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By Erwin Zodrow, De Verle P. Harris

The Smallwood mine, owned and operated by the Iron Ore Co. of Canada, is one of the largest ore producers in Canada, producing about 15 million tons of crude ore per year. Located in the Labrador Trough near, Labrador City, Newfoundland, the open-pit operation has ore consisting chiefly of specular-hematite, with some magnetite. The magnetite content of the ore as a mineral percentage is small, but it is of considerable importance in ore grading because of its effect upon milling. Being harder than specular-hematite, magnetite increases grinding time and milling costs. Specifically, higher grade magnetite (greater than 15%) usually occurs as fine grains in a fine grained siliceous rock matrix (also as larger octahedra in carbonate bands). This tends to increase the overall breaking strength in the crude ore; consequently, the hourly mill rate and the weight recovery decrease. At the same time, because of its relatively high iron content, the magnetite does contribute to the amount of iron in a block of ore. Were the concentration of the magnetite relatively constant, its presence would be of less consequence, for appropriate adjustments could be made in the milling operations. However, the quantity of magnetite present for any run of ore varies considerably; it is the magnetite prediction for a block of ore that constitutes the greatest problem in grading. THE PRESENT ORE GRADING METHOD Ore for the Smallwood mine is graded by a computerized block grading routine (using 50 x 50 x 45-ft blocks) that applies simple weighted (inverse-distance) averaging to ore grades. The results of the block grading program are not reliable with respect to magnetite concentration. Factors responsible for this poor estimation are (1) the structural setting of the deposit, and (2) mineralogical relationships. Neither of these general factors are given adequate consideration by present methods.

Jan 8, 1967

By E. W. Davis

The mixing of fine ores with fuel and burning under induced draft is called sintering in iron-ore practice and either sintering or roasting in copper and lead metallurgy. The first development of sintering was the Huntington-Heberlein process, in which fine sulfide ores mixed with fuel were charged into a pot and burned under the action of an upcast current of air introduced at the bottom of the pot. Modern development has resulted in two types of machine; the continuous Dwight-Lloyd machine, which consists of heat-resisting grates and a moving beltlike type of hearth constructed of metal, in which air is drawn downward through the bed, and the stationary Greenawalt batch process, which operates in the same manner as the Dwight-Lloyd except that the hearth is stationary. The recent rapid increase in the use of sintering has been the result of two great advances in metallurgical process—flotation and the treatment of flue dust. The Dwight-Lloyd machine is used in many plants for agglomerating flotation concentrates and at the same time reducing the sulfur content to furnace requirements and it has become standard practice to treat iron blast-furnace flue dust by either the Greenawalt or Dwight-Lloyd machine, so that it can be recharged into the furnace. The mining of low-grade magnetite iron deposits and their beneficiat-ing by grinding and magnetic separation resulted in a fine concentrate extremely detrimental to blast-furnace practice. These concentrates are sintered and made into ideal material for blast-furnace use. Incidentally, coke savings of about 400 lb. per ton of pig are reported. Sintering at Evergreen Plant The application to limonitic iron ores is the most recent development of the sintering process. The first plant in the Lake Superior region was erected by the Minnesota Sintering Co., a subsidiary of the Evergreen Mining Co., at Ironton, Minn., in 1924. This plant was designed to treat Cuyuna Range iron and manganiferous ores containing low silica, high moisture and a structure objectionable because of a large proportion

Jan 1, 1930

By E. H. Sellards

Phosphate rock like other mineral substances is found in nature in varying degrees of purity.

Jan 1, 1915

W. N. Triplett (Geology of the Silver-Lead-Zinc Deposits of the Avalos-Providencia District of Mexico, P. 583) was born in Tecumseh, Mich., and attended the University of Michigan and Massachusetts Institute of Technology. From 1912 to 1917 he worked for Moctezuma Copper Co., a Phelps Dodge subsidiary at Nacozari, Sonora, Mex. He served in Army as Second Lieutenant Field Artillery from 1917 to 1918 and from 1919 to 1922 returned to Moctezuma Copper Co. From 1922 to 1952 he has been with Compania Minera de Penoles, S. A., a subsidiary of American Metal Co., Monterrey, N. L., Mexico in Unit Dept. as chief geologist and at present is consulting geologist. Mining geology and operation is of particular interest to Mr. Triplett. He presented a previous paper before with M. W. Hayward entitled, "Occurrence of Lead-Zinc Ores in Dolomitic Limestones in Northern Mexico." Besides being an AIME member, he holds membership in Society of Economic Geologists. Fishing, hunting and photography are his favorite hobbies.

Jan 1, 1952

By W. T. Bishop

FOR many years pine oil has been used extensively as a frother for the flotation of minerals, particularly sulphides, yet the published information available to the average user on its composition, chemical and physical properties, has been rather meager. It is the purpose of this paper to discuss these points and their relationship to the frothing properties of pine oil used in flotation processes. Pine oil, as the name implies, is a liquid obtained from the processing of wood of the longleaf and other southern pines. It is a complex mixture of naturally occurring terpene derivatives, primarily alcohols, and a smaller amount of terpenes, which has found many uses in various industries. Its use as a frother in flotation processes was the first large-scale application in industry and today the mining industry still consumes large quantities of pine oil but the textile and disinfectant industries consume comparable volumes. Much is used in soap manufacture and laundry operations. The surface-active properties of pine oil are in a large degree responsible for this versatility. HISTORY The name "Naval Stores" goes back to the days when pine tar and pitch were used to caulk leaky ships and coat their ropes and rigging. Today this term is still used to include not only the oleoresinous products of the pine tree-rosin and turpentine-but other products such as pine oil, pine tar, and the many terpene and resinous compounds obtained by extracting the pine wood or tapping the tree. That part of the industry known as "wood naval stores" dates from about the beginning of this century and today produces a large part of the country's rosin and turpentine by processing pine wood. In addition, all of our natural pine oil is, supplied by the wood naval stores industry, as tapping of the live tree gives only rosin and turpentine. This latter phase is known as the "gum naval stores" industry. The first successful commercial operation of the steam and solvent process of the wood naval stores in industry was carried out by Yaryan at Cadillac, Mich., in 1909.1 This operation did not prove profitable, so Yaryan went south to utilize the longleaf pine, and built a plant at Gulfport, Miss.2 Soon after, another plant was built at Brunswick, Ga., which is still in operation, and in 1914 was reported to have processed about 500 tons of wood per day.1 In 1921 Hercules Powder Co. acquired the Yaryan interests, at which time the production of pine oil was only 3 to 5 million pounds per year and flotation was the largest customer. As time went on, technological advances were made, other companies entered the field, and the production of pine oil increased many fold. The growth of the industry was especially marked during the past 10 years, and in

Jan 1, 1946

By Arthur F. Taggart, T. C. Fitt, A. W. Thomas

IT was noticed early by operators that high recoveries and flocculation of the sulphide minerals were closely correlated in agitation-froth flotation. Later, this readily visible flocculation was found almost invariably to be due to the binding together of the oiled sulphides by minute air bubbles, and is now known to be characteristic of pulps in which at least one of the mineral species is coated with an insoluble collecting oil. In 1930 it was reported1 that in differential flotation a correlation exists between Brownian movement of particles in the pulp and their nonfloatability, and that Brownian movement and dispersion are likewise correlated, whence it would appear to follow that dispersion of a mineral particle in a flotation pulp denotes a particle condition unfavorable to flotation. In 1934 it was postulated2 that Brownian movement, dispersion and nonfloatability all flow from the condition of the surface of the dispersed particles. It was also postulated at that time that the surfaces of dispersed particles are ionized, the ionized compound being a product of reaction between a component of the particle and a. component of the pulp, of a mass solubility of the general order of a fraction of a milligram to 15 to 20 mg. per liter. It was then further asserted, and has since been confirmed by Bankoff,3 that sulphides so conditioned with soluble collectors as to be floatable flocculate without the intervention of air bubbles as binding media. The present paper comprises an inquiry into the nature of the bound and counter ions in zinc sulphide dispersed by sodium arsenate. A part of its findings was mentioned in the 1934 paper above cited.2 The tests show that: I. When powdered granular zinc sulphide is immersed in aqueous solutions of sodium arsenate, arsenate ion is abstracted from solution and anchored to the solid surface, while sulphate and lower sulphoxy ions are concurrently displaced therefrom in substantially stoichiometric quantities. 2. The ion counterbalancing the anchored arsenate ion is zinc. 3. Dispersion and Brownian movement of zinc sulphide are concurrently maxima at an arsenate-ion concentration lying between 0.01 and 0.001-molar sodium arsenate. 4. Any condition or reaction that tends to remove the zinc arsenate coating from the zinc sulphide particles decreases dispersion and Brownian movement concurrently. EXPERIMENTAL Three samples of zinc sulphide were used. Lot I was C.P. zinc sulphide, washed well beyond absence of chloride, as shown by test with silver ion. Lot 2 was prepared by precipita-

Jan 1, 1943

By W. L. Austin

THE advance made in recent times in this branch of metallurgy is indicated y the attention the subject is receiving from important American copper-producing companies. Reference to the files of publications devoted to the mining industry discloses that some 20 American companies are actively investigating the amenability of their ore, or other material, to leaching methods, and that plants of varying capacities up, to 10,000 tons per day are under construction or are projected. Several leaching works are in commercial operation. It has been frequently pointed out that no method of leaching is universally applicable, for the reason that each ore differs in some particular from apparently similar ore found elsewhere, and also because local conditions are rarely the same even where the ore closely approximates in character that being worked at some other point. For this reason the older companies are approaching the matter in a conservative manner, experimentally determining for themselves the salient features in each instance. In considering a leaching proposition three factors at once fix the attention: (1) disengaging the metal from mineralized forms in Which it is found in nature; (2) recovering the metal in a commercial state after it has been dissolved; (3) the apparatus best adapted to carrying out the several operations.

Jan 8, 1914

By George Sears

UNTIL a comparatively few years ago, interest in tantalum was limited almost wholly to its scientific investigation, but its extreme resistance to the action of even the strong mineral acids, its great avidity for the common gases, hydrogen, oxygen and nitrogen, and its capacity for transforming alternating to direct current are winning for it a place in our industrial life. Tantalum is not attacked by any single acid except hydrofluoric, nor is it affected by solutions of alkalies. Aqua regia, which readily dissolves both platinum and gold, has no action on it. This resistance to the common corrosive agents is an outstanding property of tantalum and accounts for many of the applications to which it has been put. When heated, tantalum reacts readily with oxygen and nitrogen and absorbs large volumes of hydrogen, 740 volumes being taken up at a dull red heat. This capacity for absorbing gases is being utilized to an increasing extent in the manufacture of vacuum tubes, in which tantalum is used for the metal parts, especially for grid wire. It is said to be a superior metal for this purpose, particularly in power and sending tubes, because of its low secondary emission. The use of tantalum in the manufacture of electrodes, dishes, spatulas and other laboratory apparatus appears to be fairly steady. There has been some development in its use for dental instruments, surgical tools, pen points, hypodermic needles and acidproof pumps. Recently it has been used in the manufacture of spinnerets for the rayon industry, of nozzles for the manufacture of artificial casings for sausages and of lining for plant equipment.

Jan 1, 1930

By Rudolph G. Wuerker

The scarcity of values of tensile strength of rocks has been explained by the lack of successful testing procedures. In the case of mine rock a description is given' of the difficulties encountered in testing a cylindrical specimen, such as a core, by conventional methods. Over a period of years the following method has given definite and reproducible results with the weakest as well as with the strongest rocks. It does not completely supersede the use of cores with special fixtures but is a supplement in all cases where cores cannot be obtained, as from soft rocks, or in cases where it is less expensive to prepare test specimens by cutting them out of the rock instead of drilling cores.

Jan 2, 1955

By John Griffen

THE distinguishing principle of the Tromp process is the use of a medium in the bath which is not stable, i.e., the solids will settle and the density of the medium increases with depth. A medium of uniform density can most easily be effected by agitation or by means which increase the viscosity of the medium. Either of these works against the sharpness of separation of coal from its impurities. The Tromp process grinds the medium solids to relative coarseness, allows them to settle downward in the bath without hindrance, and introduces horizontal currents of medium at intermediate levels between top and bottom of the bath. This prevents any accumulation of particles denser than the upper layer of the medium from which the clean coal is conveyed away or an accumulation of particles lighter than the bottom layer or medium whence the refuse is removed. In a relatively shallow bath making a two-product separation, the intermediate horizontal currents sweep these intermediate gravity materials away to be discharged with the refuse removed by the conveyor. Such a system provides a number of advantages. The gravity of separation can be changed simply by changing the density of the medium without changing particle size of medium solids or other conditions, as would be necessary with a system requiring uniform or stable density throughout the bath. Some installations in Europe separate at 1.40 sp gr on one shift, producing a superclean coal, and on the next shift reclean refuse from dry cleaning units and effect a separation at 1.80 sp gr. Medium solids may be much coarser in size consist, which reduces the viscosity of the medium and promotes its fluidity and in turn the sharpness of separation. Coarser medium solids with a more rapid settling rate are much more easily recoverable from the dilute medium rinsed from the products. The Tromp process is not limited to the use of medium solids having magnetic properties. Instal-

Jan 1, 1953

By John Griffen

THE distinguishing principle of the Tromp process is the use of a medium in the bath which is not stable, i.e., the solids will settle and the density of the medium increases with depth. A medium of uniform density can most easily be effected by agitation or by means which increase the viscosity of the medium. Either of these works against the sharpness of separation of coal from its impurities. The Tromp process grinds the medium solids to relative coarseness, allows them to settle downward in the bath without hindrance, and introduces horizontal currents of medium at intermediate levels between top and bottom of the bath. This prevents any accumulation of particles denser than the upper layer of the medium from which the clean coal is conveyed away or an accumulation of particles lighter than the bottom layer or medium whence the refuse is removed. In a relatively shallow bath making a two-product separation, the intermediate horizontal currents sweep these intermediate gravity materials away to be discharged with the refuse removed by the conveyor. Such a system provides a number of advantages. The gravity of separation can be changed simply by changing the density of the medium without changing particle size of medium solids or other conditions, as would be necessary with a system requiring uniform or stable density throughout the bath. Some installations in Europe separate at 1.40 sp gr on one shift, producing a superclean coal, and on the next shift reclean refuse from dry cleaning units and effect a separation at 1.80 sp gr. Medium solids may be much coarser in size consist, which reduces the viscosity of the medium and promotes its fluidity and in turn the sharpness of separation. Coarser medium solids with a more rapid settling rate are much more easily recoverable from the dilute medium rinsed from the products. The Tromp process is not limited to the use of medium solids having magnetic properties. Instal-

Jan 1, 1953

By Irwin Remson

Some unique hydrogeologic issues are inherent in the problems of siting, designing and licensing a mined geologic high-level nuclear waste repository. The problems involve hydrogeologically unfamiliar rocks for which little proven technology has been developed, long containment periods, elevated temperatures, and externally-imposed management constraints. In evaluating the existing national program, it should be recognized that hydrogeology is only one aspect of the total nuclear waste disposal problem, that the use of multiple barriers requires that the hydrogeologic system be considered in its entirety as a total system, and that engineering modifications can improve the isolation capabilities of certain barriers. Important research questions involve the mechanics of transport through dense fractured and unfractured rocks, methods for measuring vertical hydraulic conductivity, and a variety of geochemical questions. Current expectations for "high quality data" from either in situ or laboratory testing are unrealistic, and a modified approach to repository hydrogeology is needed. The dilemma is that the hydrogeological characteristics that make a potential host rock more satisfactory for respository siting are the same characteristics that are difficult to characterize and make the particular site more difficult to license. Finally, evaluation of the containment potential of any candidate site will become meaningful only with detailed underground exploration, mapping and testing in the host rock formations at the repository levels.

Jan 1, 1984

By G. C. Stone

At the conclusion of my paper on the same subject read at the Boston meeting of the Institute, I offered to send some of sample No. 2 to any chemist who wished to analyze it. Eight chemists wrote to me for samples; so far I have received results from five. I give these results in a table (on the following page), together with the results previously obtained: As to the chemists and their methods : K is an iron-works chemist whom I only know by correspondence; lie writes: "No. 27(13.64) was obtained by the method I generally use, as follows : Dissolve 0.8 grams spiegel in hydrochloric acid and a little potassium chlorate, in a half-liter flask. Boil off most of the acid, add ammonia in slight excess, redissolve in acetic acid, using rather more than is really necessary, and then add 8 or 10 grams of sodium acetate and make up to the mark with warm water. Boil hard for fifteen minutes, then allow to settle (cool?), until the liquid reaches the mark, and withdraw 300 C.C. of the nearly clear liquid. Add to this an excess of hydrochloric acid, evaporate to dryness, take up with hydrochloric acid and water, and separate the iron by two precipitations with ammonia (I have often tested the ferric hydrate for manganese, but have never found any, if the separation by ammonia was properly made). Finally, precipitate the manganese as phosphate." Nos. 28, 29 (13.35, 13.07) were by Ford's method." No. 30 (13.50) was by Troilus's method He writes, " I may add the results are quite as good as I expected, although for any element except manganese, they are not close enough for anything like accurate work." L is a firm of commercial chemists of large experience who have made a specialty of iron work. Their method is as follows : Dissolve

Jan 1, 1884

By P. H. Mell

CAN the auriferous slate deposits of the Southern mining region ever be successfully worked? is a question that has been often asked me by persons seeking investments in Southern mines. As the subject is one that has given me much thought during the past few years, I have decided to present my conclusions to the members of the Institute for their consideration. Those who have had the opportunity of exploring the region mentioned above, will readily recall to mind numerous localities, to which their attention was directed by would-be miners, as "rich and desirable properties," in which there were but few quartz seams running in every direction through fine-grained talcose slate. Most of the gold in sued formations was always found disseminated through the slate, and but a small percentage contained in the quartz. Such are the deposits I propose to discuss in this paper. Of course there are many excellent quartz mines in the South that are paying the owners good profits, and many more to my knowledge, that are not being worked for obvious reasons. But it is out of the question to suppose that these slate deposits can be practically

Jan 1, 1881

By R. C. Emmett, R. P. Klepper

The industrial practice of concentration of solids and production of clear solution by gravity sedimentation is an old technology. Through the years, many devices have been designed and built to aid this process One of the more significant developments was a revolving rake mechanism to convey settled material to a central discharge point of a circular tank, patented in 1907 (Dorr). In recent years, clarification systems employing parallel inclined plates have appeared on the market; the original device utilizing this principle was patented in 1886 (Gaillet, et al.) Numerous other methods have been invented, tested, discarded, and sometimes reinvented, all with the specific intention of improving the capacity of a particular settling area. Sedimentation theory, as expressed in Stokes' Law, shows that the rate of settling of a panicle is directly proportional to the difference in density between the particle and the surrounding liquid and, more significantly, proportional to the square of the panicle diameter. While this latter effect is less pronounced with larger particles, anything that can increase the diameter will greatly assist sedimentation and, as a result, flocculation always has been an integral part of sedimentation. Most materials suspended in aqueous media are naturally flocculent to some degree and, hence, are readily concentrated by sedimentation, although sometimes very slowly.

Jan 1, 1981

By David R. Mitchell

THE mineral pyrite (or marcasite) occurs in coal beds as balls, lenses, veinlets and bands. Several million tons are wasted annually on the refuse dumps from coal mining and coal-preparation activities. Sporadic attempts have been made in the United States to recover this pyrite for manufacture of sulphuric acid but only a few plants have succeeded in recovering it on a commercial scale. Several chemical companies in the East became concerned about supplies of pyrite early in 1943, but by late summer of that year the situation had eased. If for no other reason than national security and self-sufficiency during war-time, methods of recovering pyrite from coal-mine refuse should be worked out and made available to coal-mine operators who are potential producers of pyrite. Eastern sulphuric-acid plants are particularly likely to have their sources of raw material blocked by war conditions, so that special studies to determine where supplies of pyrite can be obtained for these plants from inland sources are desirable. Davis's1 summarization of conditions during World War I gives the following facts: During those years, the shortage of pyrite became acute. Shipments of hand-picked pyrite were made from a number of coal mines in Illinois, Indiana, western Kentucky, Ohio and Pennsylvania. A mechanical concentrating plant for separating pyrite from picking-table refuse was built at Danville, Ill., and operated for several years, and a small pyrite-concentrating plant treating washery refuse near Gillespie, Ill., operated for several months in 1918. The Consolidation Coal Co. of Fairmont, W. Va., constructed and operated a sulphuric-acid plant using pyrite recovered from coal-mine refuse. The U. S. Bureau of Mines during 1917-1919 made a comprehensive survey of pyrite-production possibilities from coal mines and estimated that there was a potential yearly production of 435,000 tons from Ohio and Pennsylvania and 928,000 tons from Kansas, Missouri, Iowa, Illinois, and Indiana mines. This estimate included only mines that could produce one per cent or more of their coal production as pyrite containing a minimum of 40 per cent sulphur. PYRITE PRODUCTION According to the Minerals Yearbook,2 approximately 660,000 long tons of pyrite was produced in the United States in 1941, with an average sulphur content of 42 per cent. The average value f.o.b. mines was $3.09 per long ton. Spanish pyrite, 48 per cent sulphur minimum, was quoted at 12 cents a unit c.i.f. U. S. ports, equal to $5.76 a ton for shipments of minimum sulphur content. Most of the pyrite produced in the United States is obtained as a by-product in the dressing of copper and zinc ores. Metal mines in the East making pyrite concentrate for the market or use in company-operated sulphuric-acid plants

Jan 1, 1944

By John F. Blandy

With the Report of Mining Statistics, for the year 1872, there was published a geological map of the United States and Territories. This is, I believe, the only map which represents the geology of Arizona, and is, as far as my observations go, correct. It is, however, on so small a scale as to be of little practical value to the miner. I know of no other maps, even of localities, of this Territory. The topographical maps are also on so small a scale as not even to serve as guides from place to place; the largest, that of Eckhoff and Ricker, being only 30 by 30 inches to represent a territory of 135,000 square miles. For these reasons, it makes it exceedingly difficult to describe the various mining centres in an intelligent manner, and equally so to examine such a hilly country as it is intended to describe in this paper. When I first came into this Territory I soon realized the troubles I had to encounter in trying to form an opinion, or even to get the needed information on the geological contour. I have, therefore, labored as best I could to get a topographical diagram of the section of country represented by the map which accompanies this paper.* The lines run by the Land Department up the valleys of the Aqua Frio, and those west of the Hassayampa, and connected east and west to the north of Prescott, enabled me to inclose correctly the space covered by the Bradshaw and Sierra Prieta mountain groups, but the territory covered by these mountains, and the most difficult part, I have had to fill up as best I could. I have met with such success as to meet the approbation of those most familiar with the country, and, with the map in hand, any one would he able to cross it in any direction. As there has not been a single line of survey made across it, this has been no small undertaking, and I have had to depend upon sights from prominent points with the pocket-compass, or, in the absence of that, to make observations, with watch in hand, and guess as near as possible the meridian direction. Rut one main wagon-road passes through the district, that from Prescott to the Peck mine.

Jan 1, 1883

By James Cudworth

THE Birmingham district of Alabama has utilized the slag from its blast furnaces consistently since the earliest development of the slag industry. Today there are producers of slag cement who started business in 1900, and who have, under a progressive policy, expanded the number of their products to meet present demands. There are producers of slag aggregates and other crushed slag products who have been successful for periods of over thirty years. There are at the present two companies, Cheney Lime and Cement Co. and the Southern Cement Co., manu-facturing puzzolan cement; three companies, Birmingham Slag Co., Woodstock Slag Co., and Swann Chemical Co., making slag aggregates and by-products; one company, Tennessee Coal, Iron and Railway Co., a subsidiary of the U. S. Steel Corporation, producing ground open-hearth basic slag for soil conditioning. Two companies, the Sloss Sheffield Steel and Iron Co. and the Woodstock Slag Co., make slag concrete in ready-mix plants and one company, the Superock Company, manufactures fine and coarse slag aggregates under a new granulation process. No Portland cement is made with slag as an ingredient, because dolomite is used so extensively as a blast-furnace flux that the magnesium content of the slag is excessive.

Jan 1, 1937

By Benjamin L. Miller

THE essential differences expressed by the different speakers participating in this symposium concern merely the relative emphasis placed on the subjects that are commonly included under the term "geophysics" and the branches of science that form the basis for investigations in this field. In order to appreciate the present situation it may be profitable to briefly refer to a few historical matters. One can find almost countless descriptions of geological phenomena long antedating the introduction of the title of "geology," which has been credited to Richard de Bury in the fourteenth century. Interpretations, when they were offered, were generally pure speculation. Only toward the close of the eighteenth century do we find theories developed as the result of observations and tested by additional observations. It is difficult to select and give proper credit to the individual who was particularly responsible for turning geology into a distinctly observational science. William Smith, who has been called the "Father of English Geology," certainly represents the period when observation was the only method used. As he traveled through the British Isles, "sometimes 10,000 miles in a year," he was continually making notes of his observations. Geikie says: "His plain, solid, matter of fact intellect never branched into theory or speculation, but occupied itself wholly in the observation of facts." William Smith, with others of his time, definitely laid firmly the foundations on which modern geology has been built. Field and laboratory observations can no longer be said to constitute the sole basis for geologic contributions but we have not laid aside the methods of Smith and his followers. It is folly to underestimate the fundamental value of the observational part of geology in the present. The objection to purely observational geology is that it is mainly qualitative and not quantitative, general and not specific. No one can deny this charge and probably there are few who do not welcome every method or process whereby we can put aside generalities for definite established values. Physics is the science that has particularly come to the aid of the geologist in this respect. CONTRIBUTIONS OF PHYSICS It is not the intent of the writer to enumerate or to evaluate all of the contributions to geologic advance in the field of physics. A few only are used for the purpose of illustration. When Clarence King, Director of the United States Geological Exploration of the Fortieth Parallel, invited Ferdinand Zirkel to study 2500 thin sections of rocks collected from the western United States, the use of the microscope came into general use. Zirkel's report was published in 1876. He was not the first to use transmitted light for microscopic rock determination, some work having been done by Henry Clifton Sorby and others some years earlier, but he was the first to put into general use this method. We may well claim that this

Jan 1, 1941

By Craig S. Hartley

An approximate expression is obtained for the energy of a closed dislocation loop in equi1ibriu)n with a constant net stress. The result obtained is valid for loops in isotropic or anisotropzc materials provided that they are suJficiently large that the energy per unit length of a segment of the loop can be approximated by that of an infinite straight dislocation tangent to the loop. It is shown that this approximation leads to very close agreement with a more rigorous calculation of the elastic energy of a circular glide loop. The Gibbs-Wulff Form, GWF, of a dislocation is the closed planar loop which has the smallest elastic self-energy of all possible loops having the same Burgers vector and enclosing a fixed area, A.' The energy of such a loop is related to the net resolved shear stress* required to expand the loop and to the stress required to activate a Frank-Read source.223 In the following sectiorls the problem of determining the form of the GWF is discussed and an approximate method for calculating its elastic self-energy is presented. It is demonstrated that the approximations employed lead to no serious errors when applied to a calculation of the elastic energy of a circular glide loop. This method is then used to obtain a closed form expression for the energy of GWFs in isotropic and anisotropic materials. THEORY Burton, Frank, and cabrera4 have proved that the relationship of the equilibrium shape of a two-dimensional array of atoms under the influence of the Gibbs free energy associated with unit length of its boundary, G(O), is that the polar plot of G(0) vs 0 is proportional to the pedal of the GWF.* The angle 0 is measured "The pedal of the polar graph ofG(0) vs0 is the envelope of tangents to the eraph.relative to some crystallographic reference direction. The difficulty in applying this result to a closed dislocation loop arises from the self-interaction of the loop. For a dislocation the energy analogous to G(0) is a function of the total configurati~n.~ Consequently the relation which determines the GWF is an integro-differential equation rather than the simple differen- tial equation which results when G(8) is a function of 0 alone. Mitchell and smialek3 and Brown~ have used the self-stress concept introduced by ~rown' to calculate the shapes of dislocations in equilibrium with an applied stress. In this approach the glide force on an element of the dislocation loop due to the interaction of the element with the rest of the loop is equated to the glide force exerted by the local applied stress. The shape of the loop is then adjusted so that the two forces above are equal at all points on the loop. It is possible to calculate the energies of such loops by noting that, for equilibrium with an applied stress, the energy is equal to pijbiAj (summation convention) where bi is the Burgers vector, p.. is the local net stress tensor, and Ai is a vector directed perpendicular to the plane of thd loop with magnitude equal to the area of the loop. Also Brown' has calculated the energy of a hypothetical polygonal GWF using the above technique and anisotropic elasticity. However, his indicated solution for the energy in the general case of an arbitrary GWF is only slightly less involved than an iterative solution of the integrodifferential equation referred to earlier. In the present work the approximation employed by DeWit and Koehler' is used to calculate the energy of a closed loop in equilibrium with an applied stress. That is, the energy of a loop segment, ds, is approximated by the product of ds and the energy per unit length of an infinite, straight dislocation in a cylinder coaxial with the tangent to the loop at the angular position of the segment. This is known as the "line tension" approximation. The inner cutoff radius of the elastic solution defines the core radius, while the outer cutoff radius is determined by some characteristic dimension of the loop. Actually, both of these radii vary with the edge-screw character of the segment. The effective core radius changes because of the orientation dependence of the Peierls width of a dislocation,8 and the outer radius should be the radial distance from the circumference of the loop to the center of symmetry of the area enclosed by the loop.g However, since the energy varies logarithmically with the ratio of these radii while depending directly on the effective elastic constants, only the effect of the latter is considered. This approximation also neglects the self-interaction of the loop segments. For small loops this will doubtless be extremely important, but for large glide loops produced by plastic deformation the self-interaction is not nearly so important in determining the energy of the loop. This point is illustrated by the following calculation of the energy of a circular loop. Consider a circular loop of radius R which lies in the XI - x, plane of an infinite isotropic continuum and whose Burgers vector makes an angle $ with xs. The first-order solution for the elastic self-energy is:'

Jan 1, 1970