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By W. G. Pfann

A simple method of obtaining multistage batch separations by crystallization was described recently. Known as zone-refining, it comprises passing short molten zones through a long solid charge. This technique can now be used on a continuous basis by means of the zone-void method described in this paper. Feed enters, at an intermediate point, a column down which molten zones travel, and waste and product leave at the ends. Materials move in the column through the agency of voids, which are introduced at the ends and travel toward the feed inlet. The voids and molten zones are moved by external heaters in a simple manner, and the principle of reflux is utilized. ANEW method of obtaining multistage separations by crystallization was described recently.' Named zone-refinina.,-, the method comwrises slowly passing a series of molten zones through a long solid charge. Solute becomes concentrated at one or the other end of the charge, depending on whether it raises or lowers the freezing point of the solvent. The separation increases with the number, P, of zone-passes, approaching a limit as P approaches infinity. Zone-refining has been highly effective in purifying germanium and other substances.2,3 and new applications are steadily increasing. Zone-refining is a batch method and as such it has certain limitations inherent in batch operation. If it could be made continuous, its scope and utility would be greatly broadened. This end has been achieved by the zone-void method described in this paper. In the zone-void method feed is introduced continuously at an intermediate point in a column down which molten zones travel, while impure waste and purified product leave at the ends. Both the flows of feed, waste and product, and also the travels of the zones, are actuated by external moving heaters in a simple manner; and the system utilizes the principle of reflux. The method provides, in the field of crystallization, the counterpart of the continuous fractiona-tion column in the field of distillation. The following will be discussed: apparatus and mode of operation, fundamental nature of the separation, design theory, and practical considerations. The method will be described in terms of a binary solute-solvent system in which the solute is an impurity to be removed and the solvent is the desired product. The distribution coefficient, k, defined as the ratio of solute concentration in the solid freezing out of a molten zone to that in the liquid in the zone, is assumed to be constant and less than one. The process is equally effective for k's greater than one and for ternary or higher order systems. Method and Apparatus The essential features of a continuous zone-refining process are represented in highly generalized form in Fig. 1. A series of molten zones, produced by moving heaters, travels slowly down the column or charge (to the left in Fig. 1). If there were no flows of feed, waste, or product, the process would simply be batch zone-refining, the action of the molten zones being to sweep solute down the column, solvent up the column. For the process to be con- tinuous, with stripping and enriching sections in the column, feed must enter, and waste and product must leave, as indicated. The zone-void process accomplishes both objectives, namely, the indicated movements of zones and the indicated flows of material. Zones are moved by moving heaters, just as in batch zone-refining. Materials are made to flow by creating voids at the waste and product exits and causing these voids to move to the feed inlet. Since there must be a net flow of material from the feed inlet to each of the outlets, the indicated movements of voids are in the desired directions, because movement of a void in a given direction corresponds to flow of material in an opposite direction. In order to produce the desired movements of voids, the column is folded into two vertical sections having the feed inlet in common at their upper ends. Voids are displaced upward by the liquids in the molten zones and their travel is actuated by the motions of the zones. Voids travel with the zones in the enriching section and move continuously. Voids travel opposite to the zones in the stripping section and move intermittently. Creation and travel of voids will now be examined in detail. The enriching section of a column in operation, with its void generator, is shown in Fig. 2. The column section is a vertical tube around which a series of closely fitting, regularly spaced heaters travel slowly upward. Each heater produces a molten region, the temperatures of the heaters and the cooling between heaters being controlled so as to maintain the molten zones approximately constant in size. A void is normally present atop the molten zone in each heater. As the heater rises, it continuously melts solid above it, which drips through the void into the molten zone and continuously freezes out solid below it, of concentration k times that of the liquid in the zone. When a molten zone and void reach the feed inlet, which is kept molten, the void is displaced by an equal volume of feed liquid. Generation of voids of controlled size in the enriching section is shown in Fig. 3. The void generator is a tube of small cross-section, provided with lateral heat-conducting fins which sense the position of the heater. Liquid can escape only when the entire outlet tube is within the heater. If any part of the outlet tube is outside the heater, liquid cannot escape,

Jan 1, 1956

W. L. SaundeRs, New York City (communication to the Secretary*):—Notwithstanding the sweeping statements made by Mr. Clarke in this paper, the friends of compressed air are not dismayed. There is no war between electricity and compressed air. Each one has its field of usefulness, and in that field each is supreme. In spite of commercial interests, in spite of prejudices and the enthusiasm of the inventor, the thing that is best will survive and flourish. At least ten years ago, our engineering papers contained large advertisements and pages of reading-matter about the application of electricity to mines, recording the introduction of numerous rock-drilling plants, and claiming that the problem had been solved, greatly to the advantage of the miner and with promise of large profits to the manufacturers of electrical apparatus. Edison and Thomson labored to apply electricity to mines, and each believed that the probabilities of success were great. This was the period of the solelloid rock-drill, which mas admirably suited, theoretically, to the percussive principle and in the development of which hundreds of thousands of dollars have been spent without satisfactory result. I have searched in vain for a standard mining equipment where electric rock-drills are in constant, commercial operation. During a recent trip made from New York to California, I visited most of the important mines of the West and failed to discover a single electric equipment, so far as this class of mining-work is concerned. If any one will inform me where there exists today an electric-drilling equipment in constant service in mines in the United States, I shall be glad to receive the information. Mr. Clarke has been for some years an active and intelligent writer on the subject of electricity for mining. Whenever his

Jan 1, 1904

By Thomas C. Baker

The Fresnillo unit of the Mexican Corporation, S. A., is situated at the old historic mining town of Fresnillo, Zacatecas, Mexico, 33 miles north of the city of Zacatecas and 750 miles south of El Paso, Tex. It is connected with the Mexican Central Railroad by a broad-gage spur 5.5 miles long, belonging to the company. Fresnillo is surrounded by a broad semi-arid valley on the Mexican plateau at an elevation of 7300 ft. The monotony of the valley is broken by a number of low hills. Near the town of Fresnillo is the " Cerro de Proano," an elliptic-shaped hill of gentle slope, rising out of the plain to a height of 325 ft.; the base has a major axis of 4500ft. and a minor axis of 3000 ft. In this hill is the silver-bearing mineralized zone, which comprises past and present mining operations. (In this paper money values are expressed throughout in American currency and the dry short ton of 2000 lb. is used.) The discovery of ore at Fresnillo is credited to the Spaniards, soon after the conquest of Mexico. There are, however, no authentic records to show the amount of work done by them. In 1832, the State of Zacatecas took possession of the property and operated it. Evidently the rich ore above the horizon of the plain had been fairly well exhausted, as an old record states that thirty shafts were used for unwatering, requiring 300 men and 1500 animals. The cost of pumping alone amounted to $150,000 a year. In spite of the fact that cheap convict labor was used, mining costs were reported as $20 and treatment charges as $20 per ton. In 1835, the state was obliged to seek foreign capital, and a company formed in London secured a controlling interest in the property. This new organization sank two shafts, one 11 by 19 ft. and the other 10 by 15 ft., to unwater the mines and extract ore. Large Cornish pumps were purchased in England and hauled overland from Vera Cruz; engines also were installed to operate the arrastres (grinding mills) in the patio process of ore treatment. Substantial buildings were erected and operations were conducted on a large scale, for that period. The patio, the largest in Mexico, was 1150 ft. square. The costs for 1850 were:

Jan 1, 1925

By Wilfred P. Sykes

AT intervals in the course of history an event occurs which, though scarcely heeded at the moment, marks in retrospect the beginning of a new era in some one field of human activity. Such a happening is perhaps more readily spotted in the field of technology than in other realms of human endeavor. Here the span of years is relatively short and the records have been kept with some degree of precision. In the current scene of our social and economic drama the art and science of metallurgy is playing a major role. Off stage will be found the metallurgist in one guise or another aiding, he trusts, in the development of processes and products which will contribute to the happiness of his fellow men. The results of his efforts appear in the form of metallic substances known as alloys built up from any two or more of the wide variety of metals which have been extracted from the mineral deposits in the earth's crust. An alloy by virtue of its inherent physical properties may seem ideally suited for human use in a special way but until this material can be produced economically it will fail to attain a place of prominence as an article of commerce. In fact many commercial alloys are being continually replaced by new or modified compositions better suited to meet the increasingly severe demands of industrial service.

Jan 1, 1939

By Oliver B. Hopkins

Peru produced approximately 17,466,620 bbl., of oil during 1937, or slightly less than the record high of 17,593,700 bbl. established during 1936. As in 1936, the entire output of the country was derived from the La Brea-Parinas, Lobitos-Restin and Zorritos fields in the northwestern part of the country. Outside of the proven areas, drilling was 'continued by the Peruvian Government in the northern province of Tumbes on the reserved zone at Zorritos. Drilling was carried out on three locations, two of which are understood to have been abandoned during the year. In southern Peru, further attention was given by Government engineers to the Pusi and Saman districts and plans are being worked out for the commencement of drilling operations in the near future in the vicinity of Pirin. Activities in the montaiia region in eastern Peru were continued by the Compafiia Petrolera El Ganso Azul. This company acquired the interest of the Selden Breck Co., and holds some 90,000 acres along the Pachitea River a few miles above its confluence with the Ucayali. During the year, the preparation of a landing place, the cutting of a 12-km. (71/2-mile) road from the river to the drill site, and the construction of a camp were undertaken. Equipment for drilling on this company's concessions has already arrived in South America. La Brea-Parinas Estate.—Production of crude oil on the La Brea-Parinas Estate of the International Petroleum Company Limited amounted to 14,722,754 bbl. during 1937, a decrease of 403,736 bbl. from the all-time high reached during 1936. The total production from 1890 to Dec. 31,1937, was 178,390,767 bbl. During 1937, a total of 141,653 ft. was drilled, 129,516 ft. in new wells and 12,137 in deepening existing wells. In all, 57 wells were completed, 47 of which produced oil, 2 were gas wells and 8 dry. holes. Twenty-nine wells were cleaned out or deepened during the year. The average depth of new wells completed during 1937 was 2367 ft. compared with 1984 ft. for the new wells completed during 1936. There was an increased use of rotary tools during the year and this method is now used to a greater extent than the cable-tool method, which formerly predominated. Of the 57 wells completed during the year, 31 were

Jan 1, 1938

By F. C. Miller

The metallurgical fuel of Colorado, Utah, and New Mexico has been a Veiny tardy member in the caravan of western industrial progress. The history of western coke has naturally been closely related to the development of the metallurgy of iron and steel and the precious metals, in the State of Colorado. It was at Leadville, with a population of 300 in 1877, that the Sentinel was published by Richard S. Allen. The Sentinel gave very full accounts of the various mineral discoveries at the new town of Leadville, which found their way to the more widely circulated journals of the East, and attracted the attention of many people. At the close of 1878, a census slowed a total of 5040 persons. The first smelter was established in 1877, at Malta, two miles from Leadville, by A. R. Meyer, but was not successful. It was succeeded by the Harrison Reduction Works, in 1878. The La Plata began with one furnace in June, 1878, and in 1879 had four furnaces in active operation. These furnaces used charcoal for fuel, and, because of hot tops, suffered a tremendous loss in lead and silver. This difficulty was overcome by the erection of 50 single-bank 10-ft. beehive ovens at Crested Butte, Colo., in 1880. The slack coal sent to these ovens was very pure, and yielded a coke carrying as little as 4.5 per cent. ash. Among the pioneers in the Leadville district were Grant, Eddy, James, Billings, Eiler, and Dickson. To these men the West owes the present expansion of its mining industry, and the erection of metallurgical processes for the treatment of precious metals. On Mar. 1, 1876, Pueblo was connected to the Atchison, Topeka & Sank Fe by the Pueblo & Arkansas Valley branch. The first smelter was erected in Pueblo by Mather and Geist. This modest plant grew into the immense Pueblo Smelting and Refining Co., now a part of the American Smelting and Refining Co. Coke for these small furnaces was made from unwashed Engleville coal, in 186 single-bank 12-ft. ovens at El Moro, in the Trinidad district, and it was not uncommon for the percentage of ash to exceed the percentage of fixed carbon in the coke. On Jan. 23, 1880, the Colorado Improvement Co. consolidated

Jan 1, 1920

By T. Lane Carter

BEFORE describing the experience with the Chinese on the Rand and the work they have accomplished, it will be necessary, sary, first, to give a brief account of labor-conditions in the Transvaal since the war, and then to show how the necessity of importation of labor arose. As is well known, the Transvaal mines are run on the dual system of labor-that is, the rough work is done by colored laborers under the superintendence of white men. From the start of mining operations in South Africa there has been the cry of shortness of native labor, due in great measure to the failure of Kaffirs to work continuously in the mines. While he works, the Kaffir is a satisfactory laborer, but his period of service is short, averaging about nine months. People unacquainted with the Kaffir have maintained that, by offering a higher wage and better accommodation, better results would be obtained from the native workers, but an increased wage simply aggravates the trouble. The Kaffir's wants are few. While at work he spends little of his money, and before long has sufficient capital with which to buy wives and become a gentleman of leisure. Doubling the wage of the Kaffir means that he acquires a competency in half the time, so that his period of service is correspondingly reduced. In 1899, before the war, there was always a cry about the scarcity of Kaffir labor. The highest number of natives at work was in July and August, 1899, when nearly 100,000 were employed. At the outbreak of hostilities the Kaffirs were scattered far and near, many doing well during the war by working for the military authorities. On the, resumption of mining operations on the Rand a serious mistake was made. Based on past experience, it was argued that if the whole industry decided to start anew with

Sep 1, 1908

CARL HENRICH (communication to the Secretary*).-I have read with much interest the discussions of my paper by Messrs. A. S. Dwight, E. P. Mathewson, Win. B. Boggs, Jos. W. Richards, and W. C. Smith. Mr. Dwight's acknowledgment that he always-in lead smelting¬obtained better results by figuring A1203 as an acid in his slags, I may take as a confirmation of my views, notwithstanding his later conversion by, the late T. S. Austin to the latter's empirical view and way of neglecting the consideration of A1203 altogether in the composition of slags-letting the slags "dissolve" in Al203. I have a strong suspicion that Mr. Austin, in a large custom smelting plant at El Paso, has been able to keep the alumina percentage of his slags sufficiently low, not to give him much trouble, although I have also a suspicion that his furnace foreman may have had a somewhat differing opinion of the practical working of the "dissolving" theory,, whenever its applicability was tested to its limits. That Austin should have conceived the notion that the Ca of CaF2 would enter into a slag as CaO, seems hardly in accord with the recognized ability of that late metallurgist. It is a well-recognized fact that even small amounts of CaF2 will reduce the viscosity of a slag; but I did not think anyone ever had an idea that CaF2, in some mysterious way, parted with its F and coupled itself with 0 to satisfy a craving for CaO on the part of 802-least of all in a lead furnace. The "dissolving" theory for CaF2 was doubtless appropriate, and an improvement on figuring the Ca of CaF2 as CaO to satisfy the demand of Si02 for RO bases. However, I cannot understand the rationality of extending this "dissolving" theory to A1203 and to ZnO. It would be interesting to have more specific data from Mr. Mathewson in regard to the actual composition-analyses-of the slags made, when he had these unusually high alumina slags in Colorado. We "old" smelters all know that within certain limits, usually found out by rather tough experience, we could safely "disregard" A1203. In fact, I believe, we never really analyzed for alumina, except in slag analyses, when we

Jan 6, 1917

By Albert Sauveur

My first paper dealing with the theories of the hardening of steel by rapid cooling was published in the Transactions of this Institute in 1896— 30 years ago-under the title "The Microstructure of Steel and the Current Theories of Hardening," hence, also, the title of the present paper. It was extensively discussed and was, I believe, one of the starting points of many subsequent papers and discussions of the same subject, dis-cusssions which at times became almost violent and which led to the formation of different schools such as the "Carbonists" and the "Allo-tropists." Some of the older members of the Institute, who took part in the debate or who were interested observers, will, I am sure, have kept a vivid remembrance of it. The controversy gradually quieted down, apparently for lack of ammunition, without any side acknowledging defeat. Recently, however, interest in it ha been revived through the claims of some that these vexed questions had at last been solved. In an effort to ascertain if possible the prevailing view of those best qualified to express an opinion a questionnaire was submitted to the following gentlemen: J. 0. Arnold Sir Robert Hadfield Edgar C. Bain W. H. Hatfield Carl Benedicks Samuel L. Hoyt N. Belaiew Kotaro Honda H. M. Boylston Zay Jeffries Harry Brearley H. Le Chatelier G. K. Burgess H. H. Lester William Campbell Francis F. Lucas H. C. H. Carpenter John A. Mathews Pierre Chevenard A. McCance P. Dejean Albert Portevin C. A. Edwards Walter Rosenhain F. Giolliti Bradley Stoughton G. Grenet F. C. Thompson Leon Guillet

Jan 1, 1926

By P. J. Burkhardt, L. V. Gregor

The oxidation kinetics of single-crystal silicon has been investigated using extremely dry oxygen as the oxidant. Two techniques were used. The first involved a flow system with which incremental thickness measurements were made. This sytem provided an oxygen ambient at atmospheric pressure which had a moisture content of less than 0.1 ppm of water. The second technique involved measuring the change in volume of oxygen with time in a closed system. A temperature range of 900O to 1200 "C and a pressure range of 20 to 760 Tory were covered. Both techniques showed that a simple parabolic rate law holds only at the higher temperatures. At lower temperatures, the data up to 5000Å can be fitted well to a linear-parabolic equation. The two constants in this rate equation are examined in terms of a physical model. The parabolic portion of the low-temperature oxidatLon fits along the high-temperature curve of an Arrhenius plot. The parabolic rate constant for the flow-system technique can be expressed by k = 2 x 10-9 exp (L 31 kcalRT) sq cm per sec. The manostatic technique gave k = 1 x 10-exp (- 23 kcalRT) sq cm per sec. By extending the thickness range to over 104. a rate law of X = At seems to fit all of the data better than the linear-Pavabolic law. Here the exponent n increases from 0.518 at 1150 V to 0.637 at 900°C. PASSIVATION of silicon planar devices through thermal oxidation is of such great importance that considerable effort has been devoted to the study of the process.17 Much of this work involves hydrothermal oxidation, in which H2O is the oxidant: whereby H2 is produced. It has been proposed that the reaction proceeds by the formation of Si-OH groups and hydroxyl diffusion through the film to react with the silicon surface. Thus, the silicon oxide layer probably contains residual hydrogen in some form after oxidation in H2O and it has already been established that hydrogen has a marked effect on the electronic properties of oxide-passivated silicon surfaces. Silicon is oxidized by oxygen at elevated temperatures; but the rate of oxide formation is considerably lower than that for 0." By using dry O2 as the sole oxidant, the presence of residual hydrogen is presumably avoided. At present, the mechanism of thermal oxidation by dry O2 is a matter for conjecture, and the presence of small amounts of H2O was reported to have a marked effect on the rate of oxide formation10 (perhaps on the electronic properties of the surface, as well). Hence, this study of the kinetics of silicon oxide growth in 0, was undertaken: 1) to determine the oxidation rate at atmospheric pressure in a system designed to exclude rigorously all traces of H2O in the ambient 0,; 2) to obtain oxidation-rate data in situ in dry O2 by means of a continuous monitoring of the amount of 0, consumed during oxide growth. These objectives are complementary—the first assesses what effects (if any) are obtained by excluding H2O from the reaction, and the second expands this information while at the same time avoiding the uncertainty inherent in relying upon incremental measurements of oxide growth to furnish kinetic data. EXPERIMENTAL PROCEDURE The conventional silica open tube in a resistance-heated oxidation furnace is subject to sources of trace H2O, even after the input O2 is thoroughly dried and the outlet gas stream is passed through a trap to prevent

Jan 1, 1967

By F. H. Deily, Jean M. Quets, Milton E. Wadsworth, John R. 222-000-000-012 Lewis, D. S. Rowley, R. J. Howe

Samples of synthetic magnetite were reduced in hydrogen-water vapor atmospheres in the temperature range 450o to 900oC. The reaction was always surface controlled, indicating the final products of reaction are nonfirotective. Three separate cases have been identified from the kinetic results: Case I, reduction of magnetite to iron below 570°C; Case II, reduction of magnetite to iron above 570°C; and Case 111, reduction of magnetite to wustite above 570 oC. In Cases I and 111 the kinetics have been explained by the formation of oxygen anion vacancies in the magnetite surface followed by associated diffusional processes. In Case 11 the observed kinetics have been related to the concentration of iron cation vacancies in the wustite layer formed, followed by associated steady-state diffusional processes. The concentration of cation vacancies in the wustite is maintained constant by the magnetite-wustite equilibrium. THE reduction of the oxides of iron has been a subject of study and interest for many years. However, few attempts have been made to interpret the results in terms of the mechanism of reduction of an iron oxide by either hydrogen or carbon monoxide. Stalhane and Malmberg' using CO, H2, and CO-Hz mixtures, developed the rate expression: where m = mass of oxide reduced, t = time, k = a constant, s = surface area, P = partial pressure of of CO or H,, and P, = partial pressure of the reducing gas at equilibrium. The rate of reaction per unit area was proportional to the difference between the partial pressure of the reducing gas and its pressure at equilibrium. Hansen, Bitsianes, and Joseph2 studied the reduction of pellets of hematite to magnetite with mixtures of CO-CO,. They concluded that below 450°C the reaction proceeded according to a model in which CO reacts with the hematite surface producing an oxygen ion vacancy. The rate controlling step was then assumed to be oxygen ion diffusion through vacancies resulting in the formation of magnetite. They derived an expression giving the rate of reduction proportional to the cO/CO, ratio. Recently McKewan3 published results for the reduction of magnetite spheres in atmospheres below 570°C. He explained his results by an equation of the form where K, is the equilibrium constant for wustite-iron equilibrium attributed to the formation of wustite as an intermediate in the reduction of magnetite. According to McKewan, Kp is an equilibrium constant for H, -HO adsorption in which oxygen is deposited on the surface from the H,Oand subsequently acts as a poison for reduction by hydrogen. Sample Preparation and Experiments. In this work the authors used the same apparatus and experimental procedure employed in the hydrogen reduction of magnetite. Sintered disk samples weighing approximately 1.5 g and measuring 1.2 cm in diameter and 0.25 cm in thickness were prepared by a method described previously.4 Partial pressures of hydrogen and water vapor were controlled by bubbling hydrogen through a series of flasks containing distilled and deionized water maintained at constant temperature in an oil bath. The total flow rate of the reacting gases—hydrogen and water vapor—was approximately 0.5 liter per min. The entire external system was maintained at a temperature above the oil bath to prevent condensation of water vapor. This was accomplished by wrapping electrical resistance elements over all surfaces. The glass column containing the weighing system-a McBain balance suspended from a gold chain-was enclosed in an aluminum tube heated by nichrome resistance wire enclosed in an insulating material. The temperature of the glass column was held constant by means of a series of thermocouples connected in parallel to a Leeds and Northrup temperature controller. This was necessary since variations in temperature resulted in expansion and contraction of the glass column and could be readily observed with the cathetometer. The spring extensions were measured through a window with a gaertner cathe-

Jan 1, 1962

By G. H. Kesler, C. E. Dryden, J. H. Oxley

Rates of heat- and mass-transfer from rods to recirculating air were determined within a one-quarter-scale model of a metals deposition bulb. The dependence of local and averaged rates of transfer upon outlet geometry, number of rods, position upon a rod, and airflow rate was established for flow patterns created by radial and tangential air inlets. The results are given a qualitative interpretation in terms of rates and distribution of metal deposition in a prototype deposition bulb. IT is well known that a number of metals can be prepared from volatile compounds containing them by causing dissociation of their compounds to occur at heated surfaces. Examples of such metals include silicon, titanium, zirconium, and aluminum, which can be prepared from their halides. While the ability to prepare high-purity metals by this technique is of importance in itself, the rate of deposition of metal also is important in considering the commercial potential of such a process. If the over-all process of deposition is broken down into separate steps of transport of materials to and from the heated deposition surface and establishment of chemical equilibrium at the surface, as was described in a recent paper,1 then since surface temperatures are usually high and surface equilibrium is attained very rapidly, the rate-controlling step can be considered as either that of transport of reactants to the surface or of transport of products other than deposited metal away from the surface. These two transport steps are related through the reaction stoichiometry. It can be shown1 that the rate and distribution of metal in such a transport-controlled process are determined by the over-all and local mass-transfer coefficients in conjunction with the equilibrium conversions at the hot surfaces. The rate relationship is: w = [KA(y a-y s)] B.E where the bracketed group is the rate of arrival of the reactant at the surface of area A as determined by the mole fraction driving force (y a - y s) and the convective transport constant K. The factor B is the weight fraction of metal in the reactant, and E is the equilibrium fractional conversion to metal. Numerical values of y, and y, are fixed by the vapor composition and the equilibrium compositim of reactant at the surface; and E can be determined by thermodynamic calculations or by experiment. However, values for the convective coefficient K are available generally only for systems of simple geometry, such as cross-flow past a rod or sphere or parallel flow past a flat plate or through a tube. Often it is necessary to work with systems of more complex geometry and in which the vapor flow may not be uniform or exactly parallel or perpendicular to the surface. It is possible, of course, to establish working correlations for these more complex systems by direct experiment; but the experiments usually are costly in both time and money. To circumvent this objection and to aid in arriving at an understanding of the relationships and interactions of the process variables, it is helpful to construct a model of the flow system in which air, water, or other convenient fluids can be substituted for the process vapors and with which mass-transfer measurements or analogous he at-transfer measurements can be made upon a simulated deposition surface. By this means, a large number of measurements can be made in a reasonable time, and the correlation of these results can be applied to the prototype system. Examples of the application of these techniques are to be found in the literature (e.g., Ref. 2). It is the purpose of this paper to illustrate these techniques by description of a model study which was done at Battelle Memorial Institute. The work to be described was of a preliminary nature; the investigation subsequently was extended to develop quantitative relationships among the significant dimensionless transport, geometric, and flow parameters. This more detailed study will be the subject of a future paper.

Jan 1, 1962

By Michel Elle, John Chipman

The equilibrium of gaseous H20-H2 mixtures with liquid iron-columbium alloys in the range 0.2 to 2.4 pct Cb shows that the activity coefficient of oxygen is strongly diminished by Cb. The oxide in equilibvium with the melt is identified as CbO2. The equi-librium constant at 1600 deg C is [%Cb][fo. % 0]2 = 2.9 x 10-4 where log fo= —0.14 [%Cb]. The deoxidizing power is comparable to that of vanadium, COLUMBIUM (niobium) is finding increasing use as an alloying element in steel. It forms several stable oxides and is removed from the steel bath by oxidizing slags. The specific oxide formed in steel-making is not known although Sazanov snd Shvarts-man,' in their study of its partition between slag and metal, have assumed this to be Cb2O5 It is the purpose of this study to determine its deoxidation equilibrium at 1600°c, the nature of the oxide formed and the interaction between columbium and oxygen in the melt. The investigation was based on the reaction H2 + O=H2O; Kl=ph2o/(pH2[%O]) [1] in which 0 signifies oxygen dissolved in the liquid Fe-Cb alloy. The method and equipment of recent studies2,3 were utilized. In brief, the molten alloy, contained in a small crucible, is held in a controlled mixture of steam, hydrogen, and argon until equilibrium is reached. It is then cooled quickly in a stream of helium and analyzed for columbium and oxygen, the latter by vacuum fusion.4 The solubility of the oxide in liquid iron is determined by visual observation of scum formation on the surface of the melt. Crucibles of MgO proved unsatisfactory because of partial reduction at the metal interface. Pure A12O3 crucibles were heavily blackened by the melt and could not be used at high concentrations of columbium. Silica crucibles were more satisfactory but these introduced some silicon into the melt thus necessitating an uncertain but small correction for its effect on the activities of the other solutes. In silica it was possible to observe the scum formation when the melt became saturated and there was no apparent reaction between scum and crucible. The procedure for saturated melts was as follows. The alloy charge composed of electrolytic iron and columbium grain was melted and held at constant temperature. The gas ratio H2O:H2 was progressively increased by raising the saturator temperature until a point was reached at which a bright film appeared on the surface and covered it completely. This film could be dissolved by raising the temperature of the melt and it reappeared when the temperature was lowered. Under a partial film covering, utilizing bare areas for temperature measurement, the melt was brought to equilibrium with the atmosphere by holding at temperature for about 1 hr as suggested by Dastur.5 INTERACTION IN THE MELT Several experiments were made without columbium to establish a base in silica crucibles. The results are shown in Table I. Except for one run, they agreed well with Floridis1 comparable results in other crucibles. The value of log K1 is taken from Table I as 0.58. This is slightly larger than Floridis' result, probably because of less elaborate safeguards against thermal diffusion. Results obtained in the Fe-Cb-0 series in which no scum formed are shown in Table 11. The equilibrium ratio Kl is defined as ph2o/(ph2[%O]). It is related to the equilibrium constant K1 as follows:

Jan 1, 1962

By H. A. Fisch, A. J. Opinsky, J. L. Bartos

Fort?-six- two-grain bounduries were studied in doped tungsten 1amp wire that had been heated to 3450°K very vapidly. Back-reflection Laue photograms were taken of the grain boundary partners and solved, using a computer. The resulting distribution of large-grain orientations was analyzed. Rotational axes were calculatedfor each grain boundary pair. The axes of least rotation show an anisotropy of rolalional angle. WhILE the orientations of large grains in straight doped tungsten wire have been studied extensively, little has been done to characterize the boundary that separates them. Rosi.1 upon seeing the jagged interlocking boundary in doped tungsten wire. inferred that the grains should have a preferred orientation, and proved it. He interprets his data as indicative of a single ideal orientation—(531)— being parallel to the wire axis. Rieck2, 3 and Mannerkoski' have essentially confirmed this finding. Opinsky, Orehotsky, and Siegle argue that the data suggest that (211)—a plane-is parallel to the wire axis instead. This (211 ) contains the (531). and hence would appear to be a more general case.5 Ahlborn and wasserman6 report that their orientation data stretch from (110) through (531) to (311). This path is the locus of {211 Recently. Opinsky has suggested that the data can be interpreted as a series of ideal orientations that can be related by coincidence relationships to the (110) fiber texture. All these investigators have determined the orientations of the large grains by the back-reflection Laue technique, and they have all obtained similar results. Only Rieck5 as methodically looked at the large grains along a wire. He was apparently not concerned with the relationships of the large grains across their common boundary, but only with their individual orientations. This research was undertaken to fill this gap in the under standing of the mechanical properties of tungsten wire. Only the crystallographic aspects of the problem will be reported here. In addition, the large number of large-grain orientations, which was accumulated in this study. will also be analyzed. EXPERIMENTAL MATERIAL AND TECHNIQUES All of the data were obtained from four pieces of the same 7-mil-diam General Electric tungsten lamp wire. Twelve-inch lengths of the cleaned wire were heated in vacuum by the flick of a switch to 90 pct of the amperes necessary for fusion (a temperature of approximately 3450°K) and held for 1 min. On the basis of other data. it is estimated that the rise time is of the order of 0.5 sec. The four pieces of wire could have come from anywhere within about 18 ft of wire. Consecutive segments of each piece of wire were mounted in bakelite and polished metallographically The polishing procedure followed that described by woods. "nly boundaries between two grains that each occupied the entire cross section of the wire were photographed and X-rayed. The metallographic sample was mounted accurately with respect to the X-ray unit. Steps were taken to read the films as accurately as possible with the conventional Greninger net. The data were then entered into computer programs that solve the Laue film by precisely the same techniques that are used in the solution of the film by means of the stereographic projection. The use of the computer has probably shifted the main source of error from the stereographic plot to the reading of the film. On the basis of several experiments, it is thought that the error associated with the entire process, from mounting the sample through the computer solution, is of the order of about one-half degree. The output of the computer is the direction cosines of the fiducial direction (the wire axis) and the locations of the three cube axes. The former data were used to calculate the differences in orientation between the two grain boundary partners, and the latter were used in the calculation of the rotational axes that could bring the two grains

Jan 1, 1970

By C. N. Reid

Slip-line studies on deformed chromium single cvystals showed the usual bcc behavior. At room temperatuve, cross slip was prevalent—slip was not confined to a given plane, but the slip direction was (111). At -10O0K, slip occuvred on (110) planes, twins on(112) planes, and cleavage on (1001 planes. A single-crystal tensile specimen with an axis close to [011] showed a pronounced yield drop and high strain rate sensitivity which zclere used to derive relevant parame tevs in a dislocation dynamics treatment. Transmission electron microscope studies confirmed the existence of (110) slip planes and showed ecidence of loops punched out by precipitates and of grown-in dislocations promoting tangling. OF recent years experimental studies have been made of the deformation characteristics of single-crystal molybdenum and tungsten, but very little has been published on the behavior of single-crystal chromium. During a study of the mechanical properties of chromium, single-crystal studies were made which have already been partially described.&apos; However, additional information was generated which was not directly relevant to the main theme of Ref. 1, and, therefore, was not reported. In view of the need for complete documentation of deformation modes, the experimental observations made on the deformation of single-crystal chromium are summarized here, together with an electron-microscope study of the associated dislocation structures. It was found that, in terms of the deformation modes, chromium is a conventional bcc metal, showing a very pronounced yield-point phenomenon. Further, it was found that the flow strength of these crystals is very sensitive to the strain rate. Finally, the crystals were observed to contain many unidentified precipitates, which often were associated with prismatic dislocation loops. EXPERIMENTAL METHODS Single crystals were grown from rods of wrought chromium by the method of zone annealing. Rods of "1/4in.-diam were supported vertically in an argon atmosphere while an induction coil was moved up the rod at 1 in. per hr. The power was adjusted to just below that required for melting, and the process produced single crystals in about 30 pct of the rods used. The orientations of the crystals, in general, lay near [011] and are summarized in Fig. 1. Before this treatment, the wrought material contained 35 pprn C, 68 ppm O, and 12 ppm N.* An analyzed single crystal *Usual metallic impurities found in iodide chromium are: Al, 5 ppm; Ca, A ppm; Cu, 2 ppm; Fe, 75 ppm; Yg, 0.5 ppm; Yn, < 3 ppm; Mo, < 3 ppm; Ni, 4 ppm; Si, < 20 ppm; Ti, < 1 ppm; V, 4 ppm; Zr, < 3 ppm. contained 10 pprn C, 79 ppm O, and 50 pprn N. Tension and compression specimens were shaped from the crystals by mechanical grinding, followed by the electrolytic removal of about 0.010 in. from the surface in a perchloric/acetic acid bath. All specimens had a gage length of 0.75 in., and tension specimens had a diameter of 0.100 in., while that of the compression samples was 0.200 in. Mechanical tests were carried out at a rate of 1.3 pct per min, and temperatures below 0°C were attained by means of a nitrogen cryostat similar to that of Wessel.2 EXPERIMENTAL RESULTS Modes of Deformation. In addition to the tensile properties of these crystals, which are described in Ref. 1, deformation markings on the surface were studied. Crystals A and F, Fig. 1, were deformed in tension at 300°K to 10 and 16 pct strain, respectively. The surfaces contained visible slip lines, about 1 C( apart, composed of both straight and wavy segments. They did not define a single plane, and so determination of the slip plane was not possible. However, the slip direction was deduced by comparing the axial orientations of the crystals before and after deformation. Fig. 2 is representative, and shows that the axis ro-

Jan 1, 1968

By Henry A. Wriedt, John Chipman

Equilibrium in the reaction of hydrogen gas with oxygen in liquid nickel, iron, and their alloys has been studied at temperatures of 1500° to 1700°C. The equilibrium con^stant, 0/p, [% O], is greater in nickel then in iron by a factor of 45 at 1594 C. In the alloy steel range, the activity coefficient of oxygen is slightly increased by the presence of nickel. NICKEL is more resistant to oxidation than is iron, in both the solid and the liquid state. The solubility of oxygen,&apos; however, is greater in nickel than in iron. The two metals and their liquid alloys constitute an interesting series of solvents in which the chemical behavior of oxygen can be studied by methods similar to those used for liquid iron.&apos; Experimental Method The furnace assembly, including the tube for preheating the entrant gas, was the same as that described by Gokcen and Chipman. " controlled mixture of water vapor, hydrogen, and argon preheated to approximately the melt temperature impinged upon the surface of the liquid metal. The charge, weighing about 35 g, was held in an alumina crucible at constant temperature in the gas stream for a prolonged period, then quenched in a stream of cold helium, sampled, and analyzed for oxygen by the vacuum fusion method. The temperature of the liquid metal was measured by a Leeds and Northrup optical pyrometer which had been checked against a similar instrument certified by the National Bureau of Standards. The freezing point of electrolytic iron in hydrogen, taken as 153j°C, was used for frequent checks. This point and the emissivity determined by Dastur and Gokcen" established the transmissivity of the optical system. The emissivities of Fe-Ni alloys at 1535" are known from the experiments of Smith and Chipman,h nd it was assumed that the variation with temperature is parallel with that of iron. Recorded temperatures are probably accurate within k5"C. Preparation of Gas Mixtures—Since the ratio H,O:H, had to be much higher for nickel than for iron, it was found convenient to construct two separate systems for gas preparation. In both cases, the ratio of argon to the sum of the other two gases was at least 4, the proportion of hydrogen and water vapor being varied to produce H,O:H, ratios from 0.2 to 70. The primary purpose of the argon was to diminish the errors caused by thermal separation&apos; in the gas phase. In addition, its presence lowered the saturation temperature required for a given H,O:H, ratio and minimized the difficulty of preventing condensation. Both systems were modifications of the one used by Dastur and Chipman.&apos; For H,O:HI ratios greater than 2, welding-grade argon purified by passage over magnesium chips at 620°C was mixed with hydrogen produced in the electrolytic cell shown in Fig. 1. The design was based on a cell used by Bodenstein and Pohl," the important features of which area nickel wire cathode and sodium hydroxide solution as the electrolyte. The rate of hydrogen evolution was controlled by a calibrated ammeter and a rheostat in the circuit, the current efficiency being taken as 100 pct. Precise control of the argon flow rate at about 300 ml per min was achieved by means of a capillary flowmeter having a controlled pressure drop. The molar flow rate was measured volumetrically before each run, and a constant flowmeter setting was maintained thereafter. The A-H, mixture passed through a water saturator of the type previously described," the saturation temperature being maintained automatically with a fluctuation of k0.04"C. The tube between saturator and furnace was heated by a resistance winding. The system was of all Pyrex construction with the exception of the stainless steel tube containing magnesium chips. This was connected with the glass tubing at the upstream end by

Jan 1, 1957

By C. B. Alcock, R. G. Hudson

Sulfur pressure measurements above FeS in equilibrium with iron have been carried out by the Knudsen orifice method. A comparison is made of the weight loss of the cell per unit time obtained in the above experiments, that calculated from Richardson and Alcock&apos;s measurements of the S2 pressure above FeS in equilibrium with iron, and the dissociation constant for diatomic sulfur from spectroscopic and thermal data. EXTENSIVE equilibrium measurements have been made to determine the sulfur potentials of a great many systems of metallurgical interest.&apos; In order to confirm their reliability, to supply data which may be of use in further thermodynamic calculations, and to establish the reliability of the Knudsen orifice in obtaining accurate thermodynamic values at high temperatures, the present investigation on the pressure of the gaseous species above FeS in equilibrium with iron has been carried out. The Knudsen orifice method has been used for these pressure measurements. Experimental The apparatus and general technique for this investigation are the same as that reported for the determination of the vapor pressure of silver.&apos; To reduce the residual gas pressure in the evacuated chamber, a titanium getter, maintained at run temperature, was introducbed. Several types of Knudsen cells were used—platinum, zircon, and fused silica. The orifice in the zircon cell was fashioned with a small diamond wheel. The same precautions were used in this investigation as were employed in the work on Mo2S2.3 The FeS-Fe mixture was prepared by heating a sample of pure FeS,, supplied by K. K. Kelley of the Bureau of Mines, with excess iron powder, cp grade, obtained from the Fisher Scientific Co. These two substances were heated in a closed Armco iron crucible at 960°C, held in a vacuum of less than 10" mm Hg for 24 hr. The mass was then removed from the cell and ground in an agate mortar. In this form it was charged to the various Knudsen cells. Heating the Knudsen cell for an additional two days was sufficient to obtain constant rates of weight loss of the cell. The data obtained in this investigation are recorded in Table I. To establish whether or not a sulfide of iron is volatile at these temperatures, 0.7646 g of the FeS-Fe mixture, described above and containing 69.2 pet Fe, was placed in the zircon Knudsen cell. Run Nos. 103 to 109 were performed on it. After the completion of these runs, the total amount of iron left in the cell was obtained by chemical analysis. It contained 0.537 g Fe, compared to 0.529 g in the original charge. Thus, there was an apparent gain in iron of 1.5 pet. This is attributed to unknown experimental error, and the conclusion is that no sulfide of iron is volatile. The vapor pressure of pure iron4 is about one thousandth that of the sulfur pressure&apos; at these temperatures. The vapor pressure of iron inside the Knudsen cell will be almost exactly that of pure iron, since in the iron-rich phase the percentage of sulfur is of the order of 0.025 pet.At this low percentage of sulfur Henry&apos;s law is probably obeyed by the sulfur. Thus, the iron will obey Raoult&apos;s law. In any event, the vapor pressure of iron will be lower than that of pure iron and, since the vapor pressure of pure iron is negligible compared to the pressure of sulfur, the weight loss of the cell due to the vaporization of iron should be negligible. Since neither iron nor FeS is volatile to an appreciable extent, the total weight loss of the cell must be due to the vaporization of sulfur. Discussion and Calculations On the assumption that S, is the only gaseous species present in appreciable quantity, its pressure

Jan 1, 1957

By C. R. Simcoe, T. J. Koppenaal

The effect of direct and alternating currents on the quench aging behavior in an Al-4 pct Cu alloy has been investigated by use of resistivity measurements. The reaction rate increases with direct current density in the investigated range of 1000 to 3000 amps per sq cm. Alternating current of a specific frequency is observed to decrease the reaction rate by a factor of about two. ErDMANN-JESNITZER et al.,1,2 investigated the effect of direct and alternating current on the quench and strain aging behavior of low-carbon iron. In both cases they observed that direct current accelerates the aging reaction and that an alternating current can completely inhibit the aging process. The purpose of the present research was to investigate these phenomena in the quench aging behavior of an Al-4 pct Cu alloy and to determine the correlation, if any, between the increase in the observed reaction rate and possible heating effects accompanying the aging with direct current. EXPERIMENTAL PROCEDURE The aluminum-base alloy used in this investigation contained 3.98 wt pct Cu (1.72 at. pct) with impurities of 0.003 pct Si, 0.002 pct Fe, and 0.001 pct Mg. The alloy was rolled into a ribbon about 0.36 mm thick and 3.7 mm wide. The ribbon was split end from end with the ends being used as electrical contacts and the central unsplit section, about 5.3 cm in length, serving as the specimen. Solution treatment was accomplished by quenching from a salt bath at 520° ± 2°C into water at 25° ±0.5°C; the specimen was immediately transferred to a liquid nitrogen bath. All aging was done at 75° ± 0.2°C in a rapidly stirred ethylene glycol bath. Resistivity measurements were made by the double potentio-metric method employing a standard resistor; for purposes of convenience, the resistance measurements were made at 77°K. The transfer of the specimen from the aging bath to a liquid nitrogen dewar was accomplished in less than 1 sec. The aging kinteics were studied with the specimen being aged under the influence of direct current, alternating current, and without any type of current. The amount of heating caused by direct currents was investigated by soldering a thermocouple on the specimen surface and measuring the temperature change after applying various current densities. The temperature was observed to increase (from 75°C, the aging temperature) about 0.8°, 3.0°, and 8.5°C with direct currents of 1000, 2000, and 3000 amp per sq cm, respectively. When employing alternating current, the circuit was monitored with an oscilloscope and adjustments made to produce a normal sine-wave pattern. RESULTS Prior investigations3&apos;4 in the aging characteristics of A1-4 wt pct Cu have shown that the resistivity initially increases, reaches a maximum, and then decreases to values significantly lower than the as-quenched resistivity. This type of behavior is seen in Fig. 1 which shows the resistivity at 77°K as a function of aging time at 75°C observed in this investigation. At this aging temperature, the resistivity maximum is seen to occur in about 1 to 1-1/2 min and it further decreases to the as-quenched value in about 24 min. The behavior observed with the application of direct currents of 1000, 2000, and 3000 amp per sq cm during aging is shown in Fig. 2. With increasing current densities, (+) ?pmax decreases and the rate of the aging process increases. The time necessary to reach the as-quenched resistivity value decreases from 24 min for aging without current to about 16, 10, and 7 min for aging with 1000, 2000, and 3000 amp per sq cm direct current, respectively. Fig. 3 shows the results obtained when two changes were made during the aging with 2000 amp per sq cm

Jan 1, 1963

By D. J. Freeh, W. E. Horst, R. C. Kellner

This paper is concerned with the description of grinding characteristics in a batch grinding system. A mathematical model was developed and used for simulating the system on an analog computer. A general equation describing the change of selected size fractions with respect to time is presented. The empirical verification of the model is discussed. In order to understand the performance of a grinding system, it would be desirable to have a mathematical description of the system&apos;s behavior. The development of a mathematical model to describe the performance of a batch dry-grinding operation was investigated. This is the first step toward reaching the objective of a practical mathematical description of a grinding system that could be employed for process control and optimization of a simple or complex grinding circuit. Although this article is concerned only with batch grinding performance, experimental work is being conducted to extend the model to continuous grinding systems. BASIC PROCESS CONSIDERATIONS In a paper dealing with the probability theory of wet ball milling, Roberts1 correlated the rate of change of oversize material, C, with energy input, E, as follows where the energy input is expressed in power/unit mass and k is a constant for each particle size. Experimental grinding studies were made by Bowdish2 to extend the previous work of Roberts. The work of Bowdish also showed that the rate of breaking of oversize particles in a ball mill is proportional to the concentration of oversize particles present. He further demonstrated that breaking of oversize particles is proportional to the surface area of the balls used for grinding. Rate equations were presented and it was concluded that grinding could be considered as a first order phenomenon according to the rate equation [2] di which is in accordance with Eq. 1. In Eq. 2, the effect of ball area is included in the constant k,. Other rate equations were reported to show the effect of a change in ball area and removal of fines during grinding. Correlation studies made by Arbiter and BhranY indicate a first-order rate equation for quartz; however, their data showed less than first-order rates existed for some of the other materials evaluated. More recently Kelsall4 has shown that the rate of breakage of any narrow size range of quartz could be described by a first-order rate equation. Several other investigators5-7 have described grinding behavior in terms of rate equations or kinetics. In general, the rate equations have been described for each particle size; however, the interactions between sizes and the overall relationships that exist have not been considered, at least not in the form of solving a group of simultaneous differential equations. Extensive work has been conducted by various investigators using a probabilistic approach which has expanded stein&apos;s&apos; earlier work. Selection and breakage matrices are incorporated in the probabilistic model as contrasted with the deterministic method presented here. A batch grinding operation may be considered as an unsteady-state process from the standpoint that the conditions within the mill are a function of time. Therefore, a plot of mass fraction of the i-th size versus time would give a set of curves as shown in Fig. 1. In these curves X , represents the mass fraction of large size material, X2 intermediate size, and X3 small size material. An examination of these curves shows a strong similarity to the curves that would be obtained from a chemical reaction of the type9 A?B?C, [3] where A would be comparable to the largest size material being broken to an intermediate size, 3, and

Jan 1, 1968

By C. Gatlin, C. E. Nemir

A common cure of lost circulation is the introduction of granular bridging agents into the mud system. Many materials, such as ground nut shells, are used for this purpose. If the trouble causing void (fracture, fissure, vug, etc.) is not too large, the granular agent forms a "bridge" across or within the opening. Successively smaller particles in the mud stream then accumulate on and/or within this bridge until normal filtration is finally established. The efficiency of many bridging agents has been studied in the laboratory using various slot testers.&apos;,&apos; Many investigators have remarked that a granular bridging material should have the proper particle size distribution. With the exception of the broad range specified in the patent of Goins and Nash,3 here is apparently no definition as to what this distribution should be. A bridge may be initiated when several particles of lost circulation material lodge against each other in a fracture or other void. Smaller particles then may bridge the openings between the larger, previously bridged particles. This process continues until the voids become quite small and the problem becomes one of filtration. It would seem logical that an optimum particle size distribution exists, i.e., one containing the proper quantity of properly sized material to fill the successively smaller voids of the bridge. The filtration characteristics of drilling fluids may be subject to a similar analysis. It has been clearly demonstrated by many workers that the filtration behavior of various muds can be altered by particle size control.&apos;.&apos; Slusser, et al, divided filtration into three periods and showed that particle sizes affecting a given period did not necessarily affect other portions of the filtration curve. An analagous problem is the proper sizing of gravel, liner slots and screen sizes in various sand-exclusion problems. Here the situation is reversed in that a proper "void" size, rather than the size of the bridging agent, is sought. The classic work of Coberly 9 forms the quantitative basis for most sand-exclusion processes. It is interesting to note that, in general, Coberly&apos;s work has been overlooked by most drilling-mud researchers. Other investigators have made various studies of the effect of particle size distribution .on drilling-mud properties. As a part of their studies, Fancher and Oliphant reported 30-minute filtration loss of a variety of mixtures of particle sizes.&apos;&apos; Gates and Bowie noted an effect of particle size distribution on filtration, as well as on other physical properties.&apos; MAXIMUM DENSITY THEORY A maximum density mixture has been mentioned as the possible solution for both lost circulation and mud filtration problems. Furnas 12 derived mathematically a method for obtaining maximum density of beds of packed solids, having either a given number of component sizes or a continuous gradation of sizes. This work was verified experimentally by Anderegg.13 or mixtures having a continuous grading of sizes, the interval between sizes is taken as successive screen sizes of interval 2 The ratio of the quantity of each size and the next smaller size is given by the equation Fig. I, number of size intervals of ratio 2 taken from Furnas&apos; paper, gives the value of n + 1 for any given values of + and K, where K is the ratio of the diameter of the smallest particles to the diameter of the largest particles. Measurement by weight assumes, of course, constant density for all particle sizes. Choosing the quantity of the smallest particle size as a unit weight, the required weights of the successively larger interials are then r1 r2 r3 . ®1,2,3. Thus, the grading curve of a maximum density mixture represents a geometric pro gression of ratio r.