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By B. M. Larsen, L. S. Darken

SOME years ago we collated all laboratory data then available to us on the distribution at equilibrium of manganese and of sulphur between metal and simple slags, and used the results in setting up an equation, which proved to be in accord with determinations of the distribution ratio of manganese and of sulphur between liquid steel and open-hearth slag, over a wide range of operating conditions. We now present an outline of our calculations and inferences on these two closely related questions, which are of especial importance because of the advisability of conserving manganese wherever possible. In general. our results show that in the open-hearth furnace equilibrium between metal and slag, with respect to both manganese and sulphur, is substantially attained during the finishing period of the heat, or in about a half hour to an hour after any additions were made. This implies that the end result will be identical whether manganese is added as alloy or metal to the liquid steel or as oxide to the slag. The proportion of total manganese retained by the steel is favored: (I) by use of the minimum amount of lime, consistent with other operating limitations, required to give a lime-silica ratio of about 2.4, which usually corresponds to a minimum practical slag volume; (2) by a high concentration in the slag of MnO relative to FeO; (3) by high operating temperature. Absorption of sulphur by the slag from the liquid metal is favored: (I) by large slag volume; (2-by a high concentration of active (or "free") lime and of manganese oxide dis) solved in the slag; (3) by low concentration of silica, iron oxide, and phosphate dissolved in the slag. DISTRIBUTION OF MANGANESE BETWEEN SLAG AND METAL AT EQUILIBRIUM On the basis that the distribution of manganese between liquid steel and slag is controlled by the reaction [FeO + Mn ;7± MnO + Fe [A] slag metal slag metal] the distribution at equilibrium, at a given temperature, is expressed by the equilibrium constant for this reaction, which is defined as [K" aFPI OFeO ? aMn] where a is the activity of the molecular species denoted by the subscript. The activity of each of the several components, although it is not known precisely, is approximately equal to the concentration of each component expressed as its mol fraction; that is, as the ratio of the number of mols of the given component to the total number of mols of all the molecular species present in the metal or slag, as the case may be. Moreover, since the activity, or concentration, of iron in the liquid metal is in fact substantially constant, the term aFe may he combined with K" to give a new constant K'. Making these changes.

Jan 1, 1942

By R. C. Ruder, C. E. Birchenall

The method of decrease in surface activity was used to determine the rates of diffusion of Co" into cobalt and into nickel. Since the absorption curves for cobalt radiation were quite complex under the conditions of these experiments, the effects of geometry and surface preparation on the diffusion results were investigated. The cobalt self-diffusion coefficients obey the equation DCoco = e-61100/RT cm2 per sec. For dilute cobalt diffusing in nickel, DConi, == 1.46 e-/R' cm2 er sec. AS part of the general program to measure the self-diffusion and dilute-solution diffusion rates of the iron-group metals, the diffusion coefficients of cobalt into cobalt and nickel have been measured using the radioactive isotope Co"'. Self-diffusion studies in iron have been previously reported by Birchenall and Mehl.' The technique of measurement used was the decrease in surface activity method described by Steigman, Shockley, and Nix.' It has been determined that scattering of the measured beta radiation by the specimen matrix is significantly influenced by the condition of the surface and the counting geometry. Accurate diffusion coefficients can be calculated from the activity data provided that the specimens have plane diffusion surfaces and that the absorption properties of the emitted radiation are determined under geometrical conditions duplicating with external absorbers the absorption and scattering in a thin film at the specimen surface as nearly as possible. The cobalt used in this research was originally in the form of hydrogen reduced rondels 99.9+ pct pure. The nickel had been prepared by the carbonyl process and was found by spectrographic analysis to contain 0.03 pct Fe, 0.04 pct Co and smaller traces of other metallic elements for a balance purity of 99.9+ pet Ni. Both materials were vacuum melted and cast in rectangular ingots. Specimens 7/8x7/8x1/4 in. were machined from these ingots. The specimens were then ground to 4-0 emery paper and annealed in hydrogen for at least a day at 1200°C. Some of the specimens were used in preliminary experimentation after which their diffusion faces were machined to remove the radioactive material from the previous diffusion experiments. After grinding, the specimens were polished using an electrolytic lapping technique described by Mazia." This lapping was continued until at least 0.005 in. was removed from the diffusion surface. The final surfaces were metallographically smooth except for a few fine scratches caused by the glass cloth. A large percentage of the area was undisturbed as determined by microscopic examination. The grain diameters of the diffusion specimens varied from 0.1 to 5 mm. There were no effects due to grain boundary diffusion in the experiments

Jan 1, 1952

[Officers and Committees of the Society of Petroleum Engineers 1 Officers and Staff of the AIME 2 Officers of AIME Sections Predominantly Petroleum in Membership 3 Society of Petroleum Engineers By-Laws 5 Alphabetical List of Members 9 Geographical List of Members 110 List of Members by Companies 127 Advertisers' Index 137]

Jan 1, 1961

By C. E. Birchenall, W. Batz, H. W. Mean

AT temperatures between 1095' and 1347ºC, 13 runs have been made on the diffusion of silicon in iron. In two of the runs the couple compositions were entirely within the loop of the Fe-Si system; the base alloys contained 0.0 and 1.0 wt pct Si. The other runs in which the couples consisted of a 2.3 wt pct Si alloy welded to a 3.7 pct Si alloy were a phase throughout. The alloys were made by melting electrolytic iron and commercially pure silicon. Trace impurities were not determined. The butt welded couples were diffused in an inert atmosphere of argon or hydrogen. After cooling, cuts of two mils or greater thickness were machined parallel to the weld interface. The chips were analyzed for silicon. When the concentration and distance data were examined on the conventional probability plot,' no marked variation of the diffusion coefficient with concentration was indicated over the narrow composition ranges employed. Therefore, a single diffusion coefficient is recorded for each run in Table I. The temperatures and atmospheres of the diffusion anneal are listed along with the compositions of the base alloys. For a iron the silicon diffusion coefficient is given by the equation: D = 0.44 e-48,000/RT where R is the gas Constant and T, the absolute temperature. However, since the scatter in the data is fairly large, the activation energy may be in error by as much as 6000 cal per g-atom. The two ? iron points do not permit estimation of the activation energy with any reasonable certainty. They do indicate that the coefficients reported by Smithells2 and Jost,3 based on the work of Fry,4 are much too high. Although very dilute solutions in iron of manganese,5 nickel,8 cobalt,7 and molybdenum8 give dif- fusion coefficients quite close to those obtained for self-diffusion in iron, the silicon values are considerably higher, though of the same order of magnitude. This seems to be consistent with the fact that the silicon atom is the only one of those listed here which is appreciably smaller than iron. The authors are grateful to the Office of Naval Research for their support of this work under Contract N6ori-47, Task order IV, Project NR 031-184, to J. K. Stanley and the Westinghouse Research Laboratories for the silicon alloys used, to several steel companies for the silicon analyses, and to C. Wells, of the Metals Research Laboratory, Carnegie Institute of Technology, for numerous suggestions during the course of the work. References 'C. Wells: Atom Movements (1951) Chapter 2. A.S.M. 2C. J. Smithells: Metals Reference Book (1949) p. 405. Interscience. Pub. Co. 3W. Jost: Diffusion (1952) p. 223. Academic Press. 4 A. Fry: Stahl und Eisen (1923) 43, p. 1039. T. Wells and R. F. Mehl: Trans. AIME (1941) 145, p. 315. "C. Wells and R. F. Mehl: Trans. AIME (1941) 145, p. 329. 7M. F. Hawkes and R. F. Mehl: Trans. AIME (1947) 172, p. 467; Metals Technology (August 1947). .J. L. Ham: Trans. A.S.M. (1945) 35, p. 331.

Jan 1, 1953

By W. F. Boericke

THE recent completion by the United States Aluminum Company of a $4,000,000 addition to its plant at Massena, N. Y., consisting of a large blooming mill and structural mill, gives this organization, a subsidiary of the Aluminum Company of America, the distinction of possessing the largest aluminum rolling mill in the world, as well as the first mil1 in this country to roll aluminum exclusively. The plant is located near the international boundary line between Canada and the United States, about 3 miles from the St. Lawrence River, to take advantage of the development of cheap hydroelectric power which is needed not only for the manufacture of structural shapes from the ingots, but in the reduction of alumina to the metal by the well-known Hall process as well. A power canal from the St. Lawrence River to the power house on the Grasse River at the plant provides for the waterflow, which, coupled with a drop of 47 ft. in 2% miles, generates 80,000 hp. through vertical turbines. An additional 60,000 hp. is purchased.

Jan 1, 1930

By R. C. Mahon

During the early history of the Lake Superior district, tamarack timber was used almost exclusively in the wines. It had the strength and lasting qualities necessary for a satisfactory mining timber. But about fifteen years ago the tamarack trees were attacked by a blight which killed nearly all of them so today no tamarack timber is available. Hemlock, spruce, and poplar have neither the necessary strength nor the lasting qualities for mining timber, but a large supply of maple and birch is available. These have ample strength but, when placed underground, fail by decay in about three years. This means that, instead of replacing the timber sets once in fifteen years, it must be done five or more times in the same space of time which involves not only incraesed timber costs but more important, an increased labor cost.

Jan 1, 1949

Admissions: Joseph C. Gordon, Chairman K. F. Anderson Allen B. Gibson H. J. Gruy R. F. Madera Dan H.-McLendon K. W. Robbins Aurel E. Smith W. F. West Advertising: John. D. Wisenbaker, Chairman Bernard F. Klein Henry N. Lyle R. E. Howard Clark R. Edgecomb, Jr. [ ]

Jan 1, 1961

By Leslie F. Tedsen, Alan E. Flanigan, John E. Dorn

IT is necessary occasionally to use aluminum-alloy sheet where moderately elevated temperatures are encountered. Considerable attention has been directed toward determining the influence of "artificial aging" on the room-temperature properties of the precipitation-hardenable alloys, as testified by numerous company reports and by references 1 to 4. Investigations on the properties at elevated temperatures are few, however,5-7 and have not always covered the range of times and temperatures of greatest interest. The present investigation was instituted to overcome this deficiency. The work was done for the Office of Production Research and Development of the War Production Board, under the supervision of the War Metallurgy Committee, as a part of the "restricted" Project NRC-548. It has been released for publication by the Office of Production Research and Development. As is well known, the high-strength aluminum alloys achieve their remarkable properties as a result of precipitation-hardening. In production they are subjected to a solution heat-treatment followed by quenching, to retain the supersaturated solid solution. The solution treatment is followed by "aging" (precipitation-hardening) either at room temperature or at a suitable elevated temperature. A considerable increase in tensile and compressive yield stresses results from precipitation at room temperature ("natural aging"). Through the elevated-temperature process ("artificial aging") it is possible to obtain values of yield stress considerably higher than those attainable by natural aging. The increase in yield stress is accompanied by a smaller gain in ultimate tensile stress and by a decrease in elongation. During [TABLE I.-Sources of Materials Used in the Testing Program MATERIAL ORIGIN AND TREATMENT 24S-T Alclad.... From Lockheed stock. 24S-RT Alclad... Direct from mill. 24S-T80 Alclad.. 24S-O Alclad from Lockheed stock, solution-heat-treated (925°F., water quench) and aged at 375°F. for t0 t % hour. 24S-T8I Alclad.. 24S-T Alclad from Lockheed stock, plant stretched up t0 I per cent and aged t0 ± % hr. at 375°F. 24S-T86 Alclad.. 24S-RT Alclad from Lockheed stock aged 534 ± 34 hr. at 375°F. 6IS-W (bare).... From Lockheed stock. 6IS-T (bare) 6IS-W (bare) from Lockheed stock aged 8 hr. at 350°F. XB7SS-T Alclad. From Lockheed stock.] the first stages of artificial aging the yield stress increases steadily until it reaches a maximum value. In this condition the material is said to be "fully aged." Further exposure results in "overaging," attended by a steady decrease in yield stress. In the production of the artificially aged materials, temperatures and times are selected to achieve full aging. The following important characteristics are associated with the process: I. The higher the temperature, the more rapidly is the fully aged condition attained.

Jan 1, 1945

Horace F. Lunt, York, Montana* :—Two years ago I visited the region described by Mr. Jennings and assisted in the examination of a somewhat similar group of deposits in the White Mesa sandstone on the Navajo Indian Reservation, 125 miles north of Flagstaff and 50 miles east of the Kaibab plateau. There, the Triassic red sandstone is less than 200 ft. thick, and is overlain by a stratum from 200 to 250 ft. thick of white sandstone, which gives the name of " White Mesa" to that locality. The white sandstone shows all phases of crossbedding in great complexity, and evidently marks a period of oscillation and subsidence of the water, or an elevation of the land, at the close of a geological epoch. The prevailing color is white or gray, but occasionally it is red. In structure, it is composed of well-worn grains of quartzsand, from which most of the cementing material has been leached out, leaving it soft and friable. Possibly the cement was ferruginous, as is indicated by occasional traces of red color. The copper-deposits consist of a replacement of the cement of one particular cross-bedded stratum of the sandstone by chrysocolla, having also at times various quantities of tenorite in grains or masses. Some specimens of the ore contain as much as 32 per cent. of copper. Generally the copper-deposits are a few hundred cubic feet in size, and no strict line of demarcation is shown between them and the surrounding sandstone, the bluish-green color of the chrysocolla gradually fading into the white of the sandstone. The ore is apparently associated with small vertical crevices or fissures. Some of the deposits show a distinct vein-structure, while others do not. The origin of the ore is not very clear. Undoubtedly the solutions, coursing through the crevices noted above, played a prominent part in its deposition, as possibly

Jan 1, 1904

By W. A. Foster

NINETY years after the Riddle nickel deposit N was discovered in Oregon in 1864, Hanna Coal & Ore Corp. began mining operations. Until 1954 much prospecting and preliminary development work had been done on the property, but no ore had been shipped other than for metallurgical testing. The deposit is being explored by churn drilling and trenching, and a few test shafts have been put down for the purpose of studying the ore in place, determining volume and moisture factors, and gathering bulk samples for pilot plant and smelter tests. In churn drilling, 6-in. casing is driven down 2 or 3 ft behind the drill bit and bottomed at each 5-ft interval. All the sludge for each cased 5-ft interval is dumped through a splitter and one eighth is saved and analyzed. Drillholes are stopped after going through the ore zone and penetrating fresh peridotite in which the nickel content is less than 0.5 pct.

Jan 8, 1957

By R. V. Norris

THE wage rates and working conditions in the anthracite. region of Pennsylvania have been governed for nearly 20 years by the award of the Anthracite Coal Strike Commission, appointed Oct. 16, 1902, by President Roosevelt. The report of this com-mission, made in March, 1903, was accepted and, with eight modifications made at various dates, has had .almost the force of law, and has kept this great indus-trial region free from strikes for almost a generation. In 1920, President Wilson appointed an Anthracite Coal Commission, and its report, accepted Aug. 30, 1920, governed wage conditions to April 1, 1922. Actually, the agreements have been for terms of two to four years, and lately, in 1916 and 1920, the employ-ees have continued at work pending the negotiation of new agreements which were made retroactive, and which have all been modifications of the original 1903 award. With the expiration, April 1, 1922, of the 1920 award approaching, Mr. Lewis, president, of the United Mine Workers of America, addressed a letter, on Feb. 20, to the operators, suggesting a meeting on March 15; this date was accepted by the latter, with the notation that the time was short. At the meeting, the Mine Workers presented 19 demands, and advised that if a satisfactory agreement was not reached by April 1.a suspension of mining would occur, contrary to the practice since 1916 of continuing work with a retro-active adjustment.

Jan 6, 1922

By J. H. Bechtold

Tensile properties of annealed molybdenum were investigated from 1000" to—200°C. In the vicinity of room temperature a well-defined transition in tensile properties occurs. Reduction in area decreases from over 80 pct to 0 pct and, simultaneously, the yield strength increases about 60,000 psi. MOLYBDENUM, tungsten, iron, and many other metals and alloys with the body-centered cubic and hexagonal close-packed crystal structures change from ductile to brittle behavior over some relatively narrow temperature range. The temperature at which this transition in ductility occurs depends on chemical composition, microstructure, and method of testing. When fine grained, completely recrystallized molybdenum of commercial purity is tested in uniaxial tension at a slow strain rate, the transition occurs at slightly below room temperature.' Iron2 and tungsten3 tested under similar conditions become brittle at temperatures close to the boiling point of nitrogen, — 195°C and at about 200°C, respectively. A sharp change in ductility is uncommon in metals with the face-centered cubic crystal structure, however, a relatively sharp transi- tion in notched bar impact properties has been observed below room temperature in a face-centered cubic copper-antimony alloy.4 A transition from ductile to brittle behavior is usually explained by the concepts originally developed by Ludwik,5 and discussed and elaborated on by others including Orowan,6 Hollomon and Jaffe,7 and Gensamer8 In brief, there are two aspects to strength, first the resistance to flow and second the resistance to fracture. Both are functions of temperature, strain, strain rate, stress system, composition, and microstructure. With decreased test temperature the flow stress required to initiate plastic deformation increases more rapidly than the fracture strength and brittle fracture occurs at that temperature where the yield strength equals or exceeds a brittle fracture strength. This investigation was conducted to determine the effects of temperature, strain, and rate of straining on the flow and fracture strengths of molybdenum above, through, and below the ductile-to-brittle transition. Other variables were held constant during testing. This information is believed to show

Jan 1, 1954

By E. W. Enqelmann

DURING January, 1933, burlap or coco matting was placed in the bottom of launders handling various products of the flotation plant of the Magna mill of the Utah Copper Co., with the hope of increasing the total recovery of gold. This was soon followed by placing various materials, such as coco matting, cotton twill, and common 10-oz. burlap on the bottom of the main tailing launder. The burlap was found to be the most economical material to use. The test was first conducted in an old wooden launder, 40 in. wide and 2000 ft. long, with 10-oz. burlap fastened

Jan 1, 1935

By N. M. Langdon

Spokane Meeting, September, 1909.) THE following corrections to the paper of Mr. Langdon (Bulletin No. 34, October, 1909, pp. 919 to 940), received after the publication of the paper in the Bulletin, will be incorporated in the paper as finally published in the forthcoming Vol. XL. of the Transactions, but are here presented for the information of members:' Page. 921. Table I., furnace M2, item 11. For " 8801 " read "0.8801." 922. Table II., furnace C, item 2, under gas. For " 0.011 C " read " 0.011 0." Furnace G, item 13, under gas. For " 5.074 air " read " 3.074 air." Item 15, 114.269 " should be " 4.289." Furnace H, item 2, under iron. For " 0.04 " read ".0.01." 923. Table II., furnace J, item 1, under iron. For " 0.95 " read " 0.93." Furnace N2, item 6, under gas. For " 0.66 CO," read 0.066 C02." 924. Table III., furnace C, item 17. For " 379 " read " 397." 927. Table IV., furnace C, item 4. For " 0.0124 " read 0.0424." Furnace G, item 15.. For " 4,060 " read " 4,066." 928. Line 2. Items 19 and 20 of heat-supply, should be items 20 and 21. 930. Line 3. Expunge remainder of paragraph after the word " supplied," and substitute the following : "As compared with the fusion-zone, the loss by radiation n C was 25.5 per cent. of the total (2,278 units) supplied to that zone, while in D it was 22.5 per cent. of the total heat (1,824 units) supplied to that zone. Finally, as compared with the reduction-zone, C lost by radiation 36.8. per cent. of the 1,580 units supplied to that zone,

May 1, 1910

By N. J. Grant, B. C. Giessen, U. Wolff

With the aid of the splat-cooling technique of rapid quenching, metastable alloy phases based on antimony ad bismuth have been prepared. At room temperature, simple cubic phases were found in the Sb + Au, 56 + Yd, and Sb + Ni systems. Another phase was retained in the Au-Bi system at -190°C; in this systent, a microcrystalline phase and a rhombohedrally distorted phase were also observed. The crystal chemistry of these phases is discussed in terms of their valence electron concentration range. A remarkable five-step Phase sequence was found upon heating and equilibration of certain metastable Au-Bi alloys. USING the splat- cooling technique of rapid quenching from the liquid,' a large number of metastable intermediate alloy phases have been prepared in recent years. Thus, Hume-Rothery phases of the hexagonal type based on the valence electron concentration have been produced in systems where they are missing in equilibrium, e.g., Ag-Ge 1 or AU-Sb. 3 In a comprehensive study of metastable alloys based on tin, simple hexagonal metastable y phases were found, raising the total of stable and metastable y phases from 3 to 13. 4 In the In-Bi system, five new metastable intermediate phases were retained.' In most cases, the new metastable phases have some crystal chemical characteristics in common: a) They have rather simple, elementlike structures with few atoms per unit cell, e.g., y phase,4'5 or the metastable primitive cubic phases in the Ag-Te and and Au-Te systems.= b) Their structures are often related to those of the terminal phases, or to elements that are straddled in their position in the periodic table by the constituent elements; this is the case for metastable ß (In-Bi) with the structure of white ß Sn,' or metastable a (Cd-sn). 4 c) They seem to represent the crystal structures appropriate to certain average group number (AGN) ranges in which no or few single-phase structures exist in equilibrium. These average group number ranges can probably be equated in the case of many elements of the Ba(Zn)-Bs(As) groups with the averaged valence electron concentration. In the present work, the splat-cooling technique has been applied to the alloys of antimony and bismuth. In equilibrium, neither element forms intermediate alloy phases with other B elements from groups Bl(Cu) to B4(Si) that contain more than 66.7 at. pct of Sb or Bi, respectively, e.g., AUSb 2. 7 Thus, antimony- or bismuth-rich phases, which might be closely related to antimony or bismuth, and which would reflect struc- tural changes occurring on alloying with small amounts of addition elements, do not exist. Also, the terminal solubility of antimony and bismuth for all B metals is very small. It was therefore of interest to investigate the influence of enforced, nonequilibrium solid solution of addition elements in antimony and bismuth on their crystal structures. It was found that additions of group B 2-B4 metals act distinctly differently than additions of group T 10 and B1 metals. The latter set of additives will be treated here. EXPERIMENTAL TECHNIQUES Alloy preparation and splat-quenching followed closely the procedures described in Refs. 1, 4, and 5; they consisted of the preparation of master alloys from high-purity starting materials (99.99+ pct) and blast-atomizing of 20-mg quantities onto copper sheets. The resulting approximately 1 to 5 u thick foils were investigated by X-ray diffraction. The cooling rates obtained are of the order of 107 to 10 8 C per set,'" causing solidification to proceed at a rat; of approximately 100 cm per sec.' Powder patterns of the resulting fine-crystalline materials were taken with filtered CuK, radiation. For antimony alloys the substrates were held at room temperature and for bismuth alloys at -190°C both during splat foil deposition and X-ray investigation. Annealing treatments at several

Jan 1, 1969

By E. A. Calnan, B. E. Williams

IN the development of a new treatment for the prediction of deformation textures,'-' it was noted that for no metals are there experimentally determined tension textures with which the predictions may be compared. There is a considerable knowledge of drawing textures and previous workers have been content to consider these as equivalent to tension textures for the purposes of comparison. It is shown, however, in the new treatment that the tension and drawing textures are not necessarily identical, the radial compression exerted by the dies in the drawing operation producing some modification of the tension texture. In particular for the face-centered cubic metals it is predicted that for drawing the final texture should be [1ll] with a spread towards [211] (a more detailed derivation of this texture has been made by Calnan3). This has been amply confirmed by experiment, see Hibbard.6 For the pure tension case, however, the treatment predicts intermediate [1ll] and [loo] textures leading to a [211] end-point, while all previous treatments have predicted the final texture as [1ll] with in some cases an additional [loo] component. Thus evidence that the pure tension end-point is the [211], or at least that [1ll] and [l00] are not the final textures, should provide a valuable test of the new treatment. Accordingly some experiments were made on aluminum. Three aluminum specimens were examined in detail, one of cold-rolled high purity rod (99.99 pct), specimen A, and two of commercial extruded rod of purity 99.4 pct, specimens B and C. The initial annealing treatments were: A, 1½ hr at 400°C; B, 2 hr at 400°C; C, 1½ hr at 650°C. The principal difficulty is that of obtaining sufficient elongation before fracture occurs. This was overcome to some extent by giving a softening heat treatment, 1 hr at 300°C, after each 15 pct of extension. Vickers hardness measurements gave values before and after the softening treatment of about 30 and 28, respectively, in comparison with the initial value of about 19 corresponding to fully annealed material. From recent observations in this laboratory it is concluded that this small recovery corresponds to a polygonization process rather than recrystallization proper and consequently the preferred orientation is unaffected. At the higher extensions, however, some slight necking of the specimens took place and it was necessary to turn them down to a uniform cross-section before

Jan 1, 1953

By R. J. Reynik

A semiempirial small flunctation theory of diff- sion in liquids is presented, which employs a fluctuation energy assumed quadratic for a small atomic or molecular displacement and Einstein's random-iralh model. The resulting diffusion equation is given by In these equations. D is the diffusivity, is the average liquid shite coordination number (at interatomic distance d. cm. T is the absolute temperature, xu. em, is (the diffusive displacement. K, is the quadratic fluctuation energy force constant, and rg, cm, are the radii oj diffusing atoms A and B, respectively. The quantities Xn and K are calculated from the computer-filled values of the slope and intercept. respectively. The radius of self-diffusing atom or radii and of diffusing atoms A and B are eta United and compared with values reported in the literature.. The predicted linear variation of diffusivity with. It tempera lure htm been observed in approximately thirty-iire metallic liquid systems, and in over seventy-fiee other liquid systems, including the organic .alcohols, liquified inert gases, and the molten salts, ALTHOUGH the average density within a macroscopic volume element of liquid is constant for fixed total number of atoms. pressure. and temperature, there exist microscopic: density fluctuations within the respective volume element. As such the microscopic volume available to an atom and its Z first nearest neighbors at any instant of time fluctuates above and below the average volume available to these atoms. If one assumes that liquid state atoms vibrate as in a solid. and further postulates that the mean position of any atom in the liquid state is not stationary. but shifts during every .vibration a distance 0 5 j 5 xo. then every atom in the liquid state continuously undergoes diffusive displacements which vary in the range 0 5 j 5 ro. Mathematically. for a binary liquid system consisting of atcrms A and B. the maximum diffusive displacement. .YO, is defined by the equation: where d is the average liquid state interatomic distance at specified liquid state coordination number Z. and v~ \ and vg are the effective radii of diffusing atoms A and B: respectively. For self-diffusion. r^ equals rg , and Eq. [I.] reduces to: It is interesting to note that Eq. [l] or [2] can be used to compute the radii of the diffusing atoms, provided one had an experimental evaluation of xo. As such. the computed radii could be compared with metallic or crystallographic ionic radii to ascerlain the electronic character of the diffusing atoms. Thus it is proposed that in the liquid state the n~otion of an atom relative to its original equilibrium position of oscillation represents the thermal vibration of any atom and its Z first nearest neighbors. while the small and variable displacements. 0 5 1 5 xc,. of the centers of oscillation represent the complex diffusive motions of the atoms at constant temperature and pressure. This is consistent with data obtained from slow neutron scattering by liquids1 ' and resembles an itinerant oscillator model of the liquid state.'" It is further postulated that the atomic displacements characterizing the liquid state diffusion process are essentially a random-walk process. As such. it nlay be described by Einstein's equation:' where D is the diffusivity. sq cm sec-'. j2 is the mean square value of the diffusive displacement. and i> is the frequency of density fluctuations giving rise to diffusion. FORMULATION OF DIFFUSION EQUATION The effective spherical volume occupied by an atom, as a consequence of a microscopic density fluctuation which enlarges the volume available to any atom, exceeds its average liquid state atomic volume by an amount: where AV is the enlarged spherical volume, v is the radius of the diffusing atom. and j is the elementary displacement distance from the original center of oscillation of the vibrating atom to a new center of oscillation position. For small atomic displacements. where c is a constant whose value depends upon the assumed geometry of the enlarged volume. For a spherical increase in volume, c equals 4nr2. Following the treatment of Furthl' and ~walin." assuming the enlarged volu~nes AL7 for the diffusing atoms are distributed in a continuunl. the probability of finding a fluctuation in the size range 0 5 j 5 xo defined by Where c includes the geometric constant cl and Eij) is the fluctuation energy causing the volume change. But the proposed model assumes all the Z first nearest-neighbor atoms are centers of oscillation. and hence the probability that any of these atoms is adjacent to a fluctuation of magnitude 05j5xo is unity. Thus:

Jan 1, 1970

By N. J. Grant, Per Knudsen, J. T. Blucher

The fatigue behavior of three SAP alloys was studied in ternzs of strain rate and temperature, at high strains. The k values in the modified Manson-Coffin equation, Nk4 = C, were less than 0.5 under all test conditions, and change with strain amplitude for the lower-oxide alloys at about 2 pct strain. Lowest k values were near 0.25. Strain rate had no effect on life at 80 F, but had an increasingly greater effect with increasing temperature above 500". Life decreased with decreasing strain rate, above 500"F, and with increasing temperature. Ductility at fracture in a tension test was indicated to be an important factor in determining 1ife in these big+-strain tests with the SAP alloys. INEVITABLY, in the course of mechanical tests at elevated temperatures, particularly if significant time at temperature is involved, there are large changes in structure; these changes make it difficult to relate behavior patterns over ranges of temperature or strain rates at high temperatures. Such changes are to be expetted in low cycle fatigue at low strain rates and high temperatures. Accordingly, it was of great interest to examine the low cycle fatigue behavior of SAP / an aluminum oxide dispersion-strengthened aluminum, a type of alloy which had shown unusual structure stability to temperatures as high as 1000" to 1150°F and resisted recrys-tallization essentially to the melting temperature.'j3 Since the matrix is pure aluminum, there are no complications of averaging, agglomeration, or phase solution. It was also desirable to check the Manson-Coffin equation4?' for the SAP alloys, namely N~E~ = , where ep is the total plastic strain amplitude, k and C are constants, and N is the number of cycles to failure. Here, too, was an opportunity to check the roles of temperature and strain rate with a very stable material. Tavernelli and coffin6 had concluded that k had a value of about 0.5 for many alloys and C was equal to ~/2, where E is the fracture ductility determined from a static tension test. The results were obtained from low-temperature tests where creep and diffusion processes are unimportant. Manson7 found k = 0.6 fitted his data reasonably well; however, in later analyses of a large amount of low cycle fatigue data generated at room temperat~re@"~ he found k to vary from 0.6 for short lives to 0.21 for long-life fatigue tests. In the latter studies,89g Manson separated the total strain range into elastic and plastic components when he found that k was influenced by the nature of the strain. The use of EL (total strain) instead of EP (total plastic strain)4'5 makes a difference in the resultant k value. The ratio of changes with temperature, strain rate, and strain; further, there are the problems in the determination of the elastic strain. Based on these considerations, and the improved fit of points in a plot of by Wells and Sullivan,' is also utilized in these studies. Anderson and wahl,14 using commercial 1100 aluminum, and Blucher and Grant,15 using 99.99 pct pure aluminum, found an increase in life with increasing test temperature. Anderson and Wahl were the first to report low cycle fatigue results from SAP materials. With increasing temperature, the role of strain rate becomes more important. In this regard, care must be exercised to differentiate between frequency (wherein strain rate may vary from zero to a maximum in each cycle, sinusoidally, for example), and constant strain rate, as used in the present study, in a saw-tooth type cycle; in the latter case, the frequency is not specified but can easily be calculated from the strain and strain rate data. It has generally been found that life in low cycle fatigue tests decreases with decreasing frequency16 or with decreasing strain rate at elevated temperatures.15 Coffin,17 reviewing Eckel's work,16 also reported that k increased with decreasing frequency for acid lead, yielding values from 4.0 at a frequency fo 6.6 cycles Per day to 1-46 at a frequency of 7440 cycles per day; the value of k decreased to 0.58 at a frequency of 2.38 x lo6 cycles per day. EXPERIMENTAL PROCEDURE Three SAP alloys, of two nominal compositions, were tested. Alcoa supplied XAP 005 as 2-in.-diam extruded bar, of nominal composition A1-7 wt pct A1203. The Danish Atomic Energy Commission supplied SAP 930 (A1-7 wt ~ct Ala3) and SAP 865 (A1-13 wt pct Al&) manufactured by Swiss Aluminium Ltd., in the form Of $-in.-diam extruded rod. Metallographic comparison of the structures of XAP 005 and SAP 930 showed the former to have a more uniform oxide distribution. Button-head specimens were machined in the longitudinal direction of the bar with 0.4 in. gage length by 0.2 in. diameter, with a fillet radius of j-B in. After machining, the specimens were electropolished in a 1 to 4 mixture of perchloric acid to methanol to remove all machining marks. All test bars were in the as-extruded condition. The fatigue tests were performed on a hydraulically activated, axial strain machine, with complete reversal of strain.15 Test conditions were:

Jan 1, 1969

T. R. HARRISON, Washington, D. C. (written discussion). *-Mr. Kowalke shows that a high resistance millivoltmeter is subject to smaller errors, due to change in resistance of the thermocouple to which it is attached, than is a low-resistance instrument. He uses as examples instruments having resistances of 30 and 2 ohms, respectively. At the Bureau of Standards, resistances above 300 ohms would be considered high and 30 ohms rather low. In the tests on calorized-iron thermocouples, a difference between the first and third calibrations of the couples serves to show changes due to the intermediate heat treatment and only under certain conditions would changes in calibrations due to changes in the wire be detected by ,a recalibration after 1 1/2 in. had been cut from the hot-junction end of the couple and the ends rewelded. The calibration of a couple depends only on the thermoelectric prop-erties of that part of the couple which lies within the region of non-uniform temperature, i.e., the temperature gradient; hence, so long as the temperature gradient falls along wires of similar thermoelectric properties no change in the electromotive force is produced by altering the metals of those parts of the circuit that are at uniform temperature. Usually at the cold-junction end of the circuit, copper leads, brass binding posts, manganin resistance coils, and various other materials form part of the circuit, but so long as all are at a uniform temperature (or if for each junction between unlike metals there is a similar opposing junction at the same temperature) no resultant thermoelectromotive force will be produced thereby. Likewise, if a length of several inches at the hot-junction end of the couple is at uniform temperature, it matters not if this section is unlike other parts of the couple, so long as there is good metallic connection and no source of e.m.f. other than thermoelectric is present. Cutting off part of the hot end of the couple within such a region of uni-form temperature would not alter the e.m.f. of the couple.

Jan 12, 1919

By J. W. Marx

A method is given for predicting the complete gravity drainage characteristics of arbitrarily long columns from centrifuge drainage measurements on reconstituted core samples. Oil residuals corresponding to hundreds of years of normal gravity depletion can be obtained in a few hours on the centrifuge. The gravity flow rate at any stage of the depletion process may be determined from the time correlation derived, and experimentally checked, in this study. INTRODUCTION Apart from the original observations of Muskat et al1, research publications2,3,4 on the subject of gravity drainage have been largely concerned with establishing in detail the saturation, S as a function of the height, z, in a draining column at any given time, t. Some form of numerical integration must be employed to obtain production rates and cumulative production even when S(z, t) is known. Furthermore, the relevant experimental work has been concentrated on drainage of a single wetting liquid from unconsolidated media. Since oil production usually concerns the drainage of a partially wetting liquid from consolidated media, in the presence of connate water, and since it is unlikely that sufficient information exists to establish S(z, t) in detail for any natural reservoir, the published research work appears to be, at best, only qualitatively applicable to production problems. With this in mind, the present study was undertaken by the writer. Experiments were planned whose results would have two advantages over existing measurements: 1. Observations were to be made on specific reservoir rock, reconstituted with formation water and formation oil. This would reduce their generality, from the research viewpoint, but increase their utility for production purposes. 2. The measurements were to be self-integrating, i.e., the phenomena were to be described and interpreted in terms of cumulative results. THEORETICAL DEVELOPMENT It was commonly known that centrifuging a liquid bearing porous medium increases the drainage rates and minimizes capillary end effects. The specific problem lay in selecting an acceleration, a, such that the mean residual saturation of a model cylinder was equal to the residual saturation of an arbitrarily long prototype column when the latter was drained by earth gravity alone. The physical conditions required to permit a valid scaling of model drainage time, tm with prototype drainage time, t, may be stated as follows: (a) At t = tm = O, So = Smo; (b) At t = tm? 8 Sr. = Smr.; (c) For all intermediate values of t and dS/dt=dsm/dtm whenever S = Sm; (d) S(z) = Sm(z) = a constant when t = tm = 0. 1 Here S = T I S(z)dz, where h is the length of the « Jo cylindrical column being drained and the subscripts S,Sm, and refer to model, initial, and residual systems, respectively. The first three conditions mean, simply, that an 3 vs t plot will be numerically identical with an S, vs t, plot,

Jan 1, 1957