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By Gordon Demetrick

3900 Yonge St. was not a typical site on which to build a condominium apartment. A steep hill covered the majority of the site. In order to use as much of this site as possible, the rear of the building was to have nine stores cut into the face of the hill. A permanent shoring system was required as the building structure was not designed to provide sufficient stabilizing elements to support the total earth pressure. The total excavation depth required was 36 m (120'-0") with the upper 12 m (40'-0") to be backsloped. The vertical face of soil to be supported was 24 m (80'-0'). The shoring system originally designed by the Structural Engineer was to support this face by installing soldier piles and inclined earth anchors. During bid preparation it became evident to us that the system as designed would be difficult and expensive to install due to wet soil conditions. An innovative design was required to overcome these problems. Anchor Shoring hired John Stephenson Consultants Ltd. to aid them in accomplishing this goal. After extensive investigation together with The Trow Group, a unique design was proposed which provided a practical solution to the shoring problem.

Jan 1, 1987

Experiment of Improving the Quality and Decreasing the Impurity of Titanium Concentrate in Panzhihua Mine in China

Sep 13, 2010

By Prosper Lamothe

El presente texto describe los distintos métodos y criterios empleados en la valoración de yacimientos o activos mineros de Chile, asimismo se realiza un análisis comparativo de los distintos métodos para explicar las distintas distorsiones, errores, riesgo e imprecisiones de cada uno de ellos. En este sentido, las empresas son concientes de los riesgos y el impacto que tienen en el valor comercial, los modelos de estimación de recurso y las reservasmineras. mineras. Por ello, las opciones reales son actualmente la técnica que permite valorar y controlar en cierto modo la cobertura de riesgo del negocio.

Sep 12, 2005

By Giovanni Barla

This paper examines the application of gelatin mixture models to the study of factors such as gravity effects, tectonic and residual stresses, anisotropy, physical nonlinearity, time-dependent behavior of the rock mass and connectedness of the geologic space. The calibration technique of gelatin mixtures, proposed by Richards and Mark in 1966, is applied to the particular problem considered. Similitude relationships between model and prototype are discussed with reference to the constitutive equations describing the physical behavior of the rock mass. The interaction between two openings in a linearly elastic medium, under conditions of plane strain, is used as an illustrative example, with the view of describing the history of stress and deformation changes on the rock medium and lining around a slusher drift while undercuts are made in block caving.

Jan 1, 1968

By S. D. Bearden

The world's barite reserve base is adequate for at least 100 years at the current consumption rate. China, India and the United States are expected to remain the leading producing countries, and the United States will continue to be the largest consumer. None of the known substitutes for barium sulfate are expected to impact existing applications. World production in 1995 was 4.41 Mt (4.86 million st), which is about 50% of capacity. Consumption is directly proportional to hydrocarbon well installation activity. Imports are expected to continue to supply more than half of the US requirements.

Jan 1, 1997

By George F. McKeregahan

Phosphate production of the Central Florida Phosphate District has been predominantly from the unique and lucrative Bone Valley Formation, with local and minor amounts coming from the underlying Hawthorn Formation. As the Bone Valley is depleted, replacement production will move progressively into areas of total Hawthorn Production. Significant changes in the characteristics and make-up of the deposit dictate required modifications in mining and beneficiation. Failure to tailor technology to fit the deposits of the future will result in vast "reserve" losses. In the Southern Extension of the Central District - two distinct "ore types" exist. These are presently referred to as the upper (high grade) zone and the lower (low grade) zone. The upper zone is somewhat similar to the Bone Valley Formation and will respond favorably to present beneficiacion practices. The lower zone is strikingly different and its response to conventional beneficiation is not acceptable. The major differences are in grain size distribution and mineralogical make-up of these grains. The Hawthorn differs from the Bone Valley by exhibiting lower grades, lower tonnage yield per acre foot, lower pebble percent of product, higher mining ratios, higher slimes (-150 mesh) content and deeper mining depths. Physical characteristic changes include more frequent occurrences of competent bands or lenses of "limerock" which are submarginal in value.

Jan 1, 1983

By R. P. King

The University of the Witwatersrand (Wits) and the minerals industry of South Africa have grown with the city of Johannesburg. The former has provided teaching and research in mining and metallurgy, while the latter has been responsible for the practical training of metallurgists and for the testing and implementation of innovative ideas proposed by the academics. This interplay between inventiveness and industrial application is illustrated by three examples: the establishment of the iron and steel industry as a result of the persistent experimentation undertaken by Professor G. H. Stanley, the first Professor of Metallurgy and Assaying at the South African School of Mines, which later became Wits; the establishment of the research organization that eventually became the Council for Mineral Technology (Mintek) - again through Professor Stanley's faith in the role of research; and the establishment at Wits of physical metallurgy as a discipline in its own right, as first suggested by Professor C. E. Mavrocordatos of Wits against the opinion of his colleagues in the industry. The Department of Metallurgy at Wits has been well supported by the minerals industry. Not only does the industry provide grants for the financial support of students, but it supplements the salaries of personnel in the Department, making possible the recruitment of top-class academic staff. At present the greatest problem is the lack of interest shown by matriculants in the metallurgical industry as a career. However, an enormous effort is being made by the Chamber of Mines, The South African Institute of Mining and Metallurgy, and the Wits Department of Metallurgy to ensure that matriculants receive appropriate information about the career prospects in the minerals industry.

Jan 1, 1983

By A. H. Heim

A method and apparatus for measuring gas porosities of rocks are described. The apparatus can be assembled from commercially available components. In principle, measurements are made by volume substitution at constant pressure. The maximum error is not more than 0.3 porosity per cent. Typical results are given. INTRODUCTION Determining the porosity of rock samples is one of the most important and yet most varied types of measurement in core analysis. Among the many techniques devised are the so-called "gas porosity" methods. An old and well known example is the Washburn-Bunting method.' The U. S. Bureau of Mines2-' described and later improved the apparatus for a now widely used method generally known as the "Boyle's law" method. In the present form of the Washburn-Bunting method,' the volume of air in the pores of a rock sample at atmospheric pressure is extracted and then collected in a graduated burette at atmospheric pressure. The volume of air is read directly as the pore volume of the sample. The absolute error in reading the collected volume of gas is independent of the total volume; thus, the relative error is larger when the volume is small, as it is for rocks of low porosity. In addition, the sample after measurement contains mercury, which limits its use for other analyses. The Bureau of Mines (or Boyle's law) method measures directly the solids volume of a sample from which the pore volume and porosity are derived, using a separate measurement of the bulk volume. Gas at a few atmospheres pressure is introduced into a sample chamber of known volume containing the rock sample. The pressure is accurately measured. Following, the gas is expanded into a burette at 1 atm, and the gas volume is read directly. From the initial pressure p, and the final pressure p2 and volume v,, the initial gas volume v1 is calculated using Boyle's law; that is, p1v1 = p2v2. Volume v, minus the volume of the empty sample chamber is the solids volume of the sample. The accuracy of the method is limited, unless corrections are made, by deviations of the gas from the "ideal" gas-law behavior assumed in the simple form of Boyle's law. The purpose of the present paper is to describe a method for measuring the gas porosity of a rock which avoids many of these difficulties. Gas volumes are measured directly with the same accuracy as the bulk volumes. Pressures of at least an order of magnitude larger than those of previous methods are employed to insure rapid penetration of the gas into the sample. While special equipment may be built to apply the method, the porosimeter may be constructed as well from commercially available components. For simplicity, the apparatus described will be referred to as the "Constant-Pressure gas porosimeter". THE CONSTANT-PRESSURE METHOD Fig. 1 shows schematically the arrangement of components comprising the present Constant-Pressure porosimeter. Briefly, the method is one of volume substitution and may be considered a null measurement. Omitting (for the present) some of the operational details, the method of measurement consists of the following three steps. 1. After evacuation, the volume of the measuring system (a ballast chamber, a manifold, two gauges and their connections) up to the sample chamber is filled with gas to a high pressure (- 1,000 psi). A sample of the gas at this pressure is trapped in one side of a sensitive differential pressure gauge to serve as the reference pressure for subsequent steps. 2. The evacuated sample chamber containing the rock sample is opened to the measuring system. As the gas expands into the chamber, the resulting decrease in pressure unbalances the differential pressure gauge. 3. The pressure is restored by means of a mercury volumetric pump. The volume of mercury injected exactly equals the free or void volume of the sample chamber (volume of empty chamber minus the solids volume of the rock within). From the injected volume and the known empty chamber volume, the solids volume is obtained and the porosity calculated. The pressure and the volume occupied by the gas are the same before and after opening the sample chamber. Expansion and compression of the gas are incidental operations and do not enter into the calculation of porosity. By the pressure balancing or nulling, the free volume of the sample chamber is merely substituted by an equal and measured volume of mercury. Since the measurements are at constant pressure, there are no compressibility corrections necessary for the sample chamber.

Study on New Tungsten Beneficiation Technological Flow Sheet of Shizhuyuan Polymetallic Mine

Sep 13, 2010

The Mining Foundation of the Southwest will host its 24th Annual American Mining Hall of Fame Awards Banquet at the Tucson El Conquistador Golf & Tennis Resort in Tucson, AZ on Saturday, Dec. 9. The Mining Foundation of the Southwest is a non-profit organization whose objectives are public education about the mineral industries. It also recognizes outstanding accomplishments in and contributions to the fields of fuel and mineral resources.

Jan 1, 2006

By O. E. Humeniuk, A. I. A. Salama, M. W. Mikhail

"The Western Research Centre (WRC) of CANMET operate a unique pilot plant facility where ongoing R&D on coal preparation and mineral processing is conducted. The pilot plant carries out two functions: coal preparation processing using state-of-the art technology and coal-liquid mixture preparation with intensive cleaning circuits that can also be used for mineral processing. In total, the pilot plant includes more than 30 different flowsheet options. The facility is dedicated to small and fine coal, and designed to be flexible and versatile.This paper describes the use of a pilot-scale facility as a research tool for process control development, fine coal beneficiation, development of coal-liquid fuels technologies, development of process models and testing and evaluation of new developments. The pilot plant is used to assist in resource development by evaluating and optimizing flowsheet selection, and producing sufficient samples for utilization tests. The facility is also an important tool for evaluating and testing samples from troublesome circuits of operating plants to find means to optimize and improve recovery, particularly of fines circuits.Detailed examples are given to demonstrate the role of a pilot scale facility in coal preparation R&D, coal industry development and optimization of coal processing operations. These examples include the development of heavy-medium cyclone computer control system, detailed evaluation of beneficiation of a coal deposit with high clay content, development of column flotation, and its role in fine cleaning circuits and treatment of ultra-fines in relation to intensive cleaning, the importance of testing coals in different processes, and cleaning processes influence on coking quality and other utilization applications. The potential of the facility for helping the mineral industry is also described."

Jan 1, 1992

By Frank R. Milliken, Robert Goodwin

In September 1937, the Ohio Copper Co. inaugurated the treatment of its copper-bearing mill tailings at Lark, Utah. These tailings had been accumulated during the regular operation of the Ohio Copper mine and mill over the period 1907 to 1919. Gravity concentration had been employed except for a comparatively short period in 1919, when flotation was used. The ore milled during that period assayed about I per cent Cu. The chief copper mineral, chalcocite, was disseminated in a shattered quartzite, mainly along fracture or cleavage planes. The quartzite gangue was extremely hard and grinding to liberation resulted in excessive sliming of the "sooty" chalcocite, with consequent high tailings losses. Recovery on the seven million tons treated was probably less than 60 per cent of the total copper content. As early as 1918, attempts had been made to sample the dump. In 1928, a complete sampling program was undertaken. The sampling consisted of seventy-four 5-in. post auger holes drilled to the full depth of the dump at regular intervals of 250 ft. Each 10-ft. portion thereof comprised a sample for analysis. Each sample was screened, rolled, divided into three parts, dried and assayed. The reject was retained for testing purposes. From the depth of the auger holes a contour map of the dump was plotted, Fig. I, which gives percentages of tonnage and copper content. The tonnage within the limit of the drill holes was estimated at about five million tons with an average content of 0.42 per cent Cu, 31 per cent of which (0.13 per cent) was acid-soluble. A screen analysis of the composite dump sample is shown in Table I. Flotation tests by several companies and individuals were then made, the results of which ranged from 62 to 74 per cent recovery. On the basis of these, a 200-ton pilot plant employing straight flotation was built and operated for a few months. Operation of this plant was unsuccessful, as no provision had been made to handle the copper-bearing solutions resulting from the water-soluble copper, a point that was overlooked in the laboratory test work. Attempts to decant the copper-bearing solution for precipitation in the usual manner ahead of flotation were not satisfactory because of low water recovery (owing to poor settling characteristics of the pulp) and contamination of the copper precipitate with unsettled slime. Low copper prices in 1931 necessitated the termination of testing. With the stimulus of higher copper prices in 1937, a review was made of metallurgical

Jan 1, 1943

By W. M. Rust, W. D, D. W. Mounce

The almost universal acceptance of electrical logging by the petroleum industry calls for a critical examination of the physical bases of the common methods. This is particularly needed for the natural potential log. The conventional explanations are based on the phenomena of electrofiltration and electro-osmosis. However, experimental data show that they fail to give a basis that is quantitatively sound. Moreover, they lead to interpretations of details of electrical logs that are erroneous. It was found experimentally that when a plug of shale is placed in a chain of dissimilar electrolytes, a current flow results. Experiments on oil-well cores and fluids similar to those existing in wells show that potentials are set up which are in reasonable agreement with those encountered in electrical logging. Doubtless other sources of potential are important but this explanation not only accounts for much of the potential but also clarifies some fairly familiar examples of misinterpretations. Introduction The extraordinary value of electrical well logging as a tool for petroleum engineers and geologists is now so uni- versally recognized that it is not necessary to point out the ways in which it can be useful. It is sufficient to mention only the saving that has resulted from the elimination of much coring that would have been necessary under former practices and the considerable additions to reserves resulting from the discovery of sands missed in coring. Paradoxically, the very remarkable success that has resulted from the application of electrical logging to correlation and completion problems has cost some of its most consistent users dearly.' The fact that some operators have placed unwarranted faith in erroneous interpretations of electrical logs does not reduce the value of the logs. It should, however, make one pause long enough to ask why experienced users should be misled. The answer to this question is not hard to find. In nearly every case, the fault has been oversimplification. This is illustrated very aptly by the familiar interpretation and theory of the natural potential log. Recording and Interpreting Logs The natural potential log is extremely simple to record precisely enough for all present-day uses. One needs only an electrode, a cable to lower the electrode through the drilling mud, a recording meter and a surface ground connection. The electrode can be elaborate but need not be. A simple brass rod 2 in, in diameter and 2 or 3 in. long is quite satisfactory. The cable need not be particularly well insulated, nor need it have a very low resistance. The recorder can be a vacuum-tube 1 References are at the end of the paper.

Jan 1, 1944

By Robert Goodwin, Frank R. Milliken

In September 1937, the Ohio Copper Co. inaugurated the treatment of its copper-bearing mill tailings at Lark, Utah. These tailings had been accumulated during the regular operation of the Ohio Copper mine and mill over the period 1907 to 1919. Gravity concentration had been employed except for a comparatively short period in 1919, when flotation was used. The ore milled during that period assayed about I per cent Cu. The chief copper mineral, chalcocite, was disseminated in a shattered quartzite, mainly along fracture or cleavage planes. The quartzite gangue was extremely hard and grinding to liberation resulted in excessive sliming of the "sooty" chalcocite, with consequent high tailings losses. Recovery on the seven million tons treated was probably less than 60 per cent of the total copper content. As early as 1918, attempts had been made to sample the dump. In 1928, a complete sampling program was undertaken. The sampling consisted of seventy-four 5-in. post auger holes drilled to the full depth of the dump at regular intervals of 250 ft. Each 10-ft. portion thereof comprised a sample for analysis. Each sample was screened, rolled, divided into three parts, dried and assayed. The reject was retained for testing purposes. From the depth of the auger holes a contour map of the dump was plotted, Fig. I, which gives percentages of tonnage and copper content. The tonnage within the limit of the drill holes was estimated at about five million tons with an average content of 0.42 per cent Cu, 31 per cent of which (0.13 per cent) was acid-soluble. A screen analysis of the composite dump sample is shown in Table I. Flotation tests by several companies and individuals were then made, the results of which ranged from 62 to 74 per cent recovery. On the basis of these, a 200-ton pilot plant employing straight flotation was built and operated for a few months. Operation of this plant was unsuccessful, as no provision had been made to handle the copper-bearing solutions resulting from the water-soluble copper, a point that was overlooked in the laboratory test work. Attempts to decant the copper-bearing solution for precipitation in the usual manner ahead of flotation were not satisfactory because of low water recovery (owing to poor settling characteristics of the pulp) and contamination of the copper precipitate with unsettled slime. Low copper prices in 1931 necessitated the termination of testing. With the stimulus of higher copper prices in 1937, a review was made of metallurgical

Jan 1, 1943

By W. D, D. W. Mounce, W. M. Rust

The almost universal acceptance of electrical logging by the petroleum industry calls for a critical examination of the physical bases of the common methods. This is particularly needed for the natural potential log. The conventional explanations are based on the phenomena of electrofiltration and electro-osmosis. However, experimental data show that they fail to give a basis that is quantitatively sound. Moreover, they lead to interpretations of details of electrical logs that are erroneous. It was found experimentally that when a plug of shale is placed in a chain of dissimilar electrolytes, a current flow results. Experiments on oil-well cores and fluids similar to those existing in wells show that potentials are set up which are in reasonable agreement with those encountered in electrical logging. Doubtless other sources of potential are important but this explanation not only accounts for much of the potential but also clarifies some fairly familiar examples of misinterpretations. Introduction The extraordinary value of electrical well logging as a tool for petroleum engineers and geologists is now so uni- versally recognized that it is not necessary to point out the ways in which it can be useful. It is sufficient to mention only the saving that has resulted from the elimination of much coring that would have been necessary under former practices and the considerable additions to reserves resulting from the discovery of sands missed in coring. Paradoxically, the very remarkable success that has resulted from the application of electrical logging to correlation and completion problems has cost some of its most consistent users dearly.' The fact that some operators have placed unwarranted faith in erroneous interpretations of electrical logs does not reduce the value of the logs. It should, however, make one pause long enough to ask why experienced users should be misled. The answer to this question is not hard to find. In nearly every case, the fault has been oversimplification. This is illustrated very aptly by the familiar interpretation and theory of the natural potential log. Recording and Interpreting Logs The natural potential log is extremely simple to record precisely enough for all present-day uses. One needs only an electrode, a cable to lower the electrode through the drilling mud, a recording meter and a surface ground connection. The electrode can be elaborate but need not be. A simple brass rod 2 in, in diameter and 2 or 3 in. long is quite satisfactory. The cable need not be particularly well insulated, nor need it have a very low resistance. The recorder can be a vacuum-tube 1 References are at the end of the paper.

Jan 1, 1944

By M. P. Du Plessis

"The paper discusses coal research in relation to the special needs of Western Canada, with its large resources of lignite and subbituminous coals. Research programs are presented under the following headings: Coal Liquefaction, Pyrolysis, Fluidized-Bed Technology, Underground Coal Gasification and Supporting Investigations. Typical processes are presented and their relevance to Canadian coals is described. The longterm plan of the Alberta Research Council for coal research and the steps taken for its implementation are discussed. Finally, some innovative concepts arising from basic research in coal chemistry are discussed.Canada's Coal ResourcesCanada is richly endowed with coal reserves. With estimated ultimate reserves of 600 billion tons in O.76-m (2.5-ft) thick seams under less than 762 m (2500 ft) of overburden, Canada rank s fourth after the USSR, the USA and Chinatu (see Table I) . Canada's reserves are incompletely explored and estimates are constantly being upgraded. Preliminary information from deeper test-hole logs suggest that similar , if not larger, tonnages occur at depths greater than 762 m (2500 ft).The types of Canadian coals and their regional Distribution(2) is shown in Figure 2. Alberta's subbituminous Plains coal represents about 70% of estimated national reserves. A large portion of the coal can be mined at relatively low cost by surface mining techniques, and it is currently being used exclusively for power generation in conventional thermal plants. This coal, however , also represents a large potential .source of liquid fuels which could equal or exceed that of oilsands and heavy oil. Table 3 compares Federal Government estimates for resources and reserves of fossil fuels in Canada and their recoverable oil content or equivalent.A conservation estimate of only the reserves of thermal coal represents an oil equivalent of 27.6 billion barrels , which equals the recoverable reserves of oil-sand bitumen and heavy oil. A more realistic estimate is probably several times this amount. Although coal can be converted to many other end products, such as fuel gas and synthesis gas for hydrogen and ammonia production, liquid fuels remain the most desirable product mainly because they can be transported more cheaply over long distances and their high energy density makes them uniquely suitable as fuels for transport and agriculture."

Jan 1, 1981

By Sarah Belair, Gauthier Deblonde, Valerie Weigel, Alexandre Chagnes, Gerard Cote

"Niobium and tantalum are strategic metals for electronic and alloys industries. They are produced by pyrometallurgy and hydrometallurgy but most of the niobium and tantalum production processes are not environmentally friendly. For instance, in the hydrometallurgical route, niobium and tantalum separation can only be achieved by liquid-liquid extraction in the presence of hydrofluoric acid by taking advantage of the difference in niobium(V) and tantalum(V) speciation in fluoride-based media. Therefore, the environmental footprint of hydrometallurgical processes for the production of niobium and tantalum could be clearly lowered by replacing HF or NH4F by greener media such as alkaline solutions in which high solubility of niobium(V) and tantalum(V) can be achieved.The development of such new efficient and environmentally friendly hydrometallurgical processes requires a fine description of the physicochemistry of niobium(V) and tantalum(V) in alkaline solutions. Unfortunately, literature data show a huge discrepancy on niobium(V) and tantalum(V) speciation in such media. This paper gives a brief overview of the niobium(V)-tantalum(V) production processes and paves the way to the development of alternative processes in alkaline media by presenting and discussing recent advances in the physicochemistry of niobium(V) and tantalum(V) in these media.INTRODUCTIONNiobium and tantalum are strategic metals since they are used for the production of alloys and super alloys, capacitors and magnets in strategic industries such as electronic, aeronautics and automobile. The main sources of niobium and tantalum are given in Table 1."

Jan 1, 2016

"Human accidents are caused by production accidents, generally ones (such as derailment of cars, falling rock, etc.) that have occurred numerous times before an employee was actually involved. Prevention of human accidents is, one of the essentials in cutting operation costs, and advocates of safety are studying economics to assist them in their work of preventing accidents.Workman's compensation insurance or compensation for human accidents is a true operating cost, and is the only purely tangible measure available which gives a measurement of the cost of accidents even though, as will be pointed out later, it represents but a portion of the total cost of human accidents.In using premiums paid for compensation insurance as a measure of the cost of accidents, it must be kept in mind that most insurance laws, as pointed out in a former paper (Serial 2590 of the Bureau of Mines) provide a waiting period before compensation for the lost-time wages starts, with the compensation limited to definite percentages of the wages. The waiting period and limited compensation combined tend to limit the amount paid to an injured workman who, if he receives 1/3 of the lost-time wage, will probably have been reimbursed as high as the average injured workman.The total or complete economic cost of human accidents, must include, in addition to compensation paid for lost time, and the portion of the lost-time wage suffered by the workman for which he is not compensated, the additional cost to the company through-(a) temporary decreased production by the breaking down of the morale, etc., (b) the breaking in of a new employee which is admittedly expensive,(c) the increased liability of human and production accidents caused to or by the new employee.Another charge against accidents, which is not included in the compensation payment, is the economic loss through the killing of as workman who has no dependents. Few of the States' laws require any compensation except burial expenses to be paid for fatalities to persons having no dependents. It is estimated by the United States Bureau of Labor Statistics that the economic loss through a fatality is 6000 shifts. If each fatality was compensated for this amount of time and at half-time wages, using an average wage of $5.00 per shift, the compensation for fatality based on the economic loss would be $15,000. but the average actual compensation paid for each fatality is about $3,000."

Jul 1, 1924

By David C. Lager

While not a new construction technique "top/down" construction is seeing increased use in high rise building construction. Using diaphragm wall, drilled shaft and mining construction techniques, top/down construction enables construction of both the below grade basements and high rise structure simultaneously. To date the top/down method has been used on at least four major building projects in the United States. This paper will review the economic, engineering, construction and schedule issues associated with top/down technology on two projects -Olympia Centre, Chicago, and One Westwood, Los Angeles. Top/Down construction is currently under consideration on several additional projects in the United States.

Jan 1, 1987

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