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By AIME

Annual production of more than 4,000,000 tons of 0.74 percent copper ore and coincident handling of over 5,000,000 tons of waste at the open-pit mine of Castle Dome Copper Co. near Miami, Ariz. takes a lot of power. Manufacturers have ever co-operated with mining companies in providing the required equipment to suit the problem. Power equipment suppliers have done much to make possible the economic and profitable production of copper from low-grade ores. In the future, as mining operations will necessarily handle even lower-grade ores, the ability of the manufacturer to supply the power and mechanical equipment to produce more metal at a fair and reasonable price will be the good right arm of the miner. About 27,000 tons of concentrate is produced from the 4,000,000 tons of ore.

Jan 1, 1948

ADVANTAGES OF LIFE MEMBERSHIP The Institute calls the attention of members to the following advantages of obtaining life membership: 1. One payment avoids the trouble of future payments. 2. The interest on $150 is less than the annual dues. 3. Provision is thus made early in life for the less productive years. 4. In case of in increase of clues at any time in the future life members are exempt from increased payments. Excerpt from, By-Laws. Article III. Section 3 Any Member or Associate not in arrears may become, by the payment of one hundred and fifty dollars at one time, a Life Member or Life Associate, and shall not be liable thereafter to pay annual dues. The money thus received shall be invested and only the income thereof used for current expenses of the Institute.

Jan 1, 1916

By C. E. Gerity

Near Bunker, Mo., in the New Lead Belt, Ozark Lead Co. operates a 6000 tpd lead-zinc mine. Mined ore is transported to the surface in three mechanized and automated steps. The mine is developed by a rectangular-shaped sublevel haulage drift 15 ft high by 28 ft wide, driven on strike below the ore zones. Ore transfer raises were driven from the sublevel at locations near the shaft, 1500 ft distant, and on subsequent 1000 ft centers. These 6 x 5-ft raises are slashed to obtain maximum storage below dump points. These dump points are located on each mining level and are of steel and concrete construction. Spiral 12 X 24-ft inclines driven from the sub-level provide access to these levels for equipment and mine utilities.

Jan 11, 1972

By James Kemp

PostScript to a paper presented at the New York meeting, February, 1915, and printed in Bulletin No. 98, February, 1915, pp. 129 to 154. The writer looked over the quarry with care in the search for fossils, having in mind shells or corals of fairly large size. In the brilliant summer sunshine, none were observed on the glaring white ledges. The impression was gained that none were present and the statement to this effect was made in the edition of this paper published in the Bulletin' of the Institute for February, 1915, p. 136. On closer examination in the laboratory it has been discovered that the limestone itself is made up of minute organisms, which are clearly revealed by microscopic examination of thin sections. The principal component of the rock is a small foraminifer, 0.1 to 0.3 in. (2.5 to 7 mm.), of the genus Orbitoides, presumably an Oligocenic form. Figs. 1 and 2. illustrate it. The accompanying description has been kindly summarized by Marjorie O'Connell, M. A., Curator in Paleontology in Columbia University, who first detected the evidences of organisms in the rock. Orbitoides kempi O'CONNELL N. SP.1 The foraminiferan which makes up the Seboruco limestone is an Orbitoides of a Species new to North America. The only Orbitoides heretofore described from this country is 0. mantelli from the lower Oligocenic of the Gulf States. This form from Cuba, then, so different in all of its characteristics from the 0. mantelli, is of great interest as perhaps forming a basis of correlation over wide areas. The most closely related Species is 0. dispansa Sowerby, which occurs in the Nummulite limestone of the Eocenic of the Bavarian . Alps, in the Priabona beds of the lower Oligocenic of Massano, and elsewhere in Italy, as described by Gümbel.2 The age of the limestone in Cuba would thus Seem to be of upper Eocenic or lower Oligocenic age, probably the latter. The fossil has the form of a sphere Surrounded by a wavy rim of horizontal extent, the whole resembling two flat-brimmed, round-crowned hats placed base to base. The total extent of the Shell ranges up to 7+ mm., while the thickness of the central sphere is 2.5 mm. in one of the largest individuals. Like all of the other Species of Orbitoides, this form begins with a Single layer of chambers which multiply in one plane and assume a circular outline; but it is in the subsequent growth that the distinguishing specific characters appear, for the chambers at the central portion of the shell increase more rapidly than do those near the periphery and in consequence a Swelling is produced which finally gives the Spherical form which is so characteristic. The rim, on the other hand, shows little chamber-increase and remains thin. This is clearly Shown in the sections figured, where the central row of larger chambers forms the equatorial zone. Radiating from this row, in section, there appear, a number of solid cones alternating with broad reticulated ones. The solid cones mark the more dense structure forming the walls surrounding the reticulated or chambered cones. These appear upon the Surface as distinct pits, whereas the solid part appears as raised walls.

Jan 7, 1915

By Lawson P. Entwistle

SUMMARY ONE of the important reserves of manganiferous iron ore is at Boston Hill, near Silver City, New Mexico. The area consists of a faulted block of gently dipping Lower Paleozoic shale, dolomite, limestone and sandstone, which have been intruded by a roughly circular mass of quartz-bearing monzonite porphyry and subordinate dikes. From a noselike protuberance of the intrusion radiate many premineral faults, which have localized much of the hypogene mineralization. Three important stages of hypogene mineralization can be recognized: (1) mesitite, a manganiferous iron magnesite, (2) quartz sulphides, and (3) barite-galena. The carbonate stage is widespread but stronger near the intrusion. The quartz may have been derived from hydrothermal alteration of the igneous rocks. Barite-galena is most important in the Chloride Flat mining district, about one mile north, where argentiferous galena provided silver for the supergene ore. The hypogene carbonate, lean in iron and manganese, has been oxidized and consequently enriched by meteoric waters containing an excess of oxygen and carbon dioxide to form ore bodies of intimately mixed hematite and pyrolusite. The ore bodies, at one place attaining a length of 1600 ft., a width of 300 ft., and a thickness of 25 ft., are largely confined to areas of brecciation and to spreads from faults in Silurian dolomite beneath soft Devonian shale.

Jan 1, 1944

By W. M. Aubrey

Lying approximately 110 miles east of Toronto, Canada, the Marmora mine produces iron ore with a content of about 40 pct Fe, primarily in the form of magnetite. Operated by the Marmoraton Mining Co., a subsidiary of Bethlehem Steel Co., the orebody is mined by open pit methods. The ore from the pit is crushed, cobbed, ground to -100 mesh, magnetically concentrated to 67 pct iron, and then pelletized in shaft furnaces. The pellets are normally shipped by rail throughout the year from Marmora to Picton on Lake Ontario where they are unloaded and stored. Subsequently, during the navigation season, the pellets are shipped to Bethlehem Steel's Lackawanna plant in Buffalo, New York, for use in the blast furnace. At Marmora, the pellet plant demand and the concentrator output are not usually equal. To counter this problem, surge capacity in the form of storage pits in combination with a 30-ft diam thick¬ener has been provided between the concentrator and the pellet plant. Two sets of controls have been installed on this thickener, one controlling the…

Jan 9, 1960

By V. W. Aubel

Among the iron-bearing ores of the world, the titaniferous iron sands of New Zealand are probably the least known to American engineers. This is not surprising in view of the fact that American ironmasters look with disfavor on any, even domestic, ores containing over 1 per cent. titanium. The possibilities of smelting titanium-bearing ores in the blast furnace are still undetermined, but the problem of their efficient reduction is becoming more important each year. There seems to be little inclination on the part of American furnace operators to tackle this problem, and they will no doubt continue to utilize the non-titanium ores at their command, leaving research and experiment to those countries not so fortunately endowed. New Zealand has, however, been intensely interested in her deposits of titanium-bearing iron sand, and during the last 50 years considerable English and New Zealand capital has been expended on this problem. The extent of the New Zealand iron-sand deposits is almost beyond measure. From Patea north to Manuka Heads, along almost the entire west coast of the North Island, these deposits exist. Wherever there is beach sand along this 300 mi. of coast line, the sand is iron bearing. It varies considerably in grade; but wherever the contour of the coast affords small bays and inlets, large dunes are found that are remarkably uniform in quality. Several of these large deposits, especially those at New Plymouth and Patea, are noted for their high iron content. The dune at New Plymouth runs between 55 and 60 per cent. of metallic iron; the panning action of the prevailing westerly winds and northwesterly currents has no doubt resulted in this concentration. Whatever the origin of this material may be, there is no doubt that deposition is going on continuously. At New Plymouth, a small artificial harbor, protected from the drifting sand by a large breakwall, has been dredged. Here sailing vessels have for years been loaded with iron sand for ballast by means of a crane and grab bucket operated from the wall of the breakwater. Thousands of tons of sand have been removed from this spot yet each succeeding storm renews the supply. The sand dune shown in Fig. 1 has been tested to a depth of 50 ft. (15 m.) without losing its

Jan 1, 1920

THE compiler, or author, of the Probierbücblein is not known, and the date of its first printing is uncertain. It was obviously not written by an assayer who wished to give a coherent description of his craft for the instruction of others; this was left for Biringuccio first to do. It is easy to believe that originally the Probierbücblein was a random collection from various sources of information useful to an assayer, probably gathered by one of the profession for his own use. It must remain a matter of speculation whether this was shown to a printer, who recognized the opportunity to turn an honest penny and made an inept attempt to give the manuscript the appearance of a coherent account by writing a preface and arranging the various items in somewhat logical sequence, or whether the assayer him- self started this job and was prevented from finishing it. That some sections of the book, especially near the be ginning, present an almost continuous story, while others are chaotic in their arrangement; that several paragraphs are printed more than once in different places; that there are paragraph headings, for which the text was never written, or lost, followed by irrelevant information-all this seems evidence of a job unfinished and points to a publisher's offering for the public's quick money. The demand must have been brisk, for metal working was a profitable profession, and the jeweler who was working with metals but did not care to become completely trained in assay methods would jump at the chance of acquiring easy knowledge. Even the great Agricola has whole sections obviously plagiarized from the Probierbücblein. Neither Biringuccio nor Ercker shows any direct influence, though they and all subsequent metallurgists will in some degree be affected by

Jan 1, 1949

By D. G. Westlake, U. F. Kocks

WHILE single crystals of most materials with cph lattice structure show essentially unlimited ductility, polycrystalline specimens of the same materials exhibit the entire range of ductilities. A difference between the ductility of single crystals and polycrystals may be associated with the special stress concentrations to be expected, for example, at the intersections of slip bands or twin lamellae with grain boundaries. Whether such stress concentrations prove catastrophic depends on the cleavage strength of the material, the size of the stress concentrations, and the speed with which they are formed. Thus, the ductility may vary in degree from material to material. Another possible reason for differences in ductility between single crystals and polycrystals is that a sufficient number of independent deformation modes must be available to insure compatibility between the macroscopic strains in neighboring grains.''2 This criterion is often taken to be a necessary condition for any polycrystal ductility whatsoever, not as one that determines different degrees of ductility; thus, a material with an insufficient number of independent deformation modes would have to be brittle as a polycrystal. The "sufficient number" is five if every grain is to accommodate arbitrary shape changes ("von Mises criterion "). We should like to argue that fewer than five independent modes may be sufficient to satisfy compatibility conditions; and that the internal stresses set up when the plastic strains are not compatible reach the theoretical fracture stress only after a significant amount of macroscopic strain has taken place which may vary in magnitude from case to case, allowing an influence on the degree of ductility. Experimental evidence for these statements is taken from the following review of the number of independent deformation modes observed in the various cph

Jan 1, 1968

By Gerald C. Mathis

FERGUS County, Mont., shown in Fig. 1, is known for its once famous gold mines near the old towns of Gilt Edge, Maiden, and Kendall. But at Heath, a small farming community near the foot-hills of the Snowy Mountains, thousands of tons of gypsum have been mined since 1916. The value of the gold taken from the mines of Fergus County runs into millions of dollars; the value of the products made from the gypsum of the Heath mine is also in the millions. The gypsum mine will continue to produce for many years, while the gold mines are closed today.

Jan 2, 1953

By A. G. Guy, T. B. Lindemer

A second intepation of the Fick law has been developed and applied to three-place data generated from the Gosting and Fujita solution of the diffusion equation. This integration provides new mathematical techniques for the analysis of experimental data. Through use of the synthetic data it is shown that for concentration-independent interdifiusion coefficients these techniques permit a more accurate determination of the coefficients than does the usual Boltzmann-Alatano analysis. Another technique, applicable to the most general concentration-dependent diffusion coefficients , can be used to determine whether given sets of coefficients are consistent with the experimental ternary concentration-distance curves. DURING the past 10 years the subject of three-component diffusion has advanced from the stage of a laboratory curiosity to the status of an accepted portion of physical metallurgy.1 In the course of this development the underlying treatment for two-component sys- tems was extended and generalized to accommodate the added component, but fundamentally the analyses currently employed for ternary systems are analogous to those previously developed for binary systems. There are several indications that an improved analysis is needed for the ternary case. First, the two cross coefficients, D312 and D321 are typically an order of magnitude smaller than the direct coefficients and consequently are difficult to determine with adequate precision. Second, instead of a single concentration-penetration curve (as in binary diffusion), there are four such curves in the usual determination of ternary diffusion coefficients. These curves have definite theoretical interrelationships, but actual experimental curves exhibit significant departures from these relationships. Finally, the amount of data needed to adequately describe the diffusion behavior of a ternary system is so large that radically new methods are needed to facilitate the gathering of these data. ICirkaldy2j4 has proposed several possible analyses of ternary diffusion data, including some of the methods in current use. A "second-integration" procedure proposed by him4 differed in important respects from that presented here and was not carried to the point of application. Two other methods have been explored by the authors and will be published separately; these are a numerical analysis technique and a method for the analysis of a single ternary diffusion couple. Still other analyses are being explored by various investigators. At present it seems likely that the final analysis of ternary diffusion that evolves will be a composite

Jan 1, 1968

By T. C. Desollar

THE group of iron-ore mines known as the Red Ore Mines, owned and operated by the Woodward Iron Co., is on Red Mountain approximately ten miles southwest of Birmingham, Ala. At the, present time No. 1 and No. 3 mines are active, No. 2 mines having been abandoned in 1928. Ore from this group of mines was first mined in 1882, and originally came from open cuts along the outcrop, but, when the "soft ore" (weathered hematite) was mined out and the harder ore was encountered, it became necessary to develop the orebody by means of slopes driven in the ore formation. The three mines to date have produced more than 22,000,000 tons, and the two operating mines now have a capacity of over 1,000,000 tons per year.

Jan 1, 1933

By William F. Ward

One often reads of the rich placer gravels in many of the citnoe-trav-elqd rivers of South America. The apparent richness of these gold-bearing gravels impresses the traveler, and in fact he may see batea after batea showing enough colors to figure over a dollar per cubic yard. These workings are called "playas" from the Spanish word playa, meaning shore or beach. Many workings have been reported in tropical rivers, but to my knowledge no dredge has made a success in such deposits. Investigation generally shows that the area of richness is limited and especially that the depth of the rich concentration is hardly ever more than a few inches. The Cauca river in Colombia, South America, is noted for its many rich playas. This river rises near .Popayan in the southern part of Colombia, flows north through a narrow valley between parallel mountain ranges and empties into the Magdalena river near Maganque. , The airline distance between source and mouth of this river is only about 500 miles. The rainfall is large and the lower Cauca appears to be about the size of the Missouri river in the United States. From its mouth up to Valdivia, in the State of Antioqua, it is navigable. Above Valdivia is a narrow gorge, above which the river is again navigable for some distance. The part of the Cauca where the play a panning is most noticeable is from Valdivia down to where the Nechi river enters the Cauca, a distance along the river of about 100 miles. The current in this part is swift, so that the stern-wheel river steamers make the trip with some difficulty. In the course of my work in this section of Colombia I have had the opportunity to make a study of several of these play a workings and will give in detail the conditions observed. The Island"Playa" The richest of the island playas is about 40 miles below Valdivia and a little below the old town of Caceres. The shape of the river and the location of the deposit are shown in Fig. 1, which indicates the condition at low water. The river at this place is about 600 ft. wide and the island about 75 ft. wide by 300 ft. long. The island is made up of coarse pebbles, some of which are as big as a man's head. In times of high water this island is under several feet of water and in a swift current. When the river lowers the current is still fast enough to prevent sand or silt from covering the coarse pebbles.

Jan 1, 1915

By T. Sterry Hunt

The deposit of rock-salt which is known to exist along the eastern shore of Lake Huron, in the province of Ontario, has lately been more completely explored than before, by a boring with a diamond drill, put down by Henry Attrill, Esq., of New York City, and the results obtained are so important in every way that I make no apology for presenting them to the Institute of Mining Engineers. I may be permitted to preface an account of this remarkable exploration, and of its results, with a historical sketch of the discovery and development of this salt-region. It was in December, 1865, that a boring was begun near the town of Goderich, in the hope of finding petroleum. In this the adventurers were disappointed, but, after passing through about 800 feet of limestone, they encountered a series of variegated marls, in which, at a, depth of 964 feet from the surface, a bed of rock-salt, 30 feet in thickness, was met with in May, 1866. The boring was carried to a depth of 1010 feet, ending in hard rock, and yielded, by pumping, a very pure saturated brine when examined by me in August of the same year. In the report of the Geological Survey of Canada for 1863-66, published early in 1867, I described this salt-well, with many geological details, and gave an analysis of the brine. In the next three years a considerable number of wells was sunk in and around Goderich, and numerous trials were made in various other parts of the region. Salt was found at Kincardine, thirty miles north-northeast from Goderich, at a depth of about 900 feet, and also at Clinton, thirteen miles southeast, at 1180 feet. Records of these wells, with analyses of the brine from them, were given by myself in a subsequent report of the Geological Survey, 1866-69, published in 1870 (pp. 211-244), together with accounts of various unsuccessful borings in the neighborhood, analyses of the brines from the various wells (including one analysis by Dr. Goessmann), with many details of the salt-manufacture at Goderich, at Syracuse, New York, and at Saginaw, Michigan. The geological character of the region was there discussed at length, and it was shown that the salt here occurs in the Onondaga or Salina formation, which

By T. Sterry Hunt

THE deposit of rock-salt which is known to exist along the eastern shore of Lake Huron, in the province of Ontario, has lately been more completely explored than before, by a boring with a diamond drill, put down by Henry Attrill, Esq., of New York City, and the results obtained are so important in every way that I make no apology for presenting them to the Institute of Mining Engineers. I may be permitted to preface an account of this remarkable exploration, and of its results, with a historical sketch of the discovery and development of this salt-region. It was in December, 1865, that a boring was begun near the town of Goderich, in the hope of finding petroleum. In this the adventurers were disappointed, but, after passing through about 800 feet of limestone, they encountered a series of variegated marls, in which, at a, depth of 964 feet from the surface, a bed of rock-salt, 30 feet in thickness, was met with in May, 1866. The boring was carried to a depth of 1010 feet, ending in hard rock, and yielded, by pumping, a very pure saturated brine when examined by me in August of the same year. In the report of the Geological Survey of Canada for 1863-66, published early in 1867, I described this salt-well, with many geological details, and gave an analysis of the brine. In the next three years a considerable number of wells was sunk in and around Goderich, and numerous trials were made in various other parts of the region. Salt was found at Kincardine, thirty miles north-northeast from Goderich, at a depth of about 900 feet, and also at Clinton, thirteen miles southeast, at 1180 feet. Records of these wells, with analyses of the brine from them, were given by myself in a subsequent report of the Geological Survey, 1866-69, published in 1870 (pp. 211-244), together with accounts of various unsuccessful borings in the neighborhood, analyses of the brines from the various wells (including one analysis by Dr. Goessmann), with many details of the salt-manufacture at Goderich, at Syracuse, New York, and at Saginaw, Michigan. The geological character of the region was there discussed at length, and it was shown that the salt here occurs in the Onondaga or Salina formation, which

Jan 1, 1877

By John Stewart

The market at present supplied by shipments from the phosphate districts of Quebec, Ontario, and New York State requires high-grade ore, carrying from 75 per cent. to 90 per cent. of phosphate of lime. In sorting out such material by hand, much valuable phosphate is necessarily left in the "culls" or refuse, besides which, much phosphate-rock of low-grade is not now mined at all, because it cannot be made available by the crude method of cobbing and hand-sorting. The utilization of such material, which would, of course, greatly benefit this industry, requires either a mechanical separation or a chemical process which would concentrate the phosphate in a form suitable for agriculture. Considering the rich phosphate now shipped as the first class, we may arrange the lower grades in three classes, as follows: Second Class.—Cull-ore from the first class, and the mass of deposits having, as gangue, pyroxene or hornblende. The following table gives the hardness and specific gravity of the minerals concerned: Hardness Spec. gravity. Apatite,....... . 5 3.1 to 3.25 Crystalline limestone (pink calcite),. 3 to 4 2.5 to 2.9 Pyroxene,..5 to 6 3.23 to 3.5 Hornblende,.5 to 6 2.9 to 3.4 Feldspar (orthoclase),. .. . 6 to 6.5 2.5 to 2.6 It is evident that when pyroxene and hornblende are present in large proportions, this ore cannot be successfully concentrated by crushing and jigging. It may be reduced to fine powder by successive treatment in a rock-breaker and a Sturtevant or Frisbee-Lucop mill, or other suitable apparatus, and in this condition it could be largely used by applying it freely upon exhausted clay soils, such as occur in Quebec and Ontario. The occupants of these once fertile river-lands are, however, hard to move in the direction of such improvements. When water-power is at hand, the cost of crushing

Jan 1, 1893

By Paul W. Zimmer, Carl E. Dutton

Iron ore in the Menominee district is mined from two iron-formations of middle Precambrian age. The older formation is present in the northeastern part; is composed mainly of hematite, magnetite, quartz, and minor silicates; and contains about 34 per cent iron. The rock has been so coarsened by meta- morphism that concentration of magnetite and hematite is feasib!e, and pellets containing more than 60 per cent iron are being produced. The older formation is also present in the southeastern part where it has 1:een only slightly metamorphosed. Ore containing more than 50 per cent iron was formerly mined from local residual concentrations of iron oxides from which silica had been sufficiently leached, or replaced by iron oxide, or affected by combinations of these processes. The younger iron-formation occurs in the western part of the district and, if unaltered, is interlayered siderite and chert. The ore in this area also contains more than 50 per cent iron and formed as local residual concentrations but in two stages. The siderite was converted to iron oxides (hematite and "limonite"), and silica was contemporaneously or subsequently removed by leaching, or replacement, or combinations of these processes.

Jan 1, 1968

By A. E. Gibson

A new feature in coal mining, where the coal is to be conveyed from a high to a lower elevation and the topography of the country is such as to preclude surface haulage.

Jan 1, 1915

By Maxwell Adams

OLIVER C. RALSTON, Salt Lake City, Utah.-We are indebted to these two gentlemen for the work which they have done with the oils derived from sage brush. Their work should not be confused, however, as the work of Mr. Adams deals with steam-distilled oils and that of Mr. Clevenger with destructively distilled oil, largely. In other words, Mr. Adams' oil is probably the original essential oil that existed' in the brush before distillation while Mr. Clevenger's oil not only contained this essential oil but also some products of destructive distillation of the wood constituents. I had noticed the work of Mr. Adams on attempting to separate the various constituents in the oils of some of the Western conifers and had sent to him to ask if he could send me small samples of some of. these pure products. This he very kindly did, and with them included some samples of oil from the common sage brush, whose characteristics he has here described, as well as a sample of oil from the common "rabbit brush." Only the sage brush oil proved of much value for flotation, but it, was very powerful, and I so informed Mr. Adams. Even in amounts as small or smaller than 1/10 lb. per ton of ore, it gave very quick and positive flotation of many ores, with high-grade concentrates and good extractions. It proved to be especially desirable for the flotation of carbonates of lead and of copper which had received an artificial coating of sulphide by treatment with a solution of a soluble sulphide. I also received a sample of crude pyroligneous acid from sage brush prepared by Dr. W. C. Ebaugh, of Salt Lake City. It did not do very good work in flotation, but it is possible that by concentration of this product to obtain the residual tar a good flotation oil might result. This has not been done as yet and I am sorry to see that Mr. Clevenger has not done this. It might be that the dissolved tar, added to the settled tar, would make a total yield of flotation oil higher than the 4 per cent. which Mr. Clevenger feels is a safe estimate. The importance of this point will be seen in the following discussion of the possible costs of sage brush oils for flotation.

Jan 10, 1916

By Leonard R. Weisberg

HE procedure of directional freezing by the Bridgman technique1 is frequently used in crystal preparation. On those occasions where the crystal is regrown, it can be advantageous to Crop part of the ingot before regrowth to achieve purification. This note describes some simple, yet interesting, observations concerning the effects of cropping an ingot between successive freezes. First, it is not effective to Crop the front end of an ingot, whether or not the distribution coefficient, k , of the impurities is greater or less than unity. This can be shown as follows. The concentration C, of an impurity in a directionally frozen ingot of length d with a uniform cross section is given by where x is the distance along the ingot, and C0 is the initial concentration per unit length. It is assumed in deriving this equation that diffusion is negligible in the solid, is complete in the melt, and that k is constant. Consider that a section of the ingot Ad is removed from the front end. Then the average impurity concentration in the remaining (d- Ad) section of the ingot can be shown by integration to be given by When the ingot is remelted and refrozen, the new impurity distribution is given by where xl is the distance along the refrozen ingot. Substituting the value of c into Eq. [3], one finds This is identical to Eq. [11 when x = (x, Ad), which represents the original impurity distribution in the (d - Ad) section of the ingot after the first directional freeze. Therefore, the cropping and re-freezing accomplished nothing. This can also be seen physically by realizing that the average impurity content in the melt after the first Ad section is frozen, is identical to that after the resulting ingot has been cropped and remelted. Hence, it is assumed in the following sections that only the tail end of the ingot is cropped. However, it must be realized that for impurities with k greater than one, the pieces cropped from the tail end are purer, and are therefore saved. After cropping an amount Ad from the tail end of an ingot, the average impurity concentration of impurities in the remaining portion of the ingot is given by wheref= d/d. For the case of k < 1, the purification is defined as c,/c. It is obvious from Eq. [5] that the purification increases asf increases, but the increase in purification is not large. For example, iff is doubled from 0.1 to 0.2, the purification increases by only 10 pct for k = 0.5, by only 24 pct for k = 0.1, and by 32 pct for k =0.01. Much smaller values off than 0.1 are not desirable since insufficient purification is achieved. These figures indicate that much larger values off do not lead to substantial improvement, especially considering that much of the original ingot is lost. Therefore, it is generally useful to Crop about 1/10 of the ingot to achieve purification. As compared to doubling the value off, it is much more helpful to remelt, refreeze, and crop the ingot twice. Using Eq. [51 reiteratively, and assuming f= 0.1, it is found that the purification after this process is found to be increased over the purification after a single freeze and cropping by 33 pct for k= 0.5, 450 pct for k = 0.1, and 4100 pct for k = 0.01. This indicates that considerable purification can be obtained by this procedure. However, if purification is the main goal, one should resort to zone refining,3

Jan 1, 1962