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By F. H. Buchella, J. F. Buchanan

The San Manuel copper deposit is located about 45 miles northeast of Tucson. The concentrator, smelter, administration building, and other plant facilities are located about seven miles southeast of the ,nine area at the new town of Sari Manuel as shown on Figure 1 (Sketch).

Jan 1, 1961

By P. E. Fitzgerald, J. C. Gindlesperger

1. The Acidizer (Trade Publication of Dowell Inc.): No. 1. Aspects of Acidizing. No. 2. Inhibited Acid. No. 3. The Value of Acidizing. No. 4. The Chemistry of Acidizing. No. 5. Jelly Seal in Acidizing. No. 6. Loosening Stuck Drill Pipe. No. 7. The Geology of Acidizing. 2. J. C. Albright: Acid Is Being Used for Cleaning Intake Wells in Water-flooded Areas. Oil Weekly (Sept. 23, 1935) 24. 3. D. H. Bancroft: Acid Tests Increase Production of Zwolle Wells, Miller County, Arkansas. Oil and Gas Jnl. (Dec. 22, 1932) 42. 4. A. H. Bell: Possible Areas for Acid Treatment in Illinois. Pub. of Illinois- Indiana Petr. Assn. and lllinois Geol. Survey (1934) 49. 5. N. A. Best: Treating Limestone Formations Consists of More than Pouring Hydrochloric Acid in the Well. Oil and Gas Jnl. (April 5, 1934) 54. 6. L. G. E. Bignell: Sealing Off Salt Water from Oil-bearing Formations. Oil and Gas Jnl. (Jan. 30, 1936) 59. 7. L. G. E, Bignell: Acidizing Upper Limestone Formation Facilitated by the Use of Jelly Seal. Oil and Gas Jnl. (March 5, 1936) 30. 8. L. G. E. Bignell: Bailing, Shooting, Tubing and Acidizing Have All Been Tried in Deep Test at Binger, Oklahoma. Oil and Gas Jnl. (May 10, 1934) 38. 9. L. G. E. Bignell: Dowel1 Incorporated Increasing Its Field Service for Acid Treatment of Wells. Oil and Gas Jnl. (June 7, 1934) 62. 10. L. C. Chamberlain, Jr. and P. E. Fitzgerald: Oil Well Acidizing in Michigan. Mich. Acad. Sci. Papers (March 1937). 11. M. E. Chapman: Some of the Theoretical and Practical Aspects of the Acid Treatment of Limestone Wells. Oil and Gas Jnl. (Oct. 12, 1933) 10. 12. C. E. Clason and J. G. Staudt: Limestone Reservoir Rocks of Kansas React Favorably to Acid Treatment. Oil and Gas Jnl. (April 25, 1935) 53. 13. W. F. Cloud: Cleaning and Reconditioning Oil Wells—Reconditioning by Use of Acid (Petroleum Production 1937), 389. University of Oklahoma Press, 1937,' 14. K. A. Covell: Developments in Eastern Production Practice. Acid Treatment of Michigan Wells. Amer. Petr. Inst. Prod. Bull. 213 (1934) 77; Oil and Gas Jnl. (May 31, 1934) 89; Oil Weekly (May 28, 1934) 17. 15. B. A. Cunningham: Acid Treatment of Lime Formations. Amer. Petr. Inst. Paper 901 (1933) 9D, 1-7. 16. 0. I. DeSchon: Pondera Production up 22,000 Barrels. Montana Oil & Min. Jnl. (Jan. 26, 1935) 1.

Jan 1, 1937

By Oscar E. Harder

THE TERM "physical metallurgy' is used in the title of this lecture in preference to "metallography ?because the former has a broader meaning with most audiences, some people thinking of the latter as being limited to work with the microscope. This distinction, how- ever, has not been held by the out- standing workers in the field of metallography, such as the late Professor Sauveur. In the broadest sense metallography is essentially the same as physical metallurgy. The American Society for Testing Materials has adopted-the following definition: "Metallography is that branch of science which relates to the constitution and structure, and their relation to the properties of metals and alloys." This definition might be improved by adding after "properties" -"and their industrial and scientific uses." Metallography has also been defined as the science of metals and alloys. Physical metallurgy is to be distinguished from process metallurgy in that the latter relates particularly to the production of metals from the ores.

Jan 1, 1940

By A. A. Toprac

The recurring problem of joint failures in ofjshore structures, coupled with the catastrophic collapse of many of these structures during Hurricane Hilda (1964), hay forced reconsideration of techniques presently used to design sfuctural joints. This paper presents results of studies conducted for this reconsiderat?on. Only right-angled T-joint,s and cross-joints where a brace was welded directly to the undisturbed surface of another tube (the chord) were considered. Tests were performed on seven T-joint and 12 oross-joint specimens of two types which were designed to give a broad but practicd range to the geometrical parameters believed to be of significance to the problem. These paramefers were expressed in dimensionless form. Each specimen of the T-joints was instrumented wirh both electrical resistance strain gauges and deflection dials. After the elastic tests were concluded, each specimen was loaded to failure by applying an axial tensile load to the brace. The cross-joints were tested to failure without measuring elastic strains. Theoretical solutions for the stresses in a cylindrical shell due to a distributed radial load over portions of its surface were numerically evaluated. The experimental results are compared with calculated values obtained using Bijlaard's and Dundrova's theoretical analyses. INTRODUCTION During the last IS years a large number of structures were built for the offshore exploration of oil both in the Gulf of Mexico and dong the Pacific Coast.' In all these offshore platforms, the tubular shape was extensively used since this shape provides outstanding strength in proportion to its weight, compared to other shapes, when all directions (x, y, z) are considered. Past use of tubes was hampered because of connection details. But with the advent of welding, it became no more difficult to connect tubular shapes than to connect rolled shapes. However, some problems have been encountered in actual construction in making welded joints that are adequate and yet economical. In trying to connect tubular members, designers have used a varied number of methods; consequently, some of the joints seem to be very expensive in detail while others appear weak and underdesigned. An inspection of offshore platforms owned by different companies indicates the use of a large number of joint arrangements and configurations. Such a variety of joint types in current service indicates the wide divergence of opinion that exists on how such joints should be designed, stiffened and strengthened. Fig. 1 shows the various types of connections that have been used in practice. This paper reviews the present state of art on tubular joints of the T and cross type, and presents results of experimental and analytical work being conducted at The U. of Texas and elsewhere. It is believed that such information will be of great help to designers for the formulation of proper design procedures for joints. CONNECTION PROBLEM Recently, cracks have been observed in several welded connections in offshore structures. Fortunately, until about 1 1/2 years ago, these failures have been localized and have not resulted in the collapse of structures or loss of life. For example, one platform installed in Louisiana during 1955 in about 60 ft of water had been subjected to four tropical hurricanes. This platform successfully withstood these forces and was later removed because operations at this location had been completed. Many joint failures were observed during the removal.

By R. E. Fryxell, E. C. Duderstadt, P. K. Conn

Permeation rates for nitrogen through are-cast tungsten were measured in the temperature range 1800° to 2600°C at nitrogen pressure differentials of 1.0 and 0.1 atm. Gas chromatography was used to measure the quantities of nitrogen which permeated through 0.26-and 0.53-mm-thick membranes. Permeation rates were proportional to the difference between the square roots of the nitrogen pressure on each side of the membrane and inversely proportional to membrane thickness, indicating that atomic nitrogen was the difjusing species and that diffusion was the rate-limiting step of the process. Permeation coefficients calculated from the rates may be represented by the equation: where P is expressed in the units cu cm (stP)-mm per 1/2 sq cm-min-atm"' and 70.0 * 0.8 is the activation energy in kcal per mole of permeating species. In a previous paper' permeation rates were reported for hydrogen and for oxygen through tungsten. The permeation cells used for the hydrogen measurements were suitable for measuring nitrogen permeation under similar conditions, so the study was extended to include nitrogen. Permeation rates of nitrogen through the polycrys-talline arc-cast tungsten membranes were measured in the temperature range 1800" to 2600°C using two membrane thicknesses and two nitrogen pressure differentials. Permeation coefficients were calculated and the activation energy of the process determined. THEORY For diatomic gases which dissociate prior to diffusion, the quantity of gas which permeates through a membrane or wall at an elevated temperature where bulk diffusion is the rate-limiting step of the process is given by the equation: where: q = total amount of gas permeating a membrane, P = temperature-dependent permeation coefficient, A = area of membrane, t = time, p1 = gas pressure of high-pressure side, p2 = gas pressure of low-pressure side, and d = thickness of membrane. When bulk diffusion is the rate-controlling step, and the solubility of the gas obeys Henry's law, a further relationship is that, for any given temperature and pressure, the permeation is the product of diffusivity and the amount in solution. The permeation coefficient, P, is temperature-dependent according to the equation: where: Po = permeation constant, Q = activation energy, R = gas constant, and T = absolute temperature. EXPERIMENTAL PROCEDURES Cell Design and Experimental Apparatus. Two of the permeation cells used for the previous measurements of hydrogen permeation are shown in Fig. 1. Each consisted of a cylindrical chamber divided into two parts by a permeation membrane fabricated from high-purity (>99.9 pct W) wrought tungsten sheet made from vacuum arc-cast tungsten. The membrane in one cell was 0.26 mm thick and the other was 0.53 mm. The fabrication of these cells was described previously.' The permeation cells were mounted vertically in a high-temperature tungsten resistance furnace and the membranes and the center portions heated to test temperatures. Temperatures were measured by sighting an optical pyrometer on the edge of the membrane through a small hole in a tungsten plate which was fastened to the side of the cell. This arrangement provided an approximate black-body condition and eliminated the need for emittance corrections. Appropriate corrections were made for the quartz window through which the temperatures were measured. Argon gas flowed through the 10-liter volume of the furnace at the rate of 4.7 liters per min. An impurity

Jan 1, 1969

DURING September, the Coal Commission pre- pared for issue a series of 18 reports on varied aspects of- the bituminous coal industry; the final report, dated Sept. 22, sums up the facts and offers recommendations addressed to Congress, to the industry, and to the public. The few following paragraphs are selected: Bituminous coal is the real foundation of that great industrial and transportation structure which enables more than a hundred million people to live in America and be so well supplied with things necessary for their health, comfort; and convenience; it also furnishes domestic fuel for two-thirds of the homes of the land. The distribution of the output of the bituminous mines tells the story: 28 per cent. goes to the railroads, 25 per cent. to the boiler houses of factories and mills of all kinds, 15 per cent. to the coke ovens and gas plants, 10 per cent, to the homes, 7 per cent. to steel plants and the same percentage to power plants and street railways, 4 per cent. is exported, 2 per cent is used for power at the coal mines, and the remaining 2 per cent. goes to the seaboard for steamship fuel. Bituminous coal enters into interstate commerce on a scale approached by no other commodity; less than a fourth of the coal mined in the United States fails to enter interstate com-merce. All but one of the 45 coal producing districts in the United States ship coal outside the State in which it is mined. Three hundred miles of cars loaded with coal is the daily output of the bituminous mines of the United States. The public-welfare element in coal is seen in the dependence of public health and safety on an unfailing supply of fuel, in the close connection between the prosperity of most industries and the uninterrupted operation of the coal mines, and in the obvious fact that without coal the great network of railroads which binds together this great country would be idle. The railroads and the public utilities, themselves so clearly obligated to render what-ever public service is demanded of them that the constitutionality of their public regulation is unquestioned, are of all industries most dependent upon coal. Thus, coal makes up over 35 per cent. of the operating cost at the gas plant and over 25 per cent. at the electric power station, and in the operating expenses of. a railroad the cost of coal is the largest single item, next to labor. The practical logic that half a century ago clothed with a public interest the steam locomotive and in later years the electric-power station must recognize a large element of public service in the coal mine that furnishes the necessary energy to both locomotive and power-plant.

Jan 10, 1923

By J. C. Borland, J. H. Rogerson

Jan 1, 1963

By Shiou-Chuan Sun

THE fact that coals of different ranks and even of the same rank differ greatly in their amenability to froth flotation is well known. In recognition of the need for an explanation of this phenomenon, two hypotheses have been suggested. Wilkins1 reported that the floatability of coals increased with an increase of the carbon content or rank. This postulate is handicapped by the fact that bituminous coals that possess moderate carbon contents are actually more floatable than anthracite coals that have high carbon contents, as shown in columns 6 and 9 of Table I. Taggart and his associates' implied that the difference of floatability between bituminous and anthracite coal was caused by the variation of carbon-hydrogen ratio. This is not applicable to the relative floatability of other coals and carbons. For example, column 11 of Table I shows that the carbon-hydrogen ratios of low-floating lignitic coal and non-floating animal charcoal are not only smaller than the moderate-floating anthracite coal, but are also similar to the high-floating bituminous coal. Furthermore, according to this hypothesis, high temperature coke-A (464), Ceylon graphite (1238), and lamp-black (357), all possessing extremely high carbon-hydrogen ratios, should be less floatable than other substances having much lower carbon- hydrogen ratios such as high volatile-B bituminous coal (11.9 to 22), anthracite coal (35.7 to 60.5), lignitic coal (15.6 to 33.6), and charcoal (13 to 26.2). However the former group is actually more floatable than the latter group.

Jan 1, 1954

By Edward Judd

CANADA'S mining industry is rapidly recovering from the depression through which it passed in 1921. Its total output of $183,029,600 in 1922 was 6.4 per cent. greater than that of 1921, and was exceeded by only three previous years, 1917, 1918, and 1920. Table 1 compares the output of a few of 'the more important items selected from preliminary data published' by the Dominion Bureau of Statistics. TABLE 1.-OUTPUT OF CERTAIN MINERAL PRODUCTS IN CANADA PER CENT. 1921 1922 CHANGE Cobalt, metal and in compounds, lb 252,000 443,800 +76.1; Copper contents of blister, matte, and exported ores, lb 47,620,820 43,321,400 - 9.0 Refined copper, lb 4,286,000 730,000 -83.0 Gold, fine oz 926,329 1,230,985 +32.8 Pig iron, sh. tons 665,676 429,024 -35.5 Lead, sh. tons 33,340 47,085 +41.2 Nickel contents of matte, etc., lb. 19,293,060 17,496,490 - 9.3 Silver, including that in base bullion, gold bullion, etc., fine, oz. 13,543,198 17,611,646 +30.0 Zinc (nearly all refined), sh. tons. 26,545 28,199 + 6.2 Asbestos shipments, sh. tons 92,761 136,657 +47.3 Coal, all grades, sh. tons 15,057,500 15,045,300 Gypsum shipments, sh. tons 386,550 441,160 +14.1 Natural gas, M. cu. ft 14,077,600 14,954,100 + 6.2 Petroleum, bbl : 187,540 178,570 - 4.8 Cement, bbl 5,752,885 6,943,968 +21.0 Brick, structural, all kinds, M. , , 109,009 127,137 +17.0 On the basis of estimated market values, the whole output of 1922 was contributed as follows: Metals, 33.4 per cent.; non-metallic minerals, 45.1 per cent.; structural materials and clay products, 21.5 percent.; this distribution indicates a return of the metal mining. industry nearly to the position of relative importance that it occupied. before 1921, in which year metals contributed only 28.7 per cent. to the total value. of output while non-metallics gave 51.1 per cent. Canadian cobalt originates entirely in the ores of the Cobalt district, which are mainly treated at smelters in southern Ontario, although some quantities of residues have been exported to England and Europe. Exports during 1922 increased even more than production, consisting of about four-fifths . cobalt oxides and salts, and one-fifth of cobalt alloys and other metal combinations.

Jan 8, 1923

By Worthen Bradley

A BETTER understanding of what is happening in the domestic quicksilver industry, and what is likely to happen, can be had after reviewing some of the highlights of the past four years. Hitting the high spots in chronological order, they are: February 1939-Army and Navy Munitions Board starts investigation on civilian and war needs of certain "strategic materials," including quicksilver, with a view to recommending stock piles. Every known producer is canvassed by the end of the year.

Jan 1, 1942

By L. H. DeWald

During the examination of various commercial brands of copper wire bars, which had exhibited different degrees of adaptability for being drawn into fine gages of wire by the present-day high speed machine, it was found that each brand had a more or less characteristic crystal macrostructure. The extremes of these macrostructures are similar FIG. 1.-EFFECT OF METAL TEMPERATURE IN CASTING ON CRYSTAL MACROSTRUCTURE OF BAR. Reading from left to right, metal temperatures were 1166" C., 1149" C., 1132" C.. 1121" C., 1093" C. to the maximum variation shown in the photomacrographs reproduced in Fig. 1. As the various brands did not differ materially in chemical composition, it was concluded that the differences in structure were the result of variations in casting technique.

Jan 1, 1931

By H. W. Dow

Quite early in the beginning of the present century, hoisting equipment underwent a radical change, when electric motors were applied to furnish the power in place of steam engines. Naturally, in the beginning, motors were not employed for large hoists: most of them were small single-drum hoists for which the motor ran continuously and the drum was clutched in for hoisting by various methods, and the down-going trips were made on the brake. In 1911 the Nordberg Manufacturing Co. of Milwaukee built for the first time a double-drum hoist powered with a first-motion direct-current motor (Fig. I). This hoist embodied many of the features that are used on larger hoists today. In the early development of motor-driven hoists a more or less natural mis- take was generally made, which only recently is being corrected. Because the electric motor has a higher speed than the steam engine, mining people in general accepted, without question, the use of small-diameter drums and the resultant finding of the rope in multiple layers, which was not at that time, the general practice on first-motion steam hoists. Small-diameter drums can usually be driven by a motor through a single reduction of gears even with relatively high motor speed, therefore the complete equipment could be obtained with a lower first cost.

Jan 1, 1946

Jan 1, 1885

By Francis Church Lincoln

I. SITUATION AND SURROUNDINGS. THE Promontorio mine is situated at the northern end of the Sierra San Francisco de Coneto, in the town of Promontorio, Partido of El Oro, State of Durango, Mexico. As shown in the sketch-map, Fig. 1, the nearest railroad station is Chinacates on the Mexican International Railroad, 82 miles north of the city of Durango. The mine is 16 miles north of the station by air-line. It is reached by means of a good wagon-road which first crosses the Guatimapé Plain, passing the ranches of San Antonio and San Julian, to Estacion-a distance of about 15.5 miles-and then entering the mountains crosses the Sierra to Promontorio-a further distance of 11.5 miles¬making in all a distance of 27 miles by road from railroad to mine. Promontorio is just beyond the summit of the range, at an elevation of about 8,000 ft. above sea-level, or 1,350 ft. above the Chinacates station. The Castillo de San Francisco, the highest peak in the Sierra, has an altitude of 10,000 ft., and the Promontorio road crosses the summit of the ridge at an elevation of 9,000 ft. by a pass just below this peak known as the Puerto del Almagre. The Promontorio mill is situated at Santa Ives, 2 miles by tram or 3 miles by wagon-road to the north of Promontorio and about 600 ft. lower. The Sierra San Francisco de Coneto decreases in height towards the north and west till it comes to an end at the Melchor Arroyo on the ranches of Melchor and Ramos. Beyond this arroyo another range, the Sierra de la Candela, begins. In the vicinity of the Promontorio mine the hills are very rugged and the surface is furrowed by ravines which contain running streams during the rainy season-July, August and

Jan 1, 1908

By C. G. Wilson

DURING the course of some experiments on the plastic deformation of gallium a standard stereo-graphic projection was prepared with (001) at the center and it was felt that this might be useful to others working with single crystals of gallium. The stereogram, given in Fig. 1, was made using the following crystallographic data (Bradley, 1935):

Jan 1, 1962

By John Chipman, Wayne L. Worrell

Using recent thermodynamic data for the carbides and oxides of tantalum, columbium, and vanadium, the stable solid phases aboue 1300°K and at 1 atm CO(g) pressure in each M-C-O system have been determined. Pourbaix-Ellingham diagrams have been constructed and are used to estimate the minimum temperatures necessary to obtain these metals by carbothermic reduction under reduced pressures. TANTALUM, columbium, and vanadium react with carbon to form the M,C and MC carbide phases. The M,C carbides have narrow homogeneity ranges, but the MC phases possess considerable ranges of homogeneity.' The free energies of formation of the MC carbides were recently measured, and those of MC and M2Ccarbides have been estimated., (The notations MC and MC denote, respectively, the carbide compositions at the carbon-rich and at the metal-rich boundaries of the homogeneous MC phase.) In this paper, these carbide data are combined with thermodynamic data for the oxides to predict the stable phases in the Ta-C-O, Cb-C-O, and V-C-O systems at specified temperatures and oxygen pressures. M-C-O PHASE DIAGRAMS The solid phases in equilibrium above 1300°K for each M-C-0 system are shown in Figs. 1, 2, and 3. Above 1300°K, the vapor would consist entirely of carbon monoxide; and these phase diagrams were obtained by specifying the vapor pressure of CO(g) to be 1 atm. The temperature at which any two solid phases become unstable is specified along the two-phase equilibrium lines in each diagram. To simplify the diagrams, all solid phases in the Ta-C-O and Cb-C-O systems are represented as stoichiometric compounds. However, the homogeneity ranges of VO and VC are indicated, because they form a complete series of solid solutions.3 It also should be noted that the homogeneity range of

Jan 1, 1964

IN speaking, on the subject, "Engineer-Citizens," at the Lehigh Valley Mineral Industries Conference dinner, on April 26, at Easton, Pa., George Otis Smith, Director of the United States Geological Survey and President of the American Institute of Mining and Metallurgical Engineers, said in part: "It would be carrying coke to Connellsville to bring to the Lehigh Valley the idea that mineral resources are the foundation of national prosperity. Unfortu-nately, however, this obvious, fact is not everywhere recognized. Too many of our economists, journalists, statesmen and other dopesters of present business con-ditions stress the human factor so strongly that they overlook the material with which men work out their destiny. To them the financial psychology of Wall Street and the political logic of Capitol Hill and the business commonplaces of Main Street all loom far larger than the geology of the Lehigh Valley or the engineering triumphs of Bethlehem, or, the creative thinking at Lehigh and Lafayette. "The present situation in the industrial and .business world is a complex of interacting causes and reacting effects not easily itemized and entered on our trial balance sheet. But, chief among the liabilities of today is the excess of production capacity in most branches of industry. The farmer has no. monopoly in his desire for relief. Whether your professional connections are with steel or cement, coal or oil, copper, or zinc, you; know too well that for, the moment America is over-engined, and you keenly realize the ever-present hazard of industry speeding up regardless of the curves or grades just around the corner.

Jan 5, 1928

The income of the Institute is derived from dues, subscriptions to MINING AND METALLURGY and sale of publications. These sources are fortunately supplemented by the interest from invested funds now amounting to over $500,000, a considerable portion constituting endowments for especial purposes. Aside from the medal funds the principal endowments are the James Douglas Fund for support of the Library, the Rocky Mountain Fund and the Seeley W. Mudd Memorial Fund. The income from the two last named is available for the support of research and a variety of other purposes. It is allocated by the Board of Directors upon recommendation of standing committees in each case. An active effort is being made to increase the endowments of the Institute, it being felt that unusual opportunities exist for research and public and professional service through the organization.

Jan 1, 1936

By Percival Roberts

I DESIRE to present this evening a few notes from the standpoint of a manufacturer upon the subject of tests of iron for structural purposes; not that I have any new facts to which to call your attention, but rather a statement of a few of the objectionable features of the present modes of operation, showing the absolute necessity of important and very radical changes. At the present time, as most of you are well aware, proposals for materials are accompanied by certain specifications as to quality and tests to which the manufactured article must conform. Evolved in many cases from the inner consciousness of some one more expert in theory than in practice, we find a few of the specifications to be good, many bad, and some indifferent. Appended are specimens of specifications of the most prominent engineers and railroad companies, which may be taken as representing the best and most intelligently framed specifications which we now have, arid yet in some pints scarcely satisfactory, owing to misunderstanding of tests as now made. To show the very varied opinions held as to proper quality of iron for bridge-work, I give the tests of two lots of fron made by inspectors with the results, which were referred to the maker with the following commensts : Lot No. 1. Teat of Iron for Eyebars. Reduced area. Elongation. Size. Per cent. Per cent. Breaking load. 4" x 1 3/8 26 25 68,500 Bent 120° around 1 1/2" bar with fracture. Reduced area. Elongation. Size. Percent. Percent. Breaking load. 6" x 1 7/15 24 24 48,820 Bent 110° around 2" bar. This iron should bend 180° without fracture, and is therefore rejected. Lot No. 2. Test of Iron for Brirlye. All measurements taken upon a parallel section of 10". Iron for tension members. Breaking load Elongation. size. per aquare inch. Percent. 1 5/8 49,600 20 14 61,600 27

Jan 1, 1882

By J. Gurland

A method of measuring the degree of contact between grains of 1 phase in multiphase alloys is derived. It is shown that the number and the areas of contacts between grains can be determined by metallographic analysis. Relations between the area of contact, the dihedral angle, and the mean free path of spherical grains are developed. It is often desirable to interpret the mechanical behavior of alloys in terms of structural features observed under the microscope. A quantitative description of microstructures of multi-phase alloys requires consideration of geometrical and topological factors such as the amount, size, and shape of grains and the continuity of the constituent phases. The number and dimensions of grains may be metallographically determined by applying the methods described by Smith and Guttman1 and by Fullman2 in their papers on the measurement of particle size and internal boundaries in opaque bodies. The present work intends to show that the same methods can be used to evaluate some of the parameters of phase continuity; namely, contiguity, number of contacts, and areas of contact of grains of 1 phase. Application of these concepts may be found in such problems as the calculation of electrical conductivity of 2-phase alloys, or the evaluation of the length of fracture path through grains of a brittle phase more or less dispersed in a matrix. I. DEFINITION The following definitions and derivations are based on 2-phase alloys, of which the units of the microstructure are grains. Contiguity is defined as the average fraction of surface area shared by 1 grain of a phase with all neighboring grains of the same phase. In a 2-phase alloy of constituents A and B, the contiguity of phase B is given by: where Cb is the contiguity of phase B aBß is the average area of contact between a grain of phase B and adjacent grains of phase B, aAB is the average area of contact between a grain of phase B and adjacent grains of phase A. The contiguity is a measure of the average degree of contact between grains of phase B in the 2-phase mixture. The ratio varies from 0 to 1 as the distribution of phase B changes from a completely dispersed to a fully agglomerated structure. Smith and Guttman1 have shown that the relative areas of 2 kinds of interfaces in a volume are directly proportional to the number of interfaces of each type intersected by a random line. The lines can be drawn on metallographically prepared surfaces as long as these are random sections through the sample. The contiguity ratio of phase B then becomes: Cb = 2NBB/NAB + 2N BB [2] where: NBB is the number of interfaces between grains of phase B intersected per unit length of random line. Nab is the number of interfaces between grains of phase B and grains of phase A intersected per unit length of random line. The factor 2 arises in Eq. [2] because each interface B-B is associated with 2 grains of B-phase, whereas the interface A-B involves only 1 grain of B-phase. The calculations of contiguity do not require any assumption as to volume fraction, particle size, or particle shape. Fullman2 gives an expression for the determination of the mean free path between particles. The mean free path PB between grains of phase A, i.e., through grains or agglomerates of phase B, may be found from the relationship: PB =2fB/NAB [3] where fB is the volume fraction of phase B. The calculation of the mean free path is independent of grain shape and grain size distribution. The calculation of the number of contacts and of contact area requires assumptions of grain shape, grain size, and contact shape. In the case of uni-

Jan 1, 1959