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By Benjamin F. Merembeck

A mutispectral scanner (MSS) obtains remotely sensed data of the earth's surface in vector form, one vector element for each spectral sensing band of the MSS. Data generated by either airborne or orbiting MSS systems are organized in a lattice of scan lines and elements within scan lines. Each element, called a pixel, is represented by an observational vector and corresponds to a relatively small specific area on the ground. The total observations for a sensed scene frequently are in the millions and are composed of a number of populations, each representing a different land form category. Based on samples from the populations, the mean vectors, or spectral signatures, and the covariance matrices for the categories may be estimated. From these, an among category covariance matrix and a combined within category covariance matrix can be found. The total among category variance is the trace of the among category covariance matrix. Canonical analysis finds a linear transformation matrix such that the first transform variable accounts for the maximum possible part of the total among category variance. Similarly, the second transform variable, orthogonal to the first, accounts for the maximum possible part of the remainder of the total variance, and so on. Such transformation often results in over 95 percent of the total variance accounted for in the first three canonical variables, even though the initial number of spectral bands exceeded twenty. Transformation of bulk data into three canonical variates allows color map products to be developed by assigning each variable to a different basic color. Such color products are believed to be more useful for photo-interpretation than color products resulting from any combinations of three of the initial spectral bands.

Jan 1, 1977

By Frank L. Nason

(New York meeting, February, 1912) IN the year 1904 an eminent Swedish geologist prepared a report on the iron-ore reserves of the world. His estimates follow: Countries. Tons. United States, 1,100,000,000 Great Britain, . 1,000,000,000 Germany, 2,200, 000, 000 Spain, 500,000,000 Russia and Finland, 1,500,000,000 France, 1.500, 000, 000 Sweden, . 1,000,000,000 Austria-Hungary, . 1,000,000,000 Other countries, 1,200,000,000 Total, . 10,000, 000, 000 The iron-ore allotted to the United States by the Swedish geologist is barely sufficient to last 20 years at the present rate of consumption. On the other hand (according to Edwin C. Eckel,1 from whom the above and following statistics are quoted), there is hardly need for worry on the part of our iron industries for the, next two centuries or more. Upon the basis of careful work by the U. S. Geological Survey, in which Mr. Eckel has taken an important part, the following estimates arc definitely, but by no means finally, given for the United States District. Tons. Lake Superior District, . . 1,500,000,000 to 2,000,000,000 Alabama, red hematite. . . 1,000,000,000 brown hematite, 725,000,000 Georgia, red hematite, 200,000,000 brown hematite, 125,000,000 Tennessee red hematite, . 6110,000,000 I brown hematite, 225,000,000 Virginia., red hematite, 50,000,000 brown hematite, 300,000,000 Total, . . 4,725,000,000 to :5,225,000,000

Jul 1, 1912

By T. D. Yensen

It is safe to say that of all the different materials that go to make up electrical machinery, iron is the most important. Upon its magnetic and electrical quality depends not only the efficiency of the machine but, to a very large extent, the cost. Aside from the mechanical strength, there are three characteristics of iron that are of importance in this connection, viz., magnetic hysteresis, electrical resistance, and magnetic permeability. In the homopolar machine, where the magnetic flux is unidirectional, permeability is the only important factor, but in all other machines the flux is reversed in one or more parts and causes losses due to hysteresis and eddy currents. The eddy-current loss depends largely upon the electrical resistance of the iron; the higher the resistance the lower the loss, under otherwise identical conditions. These hysteresis and eddy-current losses cause heating of the machine, and as they depend upon the magnetic density in the iron, this density must be regulated so that the heating shall not be excessive. If the hysteresis and eddy-current losses and the permeability of the magnetic circuit will permit an increase in the magnetic density, or, in other words, a decrease in the amount of iron, this in turn will mean a decrease in the amount of copper needed, with a consequent decrease in the copper loss. It is thus seen that, indirectly as well as directly, the above characteristics have an important bearing on both the efficiency and the cost of electrical machinery. In general, it may be said that iron for electrical machinery should have the following characteristics: (1) low hysteresis loss, (2) high electrical resistance, and (3) high permeability. These are the characteristics that investigators have been striving to attain since electrical machinery first came into use. Until the beginning of the present century, Swedish charcoal iron was regarded as the best grade of iron for magnetic purposes, and even now it ranks high among the various grades used. About that time Sir Robert Hadfield1 produced a number of iron alloys that revolution-

Jan 1, 1916

By H. R. Hanley, D. F. Walsh, C. Y. Clayton

Lead-refining practice at the Bunker Hill differs to some extent from that of other United States refineries using the Parkes process, in that the Bunker Hill has reverted to a custom used years ago of making two kinds of skims, or crusts, in the desilverizing kettles. Also, this was the first refinery to adopt the liquation process for silver skims as developed in Australia. Both of these ideas were brought to the attention of the operator by H. S. J. Sommerset, in the summer of 1924, while he was visiting metallurgical plants in the United States, when he was general superintendent of the Broken Hill Associated Smelters Pty., Ltd., of Port Pirie, South Australia. Since Mr. Sommerset's visit, United States patents on the liquation process have been issued to George Kenneth Williams, of Port Pirie, South Australia. At the Bunker Hill, the lead bullion is conveyed from the blast furnaces to the refinery in brick-lined cast-steel pots, each having a capacity of 5 tons, by a 20-ton electric crane, to which is suspended a Fairbanks-Morse suspension-type scale on which the gross, tare and net weights are obtained. The bullion is poured from the small bullion pots into either one of two kettles of 105 tons capacity, and when a kettle is entirely filled the heavy dross is removed by skimming it into a 5-ton pot suspended by the crane. The crane operator becomes proficient in the manipulation and a kettle is skimmed in a very short time. After the kettle is skimmed clean the bullion is pumped to a kettle of the same size alongside, where the bullion is cooled until it has almost frozen. By using two kettles for the drossing operation, one to accumulate the bullion where the heavy dross is removed, and then pumping to a clean kettle comparatively free of hangings, etc., it is possible to reduce the copper content much lower than if only one kettle is used in the operation. The average yearly analysis of bullion is given in Table 1. During July, August, September, and October, when a considerable quantity of high-grade silver ore from the Yukon Territory is smelted,

Jan 1, 1930

By Harry K. Ihrig

The hot-working of iron and steel is an art dating back to antiquity, but until about 25 years ago, relatively few alloying elements were used, and these were present only in small percentages. With the exception of sulphur, the amounts of other elements in steels did not markedly affect their hot-workability. The references in the literature on the effect of other elements on the hot-workability of steel are usually reports of failure of these steels in forging or rolling.1-8 With the increased use of alloying elements, and their use in larger amounts, it was observed that many of the new steels were red short in certain critical ranges or at all hot-working temperatures. The stainless steels are particularly difficult to hot-work. The determining of the correct conditions for piercing, rolling and forging of these alloys by experimentation in the mill often results in large losses of these expensive metals. It also is found that the hot-workability limits of many types vary from heat to heat, and hence poor results are obtained on changing to a new heat after a previous one has rolled satisfactorily. To determine the effect on hot-workability of iron to which various elements have been added, it was necessary to devise a method that could be used on small quantities of metal. In such a method, the minimum number of variables should be present, and the procedure should be simple, quick and correlatable with large-scale hot-working operations. Sauveur,9 in the first Henry Marion Howe lecture in 1924, described the effect of carbon on the ductility of steels in torsion near their critical points. He found that carbon increases the plasticity of gamma iron. In the 1930 Campbell Memorial lecture,10 he gives the effect of carbon, chromium, and chromium and nickel on the ductility of steels under 2000°F. in torsion. Ellis11 has studied the malleability of steels at various elevated temperatures by means of a single-blow drop-hammer test. In this test the percentage decrease in height of standard cylinders is taken as a measure of their malleability. He has shown that in the low-alloy steels studied, carbon has a greater effect than nickel, chromium and vanadium. In 1938 the first tests were run on a new quantitative hot-workability test in the laboratories of the Globe Steel Tubes CO. Thum12 mentioned it in 1940. An illustration of the apparatus was published in January 1942.'' The effect of a few alloying elements on the hot-workability of metals was shown in a description of the test in 1944.14 Description of Test Method The method adopted after a trial of several others is a rapid twisting of bars to failure in a furnace. The standard-size bar was chosen as 9/16 in. It is prepared from larger pieces by forging and cold-

Jan 1, 1947

By Harry K. Ihrig

The hot-working of iron and steel is an art dating back to antiquity, but until about 25 years ago, relatively few alloying elements were used, and these were present only in small percentages. With the exception of sulphur, the amounts of other elements in steels did not markedly affect their hot-workability. The references in the literature on the effect of other elements on the hot-workability of steel are usually reports of failure of these steels in forging or rolling.1-8 With the increased use of alloying elements, and their use in larger amounts, it was observed that many of the new steels were red short in certain critical ranges or at all hot-working temperatures. The stainless steels are particularly difficult to hot-work. The determining of the correct conditions for piercing, rolling and forging of these alloys by experimentation in the mill often results in large losses of these expensive metals. It also is found that the hot-workability limits of many types vary from heat to heat, and hence poor results are obtained on changing to a new heat after a previous one has rolled satisfactorily. To determine the effect on hot-workability of iron to which various elements have been added, it was necessary to devise a method that could be used on small quantities of metal. In such a method, the minimum number of variables should be present, and the procedure should be simple, quick and correlatable with large-scale hot-working operations. Sauveur,9 in the first Henry Marion Howe lecture in 1924, described the effect of carbon on the ductility of steels in torsion near their critical points. He found that carbon increases the plasticity of gamma iron. In the 1930 Campbell Memorial lecture,10 he gives the effect of carbon, chromium, and chromium and nickel on the ductility of steels under 2000°F. in torsion. Ellis11 has studied the malleability of steels at various elevated temperatures by means of a single-blow drop-hammer test. In this test the percentage decrease in height of standard cylinders is taken as a measure of their malleability. He has shown that in the low-alloy steels studied, carbon has a greater effect than nickel, chromium and vanadium. In 1938 the first tests were run on a new quantitative hot-workability test in the laboratories of the Globe Steel Tubes CO. Thum12 mentioned it in 1940. An illustration of the apparatus was published in January 1942.'' The effect of a few alloying elements on the hot-workability of metals was shown in a description of the test in 1944.14 Description of Test Method The method adopted after a trial of several others is a rapid twisting of bars to failure in a furnace. The standard-size bar was chosen as 9/16 in. It is prepared from larger pieces by forging and cold-

Jan 1, 1947

By E. W. Pehrson, J. W. Furness

THE method of presentation in the accompanying charts is based upon the well-known formula: production plus imports minus exports equals apparent consumption. Thus for each area for which data are shown there are two columns of equal height, one representing production plus imports, the other apparent consumption plus exports. Usually no account has been taken of increases or decreases in stocks. All columns and flow lines are drawn to a linear scale which is supplemented by figures showing the actual quantities represented. Owing to the small area occupied by the European countries on the world map it was impossible to show the details of the trade of the individual countries. All of Europe (except Russia), therefore, is shown as a single unit. However, statistics of production and consumption indicated elsewhere on the charts show the degree of self-sufficiency enjoyed by the major European powers.

Jan 1, 1936

[A AALSETH, Earl P (M 51) Consult Geol Engr 2019 Eldorado Dr, Billings, Monl ABADIE, Henry G (M 43) Asst to Supt of Oper Long Beach Oil Dev Co 925 Harbor Plaza, Long Beach 2, Calif ABBE, T Waldo (A 56) Asst Dist Oper Supt Sun Oil Co PO Box 66, Stowell, Tax ABBOTT, Fred E Jr (M 59) Abqaiq Dist Mgr Arabian American Oil Co Dhahran, Saudi, Arabia ABBOTT, Clifton T (A 60) Apartado 677, Maracaibo, Venezuela ABBOTT, J L (M 56) Partner Pritchard & Abbott 1010 Ft Worth Natl Bk Bldg, Fort Worth 2, Tex ABBOTT, Richard H (J 51) Partner Abbott & Howard 422 W Hermosa San Antonio 12, Tex .ABBOTT, William G (M 50) Div Mgr Rice Engrg & Operating Inc Box 1142, Hobbs, N. M. ABDERHALDEN, Ronald R (J 59) Prod Engr Continental Oil Co Box 100, Carmi, III ABEL, Malcolm D (J 50) Gen Partner Abel & Bancroft PO Box 865, Midland, Tex ABEL, Ramond L (M 28) Prof of Chem Eng Univ of Pittsburgh, Pittsburgh 13, Pa ABEL, Wayne K (M 57) 1513 Patton Drive, Odessa, Tex ABELL, Joseph M (J 55) Petr Engr Tennessee Gas & Oil Co Box 1772, Casper, Wyo ABELS, Thomas A (J 60) Exploit Engr Shell Oil Co Box 193, New Orleans 3, La ABENDROTH, G F (M 46) Dring Prod Supt Lyons & Logan 1500 Beck Bldg, Shreveport, La ABERCROMBIE, Bolling A (M 60) Mgr Product Planning Axelson-Garrett PO Box 2427, Longview, Tex ABERCROMBIE, C T (160) Prod Engr Cities Ser Petr Co Box 472, Brownfield, Tex ABERCROMBIE, H L Jr (J 55) Prod Engr Mobil Oil Co Room 1800 Gr PI Life Bldg, Lubbock, Tex ABERCROMBIE, Robert (J 57) Prod Engr Mobil Oil Co PO Box 1770 Shreveport, La ABERG, Richard S (M 57) Area Prod Geol Shell Oil Co of Canada, Box 100 Calgary, Alta, Canada]

Jan 1, 1961

By D. C. Lindley, D. H. Gaucher

The displacement of oil by water in a waterflood project is accomplished by the action of transient viscous, gravitational and capillary forces which drive fluid through interconnecting pore spaces toward production wells. The relative importance of each of these forces to the effectiveness of the displacement and the production history depends on properties of the reservoir itself and the manner in which it is operated. There has been considerable discussion'-3 concerning the importance of these factors and the extent to which they control the performance of individual waterflood projects. No data have been presented, however, to demonstrate the effect on waterflood behavior of variations in rock permeability, water-injection rates and mobility ratios in three-dimensional reservoir systems in which viscous, gravitational and capillary forces are allowed to assume the proper relative influence on fluid flow. Much information relevant to water flooding has been gained from the study of field case histories. But, the complexity of the systems involved, the difficulty of defining geometry and obtaining sufficient data, and the fact that the same reservoir is never flooded twice with the same initial conditions, all obscure the role of process variables such as rate. Further, mathematical calculations of waterflood behavior are restricted at this time by available mathematical techniques to highly simplified situations. Scaled models, however, do offer an approach at the present time to evaluation of the effects of the pertinent variables. Several investigators have predicted prototype reservoir behavior from observations of model waterflood performance under a variety of conditions. Two-dimensional aspects of waterflood pattern efficiency have been investigated by Muskat, Aronofsky, Dyes, et al, raig, et al,' and Rapoport, et al. he effects of gravity segregation, viscous fingering and permeability stratification have also been studied in two-dimensional models. Craig, et al," studied the importance of gravitational forces on frontal displacement in three-dimensional models with wells on a five-spot pattern. This work in- vestigates the tendency for water to segregate in homogeneous reservoirs because of gravity and to under-run the oil for a range of water-inject ion rates. The effects of permeability stratifications were investigated by these authors using miscible fluids to simulate water-channeling through permeable strata in systems of negligible capillary force. In this investigation, a three-dimensional model of a five-spot pattern flood was designed to represent typical prototype conditions, and the sand and liquid properties were selected so that capillary, gravitational and viscous pressure gradients were scaled. It was not, however, possible to achieve exact similitude regarding viscous fingering when the more viscous oil was used. The effects of rock stratification on waterflood behavior were studied by changing both the permeability ratio and the position of the more permeable sand stratum in a two-layered, horizontal model. For each type of stratification, constant-rate floods were performed and the rates were varied, in separate experiments, over a tenfold range. To observe the effect of mobility ratio on flood performance, two series of constant-injection-rate floods were performed on the most highly stratified reservoir at a water-oil viscosity ratio of one.

By Robert Bosworth

THE liability for damages to the surface caused by subsidence is an ever present threat in all underground mining. In ordinary lode mining, this threat rarely materializes into an action, due to the method of mining metalliferous ores, the dip of the veins, and the nature of the ground itself. In the mining of coal, however, this threat is very real. The coal frequently lies close to the surface, in beds underlying large areas of land of which the surface is suitable for agricultural or urban development. Furthermore, the coal is generally mined by the "room and pillar " method and when the pillars of coal are removed, the subjacent support is destroyed. This question of the duty of surface support has now become a very live one in Colorado. What was waste prairie land a few years ago has become valuable agricultural land dotted here and there with growing towns. Frequent references will be made here to Colorado conditions and adjudicated cases, but those conditions and cases and the conclusions to be drawn therefrom are applicable to all coal-mining states. Briefly stated, the question is "Does the owner of the substrata or underlying mineral owe any duty of surface support to the owner of the superjacent strata or surface?" There is no absolute duty of support owed by the mineral owner and this assertion is made with full knowledge of numerous expressions to the contrary by courts of Pennsylvania, Illinois, Colorado and other coal-mining states. Whether or not any duty exists depends upon the circumstances surrounding each case, and since in the nature of things those circumstances are rarely identical, there can be no absolute rule.

Jan 1, 1928

By M. G. Corson

INFORMATION regarding the use of manganese alloys has hitherto been incomplete and available only from widely scattered sources. This paper attempts a systematic description of properties and uses of alloys other than manganese bronze, manganin and duralumin, which are probably the only non-ferrous alloys associated with manganese in the minds of most metallurgists.1 PROPERTIES OF MANGANESE Manganese can react either acid or basic; it is hard to obtain in the pure state; it has two different crystalline lattice structures, both of the cubic system, one stable above 850° C. and the other below 650° C., both coexisting in the intermediate range. Although the commercial product is hard and brittle, the pure metal seems to be ductile. In fact Zhemchuzhny, in Russia, was able to obtain ductile manganese and draw it to fine wires by the simple expedient of adding about 3 per cent. copper to the alumino-thermic product. Copper most probably brings the sili-cides, aluminides, nitrides and carbides present in the commercial product into a much less harmful form of distribution. One industrial use that can be foreseen for wrought manganese articles is as anodes for electrolytic processes in sulfate and nitrate solutions, particularly with high voltages. A practically insoluble skin of manganese peroxide is likely to form in such cases and an insoluble and strong anode material will be available.

Jan 5, 1927

By W. S. Row

This mine is operated at 4000 to 4500 tons daily through a single shaft, with one rock hoist and one service hoist. Latest shaft construction is concrete with wooden dividers. Economics of drifters and air-leg drills are compared, as well as costs of shrinkage and sub-level stoping. Economy of large haulage equipment and underground crushing is shown.

Jan 3, 1953

THE decades immediately before and after the end of the nineteenth century (1890-1910) were a period of increased activity in mineral industry education. One reason for this, undoubtedly, was the rapid increase in mineral production in the decade 1880-1890; pig iron and copper production tripled; coal, lead, and zinc output more than doubled. Most of the other mineral substances followed the same general trend. Aluminum production began in 1886; petroleum output, which in 1888 was less than it was in 1882, almost doubled in the next three years. Gold alone showed no appreciable change until its discovery at Cripple Creek in 1891, followed by the Klondike in 1896, brought to boiling a public interest in minerals that had been simmering for some years previously. The first cyanide plant in the United States was erected at Bodie in 1892, and the first chlorination plant at Cripple Creek* the next year. Silver- lead smelting had already greatly developed, and the metallurgy of copper was almost transformed. The hearth area and smelting capacity of copper reverberatory furnaces more than quadrupled between 1878 and 1894; matte converters were first erected at Butte in 1884. Copper production of the United States in 1899 was 20 times that of 1872. While it was the increased technology used in mineral production that really made the field attractive for educated young men, undoubtedly they did not realize that, and were impressed mainly by the quantitative increase in output. Another factor was the increased general interest in engineering education; three times as many men took engineering degrees in the United States in 1890 as in 1880; 1892 showed almost a 56 per cent increase over 1890. Industry had come to recognize that technical training was worth while. The mineral industry lagged somewhat at first; the total number of mining degrees

Jan 1, 1941

By G. B. Misra

While investigating on the aerodynamic resistance of airways supported with peripheral timber sets, at regular intervals, the following theoretical equations were developed by the author to estimate the resistance coefficient of such airways: [ ] for S < 1, where f is Darcy-Weisbach resistance coefficient of the airway, C is modified drag coefficient of the supporting member, D is equivalent diameter of the bare airway, 8 is ratio of the approach velocity over the sets to the average velocity of the bare airway, A is cross-sectional area of the bare airway, a is projected frontal area of the sets, A., is cross-sectional area of the air stream at the vena contracta inside the set, S is spacing of the sets, f, is resistance coefficient of the bare airway, l is length of aerodynamic influence of sets, p is perimeter of the bare airway, p, is setted portion of the perimeter of the bare airway, pe is unsetted portion of the perimeter of the bare airway, and P shielding factor. The equations were verified experimentally in a model rectangular airway supported with one- (bars), three-, and four-piece sets of square-section timber of three different sizes and were found to hold true. The work has been further extended to one-, three-, and four-piece sets of round timber of 2.6, 3.2, and 3.8 cm diam with the same experimental set up. Tests have been carried out for spacings of 25, 50, 75, 100, 150, and 200 cm over a regime of flow defined by the Reynolds number (with respect to the equivalent diameter of the bare duct) ranging from about 1.5 X 106 to 5 X 106 using the same experimental techniques. The values of f are calculated in the manner indicated in [Ref. 1]. Unlike with square-section timber, the resistance coefficient f of the airway setted with round timber shows a distinct variation with the Reynolds number of flow. This conforms to observations made by Sales and Hinsley.2 In order to have a comparable value of f for all types of sets with all sizes of timber, it was necessary to select the value of f at a fixed Reynolds number of flow. Since f is chiefly a function of the drag coefficient of the sets, the appropriate Reynolds number RE is that with respect to the diameter of timber in the set. Considering the diameters of timber used and the regime of flow over which measurements were made, f was chosen at a value of RE = 20,000 in all cases. The f vs. S curves are maximal in nature and in conformity with theory, the f vs. 1/S curves are straight lines up to a value of S = 1 beyond which they show a distinct flexure. The observed values of 1, the length of aerodynamic influence of sets, agree with the relation 1 = 42 e, developed for square-section timber sets, thus suggesting that the shape of timber has little influence on the length of aerodynamic influence. The value of the modified drag coefficient CD for round timber was calculated in the same way as for square timber in Ref. 1, taking the contraction factor Z = 1.5 for round-edged constrictions. CD has an average value of 0.96 with a standard deviation of 6.08% as compared to the free stream drag coefficient of 1.2 at RE = 20,000 for long cylindrical obstructions The shielding factor [ ] is plotted against S/1 in [Fig. 1]. The curves are more or less independent of the size of timber, but are different for the different types of sets, possibly due to their different degree of symmetry. Values of f calculated by the author&apos;s [Eqs. 1 and 2], using experimental values of CD&apos; and [ ] and taking I = 42 e, are plotted in [Fig. 2] against experimentally measured values of f for different types of sets with different sizes of round timber. The values agree closely with a standard deviation of only 5%, thus establishing the veracity of the theoretical equations developed by the author for round timber as well. A comparison was made between the Xenofontowa4 equations (the only other reasonable relations available for the estimation of the resistance coefficient of supported airways) and the author&apos;s [Eqs. 1 and 2] by comparing in [Fig. 3] the values of the resistance coefficient f computed by the Xenofontowa relations with those experimentally measured by the author. In order to make

Jan 1, 1975

By D. Turnbull, J. C. Fisher

ACCORDING to the "reaction-path" modell,2 of martensite nucleation, the shear angle of the embryonic martensite plate must be treated as a variable, and included in any calculation of nucleus critical size. Also, as can be deduced from this model, the interfacial free energy between austenite and martensite does not reach its final value until the shear is completed. It is zero for zero shear angle. However, in order to account for the kinetics of the martensite transformation, some sort of interfacial energy barrier appears to be necessary even with the reaction-path model, for otherwise the volume and the energy of formation of the critical size nucleus both collapse to zero.3 Cohen independently suggested that surface energy could be incorporated into the reaction-path model, with the overall free energy of a martensite embryo being a function of its volume and shear angle.&apos; It is possible to estimate the energy associated with the formation of a critical-size martensite nucleus starting with the reaction-path model and including a surface free-energy barrier. As the dependence of interfacial free energy upon shear angle is unknown, a simple type of dependence will be assumed, with the belief that the true dependence would not lead to appreciably different results. Consider the work required to form a lenticular martensite plate with radius r, thickness t, and shear angle 8. There are three contributions; one being the interfacial free energy, one being the free energy change in the martensite plate, and one being the free energy increase in the surrounding austenite. The interfacial free energy u is assumed to depend upon the shear angle 0 according to the relationship s=s0(?/?0)n [1] where 8, is the equilibrium shear angle and n is an exponent that may lie in the range 0 n 2. The work required to form the interfaces of a martensite plate then is W. = 2pr² s0(?/?0)n [2] The free energy change per unit volume of martensite is composed of two parts, one the ordinary volume free energy ?f1. which is negative, and the other the elastic strain energy G?m²/2, where G is the shear modulus and 7, the shear strain relative to the martensite structure. This expression for the strain energy is valid only when the shear strain ym, is sufficiently small that the martensite is within its linear elastic range. There is no doubt that ym, lies beyond the linear elastic range for embryos that are considerably subcritical. However, for critical nuclei it will be shown that ym, is 1.5 pct or less, within the linear elastic range of martensite. For embryos of nearly critical size, then, the strain energy of the martensite is correctly given by G?m²/2. The shear strain in the martensite is ym, = 8, — 8, and the work required to form the strained martensite is Wm --= (pr²t/2) [?fv + G(?O - ?)²/2] [3] The free energy change in the austenite is entirely that due to elastic distortion. The elastic strain is not uniformly distributed in the austenite, being large near the martensite plate and small elsewhere. Approximately, however, the energy corresponds to a uniform shear strain ya= (?t/2)/r [4] throughout the volume 4pr³/3 surrounding the plate. The work required to strain the surrounding austenite then is Wa = (4pr³/3) (G?a²/2) = (G?²/6) prt² [51 For simplicity, the same shear modulus G is assumed for each structure. The total free energy for forming a plate then is W = W3 + Wm + Wa. = 2pr² s0 (?/p?0)n + (pr²t/2) [?fr+G(?0-?)²/2] + (G?²6) prt2 [6] This expression is correct for nuclei and for embryos of nearly critical size, where, as will be shown, the strain energy in the martensite is correctly given by the expression G (? — ?)². Having W as a function of r, t, and 8, as in Eq. 6, there is a saddle-point where W has a stationary value, W subsequently decreasing indefinitely as the nucleus volume increases along the reaction path. The stationary value of W is the energy of the critical nucleus. The critical nucleus has radius, thickness, and shear angle such that ?W/?r - awlat: = ?W/?p? = 0. Performing these differentiations and calculating the critical nucleus energy, W* = [8192p(G?/6)²;s/27 ?fv4] [7] where a= (?/?0)3n+1[l +G(8"-8)&apos;/2af.]&apos; [7a] and where 8 is to be determined from the equation (1 + 3n/4) + G8(6O - (9)/[Af. +G(6>o-6>)72] = 0 [8] For ?f, near —200 cal per mol or —10" ergs per cc, and 8, near 1/6, as for iron-base alloys, Eq. 8 gives ?0 - ? ~ - (4 + 3n) ?f1./4G0O [9] as the difference between the equilibrium shear angle and the actual shear angle for a critical nu-

Jan 1, 1954

By John Gann

THE following investigation constitutes a brief resume of the more important binary magnesium alloys from the standpoint of metallographic technique, and the effect of heat treatment on structure and properties. The comparative newness of the subject justifies this procedure as a preface to a more detailed study of each individual series of alloys. The work was started with the idea of practical application in the industry rather than as a theoretical investigation. The alloy compositions studied were selected as those most likely to show whether heat treatment would produce beneficial results. Furthermore, it was considered satisfactory to use commercial 99.9 per cent. magnesium, the best commercial grade of alloying ingredients, and to limit the time of heat treatment at the expense of incomplete equilibrium. These facts must be kept in mind when examining the results obtained, and the conclusions drawn.

Jan 1, 1928

By W. H. Bassett, C. H. Davis

ALTHOUGH brasses and bronzes have been made for ages, a systematic study of their physical properties has been carried out only during the years of the present century. Among these properties may be included those which are to be detected by means of microscopic examination; in other. words by the science of metallography. The earlier workers in this field, both in this country and abroad, gave their attention to steel. When the senior author explored the situation in 1902, there was little encouragement to be found in undertaking the study of the non-ferrous alloys. A start was made, and the metallography of the brasses and bronzes, as well as of the copper-nickel-zinc alloys developed materially under his direction. Annealing experiments were begun in 1902, and in the succeeding years the effect of temperature, and the influence of previous working, on the grain size of brass were studied. The conclusions so well known and widely published today were largely reached during those earlier years. . In 1905 the first complete annealing series were made. By this it is meant that brass and copper sheet, 5 B & S Nos. hard, was machined into tensile test specimens, then annealed under accurate control for 30 min. at temperatures up to the melting point of the material. Various determinations were made, including tensile strength and elongation in 2 in. There rapidly followed similar series on all of the copper-zinc alloys from 100 to 60 per cent. copper, on the bronzes, cupronickels, and on copper-zinc-nickel alloys. At this point there was published by Grard, in October, 1909,1 the very comprehensive and complete work on the tensile properties of cartridge brass, 90-10 copper-zinc, and electrolytic copper. The excellent photomicrographs in that paper illustrated the changes in structure produced by cold rolling as well as by annealing at different temperatures, but where Grard&apos;s work was confined to copper and to two alloys, the investigations in this laboratory have been over the entire fields of the commercial copper-zinc alloys, copper-tin alloys, representative copper-nickel and copper-nickel-zinc alloys as well as aluminum bronzes and others of a more special nature.

Jan 1, 1928

By Neville J. Price

In order that the reader may not be misled, I feel it necessary to comment upon the title of this paper. "Laws of Rock Behavior," one may take as being part of the all-embracing "Law of Nature" and this, according to the Oxford Dictionary, relates to the principles of conduct recognized as being pleasing to God. I feel it would be presumptuous to erect a code of rock behavior on this basis, so turn to a secondary definition, namely that a "Law" is that which is intrinsically reasonable. It is extremely unlikely that any group of geologists, or workers in rock mechanics would be in complete agreement about what could be taken to be "intrinsically reasonable." Therefore, this paper does not present any deified utterances, but rather deals with a few aspects of rock behavior which I consider to be intrinsically reasonable and with which I hope the reader will concur. The mode of behavior of rocks in the Earth&apos;s crust covers the range from wholly brittle to completely ductile ; with a deformation time scale which may be measured in milliseconds, for some events such as meteoritic impact, or in millions of years for the tectonic deformation involved in mountain building. A complete survey is, of course, outside the scope of an introductory paper, so I must be both brief and selective in my treatment. Any attempt to establish the mode of rock behavior in the Earth&apos;s crust should take into account data and relationships established in laboratory experiments and correlate these with field evidence. Consequently, the first section of this paper presents a brief discussion of the experimental aspects of rock mechanics which are pertinent to the subsequent discussion.

Jan 1, 1970

By R. P. Marshall, L. P. Costas

The solid solubility of lithium in aluminum was determined by two independent techniques, electrical resistivity and microhardness, and the results are in close agreement. The solubility limits X-ray diffraction studies of the intermetallic compound LiAl indicate that its composition is nearly independent of temperature when in equilibrium with the terminal solid solution of aluminum. THE investigation of the aluminum-rich portion of the aluminum-lithium system at the Savannah River Laboratory was prompted by the observation that over-aged alloys consistently differed from the equilibrium states predicted by the latest published diagrams. Chemical analyses of these alloys showed their impurity contents to be quite low; therefore, the results obtained should have very nearly coincided with true equilibrium. A survey of the literature disclosed that previous studies had been made with metallographicig or electrical resistivity methods,4&apos;5 but that agreement between results and technique was poor as evidenced in Fig. 1, which also includes the present results for comparison. The discrepancies have been attributed to impurities,3 and this is undoubtedly true in the early work.1&apos;4&apos;5 The latest Studies,&apos;&apos;~ conducted with starting materials of higher purity, employed metallographic analysis, a technique that is quite sensitive to local homogeneity and depends strongly on subjective interpretation. In the present work the problem of defining solubility limits was approached in two ways. The first measured a physical property, electrical resistivity, at the equilibrium temperature. The second, a micro-hardness characterization of a diffusion zone, is a room temperature evaluation of a mechanical property under conditions removed from equilibrium. A close correlation between two such basically different approaches would strongly justify confidence in the results. I) MEASUREMENT OF SOLUBILITY OF LITHIUM IN ALUMINUM BY ELECTRICAL RESISTIVITY Experimental Procedure. Alloys for electrical resistivity measurements were made by melting and

Jan 1, 1962

By H. H. Kellogg, T. R. Ingraham

Three anhydrous zinc sulfates have been identified. They are: ZnSO,(a), stable below 1007°K; ZnS04(/3), stable above 1007OK; and ZnO.ZZnSO,. The decomposition pressure of each sulfate has been measured and the following relations calculated from the results: The measured data have been combined with the known themzodynamic properties of ZnS, ZnO, Zn, SO,, and SO, to yield univariant and bivariant phase diagrams for the system Zn-S-0. The application of these diagrams to problems of roasting zinc concentrates is discussed. PRESENT knowledge of the equilibrium chemistry of the system Zn-S:O, so essential to scientific control of zinc-blende roasting, is deficient in several respects. A basic sulfate of zinc has been reported by many investigators, but its composition is in doubt and its thermodynamic properties have not been measured. Our scanty knowledge of the properties of the normal sulfate at roasting temperatures is based on old and inexact studies. A crystal transformation in the normal sulfate, involving a sizable heat effect, has been noted by several investigators but has never been quantified. The studies reported herein were designed to fill these gaps in knowledge and to make possible a reasonably complete thermodynamic description of the system Zn-S-0 at roasting temperatures. The results make possible a far more exact understanding of zinc roasting chemistry than was hitherto possible. EXPERIMENTAL The principal experimental technique employed was the measurement of the total gas pressure developed from decomposition of either ZnSO, or ZnO2ZnS0, in a closed system. The apparatus employed was essentially the same as that described by Warner and lngrahaml and Flengas and tngraham.&apos; The unusual feature is a flexible Pyrex bellows used to separate the reaction gas mixture (S03, SOz, and 02) from the mercury in the manometer and thus prevent corrosion of the mercury by SO3. The bellows operates without evidence of hysteresis and, barring accidents, may be used for several months. The response of the bellows varies from manometer to manometer, but is generally of the order of 0.6-cm displacement for a l-cm change in pressure. The response for all manometers has been linear over the range 0 to 1 atm. To prevent condensation and polymerization of sulfur trioxide, the bellows-manometer was maintained at 100.0" * 0.5" by a circulating bath of silicone oil. The connecting tubing between the manometer and the furnace was maintained at 100.0" * 0.2"* also, with a stirred air bath. The open end of the manometer was connected with a chamber which was maintained at a known pressure. The pressure could be varied so that readings of the height of the mercury column, measured with a cathetometer, could be made with both rising and falling mercury column. By using the average of the readings, any error due to sticking of the mercury column was minimized. The sample was placed in a 2-in.-long platinum boat formed into the shape of a half-cylinder. The sample was prepared as a fine powder and pressed against the inner wall of the platinum boat. A silica thermocouple well, covered with a platinum sleeve, was placed lengthwise along the center of the boat. The temperature of the sample was read on a calibrated Pt-10 pct Rh theirnocouple. The temperature profile of the furnace was constant within ± 0.2 C over the length of furnace occupied by the sample. The horizontal furnace used to contain the sample and the quartz reaction tube was electrically heated, with the control thermocouple placed 1/4 in. from the windings. A Brown Pyro-O-Vane temperature controller with a 3-sec response time was used to maintain the furnace temperature. Before beginning a run, the apparatus, including the bellows manometer, was thoroughly washed in sib with acid and distilled water to remove any

Jan 1, 1963