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By T. W. Atkins

ATHOUGH the magnesium industry in this country is about thirty years old, not until American industry began to amaze the rest of the world and confound our enemies with the extent and variety of our war production did the industry begin to come into its own. At the outset of the war, only three companies were producing and fabricating magnesium in this country. Today, about sixty companies are producing, casting, forging, extruding, rolling, and stamping this lightweight champion of metals. Experience in alloying, processing. and fabricating the metal gained during the war years is now being translated into hundreds of civilian peacetime applications. In no sense should magnesium be considered as a substitute for other metals. It has come into popular favor because If many unique properties in addition to is being the lightest known structural metal. These attributes are toughness, igidity, corrosion-resistance, and the ease with which it can be machined and worked. Magnesium is the third most abundant element in nature. Sea water, magnesite,

Jan 1, 1946

By T. L. Johnston

MUCH has been said and written about deep mine shafts and deep drill holes as man in his search for mineral wealth digs deeper into the earth's crust. Each year some new extra depth is heralded as a record, but with unlimited possibilities of going still deeper. In contrast to "digging deep," "mining high" is limited by the height of the mountains (Mt. Everest being the maximum with its 29,000-ft. elevation) and also by the extent of human endurance. An ex- ample of what might be called near- stratosphere mining in what is probably the highest mine worked by compressed air in the world is seen in a recent project in the Andes mountains of southwestern Bolivia.

Jan 1, 1939

By H. H. Stout

THE high copper price during the war stimulated the capacity to produce far beyond a possible normal consumption. The curves in Fig. 1 show this. The line YZ indicates, what the world production and consumption of primary copper nor-mally would have been, had not the 3 war upset the rhythm of industry. Granting that the maximum world production of 3,150,000,000 lb. in 1917 was obtained by crowding both the equipment and the grade of ore mined, yet in many instances addi-tional capital was invested, upon which the producer will be driven to earn at least a reasonable interest. During the period of deflation, or C liquidation, which we have entered, the consumption of copper will nat-urally be below the normal. Fig. 1 shows the actual consumption ex-pressed-in per cent. of normal : 1919, 96 per cent.; 1920, 94 per cent.; 1921, 70 per cent. The copper industry, consequently, faces: (1) Potential over-production capacity; I (2) Diminished consumption. To deny the existence of these factors would be illogical. To minimize the menace of this potential producing capacity might lead to regret. All past attempts at artificial control have not proved very successful. Obviously the remedy is to increase, if possible, the consumption of copper to a point where these factors cease to be dangerous. In ultimate analysis, this means: Produce an article so cheap and so good that no one can afford to use substitutes. The problem can be solved by: (1) Re-ducing price; (2) Improving product offered.

Jan 11, 1922

By Olav Idelgeland

FROM indirect evidence point defects have been believed to influence the fatigue behavior of metals and alloys.1,2 Measurements of changes in resistivity made after cyclicstressing at low temperatures indicate that a very high density of defects is present, part of which may be removed by room-temperature annealing.3'4 These results are consistent with the generation of a high number of point defects at low temperatures. Corresponding measurements made after room-temperature stressing did not show any recovery effects.3 This was attributed to a stabilization of the dislocation network after a few thousand cycles without generation of vacancies. In this laboratory resistance measurements of copper single crystals, shaped as normal fatigue specimens ,5 have been made with a Kelvin double bridge at room temperature during and after cyclic stressing at 80 cps by comparing with a dummy at a close and constant temperature. Temperature differences were measured to ±0.025°C with fine thermocouples taped onto the gage lengths. Potential leads were tin-soldered into small holes in the gage length to give stable values. Corrections for differences in temperature and changes in mean length of the specimen were made according to the formula:

Jan 1, 1968

The fundamentals of blasting involve both the properties of explosives and of the rock being blasted. Four of the most important explosive properties appear to be energy density, bulk density, rate of energy release and the pressure- time history of the gases produced. Important rock properties are density and porosity, strength, and energy absorption including the effective moduli of elasticity. Rock structure also has a marked effect on its properties: for example, joints, bedding, and fracture alteration. Several mechanisms enter into rock fragmentation by blasting. These include slabbing, radial fracturing, crushing and bursting by the gas bubble. All of these factors are closely related to properties of both explosives and rock. Slabbing depends upon the first generated stress wave, whose shape and magnitude are a result of the pressure generated by the explosive, its time history and the resultant response of the rock, including its ability to sustain the stress wave. Actual slabbing, in turn, is a function of the magnitude and shape of the pressure pulse and the tensile strength of rock. Further fragmentation depends to a great extent upon the amount of gas in the bubble and its energy and pressure.

Jan 10, 1967

By H. l. Burghoff

DURING the course of preparation of crystals of alpha brass for an investigation of their creep characteristics, a number of critically oriented crystals were produced. In each of these specimens, P0, the specimen axis, lay near some important crystallographic direction or on or near the border of two possible slip systems. Because of the unusual nature of their orientations, it was considered of interest to deform these speci-mens in simple tension and to study orientation changes and any unusual occurrences, different from what would be expected for specimens in which only one slip system had distinctly the highest maximum resolved shear stress. Choice of actual operating slip system in a crystal offering an immedi-ate possibility of two slip systems would be expected to be due to chance, defect, or some inhomogeneity. Even in an ideally perfect crystal so oriented, the natural oscillations of the atoms about their lattice positions would give rise to a condition wherein one slip system would be favored over the other at the critical shear stress. In the large, nonperfect crystals of the present investigation, slip on both systems, but in different portions of the specimen, might occasionally be expected.

Jan 1, 1940

By Kenneth E. Mathews, Ross D. Hammett, S. Byron Stewart

Theoretical models have been important throughout the history of engineering as a means of understanding past experiences and predicting future performance. Most modelling involves assumptions and a degree of idealization, and it is shown that it is important that the effects of these be recognized when making use of models. One of the principal concerns in underground mining is the effect of the excavations on the states of stress in the rock adjacent to these excavations. As mining proceeds to depth, stress concentrations may be sufficiently high to cause inelastic behaviour of the rock and yielding along joint surfaces. At this stage, attention must be given to the sequencing of the mining process to ensure that the ground control techniques applied are optimized. Increasing use is being made of computer modelling techniques to assist with design. Three case studies are presented to illustrate the application of computer models in mine planning and ground control. In all cases, the data available for design was limited, but the mines were fully developed and openings could be inspected. The mining methods studied are cut and fill stoping, room and pillar stoping, and longhole stoping.

Jan 1, 1983

By R. E. Hook, R. L. McGaughey, A. M. Adair

The initial yielding characteristics of a vacuum-melted iron have been measured as a function of thertnal history after slow cooling or quenching from a 700°C recrystallizntion anneal. A thermal history favoring the segregation of interstitials to grairz boundaries results in a material having high values of upper and lower yield stress and long, irregutar Luders' plateaus, wheueas specimens treated to minimize grain boundary segregation have significantly lower values of these yielding characteristics. The struc- ture of typical grain boundary areas as revealed by electron transmission microscopy is consistent with these findings. The grain boundaries in iron are considered to be principally responsible for the release of dislocations during macroscopic yielding and it is suggested that strong locking results when a substantial amount of grain boundary segregution is present; it follows that weak locking results from a more random distribution of interstitials to grown in dislocations. RECENT years have seen an increased emphasis placed on a more quantitative study of the influence of grain boundaries on the yield behavior of bcc metals. The earlier picturk of dislocation pileups at grain boundaries building up a sufficient stress concentration to unlock dislocations in neighboring grains1

Jan 1, 1967

By W. Rogers Wade, Alfred Wandtke

The Pilares mine of the Moctezuma Copper Co. is situated at Los Pilares de Nacozari, Sonora, Mexico, about 75 mi. (120.7 km.) south of the international boundary and about 7 mi. (11.26 km.) east of the town of Nacozari de Garcia. It is situated at an elevation of 5000 ft. (1524 m.) in one of the northward trending ridges that form part of the mountain mass that culminates in the Sierra Madre de Mexico. To the east, south, and west, the topography is rugged and diversified; to the north less diversity exists, ranges of mountains rise sharply out of almost level ground and give the basin range structure characteristic of the Southwest. The climate is dry, the average rainfall of 15 in. (38 cm.) being confined almost entirely to the months of June, July, and August. The winter consists of a few days of disagreeable weather when a little snow may fall; the remainder of the year is thoroughly delightful. Vegetation is typical of a semi-arid region. In the canons near the mine, where water flows intermittently, willows thrive; on the northern slopes of some of the mountains and in some of the broader canons pines may even become abundant. The dominant rocks are flows and pyroclastics which are cut by dykes, stocks, and batholiths. The mountain just west of Nacozari is, in part, composed of limestone of an unknown age which occurs as a syncline and is undoubtedly a part of a prevolcanic land surface. Overlying the limestone and faulted against it, are the volcanics; cutting the limestone is a coarse biotite granite. Whether the granite is older or younger than the volcanics has not been definitely established. No attempt has been made to differentiate the rock types of the volcanic~, of which there are exposed 3000 ft. (914 m.) in thickness of basic and acid flows (andesites, latites, and rhyolites) and andesite and latite tuffs and breccias. The latite breccias, the youngest of these volcanic~, cover the highest mountains in the immediate vicinity. The

Jan 1, 1920

By D. E. Swets, R. C. Frank

It is well known that hydrogen is introduced into iron or steel as a result of many chemical processes (acid pickling, electrolytic cleaning, plating, etc.). One of the reactions that has been of recent interest1 is the reaction between an iron surface and water vapor. It was shown a few years ago2-4 that hydrogen can be introduced into steel at an accelerated rate during abrasion as a result of this reaction. Grun-berg and Scott have also observed that water in mineral oil lubricants increases pitting failure in ball bearings5 and they have suggested that hydrogen from the water is the primary cause of this effect.' In this laboratory, the question was raised as to whether or not hydrogen is also introduced into the metal surface of a bearing as a result of the decomposition of the hydrocarbon lubricant itself, and an experiment was performed to try to find a satisfactory answer. All steel parts contain some residual hydrogen. Therefore, it appeared that the best way to carry out this experiment without the need for highly accurate quantitative analyses was to use deuterium as a tracer. The natural abundance of deuterium in H2 is only 0.015 pct. The tracer was obtained in the form of deuteroparaffin (CD,(CDJ, CD,) and 0.25 g were dissolved in 20 cc of mineral oil to form the lubricant to be used in the tests. The bearings used were New Departure Type QOLOO ball bearings with a ball diam of 0.187 in. Prior to adding the mineral oil-deuteroparaffin lubricant, the bearings were cleaned in warm trichloroethylene to remove the packing grease. After packing with the new deuterated lubricant, the bearings were operated in a bearing fatigue test machine under a radial load of 190 lb and a thrust load of 190 lb at a speed of 3800 rpm. The expected life under these conditions is about 500 hr. Two tests were made; one for a period of 27 hr and the other for a period of 102 hr. The bearings achieved a temperature of 120o F during the tests. When the tests were stopped the balls were mechanically removed from the bearings and were immediately placed in liquid nitrogen to reduce degassing until the analysis for deuterium could be made. Before analyzing, the balls were warmed to room temperature and scrubbed with several degreasing agents to remove all traces of the deuteroparaffin mixture. This cleaning procedure was shown to be satisfactory by running a control test in which one ball bearing was subjected to all parts of the test except running in the fatigue machine. The hydrogen and deuterium were removed from the balls using a hot extraction apparatus attached to a mass spectrometer. Four balls from each bearing were analyzed. Each one was analyzed separately by removing it from a cold storage volume of the hot extraction apparatus and transferring it to the oven tube with a magnet. As the gases were evolved they were analyzed with the mass spectrometer. Since the hydrogen and deuterium pass through steel in the atomic form and since there are many more hydrogen atoms than deuterium atoms in the sample, the probability of forming an HD molecule is greater than forming a D2 molecule. For this reason the evolution of HD and H was followed as each ball was placed in the oven. The results showed that as each ball from the test bearing was dropped into the oven, the mass spectrometer recording of the HD evolution increased by about ten divisions. When balls from the control test bearing were dropped into the oven, the increase was about one division or less. The hydrocarbon background in the mass spectrometer was also monitored to see if hydrocarbons or deuterocarbons were given off when the balls were dropped into the oven, but no change in the hydrocarbon peaks was observed. Since the balls contained a fair amount of residual hydrogen, isotope ratio measurements were made on the gas obtained from each ball. The D/H value found for those balls which had been operated in the fatigue testing machine was consistently about 0.3

Jan 1, 1962

THE illustration below shows the design of the face of the clock to be erected as a memorial to the American engineers who gave their lives overseas in the World War. It will be placed in the tower of the library at Louvain, which has been rebuilt through contributions from America. Large clocks seldom have figures on their faces, and each hour on this one will be marked by a gold star, the four faces containing 48 stars, one for each State of the Union. Contributions toward the memorial have been received from every one of the States, and from Alaska and Hawaii as well, but additional subscriptions are invited by the Com-mittee which is arranging for the memorial.

Jan 3, 1928

(The following -list, contains the navies of those members of the Institute of whose connection with military service we have only recently become acquainted; it also includes the names of a few who have recently been promoted or transferred. A com-plete list was published in the Year Book, issued as a supplement of the Bulletin for March, 1918.) ADDICKS, LAWRENCE, Naval Consulting Board. ALINE, P. A., Camp Lewis. BARCUS, WALTER .J. E., Captain, Ordnance Department. BAUSH, JOHN R., Private, 1st Army Headquarters Regiment, Co. M. BENNETT, A. F., Lieutenant. BILLINGSLEY, PAUL, Engineer Officer, Aviation Section, Signal Officers' Reserve Corps. BOOTH, L. E., Ordnance Department. BROWN, JAMES F., 2d, 1st Lieutenant, Ordnance Reserve Corps, A. E. F.

Jan 4, 1918

By Philip D. Wilson

SPEED is essentiaI in this war program and it is hard to keep up with developments. When the title of this paper was chosen, the contemplated magnesium production for which plants were then under construction was some 200,000 tons of metal per year or sixty times the 3350-ton production in prewar 1939. A few- days later an analysis of the President's 185,000-plane pro-gram, incendiary bomb schedules, and the additional requirements of the Army. Navy and Maritime Commission made it apparent that a much greater amount of magnesium must be provided in 1943. The new figures are huge but the censor will not per-mit their disclosure.

Jan 1, 1942

By Ralph Arnold

Since 1915, when Elk Basin field was brought in, eight oil fields have been developed in Montana and the production has arisen from 50,000 bbl. in 1916 to 8,000,000 bbl. in 1926. The production for 1927 was 5,121,600 bbl. and the total up to the end of 1927 was 27,138,239 barrels. The eight fields, with their year of discovery are: Elk Basin, Carbon County (1915); Devil's Basin, Petroleum County (1919); Cat Creek, Petroleum County (1920); Soap Creek, Big Horn County (1921); Kevin-Sunburst, Toole County (1922); Lake Basin, Stillwater County (1924); Pondera, Pondera and Teton counties (1927); and Bannatyne, Pondera and Teton counties (1927). About 170 wildcat wells have been drilled in the state of which 8 were successful and 162 gas wells or dry. Hence, only one out of 21, or 5 per cent. of the wildcats have been successful. The average depth of the wells has been 1600 ft. and the average cost $32,000 apiece. • Up to Jan. 1, 1927, a total of 1376 wells have been drilled in the producing oil and gas fields of the state, of which 904, or 66 per cent., were successful oil wells; 82, or 6 per cent. were gas; and 390, or 28 per cent, were dry. The percentage of dry wells is excessive as compared to the wells in other states, due to the uncertainties of limestone reservoir rocks. The total production of oil to Jan. 1, 1927, has been 22,016,639 bbl. and of gas 7,265,330,000 cu. ft. The average price at the well for the oil has been $1.47 per bbl. and for gas about 4 c. per 1000 cu. ft. The value at the point of consumption has been about 23 c. per 1000 cu. ft. The total revenue derived from crude oil has been $32,277,119, and from gas 8350,613, or a total income to the producer of $32,727,832. Each well drilled in the state has already (to Jan. 1, 1927) averaged a return of over $21,000. The total number of domestic (Montana) oil and gas companies organized, since the first in 1885, has been 844, of which 702 are still alive and 142 dead. Oil and gas companies registered for operation within the state to Jan. 1, 1927, but with outside charters, are 143, of which 66 are alive and 77 are dead. Outside the few distributing companies, which are included in these figures, the grand total of 997 companies which have

Jan 1, 1928

By Karl W. Mote

CALIFORNIA'S iron and steel industry had its beginning in San Francisco in 1849 when the first iron casting was poured at the old Union Iron Works. Soon after, in 1856 at Grass Valley, enough iron ore was smelted to supply pig iron for the castings of a quartz mill there. From 1880 to 1886, iron ore was produced from the Hotaling mine in Placer County and converted to pig iron in a local blast furnace using charcoal. From 1907 to 1914, the Noble Electric Steel Co. produced pig iron from iron ore mined at the Shasta Iron Co. mine, and followed this for three years in the production of ferro-alloys. Between 1917 and 1941, the State's industry in- creased its capacity for open hearth and electric furnace scrap treatment, but the real impetus was supplied by the need for more steel at the beginning of World War II. The result was the State's first integrated steel plant-the Kaiser Steel Corp. facilities at Fontana.

Jan 7, 1958

R. F. McELVENNY.- The next item is: "Center and other methods, vs. side charging." That was all discussed in the Carson case, and I do not know but what many of the plants are still using center charging. Some are using side charging. Did I understand that where you use the wet charge it is all side charging on the wet ore? B.-G. C. HONEYMAN.- We were on center charging for about a year with wet ore. R. F. McELVENNY.- Then you went to side charging. Has anyone any remarks to make on side versus center charging? E. A. BARNARD.- We have one side and one center, both on deep bath. It is an experimental proposition so far, but the side charge looks very favorable.. R. F. McELVENNY.- This is with calcine? E. A. BARNARD.- This is with calcine on a floating charge proposition.. They are both water jacket. The charge acts very similar on both center and side charging. The calcine spreads much the same as it does on the center charge. It will run down 75 ft. on the furnace side as well as the center. The advantage is in taking care of secondaries and things of that nature. C. BARDWELL.- Do you get any side wall protection from it? E. A. BARNARD.- No. R. F. McKENZIE.- Do you not project the side wall up to protect the skewback? E. A. BARNARD.- There is a slot projection down around the top of the bath; but the repairs on the side wall have been practically the same; that is, they, have been practically the same as they have on the center charge. A. H. RICHARDS.- A point I would like to make is that if you have any doubt about the center charging, we feel that we get better tonnages and lower fuel ratios and better slags with center charging than we ever got with side. Different kinds of charges would, of course, vary, and I could readily see that if you had the same advantage with deep bath smelting that you mention you would probably get just as good a slag and as good fuel ratios. E. A. BARNARD.- In fact, I think the calcine charge spreads more on the side than on the center charge. A. H. RICHARDS.- If you maintain a deep bath. E. A. BARNARD.- That is one thing we have to be careful about, to hold the charge back.

Jan 1, 1930

By D. R. THOMAS

GENERALLY speaking, the production of other metals in Mexico fluctuates with that of silver. The first commercial discovery of mineral was in Taxco, Guerrero, in 1552. Five years later, the patio process was introduced at Pachuca, by Bartolome de Medina. In 1884, the main line of the Mexican Central R. R. was completed and a few years later, the National railway. In 1907, the patio process, after 350 years of successful operation, was replaced by cyanidation. Soon after the completion of the railroads, smelters were built at various points and provided means of treating ores that could not be treated by any of the processes existing at that time, such as patio, lixiviation, or pan amalgamation. As a result, a number of mines were developed along the railroads and even far \ out in the mountains. In order to facilitate the shipment of this ore to the smelters, purchasing agencies were established, which for a time were very profitable; most of these agencies are now permanently closed.

Jan 1, 1921

By Archer E. Wheeler

IN the copper industry, the year 1942 was one of striving for larger tonnage and increased production. The demands of the war program placed copper high in the list of strategic metals and the Government encouraged production by offering a premium of 5c. per pound for copper output in excess of the 1941 quotas. This had the effect of increasing the tempo of existing operations and also of initiating a number of projects which will eventually result in production from sources not hitherto exploited. No radically new methods of copper reduction were reported.

Jan 1, 1943

By Francis J. Dennis

(San Francisco Meeting, October, 1911.) MANY factors govern the value of dredging-ground, and much capital can be wasted by the mistaken policy of contracting for the purchase of property and the installation of machinery before a thorough, examination has been made. To the uninitiated investor the presence of gold is generally the criterion,, and very superficial evidence is necessary to satisfy him as to this point. He considers the comprehensive report of a competent engineer as a wasteful extravagance and cannot understand why the engineer requires so much time and money to ascertain the information on which to base his conclusions, when the promoter can furnish him such pleasing and satisfactory data with but little expenditure of time and money. The uninitiated investor will often optimistically risk capital for purchase and equipment, and not until the venture comes to grief does he learn that the conditions are wholly unsuited for dredging. In many instances, a short preliminary examination by a competent engineer would have disclosed these facts. The mere presence of gold is by no means sufficient; some of the other factors necessary to be ascertained in determining the value of placer-ground for dredging-purposes are : (1) character and distribution of gold, and how much can economically be recovered; (2) character of bedding underlying the gravel, its contour, and whether its gold can be recovered by ordinary dredging-operations; (3) area and depths of gravel, surface contour, over-burden, water-level, proportion of fine material and boulders, and the presence of any material which might interfere with the dredging-operations and the recovery of the gold; (4) water-supply, power available, labor, transportation, and supplies, and cost of these ; (5) climatic condi-tions; (6) title to property, cost and royalties, and legal obstacles to carrying on dredging-operations. A brief reconnaissance may be sufficient to determine that some of the essential conditions for successful dredging are

Apr 1, 1912

By J. Lewis, J. Harper, M. F. Ashby

A grain boundary in a metal interacts with second-phase particles, which exert a pinning force (first estimated by Zener) on the boundary opposing its motion. We have computed the shape of boundaries which interact with more or less spherical second-phase particles and have constructed a soap-film model to reproduce the shape of the boundary surface. An important result is that measurement of this shape allows the pressure, or driving force, on the boundary to be measured. We hare applied this technique to grain boundaries in two alloys and hate measured the pinning force exerted by single second-phase jwrticles on the boundaries. It is in good agreement with Zener's estimate. J\. boundary between two grains, or two bulk phases, interacts with small inclusions or particles of a second phase, whether they are gas or solid. This interaction means that the boundary, forced to migrate by a difference in free energy between the material of the two grains or phases which it separates, exerts a force on a particle which it touches, tending to drag it forward. (The movement of inclusions through metals under the influence of this force, has, in fact, been observed. 1-3) Equally, the particle can be thought of as exerting a pinning force on the boundary, tending to hold it back. Zener (in a celebrated private communication4) first realized that this interaction, and the resulting pinning force, existed. His calculation of its magnitude was crude but adequate: a spherical inclusion of radius r blanks off an area nr2 of the boundary on which it sits; since the boundary has an energy of rMM x per unit area, the blanlung-olf decreases the energy of the system by MM: this energy is returned to the system if the boundary is pulled free from the inclusion— a forward movement of the boundary by a distance r will do this—so that the maximum pinning force is Trrym.M- A similar argument can be made for inter-phase boundaries. The nature of the particle itself did not enter this, or two subsequent treatments.5,6 When it is considered, tic leifthe energyoftheb a) The boundary may enter and pass through the particle if the energy of the boundary is lower within the particle than in the matrix. Fig. l(r/). Certain coherent precipitate particles behave like this. h) More usually, the boundary will bend round the particle, enveloping and bypassing it. Fig. l(b). In doing so, it changes the structure and energy of the interface between the particle and its matrix. This means that the boundary does not touch the particle surface at right angles, as early treatments assumed,5'9 but at some angle a which depends on this change in surface energy of the particle, and can be calculated from the equilibrium of surface tensions. Most precipitate particles and inclusions behave like this. Gas bubbles or liquid drops can be regarded as belonging to either group. The progress of bypassing is conveniently measured by the angle shown in Fig. 1. When the nature of the particle is ignored, its maximum pinning force is exerted when - 45 deg. When it is considered, this critical value of is found to depend on a and thus on the nature of the particle. The maximum pinning force lies between nryMM and 2jtjMM (Appendix 1). not very different from Zener's result. In reality, a boundary between crystals has a specific energy and tension which varies with the orientation of the boundary. Furthermore, recent experiments7 indicate that such a boundary is not atom-ically smooth, but has steps on it: migration of the boundary corresponds to the sweeping of these steps across the boundary surface, like the Frank model of crystal growth from the vapor. This means that the interaction of a boundary with particles should really be considered in terms of the way in which particles hinder the movement of these steps. To suppose a grain boundary or interphase boundary to be smooth, and to ignore the variation of its energy with orientation, is to liken it to a soap film. The advantage of this soap film approximation, which we have used throughout this paper, is that interaction energies and boundary shapes can be calculated easily. We have done this by numerical computation and by using a soap film model, and have compared the results with grain boundaries in an aluminum-based and a copper-based alloy. It turns out that the shape of the boundary which bulges between particles allows the pressure an it to be calculated; that is, the local driving force an the boundary can be measured. This has allowed us to check the Zener relationship experimentally.

Jan 1, 1970