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By B. W. Gandrud, R. G. Meara, O&apos

In 1034 the Southern Experiment Station of the U.S. Bureau of Mines in cooperation with the University of Alabama began an investigation of the availability of kyanite ores as a source of raw material for the manufacture of refractories. Under this program, gravity concentration and flotation tests have been made on two varieties of Georgia kyariite ore, mica schist and massive. Most of the attention has been directed to the mica schist ores, as they are more widely distributed and seem to offer greater economic possibilities than the massive ores. It is evident that the preparation of kyanite for use as a refractory material involves other considerations than the mere elimination of impurities. A concentration process that eliminates impurities satisfactorily may have to be followed by some additional treatment, since the final product must be of a coarseness and size ratio that will make it suitable for refractories manufacture. So far in the investigation at the Southern Experiment Station of the U.S. Bureau of Mines only the concentration problem has been considered, and this paper is intended as an interim report. Ores The schist ores contain 1 to 9 per cent of kyanite crystals embedded in mica and quartz, with smaller amounts of graphite, garnet and iron oxide and minor amounts of other heavy minerals. The garnet content varies from a trace to a few per cent. The minerals are easily released by moderate grinding. The size of the kyanite ranges from fine needles to crystals 1 1/2 in. long, 1/2 in. wide and 1/4 in. thick. The garnet, quartz and iron oxide grains have a smaller mean mesh than most of the kyanite. The maximum size of the garnet crystals corresponds to about 14 mesh and that of the sand grains is considerably less. Most of the iron oxide is still finer, for the minus 100-mesh size is greatly enriched in Fe²O3. The massive ore consists of radiating masses of kyanite interlocked with quartz, mica, corundum and small amounts of other heavy minerals.

Jan 1, 1938

By Lewis M. Haupt

IT has given me great pleasure to read, in the papers recently published by this Society, the discussions on the subject of Technical Education, which were developed at the joint meeting held at the Franklin Institute in June, 1876; and since it was impossible for me to be present, I desire to improve this my first opportunity of adding the weight of my testimony and experience to what has been so ably presented by others. It is a subject about which the people need to be kept agitated, that their views may expand with the demands made for a higher and more thorough education. It is the public at large, the capitalist, the manufacturer, and the laborer, who are to be benefited more or less by this elevation of the standard of our professional schools, and it is but just, therefore, that the schools should look to them for the means with which to accomplish so desirable an object. It is no doubt to the interest of a metallurgist to employ a skilled laborer who will prevent waste by properly proportioning his materials ; by regulating the supplies of air and fuel ; by arranging his plant in the most economical manner, and by disposing of his products to the greatest advantage. The engineer is benefited by selecting for an assistant a person able to determine the values of his factors of safety for the same materials in different forms and positions, avoiding expensive suits for damages and cost of reconstruction; he should be able to so locate a road as best to fulfil the requirements of a through traffic, and yet develop local industries. But I need not multiply instances to show what all will readily concede, viz.: the advantages of a theoretical education ; that was fully demonstrated at the previous special meeting, but it is still an open question whether the practical instruction should precede, accompany, or follow the theory.

Jan 1, 1877

By Richard A. Brown

The direct precipitation of uranium with hydrogen peroxide has been known since 1877. Commercial use of the process began in the 1960s. During 1967 the US Bureau of Mines (USBM) assisted the Climax Uranium Co., Grand Junction, CO in the development of a uranyl peroxide precipitation process to control a molybdenum impurity problem (Shabbir and Tame, 1978). Atlas Minerals, Moab, UT has used hydrogen peroxide to control vanadium and sodium levels in uranium concentrates since 1969 (Caropresso and Badger, 1973). Recently, the use of hydrogen peroxide by the uranium industry has grown, particularly since the increased demand for uranium has led to the processing of low grade ores. Impurities present in low-grade ores can be concentrated with the uranium during milling and will substantially complicate the refining of uranium yellowcake concentrates. Consequently, commercial nuclear fuel processors have imposed stringent specifications and penalties to control these impurities. The ability to produce a pure uranium yellowcake can eliminate penalty or reprocessing costs. Hydrogen peroxide precipitation of uranium is specific and quantitative, producing a very high purity product. Although the hydrogen peroxide precipitation of uranium has, and continues to be used primarily as means of producing a high purity yellowcake, it has also become an important process due to the superior physical properties of the precipitate. Under normal operating conditions, the precipitate produced by the reaction of hydrogen peroxide and uranium is dense, easily filtered and dried. The final dry yellowcake is pure, high U308 assay product. Consequently, processing costs such as filtering, drying and/or calcining and drumming, can be reduced compared to ammonia, caustic or Mag-Ox precipitation.

Jan 1, 1982

By John Porter

THE requirements of the standard specifications under which Portland cement is sold have materially increased within the past 10 years, but practically all companies are now furnishing cement better than these requirements; in some cases exceeding them by nearly 100 per cent. From a sales standpoint, it is desirable to have a product that is uniform to a high degree and free from occasional quality troubles. A failure in quality, even if it affects only a few hundred barrels out of a yearly output of a million or more, is apt to be talked about in the trade and to affect the salability of the entire output. For these reasons, there has recently been great activity along the lines of quality control and improvement; and some of the most interesting problems of the industry are in this field. From the manufacturing standpoint, the quality of cement is chiefly a matter of uniform and proper chemical composition of the raw mix fed to the kilns plus proper burning in the kilns; the fineness to which the cement is ground, the proportions of gypsum, the method of seasoning, and the like are contributory factors. Uniform chemical composition of the raw mix has been one of the most difficult problems to solve. Most plants will use from 1000 to 3000 tons of rock per day and in but few cases is this material as it lies in the quarry even approximately uniform in composition. The problem, then, is to quarry and mix this raw material in such a manner that every handful passing through the kilns will have practically the same analysis as every other handful. To accomplish this purpose there are two methods of preparation: the wet process and the dry.

Jan 1, 1925

By R. G. Ward

The temperature gradient in the subhearth metal or "salamandern of the iron bhst furnace results in the establishment of gradients in the concentrations of silicon, manganese, carbon, and sulfur. The temperature and compositional variations observed in three blast furnaces are analyzed according to irreversible thermodynamics and the systems appear to be close to the steady state condition. Apparent heats of transport, Q, for silicon, manganese, carbon, and sulfur are found to be respectively -17.5, -5, -2.1, and+22k cal per g mol. In conclusion the significance of thermal diffusion in extraction metallurgy is briefly discussed. INCREASING interest has been shown in recent years in the application of irreversible thermodynamics to metallurgical problems. In particular studies have been made of the transport of matter in thermal gradients1-' and under chemical gradients imposed by a binary solvent However, no detailed example in extraction metallurgy has been reported although gradients are the essence of many extractive processes. The case of the distribution of elements in molten blast furnace iron under a thermal gradient is discussed here. DATA In blast furnace operation the hearth bottom is often extensively destroyed by molten metal, and the metal may penetrate perhaps 10 ft into the furnace foundations forming a "bear" or "salamander". Several hundred tons of molten metal may thus exist beneath the level of the conventional tap hole and remain relatively undisturbed for several years under a thermal gradient. This system is subject to little convective stirring because the temperature decreases from top to bottom, and mechanical stirring due to movements in the stack and to tapping operations is unlikely to penetrate far into the metal. The system may thus be regarded as static

Jan 1, 1963

By H. B. Fuqua, B. E. Thompson

The area discussed herein, commonly known as the North Texas district, embraces the following 10 counties: Archer, Baylor, Clay, Cooke, Foard, Hardeman, Knox, Montague, Wichita and Wilbarger. It is underlain by two major structural features. The northernmost portion of the district, including Coolie, Montague, northern Clay, Wichita, Wilbarger, Foard and Hardeman Counties, is underlain by the system of buried mountains known as the Red River uplift, which is parallel to and closely related to the Wichita-Amarillo uplift of Oklahoma and the Texas Panhandle. While the presence of a great majority of the numerous oil fields of the area is traceable to this feature, the production in Archer, southwestern Clay and southeastern Baylor Counties is due to the influence of what is known as the Cisco arch (so called because of its influence on Cisco deposition), the axis of which extends in a northwest-southeast direction across southwestern Wichita County into Archer County. Developments during 1938 Important discoveries in the district were considerably more numerous and of more economic importance than for several years. In addition to a number of small, relatively unimportant discoveries and to the usual local extensions to the various producing fields in the several counties, at least eight fields, most of them apparently of considerable areal extent and importance, were found. The Helmerich and Payne, Incorporated and Blackwell Oil and Gas Company No. 1 Wilson. 4 miles southeast of the town of Holliday, in north central Archer County, encountered a pay of Strawn age at a depth of 3841 to 3858 ft., and was completed for an initial production of 1952 bbl. T'his well opened a new deep pool in the K. M. A. producing zone 8 miles southeast of the K. M. A. production. Subsequently an additional deeper horizon, also of lowcr Strawn age, was discovered by wells that failed to yield commerecial oil from the horizon of the discovery well.

Jan 1, 1939

Discussion of the paper of ALBERT SAUVEUR, presented at the Pittsburgh meeting, October, 1914, and printed in Bulletin No. 93, September, 1914, pp. 2439 to 2449 G. K. BURGESS, Washington, D. C.-This very instructive contribution by Professor Sauveur to our knowledge of that puzzling substance, Hadfield's manganese steel, should not only be read in connection with the paper of Messrs. Hopkinson and Hadfield referred to by Professor Sauveur (Bulletin No. 87, pp. 513 to 530, March, 1914); but one should also have in mind, as throwing much additional light upon the questions raised, two papers recently presented before the Iron and Steel Institute, the one by Sir Robert Hadfield (Journal of the Iron and Steel Institute No. II, 1913) on Heating and Cooling Curves of Manganese Steel, the other by Messrs. Hadfield and Hopkinson (ibid., No. I, 1914) treating of the Magnetic and Mechanical Properties of Manganese Steel. We then have brought together for this substance, the thermal, magnetic, and mechanical properties as well as the resulting microstructure, for the definite heat treatments described, and in particular after long annealing between 500° and 700° C. Sir Robert Hadfield and Professor Hopkinson see in the properties found for manganese steel (of C = 1.25 and Mn = 12.5 per cent.) a demonstration of the untenableness of the allotropic theory of iron, whereas Professor Sauveur reaches the contrary conclusion, that some of the facts observed can be explained only in terms of the existence of beta iron in steel of this composition. There is another possible hypothesis: namely, that these several series of experiments shed no light on the subject of the allotropy of iron, or at least as regards the existence of beta iron. However heretical it may sound, I am inclined to this last belief.

Jan 4, 1915

By William Schriever

The flow of a gas-free liquid through a spherical-grain sand has been investigated by S1ichter.l By theoretical considerations involving a rather large number of approximations he arrives at the following flow-formula: V = CPd2At NLB{1 - m) where V is the volume of liquid delivered in time t through a cylindrical column of sand of length L and cross-sectional area A by a pressure-drop P when the sand grains of diameter d are packed to a porosity m and the coefficient of viscosity of the liquid is n. C and B are constants which were determined from geometrical relations; B was in reality a function of . Values of B(l — m) for various values of m were given in a table. In the same Annual Report of the U. S. Geological Survey, King reported the results of his experiments on the flow of water through porous media. He found that there was a departure of about 86 per cent. from a linear relationship between rate of flow and pressure, for a specimen of Dunnville sandstone for pressure drops not exceeding 60 cm. of mercury. The specimen was approximately 4 cm. in diameter and 5.1 cm. in length. Over the same range of pressure he found a departure of 45 per cent. for a specimen of Madison sandstone. For unconsolidated sands he found departures as great as 49 per cent. for pressure drops of 70 cm. of mercury; for pressure drops not exceeding a few inches of water he obtained a close approximation to a linear relation. He also investi-

Jan 1, 1930

By Charles W. Goodale

The attention of the Institute has been called by Prof. John A. Church* and Mr. W. Lawrence Austin? to the free-milling ores of the Tombstone mines and their treatment, but the silver-bearing man ganese ores of the district have received only a passing notice. As these ores show some interesting peculiarities, and have yielded not less than 750,000 ounces of silver, they are worthy of some study. The Knoxville, Lucky Cuss, Luck Sure, and Wedge mines (named in the order of their importance) are situated along the northern border of the district. They have been the leading producers of this manganese ore, and possess the same general characteristics. Special attention will be given to the Knoxville, as it has been the one most extensively developed. The limestone belt, in which the Knoxville ore bodies occur, has an easterly and westerly trend, is about 1680 feet wide, and rests on granite on the north, the plane of contact being nearly vertical. It is overlain by quartzite, the contact-plane having a dip of 82°. Some mining has been done along these contacts, and a considerable amount of pay ore has been extracted, but development has been very superficial. The ore found along these contact planes contains very little manganese, and differs entirely from the ore in the lime stones. No attempt will he made to assign this limestone country-rock to a particular geological horizon, as no fossils have been found in it. Prof. Blake, in a paper on "The Geology and Veins of Tombstone, Arizona" (Trans., x., 334), speaks of the middle and upper strati-

Jan 1, 1889

By C. C. RAE

The Texas Panhandle produced 18,677,000 bbl. of oil in 1932 as against 25,064,000 in 1931. The decline was caused by smaller market demand, since the Railroad Commission potential increased from 105,528 to 149,260 bbl. during the year. Well Completions, 1932 The development during 1932 compares with 1931' as follows: Year Wells Drilled Dry Holes Gas Wells Oil Wells Initial Pro- duction, Bbl. 1931 200 6 77 117 347 1932 136 18 28 90 603 Crude oil prices, small market demand, and lower allowable rate of production caused less drilling. Expiration of leases was one reason for a greater number of dry holes through forced drilling of questionable areas. The small number of gas wells reflected the influence of the business depression upon industrial and domestic gas demand, together with difficulties of franchise negotiations or pipe line extensions under present conditions. Probably much of the gas-well drilling was done on expiration leases, or to protect against drainage, and equalize withdrawals as between the various units held by each gas pipe line company. The increase in average initial daily production was due chiefly to excellent granite wash wells in the LeFors district developed by the Texas Co. and Skelly Oil Company. In the Panhandle district, comprising a major anticline with almost a million productive gas acres, the pools tend to merge in time, the development being confined to more productive areas. Hence separation into pools becomes a matter of time of development with some effort to keep dolomite, archosic and granite wash production separate. Many pools, like the Finley and Bowers, have mainly one type, but many leases and even individual wells produce from two zones. The oil production is usually closely associated with sea level, where proper porous formations

Jan 1, 1933

By F. E. Marcy

IT is not my purpose to write a lengthy article or to attempt the solotion of the problem I am presenting, but to call attention to what I believe an important issue, hoping that it may arouse in some one, or in some company, a sense of responsibility. I am referring particularly to modern up-to-date milling plants discharging tailings which under existing conditions cannot be further treated or from which a recovery cannot be made at a profit, but where a quantitative and qualitative analysis shows that a portion of these tailings might profitably bee treated, at some future time when our metallurgical knowledge has advanced, when we have cheaper power, chemicals, labor or other advantageous conditions. Early Methods In our early milling methods very little attention was given to the care of tailings. It was thought that if the mill could be located by a stream or a river where the final disposal of the tailings could be forever lost sight of, it was highly desirable. We can now see acid estimate what was lost in these rich tailings, not recoverable from the streams and the great rivers. Fortunately for many, the depositing of tailings in these streams and rivers was objected to by the farmers and finally prohibited by the State Legislatures. In looking back over our past milling methods, it seems that, the first endeavor was to make the maximum amount of money for a particular period, or year, regardless of the future, the depletion of the mine, or the conservation of the total mineral content. The dumping and sluicing of 3,000 tons per day, for a period of many years, of a copper tailing carrying

Jan 8, 1917

By John W. Tieman

Coal is a term applied to vegetable matter (trees, grasses, etc.) which was subjected to heat and pressure through geologic ages. This resulted in a change in both the physical and chemical properties. Because its chemical composition is variable, geologists classify coal as a heterogeneous mineral rather than a homogeneous mineral. Peat represents the initial, unconsolidated stage in the development of coal. This coalification continues with time and the application of temperature and pressure to lignite, subbituminous, bituminous, and anthracite toward the theoretical graphite end member. PHYSICAL PROPERTIES OF COAL The physical properties are concerned with the characteristics of coal in its natural state, or prior to its end use as a fuel. For example, the hardness and grindability of coal determine the maintenance cost for coal mining, handling, and pulverizing equipment; the specific gravity of coal and its associated minerals determines the coal preparation technique used in a cleaning plant as well as the capacity of coal bins, boats and size of cargo, and other coal storage facilities. The physical properties are, of course, dependent on the chemical constituents of coal, and all properties are interrelated. Specific Gravity The specific gravity (sp gr) of a solid is the ratio of the weight of a cubic foot of the solid to the weight of a cubic foot of water. The specific gravity of pure coal has been reported to range between 1.23 to 1.72 and increases with the change in rank from lignite to anthracite. This means that it is 1.23 to 1.72 times heavier than water.

Jan 1, 1981

The Library of the above-named Societies is open from 9 A.M. to 9 P.M. on all week-clays, except holidays, from September 1 to June 30, and from 9 A.M. to 6 P.M. during July and August. The Library contains about 55,000 volumes, including sets of technical periodicals and the publications of scientific and technical societies. Members of the Institute, with few exceptions, are forced to spend a portion of their time in localities isolated from sources of information. To these the Library can render valuable service through correspondence; letters requesting information will receive special attention. The Library is prepared to furnish references' and copies of articles on-mining and metallurgical subjects; to determine the existence of mining-maps, and to furnish general information as to the geology and mineral resources of all countries. All communications should be made as definite as possible so that the information received may be what is desired and not include collateral matter which may not be of interest. The time spent in searching for such collateral matter will be saved, and the information will be sent more promptly and in more usable shape. The members of the Institute can be of service to the Library by forwarding copies of mining-reports, maps privately issued, and similar material, which will be classified, indexed, and made available to other members. Suggestions for additions to the Library, either by purchase or personal solicitation as gifts, will be welcomed. It is hoped that members while in the city will use the Library freely, and assurance is given that most careful service will be rendered to them.

Jan 7, 1913

By E. M. Wise, R. V. Vines

It is known qualitatively that the recrystallization behavior of platinum is dependent upon the amount and particularly the nature of impurities present, the amount of prior cold-work and the annealing time and temperature, but published data are limited. A study of the effects of cold-work and annealing temperature on the hardness of a sample of very pure platinum was undertaken to supply part of this information. Conclusions 1. The platinum used in the experiments had a probable platinum content of 99.99+ per cent, and had the following mechanical properties in the completely softened condition: Vickers hardness number, 39.4; ultimate tensile strength, 19,340 lb. per sq. in.; proportioilal limit, very low; elongation, 37.5 per cent in 2 inclles. 2. The effect of cold-rolling on the hardness is shown in Fig. 1. The hardness increases rapidly up to 10 to 15 per cent reduction and more slowly up to about 75 per cent reduction, beyond which it increases more rapidly. 3. The recrystallization temperatures for a 15-min. anneal, after cold-rolling 19, 39.5, 50.8, 66, 80.5 and 89.5 per cent reduction in thickness, are approximately 765°, 700°, 635°, 600°, 545' and 425°C., respectively. 4. The recrystallized grain size of this platinum is a function of the percentage of cold reduction, being larger the lower the percentage of cold-work. 5. Little or 110 grain grourtll resulted from subjecting recrystallized samples to higher temperatures or annealing for longer times. Prior Work As already mentioned, data on the recrystallization of platinum are scarce. Gmelin'sl handbook, which summarizes data published earlier than August 1938, lists values ranging from 400' to 810°C. for the minimum temperature of recrystallization of samples with rather indefinite

Jan 1, 1940

By A. L. Field

WOOLSEY McA. JOHNSON, Hartford, Conn. (written discussion).¬When ;we regard the number of British thermal units running into the billions that-must be applied to metallurgical slags in the United States, we cannot but conclude that the physical chemistry of-slags is a very important subject when measured in dollars and cents. A further contemplation of the subject shows us that it has been hitherto treated in too purely a practical manner. It is needless to comment at length on the cost of these heat units and on the cost of fluxes to produce these metallurgical slags, for, it amounts to tens of millions of dollars annually. Accordingly, this research is of value to the country. But we must,all balance our results against our efforts. Therefore, while the speaker is unwilling to criticise unduly this meritorious research, lie does criticise it in the interest of the profession for the reason that it seems to him too highly theoretical. The article is much too, scientific to produce results at a minimum cost. Let us explain our meaning. It has been said that there are always two sides to a question. It may be further said that there are always three sides to a question, the two extremes and the middle ground. In any industrial research there are the highly theoretical side, the purely practical side, and the theoretico-practical side. To study a slag and be practical in the studying, there is something needed that represents in the laboratory (or in microcosm) what actually happens macrocosmically in the blast furnace. There is such a thing as the art of metallurgical research occupying the middle ground between theory and practice.

Jan 4, 1917

Jan 1, 1944

Jan 1, 1946

(Under this heading will be published notes sent to the Secretary of the Institute by members or other persons introduced by members.) Member, aged 34, married, technical graduate, 10 years' experience as mining engineer and mine superintendent, desires position. Can show low cost records and good references. No. 176.

Jan 1, 1916

By N. De Nevers

A calculation method has been developed for carbonated water flooding. This method takes into account the effects of oil viscosity reduction and oil swelling, due to carbon dioxide transferred to the reservoir oil from the carbonated flood water. It shows the effect of changes in carbonation pressure and carbonated water slug size. The method is based on a Buckley-Leverett-type linear flow model. The mathematical approach is similar to that developed by Welge, et al, for enriched gas drives. However, it contains a very important advance over the previous papers in its solution to the problem of injection of a "slug" of carbonated water rather than continuous injection of fluid of constant composition. The method also shows the chromatographic nature of the transport of Co 2 in a carbonated water flood. Sample calculations indicate that viscosity reduction is the most important source of incremental oil recovery. Swelling contributes to a lesser extent. Raising the carbonation pressure increases recovery, but this effect diminishes as pressure is increased. increasing the slug size also increases recovery, but again this effect diminishes as slug size is increased. INTRODUCTION In recent years there has been considerable interest in carbonated water flooding as a secondary recovery method. Several carbonated waterflood field tests are now in progress.1'3 Yet there is no published method for predicting the results of a carbonated water flood. This paper presents a method for predicting the oil recovery for ; carbonated water flood. In a carbonated water flood. a carbonated water slug is injected into the reservoir. Then this slug is driven forward by injecting plain water behind it. The field operator must choose the carbonated water slug size and the CO2:water ratio in the slug. The calculation method presented here shows the effects of both slug size and CO2:water ratio on oil recovery. The calculation assumes that the addition of carbon dioxide to flood water increases the oil recovery by two mechanisms: 1. Carbon dioxide transfers from the flood water to the oil, thereby reducing the viscosity of the oil. At the lower viscosity, the oil flows more readily and is more easily swept out by flood water. 2. The carbon dioxide which transfers to the oil phase causes the oil phase to swell. Assume that the residual oil saturation (volume per cent of pore space) is the same whether the oil is carbonated or not. Then the same volume will contain less stock tank oil if it is carbonated, due to oil swelling. The plain water driving the carbonated water slug forward will strip the CO2 out of this residual oil., causing this oil to shrink. This swelling-followed-by-shrinking leaves behind a lower residual oil saturation than would have been left behind by a plain water flood. Since some oils swell to almost twice their original volume at reasonable CO2 pressures, this effect may be large. Two additional benefits sometimes claimed for carbonated water flooding are: 1. Adding CO2 to flood water greatly increases the water injectivity in some cases.1 (Injectivity = BPD of water injected/ft of sand x differential bottom-hole pressure, psi.) CO2 forms a weak acid in water; injecting carbonated water is, therefore, somewhat like acid treating. If a formation responds to acid treating, it will probably have a higher injectivity for carbonated water than for plain water. Although the increased injectivity increases the profitability of a carbonated water flood over a plain water flood, it does not change the production curve based on total fluid injected. Therefore, the method presented here does not show any effect of increased injectivity. 2. It is claimed in one patent4 that carbon dioxide will react with some constituents of the oil to form detergents. These detergents are expected to increase the oil recovery. There is little data available to support this idea. The calculation method presented here takes no credit for extra oil recovery due to the formation of any such detergents.

Jan 1, 1965

By F. X. Tartaron

This paper deals with basic physical phenomena, which when combined and interpreted, lead to the same mathematical equations that describe comminution phenomena. Thus, a physical model is described that corresponds to the mathematical model presented in the writer's previous papers. '12 In the mathematical model, the energy consumed in breakage is related to the volume or weight of material broken and the size of particles broken. The equation E=2.303 Ck-a log x1/x2 was derived by multiplying the volume or weight of each size in an ideal Gates-Gaudin-Schumann size distribution by an energy factor. The product of these two factors gives the energy distribution among the different sizes in a single size distribution. The energy of breakage of a specific constant weight of one size distribution to another size distribution is given by the equation E = constant/kn-1. In this case, where the volume or weight is constant, the energy is proportional to the size factor 1/kn-1. In what follows, a physical theory will be presented showing that the energy consumed in comminution is proportional to the volume or weight of the material broken and to the reciprocal of the size of this material raised to a constant exponent. THE VOLUME FACTOR The atomic theory of matter reveals that in solids, atoms or ions are arranged so as to be in equilibrium at specific distances from one another. Although the atoms or ions are oscillating, there is a definite determinable mean distance between them and this distance is a balance between repulsive and attractive electrical forces. It therefore requires force to separate the atoms or ions and when an outside force is applied, it first produces strain in increasing the distance between the atoms or ions. This strain increases to the breakage limit on application of sufficient force. In brittle materials, there is negligible plasticity and when an elastic limit is exceeded, breakage takes place. The work done is the force applied per unit area times the cross sectional area of the ideal particle multiplied by the maximum strain per unit length at right angles to the area times the length of the particle. Thus the work done is proportional to the area times the length, which is equivalent to the volume of the ideal particle. If more than one feed particle is considered broken, each particle must be subjected to sufficient strain so that the breakage limit of its contained atoms or ions is reached in order for the particle to be broken. Thus, the energy of breakage is proportional to the total volume of the particles broken. If the particles are of different sizes, the size factor must be included to get a correct determination of energy of breakage. In the preceding, it has been assumed that there is a constant binding force between the atoms throughout the volume being strained. This, of course, is not true. It is known that there are many irregularities in the structure of matter and the binding force differs markedly in different portions. But the differences are only discernible by examining extremely small subdivisions of matter. In one order of magnitude of volume, cracks can be discerned separately from non-cracked neighboring material. In a smaller subdivision of volume, lattice dislocations can be isolated. When these situations are brought into focus, mechanisms of their behavior can be learned, leading to a fuller understanding of phenomena that occur in larger scale subdivisions of matter. Very often, however, the mechanisms that operate in small scale subdivisions have negligible effect in those of large scale, and there still is a place for deriving a mechanism for large scale conditions. The quantum theory is extremely valuable for use with photons and electrons, but is of negligible use with ordinary atoms and molecules. This paper deals with relatively large scale subdivisions of volume present in comminution phenomena. Hence, the effects of cracks, lattice dislocations, misplaced atoms, etc., are smoothed out in an average, constant for each relatively large subdivision of volume. This attitude is supported by experience. If two 10 cc samples of the same ore were ground identically, the same product would be obtained. However, if two samples, each a cubic micron, were conceived to be broken, then one sample might contain a crack and the other not, hence a different product would be obtained. Experience shows that ordinary samples used in comminution, behave as though no irregularity existed

Jan 1, 1964