic Energy Commission expects to put eight to ten diamond drilling rigs into the area 11 miles southwest of Blanding, San Juan Co., Utah early this year. The Commission's primary objective is the Salt Wash member of the Morrison formation. Holes 140 ft deep are expected to be drilled, with solid bit drilling through overburden, mudstone, shale and sandstone overlying the area.

Jan 1, 1951

By J. C. Fisher, J. H. Hollomon

The fundamental problem concerning the fracture of both crystalline and noncrystalline solids is the divergence between the actua1 and the theorcticallY computed fracture stresses; the stress required for fracture, computed from the forces between atoms, is many times that actually observed with commcrcinlly available materials. Computatiolls have been made,,2 indicating that the theoretical fracture stress should be from 100 to 1000 times that actually observed. There are other incidental problems that have arisen, perhaps the most importallt of which is the problem of size effect often observed in the measurement of the fracture stress of non-metallic solids, such as glass. Another effect conccrns the relation between deformation and the stress required for fracture, Experiments recently made with pearlitic steels indicate that the tensile fracture stress increases with increasing tensile deformation and decreases with increasing prior com-pressive deformation, This marked ani-sotropy of the effect of deformation on the fracture stress is in contrast with the essential isotropy of the flow stress. Early experiments on rock salt crystals by Joffe, et al.3 have illustrated the effect of tensile strain in increasing the tensile stress required for fracture. A consistent theory must be constructed that will explain not only the divergence, of the measured fracture stress from the theoretical value, the size effect, and the ergence of deformation; but will also explain and predict the effects of combined stress, of temperature, of strain rate, and of metallurgical structure. With respect to this last variable, it has now been relatively well established that the carbide particle is the clement of structure controlling the fracture of steels. In steels carbide particles vary in shape from plates to spheroids. It has been found that not only docs the magnitude Of the Fracture stress depend upon the size and shape of these particles. but also its dcpendencc upon strain is affected by changes in 'hap' an' size Or the particles. The precipitate resulting from the age hardening Of duralumin also modifies the fracture stress of this alloy. Nonmetallic inclusions greatly lower the fracture stress of all metals. The magnitude of the lowering depends 0' the size and shape of the included particles. In glass, the major source of the low fracture stress has been fairly conclusively demonstrate' by Griffith4 '0 arise from real flaws or cracks present in the material. He showed that the stress concentration at the end of a defect was of suficient magnitude to raise the stress at this location to a value comparable with the theoretical strength Of the material. If the cracks were reduced in size, Griffith showed that the observed fracture slrength the by virtue Of the decrease in stress concentration. He also pointed out that cracks disposed perpendicularly to the applied tensile stress would be more effective in lowering the fracture

Jan 1, 1947

By J. H. Hollomon, J. C. Fisher

The fundamental problem concerning the fracture of both crystalline and noncrystalline solids is the divergence between the actua1 and the theorcticallY computed fracture stresses; the stress required for fracture, computed from the forces between atoms, is many times that actually observed with commcrcinlly available materials. Computatiolls have been made,,2 indicating that the theoretical fracture stress should be from 100 to 1000 times that actually observed. There are other incidental problems that have arisen, perhaps the most importallt of which is the problem of size effect often observed in the measurement of the fracture stress of non-metallic solids, such as glass. Another effect conccrns the relation between deformation and the stress required for fracture, Experiments recently made with pearlitic steels indicate that the tensile fracture stress increases with increasing tensile deformation and decreases with increasing prior com-pressive deformation, This marked ani-sotropy of the effect of deformation on the fracture stress is in contrast with the essential isotropy of the flow stress. Early experiments on rock salt crystals by Joffe, et al.3 have illustrated the effect of tensile strain in increasing the tensile stress required for fracture. A consistent theory must be constructed that will explain not only the divergence, of the measured fracture stress from the theoretical value, the size effect, and the ergence of deformation; but will also explain and predict the effects of combined stress, of temperature, of strain rate, and of metallurgical structure. With respect to this last variable, it has now been relatively well established that the carbide particle is the clement of structure controlling the fracture of steels. In steels carbide particles vary in shape from plates to spheroids. It has been found that not only docs the magnitude Of the Fracture stress depend upon the size and shape of these particles. but also its dcpendencc upon strain is affected by changes in 'hap' an' size Or the particles. The precipitate resulting from the age hardening Of duralumin also modifies the fracture stress of this alloy. Nonmetallic inclusions greatly lower the fracture stress of all metals. The magnitude of the lowering depends 0' the size and shape of the included particles. In glass, the major source of the low fracture stress has been fairly conclusively demonstrate' by Griffith4 '0 arise from real flaws or cracks present in the material. He showed that the stress concentration at the end of a defect was of suficient magnitude to raise the stress at this location to a value comparable with the theoretical strength Of the material. If the cracks were reduced in size, Griffith showed that the observed fracture slrength the by virtue Of the decrease in stress concentration. He also pointed out that cracks disposed perpendicularly to the applied tensile stress would be more effective in lowering the fracture

Jan 1, 1947

By Arthur F. Taggart

MR. CHAIRMAN: Congratulations! Your four-ring milling show this year was a dandy. It cleared our minds, for a few hours at least, of what Hitler, Hirohito, the New Deal, and the tribe in the Treasury are trying to do to strangle American enterprise. We mustn't forget this, but it's a relief to get our thoughts away from it occasionally. GRINDING-There was a further contribution to the excellent work that the Allis-Chalmers laboratory staff has been doing for the grinding fraternity in compiling-and publishing-a carefully quantitative list of comparative resistances of ores and other materials to comminution (T.P. 1579, Bond-Maxson). A diagnostic accuracy of ± 10 per cent was claimed for estimates based on these figures. Are they really that good? How about some of you men in the field writing M&M about it?

Jan 1, 1943

By J. B. Tyrell

A SHORT time ago I paid a visit to the alluvial gold fields on the tributaries of the Chaudière River in Beauce County, Quebec, in company with A. 0. Dufresne, late manager of the Champs d'Or Rigaud-Veaudreuil, and now Assistant to the Superintendent of Mines of the Province of Quebec. As the conditions under which the gold occurs in this district are not very generally known, and present some interesting features, a brief description of these conditions, and a consideration of the causes which gave rise to them, may be of interest to other mining engineers. During the latter half of last century the country was visited by many mining engineers and geologists, and many references to it may be found in the reports of the Geological Survey of Canada between 1848 and 1911. The most important of these are by J. A. Dresser and J. Keele and the late Robert Chalmers. The Department of Colonization and Mines of the Province of Quebec also published a report with map on the district by J. Obalski. From the earliest times the valley of the Chaudière River formed one of the main avenues of approach to the St. Lawrence in the vicinity of Quebec from the country to the south as far as the seaboard of the States of Maine and Massachusetts. The Indians had a well-known trail along the banks of the stream, and armed troops and foraging parties constantly moved backward and forward along it between Quebec and New England in those insecure times before the ceding of Canada to Great Britain. Even yet the natural advantages of this old military route are recognized, and the government of the -Province of Quebec has now under construction along it a magnificent highway from Quebec to the International Boundary Line, which is to form part of a through highway from that city to Boston; The land along the valley is naturally well suited for agriculture, and about the end of the eighteenth and the beginning of the nineteenth centuries farmers began to go back from the St. Lawrence, and to occupy the higher lands along the upper portions of the Chaudière Valley. This settlement has gone on until now the country is peopled with a prosperous agricultural population.

Jan 3, 1915

By Finney, W. R.

MUCH has been said and written of the "Big Inch," of the terrific obstacles encountered in its construction, of the colorful and tough men engaged in its building, but little has been publicized of the engineering and economic problems behind the scenes. Long before Pearl Harbor it was apparent to the petroleum industry that a critical oil shortage could be expected along the Atlantic seaboard, owing to delay in tanker deliveries as a result of convoy movements, and to allocation of vessels for foreign shipments. This area, with a normal consumption of approximately 1,800,000 barrels per day of oil and products, was almost entirely supplied by tanker. Pipe lines supplied an average of only 20,000 barrels per day in 1939, 40,300 barrels per day in 1940, and 55,000 barrels per day in 1941. A small amount of oil and products was also delivered via barge.

Jan 1, 1943

By M. L. Requa

EVERY forward step in civilization brings with it an increase in population and increasing demand for raw materials. Modern civilization, because of its industrial development, depends more and more for its well-being on ample supplies of raw materials; the higher the type of that civilization, the greater its dependence. No fact is more obvious than that the raw materials should be put to use with greatest prudence and efficiency. National life is not a matter of a decade or a century. Conservation is no longer a matter for political discussion; it is a vital element in the future welfare of all nations. Unfortunately, to the minds of many, conservation means the locking up of natural resources, their arbitrary withdrawal, bringing about, in short, a condition of industrial stagnation. This has occurred in past centuries through misdirected governmental effort. Two eminent engineers have variously defined conservation as follows:

Jan 1, 1925

By Larry Dale

An approach for predicting the development of mineral resources on public lands has been developed as an aid to resource agencies. It consists of new techniques for evaluating the economic potential of the resource, the uncertainty about mine cost estimates, and the uncertainty about the occurrance of mineral deposits. New mineral sup- plies from inferred and hypothetical resources can be predicted by using these techniques. A case study illustrates their application in predicting development of copper resources in western Montana.

Jan 1, 1982

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