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By Robert C. Emmett, Donald A. Dahlstrom

FOR many years gravitational classification has been employed as a basic tool in beneficiation of minerals and coal. While improvements have been made to increase efficiency and fields of application, the basic flow pattern has remained relatively unchanged in most gravitational classifiers. Feed slurry is introduced into a settling pool wherein the coarser solids settle against either an upward or horizontal fluid current, or a combination of both, and are withdrawn in a concentrated underflow stream. The finer solids below the classification point possess too low a settling velocity and thus are primarily swept out through a weir overflow by the bulk of the fluid. Because of its simplicity, efficiency, and low power and maintenance costs, gravitational classification finds a wide acceptance for separations in the range of 20 to 325 mesh.

Jan 10, 1953

By R. F. Mitchell, G. F. Dillon, A. F. Armington

In this paper the present methods of boron preparation are discussed with emphasis on the iodide intermediate. Several methods of boron triiodide preparation were investigated, the most satisfactory method being the preparation from the elements. A yield of 60 pct based on iodine is found for this method. Zone-refining, sublinzation, distillation, and fractional-recrystallization results are given for the boron triiodide, with distillation producing the best results. Several methods of decomposition are also discussed. The purity of the resulting iodide boron approximates the puritjl of the best available bromide boron, ELEMENTAL boron has been suggested as a possible high-temperature semiconductor by several workers,' but has never been exploited as a device material. The principal difficulty with boron is the unavailability of pure crystalline material from which accurate information on electrical properties could be obtained. Most boron crystals presently produced are very imperfect in structure and of questionable purity, particularly in relation to carbon content. Several methods of boron purification have been reported in the past few years, all of which produce material with a purity better than 99.0 pct. Most of these methods have been the subject of a recent review by Starks' and will not be elaborated upon in this report. However, of all the purification methods reported, only those using halide intermediates produce a purity approaching that usually required for electronic applications. The bromide intermediate has been most used for the preparation of high-purity boron.'y3 This material is easily prepared from the elements and can be effectively purified by distillation and decomposed by hydrogen reduction. The resulting product contains a trace of silicon, and an uncertain amount of carbon, believed to be approximately 100 ppm. It has been recently reported by Russian workers that high-purity boron can be produced using an iodide intermediate.' In the work cited, boron is reported free of spectro-scopically determined impurities, but the reported detection limits are quite high (- 100 ppm). In addition, no data is given on the carbon content of the product. In the present paper, boron triiodide was chosen as the intermediate for several reasons. First, carbon tetraiodide, which could be a major impurity, is reported to be unstable above 200" and hence could be easily separated from the boron triiodide by its decomposition, since temperatures greater than this are attained during the purification process. The low melting point (45°C) and boiling point (20B°C) and the relatively high vapor pressure of boron triiodide should allow the application of any physical purification technique to the material. The possibility of a lower decomposition temperature than that used for the bromide process is another advantage which might cut down extraneous contamination. The iodide, however, does have certain disadvantages when compared with the bromide, the production cost being the most significant. This is the result of a higher halide-to-boron weight ratio, which means more intermediate must be employed. The cost of the starting material is also greater for the iodide. This cost could be considerably reduced however, by recycling the iodine byproduct. Epitaxial growth of boron, which is probably the best method of producing junctions, should be possible with either the bromide or the iodide as the intermediate. However, this has been attempted only on a limited scale up to the present time because of the unavailability of good crystals. The authors have been relatively successful in laying down a heterotaxy of boron on silicon, however. This will be reported at a later date. Several crystalline modifications have been reported for boron, four of which are now believed to be real.' These are the a! and 0 rhombohedral and the a, and 0 tetragonal. In general, the a! rhombohedral is the low-temperature form and the B rhombohedral is the high-temperature form. The tetragonal structures are detected between 1000"

Jan 1, 1964

By Richard Pearce

WHILST most of the silver- and copper-bearing veins of Butte have characters somewhat similar, the Gagnon vein has certain rather remarkable features which are not noticed in any of the other mines. The silver-veins proper, as illustrated in the Alice, Lexington, Moulton, and many others, have certain well-known typical characters. Manganese is always present in variable quantities as rhodocrosite or rhodonite, associated with quartz, pyrite, and sphalerite, and with little or no copper. The copper-veins also have certain mineralogical characteristics, which are very similar, or different only in minor points. Chalcocite, chalcopyrite, bornite, enargite, with variable quantities of pyrite, may be said to represent the general mineralogical features of these lodes. It is worth noticing that while the silver-bearing lodes have more or less sphalerite, this mineral is almost entirely

Jan 1, 1888

By H. W. Hitzrot, R. A. Limons, L. V. Fegan

The authors have developed and tested a new method for measuring pellet-bed temperatures in the traveling-grate or the shaft furnace. This method-using silver-palladium alloy wires as indicators-is less costly and less time-consuming than existing methods. Silver palladium wires, having specific melting points in the 2000° to 2500°F range, are enclosed in ceramic capsules. Each capsule is placed in a nichrome wire basket filled with a sample of green pellets, the baskets being the means for recovering the capsule after firing. After the encapsulated wires have been exposed to the firing cycle, the alloy wires are examined to determine the maximum temperatures attained by the pellet sample. This gives accurate, rapid determinations of maximum temperatures attained during pellet induration in either the traveling-grate or shaft furnace.

Jan 6, 1965

By AIME AIME

OPPORTUNITY may not be knocking but it, at least, is waiting for you, your family and your friends in that amazing republic south of the Rio Grande. For the first time we are able to publish the official itinerary for the forth-coming Mexico City meeting of 1936. As shown on Page 351, the deluxe special train leaves St. Louis on Thursday. Nov. 5 at 5:30 p.m., returning to St. Louis on Nov. 18 at 8:15 a. m. The schedule provides seven days and six nights in Mexico City with numerous excursions to nearby towns and resorts. The oldest surviving city in' North America is Mexico City, dating back at least to the twelfth century. It was the Aztec capital when Cortez arrived in 1519. The famous cathedral still standing was built on a foundation of sculptured Indian images and the remains of a great Aztec temple. Today it is a city of romance.

Jan 1, 1936

By T. F. Witherbee

The subject of an article in the Engineering and Mining Journal for October 13th, 1877, namely, Blast Furnace Treatment of Silicious Iron Ores,, is of great interest to myself, and doubtless to many others who hare been troubled with a seemingly unaccountable percentage of silicon in their pig iron. It is to be regretted that the author of the article did not give us complete details of his charges, and thus prevent a possibly fatal error in the very beginning of the discussion of the points raised in his communication. As it now stands, I think we will have to fall back upon the statement that, " every conceivable mixture of fluxes and ores (A and B) has been used." Let us first, in order to simplify the calculations, do with she

Jan 1, 1879

By L. N. Brown

The use of sheet and strip metal has increascd rapidly during the last few years and manufacturers have been called upon for an ever-increasing tonnage, better drawing quality, and better surface. The automobile industry is probably the most insistent in striving for a better product and a desire to reduce costs. Confronted by these demands, the mills have directed their efforts toward the delivery of material. Their personnel has been occupied largely with the problems incident to production, as any increase forced the use of new sources of raw material with their problems. These problems, combined with those met in the daily routine, have demanded immediate attention, with the result that the standardizing of heat treatments, quality, or temper, etc., have been neglected. Considerable work in standardizing has been done by many companies, but no acceptable method has been developed. The following method, therefore, is given with the hope that some method that can be accepted by the manufacturers and users may be developed. The problem of selecting a material with such properties that the losses in processing are a minimum is interesting and difficult. A description of the properties required is likewise difficult, largely because of loose terms. Another handicap is the number of methods of testing which have not been standardized and concerning which little information is available. In the selection of drawing or forming stock, it is advisable to eliminate as many variables as possible; consequently the method of testing the material is of the utmost importance. The method should be rapid and comparatively easy of application, as it is more important that a large percentage of the stock be tested with reasonable accuracy than that

Jan 1, 1923

By L. N. Brown

The use of sheet and strip metal has increascd rapidly during the last few years and manufacturers have been called upon for an ever-increasing tonnage, better drawing quality, and better surface. The automobile industry is probably the most insistent in striving for a better product and a desire to reduce costs. Confronted by these demands, the mills have directed their efforts toward the delivery of material. Their personnel has been occupied largely with the problems incident to production, as any increase forced the use of new sources of raw material with their problems. These problems, combined with those met in the daily routine, have demanded immediate attention, with the result that the standardizing of heat treatments, quality, or temper, etc., have been neglected. Considerable work in standardizing has been done by many companies, but no acceptable method has been developed. The following method, therefore, is given with the hope that some method that can be accepted by the manufacturers and users may be developed. The problem of selecting a material with such properties that the losses in processing are a minimum is interesting and difficult. A description of the properties required is likewise difficult, largely because of loose terms. Another handicap is the number of methods of testing which have not been standardized and concerning which little information is available. In the selection of drawing or forming stock, it is advisable to eliminate as many variables as possible; consequently the method of testing the material is of the utmost importance. The method should be rapid and comparatively easy of application, as it is more important that a large percentage of the stock be tested with reasonable accuracy than that

Jan 1, 1923

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Jan 1, 1938

By F. N. Rhines, T. E. Leonitis

The oxide scale that forms upon magnesium at elevated temperatures is non-protective in the sense that the rate of oxidation is constant and thus does not decrease with the growth of the scale as it does with other common metals. This generality was first stated by Pilling and Bedworth' and has been verified by Suzuki2 and by ScheiL3 Pilling and Bcdworth argued that the nonprotective characteristic could be predicted from the fact that magnesium oxide occupies less space than does the metal from which it springs, wherefore the scale is not expected to cover the metal so completely as to exclude all direct access to the atmosphere. Linear oxidation is thought by Scheil to be common to all cases where the reaction occurs at the oxide-metal interface. According to Suzuki," he product of high-temperature oxidation in the air is MgO contaminated with no more than traces of a nitride. When the metal is allowed to burn freely a fume composed of cubic crystals of Mg04 is given off. Delavaults observed that excrescences form upon liquid magnesium and alloys in thc course of oxidation. Beyond this it is known that the use of atmospheres containing small quantities of sulphur dioxide6 or carbon dioxide serve to retard the oxidation of solid magnesium and that beryllium' and calciums minimize the oxidation of molten magnesium exposed to the air. Many studies have been devoted to the nature and rates of "protective" oxidation, as exemplified by the cases of copper and iron, wherein the rate is characteristically parabolic. The theory of parabolic oxidation is well developed.~ Linear oxidation, on the other hand, has received but little attention and the theories proposed by Pilling and Bedworth and by Schcil have yet to withstand careful examination. There exists no comprehensive survey of the high-temperature oxidation of magnesium (or of any other metal that exhibits linear oxidation) over a broad range of temperature, under a variety of atmospheric conditions and covering a large group of alloys. It has been the purpose of the present investigation to provide such a survey, with the object of gaining a fuller understanding of linear oxidation, especially as applied to magnesium. Experimental Procedure and Results The experimental studies undertaken were of two kinds: (I) measurement of the rate of oxidation as influenced by the 6c

Jan 1, 1946

By T. E. Leonitis, F. N. Rhines

The oxide scale that forms upon magnesium at elevated temperatures is non-protective in the sense that the rate of oxidation is constant and thus does not decrease with the growth of the scale as it does with other common metals. This generality was first stated by Pilling and Bedworth' and has been verified by Suzuki2 and by ScheiL3 Pilling and Bcdworth argued that the nonprotective characteristic could be predicted from the fact that magnesium oxide occupies less space than does the metal from which it springs, wherefore the scale is not expected to cover the metal so completely as to exclude all direct access to the atmosphere. Linear oxidation is thought by Scheil to be common to all cases where the reaction occurs at the oxide-metal interface. According to Suzuki," he product of high-temperature oxidation in the air is MgO contaminated with no more than traces of a nitride. When the metal is allowed to burn freely a fume composed of cubic crystals of Mg04 is given off. Delavaults observed that excrescences form upon liquid magnesium and alloys in thc course of oxidation. Beyond this it is known that the use of atmospheres containing small quantities of sulphur dioxide6 or carbon dioxide serve to retard the oxidation of solid magnesium and that beryllium' and calciums minimize the oxidation of molten magnesium exposed to the air. Many studies have been devoted to the nature and rates of "protective" oxidation, as exemplified by the cases of copper and iron, wherein the rate is characteristically parabolic. The theory of parabolic oxidation is well developed.~ Linear oxidation, on the other hand, has received but little attention and the theories proposed by Pilling and Bedworth and by Schcil have yet to withstand careful examination. There exists no comprehensive survey of the high-temperature oxidation of magnesium (or of any other metal that exhibits linear oxidation) over a broad range of temperature, under a variety of atmospheric conditions and covering a large group of alloys. It has been the purpose of the present investigation to provide such a survey, with the object of gaining a fuller understanding of linear oxidation, especially as applied to magnesium. Experimental Procedure and Results The experimental studies undertaken were of two kinds: (I) measurement of the rate of oxidation as influenced by the 6c

Jan 1, 1946

By A. P. Watt

Foreword...............................................................323 Location of District..................................................... 324 Geology and Mining..................................................... 325 Topography and Climate................................................. 325 Lcad Production of the District...........................................325 Operating Companies in Southeast Missouri................................ 327 History of the District................................................... 329 Present Method of Treating the Ore....................................... 335 Character of Ore Treated...........................................338 Chemical Analyses............................................. 339 Description of Polished Specimens.................................340 The Concentration Problem of the District............................. 341 Handpicking at Mine La Motte....................................... 343 Crushing............................................................344 Roll Practice in the District.......................................... 346 Screening Practice................................................... 347 Jigging the Ore..................................................... 347 Bull Jigging.................................................... 348 Hancock-jig Practice............................................ 348 Classification of the Ores.............................................. 350 Table Treatment....:............................................... 352 Regrinding of Middling.............................................. 354 Description of Marathon Mill..................................... 358 Results of Preliminary Tests.....................................359 Rod Wear in the Marathon Mill.................................. 367 Steel Consumption.............................................. 368 Design of Marathon Mills.............. :......................... 368 Treatment of Table Middling........................................ 368 Slime Concentration................................................. 370 Methods Used in the Past.......................................370 Present Methods of Treatment................................... 371 Flotation of Slime.......................;........................ 371

Jan 1, 1918

A shrinkage stope is an overhand stope in which the broken ore accumulates until the stope is completed to, or near, the level above. As broken ore generally occupies at least 60 per cent. more space than ore in place, about a third of this must be drawn out as the stope advances to leave a working space under the back. The ore remaining supports the miners and gives temporary support to walls, and is all withdrawn when the stope is finished. The shrinkage-stope method is applicable to steep-dipping deposits of strong ore with strong walls. It may be applied to narrow or wide veins, and is simple and cheap. Five examples, which include important and varied types of deposits, are given: namely, Kennecott, Homestake, Jarbidge district, Mogollon district, and Cripple Creek district.

Jan 1, 1925

By Arthur Knapp

NEARLY every technical man is called upon at some time in his life to deliver a paper before a technical audience or to write a technical paper for publication. It is not necessary to be an accomplished public speaker to deliver a technical paper successfully; it is only necessary to bear in mind a few obvious points. Poorly presented papers are nearly always the result of a few errors of deportment, but they are vital and at the same time so obvious that they are often overlooked. Experience is a good teacher but a little study and careful preparation will moderate the suffering of both an amateur speaker and his audience. An author's paper suffers, through poor delivery, in direct proportion to the suffering of his audience. The best test of a paper is to have it read aloud to the author. This will bring out faults not apparent when read silently by the author. Some of the things which will probably need correcting are improper phrasing, noneuphonic sequences, and long or involved sentences. Frequently authors write their papers in short crisp sentences for oral presentation, then rewrite them for publication.

Jan 1, 1942

By Will Clark

HE who enters a mining claim within an Indian reservation of the United States of America acquires no rights thereby, because of the fact that the lands within such Indian reservation are not a part of the public domain, and cannot be located or acquired as mineral land. However, where such an entry is authorized as to a particular reservation by an Act of Congress, such claims as may be entered under such authorization are thereby segregated from the reservation, and the Indian title is extinguished. Under the Choctaw Constitution, any citizen of that nation, in other words any Choctaw Indian, who discovered a coal mine, acquired an exclusive right to all coal within a radius of 1 mile. The laws of the Chickasaw nation provided for the formation of corporations to develop coal and other mines, with authority to contract with others to develop and work the mines. Under these laws, leases were made; but Congress subsequently abrogated all existing leases, prohibited all persons from receiving royalties from such mines, and provided that all coal within the nation should remain the common property of the tribes. Such leases are now expressly prohibited by an Act of Congress (32 United States Statutes at Large, 655). All leases of mineral lands upon Indian reservations must now be made under regulations promulgated by the Secretary of the Interior, and the royalties must be paid into the United States Treasury for the benefit of the tribes. In Canada the Indians have no rights to the royal mines and minerals, and the government can make no stipulation with the Indians which would affect the rights of the Province in which the lands are situated. Therefore, while it is true that under our present law no rights can be acquired to a mining claim within an Indian reservation, it seems to be fully within the authority of Congress to make laws, giving such rights to mineral locators as it may deem necessary or expedient.

Jan 6, 1914

By Thomas T. Read

THE benefits derived from stabilization of industry that might possibly be attained through some scheme of centralized economic planning have been much discussed of recent months, and opinions on the subject range from those who believe that some agency like the War Industries Board would be practicable to create and wholly beneficial in effects, to those who are equally convinced that none of the suggestions so far advanced are at all practicable, or likely to be productive of more of good than of evil. The discussion has been on the general topic, but-many of those who have written or spoken on it have introduced economic problems of the pinera1 industry; for example, Newton D. Baker, who referred to the coal industry in his address on economic planning at the Williamstown Institute of Politics on July 31, and then went on to say, "Industrial progress is made by the development of new things, but new things upset the equilibrium of any plan. Who could have planned the industrial effects of the development of the railroads, or the economic changes which you have seen attend the development of the internal combustion engine. Obviously, unless we are prepared to put world economics in a strait-jacket and, like the encyclopedists, write its full history on the theory that further progress is impossible, no such plan could be made for nations which are forging ahead as is entirely rational for nations which are still catching up."

Jan 1, 1931

Abbey. Robert Graham, District Mgr.. The W. W. Sly Mfg. Co., 50 Church St., New York, N. Y. '21 Abbott, Clarence E., V.P., Charge of Raw Materials, Tenn. Coal, Iron & R. R. Co., 1242 Brown-Marx Bldg., Birmingham, Ala. '04 Abbott, Louis Benjamin, Chief Engr., Consolidation Coal Co., Watson Bldg., Fairmont, W. Va. '15 Abeel, George H., Jr., Cons. Min. Engr 12S1, S. Canon Dr., Beverly Hills, Cal. '18 4 -Abel, Raymond L., Asst. Prof., Dept. of Pet. Refin.. Univ. of Pittsburgh. Pittsburgh, Pa. '28 Abel, Walter D., Cons. Engr 650 S. Grand Ave., Los Angeles, Cal. '82 Abele. Louis T., Min, & Met. Engr., Supt., Texas Hill Mine Coulterville, Cal. '31 Abell, Leo M Sullivan Concentrator, Chapman Camp, B. C., Canada '31 Abernathy, George Elmer, Prof. of Geol. & Min., Kansas State Teachers College. Pittsburg, Kan. '20 Aborn, Robert H., Asst. Met., Research Lab., U. S. Steel Corp., Lincoln Highway, Kearny, N. J. '19 Abraham, W. E. V., Member, Geological Staff of Burmah Oil Co., Ltd., Nyaunghla, Upper Burma, India. '28 Abstein, Henry T., Engr. & Mgr., Profile-Tamarack Mines Co Yellow Pine, Idaho '27 Acker, E. O'C., Met 128 East Washington Lane, Germantown, Philadelphia, Pa. '86 Ackerman, D. E., Met., Research Lab., International Nickel Co., Inc Bayonne, N: J. '24 Ackerman, George F., Engr., Real del Monte y Pachuca Min. Co., Apt. 3, Pachuca, Hgo., Mexico '29 *Acres. T. H.. Geol. Dept., Valuation & Pet. Engrg., Richfield Oil Co., 555 S. Flower St., Los Angeles, Cal. '29 Adachi, Jinzoo Address Wanted '88

Jan 1, 1934

By Chas. F. Jackson

IN these days the headlines and spotlight have been focused largely upon the new processes developed and new plants erected to meet the multiplied demands for mineral products required for prosecution of the war. By comparison, the less spectacular achievements of the miner, who is meeting the demand for raw material without which these processes and plants would be useless, have received little attention. Attendance at the mining meetings here reported was small, averaging about 35 to 40, but interest was as keen as ever, and evidenced to your reporter that the miner is no less on the job than is the metallurgist. It is evident that the mine operators are not neglecting any improved methods and practices in their struggle to produce more in the face of diminishing labor supply.

Jan 1, 1943

By Rollin E. Hook, Attwell M. Adair

The yield and fracture behavior of recrystallized chromiztm have been studied in order to gain an understanding of the recrystallization embrittlement-rheotropic recovery phenomenon. The duc tile-brittle tensile transition temperature of recrystallized chromium was found to vary from 225 ° to -80°C as the ratio of specimen diameter/mean planar grain size decreased. The applicability of this observation to other bcc metals is briefly discussed. Brittle fracture in recrystallized chromium was found to be initiated predominately from intercrystalline rupture nuclei. Single crystals exhibit a high degree of ductility at 23 "C. The experimental data indicate that grain boundaries play a significant part in the yield and fracture behavim. Pres training significantly reduces the transition temperature, and high temperature aging does not result in re-embrittle-ment until complete recovery or re crystallization occurs. SEVERAL theories have been used to explain the recrystallization embrittlement-rheotropic recovery phenomenon in chromium. Wain, Henderson, and ohnstone' propose a Cottrell dislocation locking mechanism due to nitrogen, and Weaver and Gross and weaver 3 propose a strain-induced precipitation mechanism involving a chromium nitride precipitate. The researches of many investigators seem to leave little doubt that brittleness in chromium is promoted by interstitial impurities. Smith and seybolt4 have shown that the ductile-brittle transition temperature is lowered as the interstitial content is reduced. weaver3 provides evidence for a 150°C reduction in the tensile transition temperature as the nitrogen content is reduced from 20 to 5 ppm. Maykuth and affee' have suggested that the amount and orientation of grain boundary impurities may be responsible for the brittle nature of recrystallized chromium. This suggestion was based on their findings that wrought iodide chromium possessing a fiberous grain structure is ductile in tension at room temperature while a recrystallized grain structure is completely brittle. Previous investigations have not studied this phenomenon sufficiently to determine its cause. Perhaps this has been largely due to previous experimental findings that brittle fracture observed in chromium has been almost entirely transgranular.' In addition McNeil and imb,' who investigated coarse-grained as-cast chromium, describe the point of initiation of fracture as cleavage, close to the (100) plane, near or at grain bound-daries, or at included particles or voids. However, Hook, Adair, and ipsitt found that fracture in coarse-grained recrystallized chromium is initiated by intergranular rupture and then propagates nearly entirely by cleavage. This result, together with their finding that room temperature ductility in bending is observed for single crystals and coarse-grained polycrystalline specimens for which the number of grains through the specimen diameter is small, suggests that grain boundaries may play an important role in the brittle behavior of chromium. The recrystallization embrittlement problem can be resolved into two questions. These are, whether the controlling mechanism is predominately one of crack initiation or crack propagation, and whether brittle fracture is initiated predominately by slip or twin induced intergranular rupture or by cleavage. The following research was designed to study the role of grain boundaries on the brittle fracture of chromium in an effort to resolve these questions. EXPERIMENTAL PROCEDURES, RESULTS, AND DISCUSSION General Procedure. All tensile specimens (except 0.04 in. diam wires) were prepared from 1/4 in. diam swaged rod fabricated from one ingot. Details of fabrication are given elewhere. The results of impurity analysis for the swaged rod and for the

Jan 1, 1963

By Roland de Wit

Conclusions reached in a paper by weertmanl are amplified in a mathematical and graphical way. It is shown that in a stressed crystal a straight dis-location may be in a position of unstable equilibrium with respect to helix development, and how a small perturbation may start the dislocation off on its helical path. Helix development occurs by diffision; bulk diffusion is necessary for development from a screw, but core diffision is sufficient for development from an edge dislocation. For a mixed dislocation helix development can take place by core diffusion if the helix also climbs; a diffusion reversal takes place when the slope of the helix equals the slope of the Burgers vector. The work done on a crystal by the external forces is graphically shown to be consistent with the direction of motion of the dislocation in helix development. Finally a detailed mechanism for tangle formation from helices is presented. In the course of helix development a glide situation may be reached where a segment of each helix loop lies in a slip plane in which it can expand by glide. Thus is it visualized how a helix can deteriorate into a tangle. A paper by weertmanl proposes dislocation-tangle formation by a helical dislocation mechanism. The present paper amplifies Weertman's arguments in a mathematical and graphical way and presents some further ramifications of the proposed model. The importance of dislocation tangles is discussed in Weertman's paper and the references cited therein. The mechanism of their formation is not yet understood. Weertman proposes that in cold-worked crystals conditions exist suitable for the conversion of straight dislocations into helices and subsequently into tangles. Helix formation occurs by a diffusion process and Weertman proposes that at low temperatures only core diffusion is important. The present paper necessarily repeats some of Weertman's work. Since the mathematical development and notation used are slightly different from his, this was thought necessary for clarity. GEOMETRY OF THE HELIX weertman2 has shown that the equilibrium form of any dislocation line is a helix if it is assumed that the energy per unit length (line tension) of the dis- location is constant. For the special case that no external forces act on the dislocation, the helix reduces to a straight line. We shall assume in this paper that the dislocation has a helical form even when it is not in equilibrium. The parametric equation of a helix is, see Fig. l: where a is the radius of the cylinder tangent to the helix, and 270 the pitch of the helix. The pitch is related to v, the number of turns per unit length (along the axis) by the relation: When a = 0 Eq. [I] gives a straight line in the z direction. The growth of a straight dislocation into a helix is now described mathematically by letting a vary from zero to its final value. The tangent to the helix is given by where is the path length along the helix. This gives the direction of t and since its magnitude is unity we must have So that dcp/ds = (a2 +p2)-"'. The curvature of the helix is given by where n = -(cos + sin) is a unit vector normal to the helix. Note that the vectors k and n always point toward the axis of the helix, Fig. 1. FORCE ON THE HELIX The external force which makes the straight dis-

Jan 1, 1963