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By CHAS. A. R. LAMELY

In the extreme northeast corner of the State of Washington, on the Canadian border, lies the Metaline mining district. This district is old in history, but young in production. The Metaline district is a zinc-lead area of the replacement type in dolomite and limestone. The ore bodies of the Josephine horizon are in many ways similar to the ore bodies of the famous Tri-State zinc fields. The beds are faulted and folded and have varyng low dips in varying directions, and underlie large areas of the district. Production started in 1927 on a very limited basis. The property is now mining and milling 700 tons per day. The mine is opened by adit tunnels and a vertical shaft. As the ore horizons gained depth, it was necessary to sink inclines to follow the ore horizon (see Fig 1). From 1927 to date, approximately 600,000 ft of diamond drill was put down This work indicated that sufficient tonnage existed to justify a redesigning of the whole operation, surface and under- ground. After four years of general study, the following program was planned :

Jan 1, 1949

By R. S. Dean

AMONG naturally occurring inorganic compounds, magnetite has many unusual and interesting properties, and it is the purpose of this paper to call attention to these properties and review possible uses of magnetite that might be based on them; in other words, to see what uses may be found for magnetite as a physical rather than as a chemical entity, as a mineral rather than as an iron ore. The Mineral Physics Studies initiated in the Metallurgical Division of the U. S. Bureau of Mines a few years ago gathered together much information on mineral properties, and they are therefore the principal source of material for this paper.

Jan 1, 1937

(Under this heading will be published notes sent to the Secretary of the Institute by members or other persons introduced by members. ) Member, age 33, single, desires position as null superintendent or charge of mine and mill. Twelve years' milling, cyaniding and flotation in the southwest and Mexico. Will go anywhere. No. 458. Member, mining engineer and geologist, graduated, from- mining college, age 27, single, exempt, with practice in metal mining, surveying of any kind, field geology and ore testing, desires to .engage as geologist or mining engineer with a reputable concern in the west or east of. U. S. Hard worker and reliable. No: 459.

Jan 6, 1918

By Paul Soros

Terminal facilities were recently completed at Conneaut, Ohio, on Lake Erie, for the Bessemer and Erie Railroad Co. (a wholly-owned subsidiary of U.S. Steel Corp.) which may become the blue- print for all future coal shipping terminals. Design and engineering of the new facility was by Soros Associates, New York, N. Y. Unlike terminals of conventional design, for example, those at Toledo and Newport News, which load coal directly from the railroad car to the vessel, the new installation passes the coal into temporary storage, loads the vessel from temporary storage and provides alternative reclaiming systems in case of major system failure.

Jan 1, 1966

By Mark Malamphy

DURING colonial times, Brazil was famous for the richness of her alluvial gold deposits. Paul Ferrand has estimated that the gold produced during the period from 1700 to 1820 was the equivalent of some 64 million pounds sterling. Since that time, most of the more prolific alluvial deposits have been exhausted. A few gold mines are still func-tioning, notably the Morro Velho mine, which is one of the deepest mines in the world. Today, the gold production of Brazil is insignificant when compared with world figures, but there are still many gold-bearing regions and it is probable that in at least some of them profitable returns would result from an exploitation program taking advantage of all the most modern innovations in gold mining and ore treatment on a large scale. In order to demonstrate the value of some of these abandoned pros-pects and stir up interest in increasing the national gold production, the government has stimulated research. Experimental plants have been and are being established in various places, and tests on large quantities of ores are being carried out on a semicommercial basis. The Geological Survey of the State of Minas Geraes is very active in this line and the Federal Institution is also showing an increased interest in the matter. One of the lesser known gold-bearing regions of Brazil is in the vicinity of Lavras, in the State of Rio Grande do Sul. Gold was first reported from this region in the early part of the nineteenth century. In 1811, D. João VI sent an experienced prospector from Minas Geraes to investi-gate the validity of the reports. According to the reports of Baron

Jan 1, 1934

By J. C. Irvine

Meramec Mining Co. has put into operation a crushing and conveying system on its newly established 2475-ft level, 200 ft below the lowest production. To develop this level without interrupting hoisting or mine haulage, a 15.8% decline was driven from the 2275-ft level. A 5-cu-yd LHD diesel loader and a diesel-powered drilling jumbo were put into operation midway down the decline, and were used to develop the remainder of the decline and the entire level. Development of the ore pass system to the crusher required the construction of Swedish-type dumps on the main haulage-ways of all production levels with a minimum disruption of ore haulage. Concrete was handled by both rail-mounted and rubber-tired vehicles. The system features four Swedish-type dumps with control chutes at the lower three dumps, a 42-in. gyratory crusher with attendant feeders, and an 1800-ft long roof suspended conveyor feeding two 5000-ton ore bins. The crushed ore from these bins is conveyed to the lower of the mine's two original loading stations for hoisting. The retention of the original dumping and ore pass system as an alternate route has given mine production a unique flexibility. Operation for 22 months has permitted evaluation of the system from a long-term standpoint.

Jan 1, 1973

By T. H. Alden

A correlation has been found in rock-salt structure single crystals between the latent hardening, measured by the direct stress activation of oblique slip systems, and the stress-strain behavior in simple compression. Materials with high latent hardening, like LiF, strain-harden at a low rate (Stage I) even when severely constrained. KCl, in contrast, shows low latent hardening and a tendency to strain-harden at a high rate (Stage 11). This correlation suggests that oblique slip is essential for Stage II hardening of these materials. THE role of secondary slip in the strain hardening of metal single crystals is a topic of lively controversy. On the one hand are theories in which secondary dislocations participate directly in Stage II hardening in the fcc metals, for example through the production of sessile dislocations,1 forest intersections, or jog formation. Much of the experimental evidence on which these theories are based has been reviewed by Clarebrough and Hargreaves.~ On the other hand, a recent theory5 denies that secondary slip has an essential role in Stage II hardening or in the transition from Stage I to Stage 11. In the latter view, Stage I is not terminated by an increase in the activity of secondary systems but by the exhaustion of undeformed material.6 The experiments reported in this paper will not resolve this controversy since the materials being studied are cubic ionic crystals rather than metals. However, the results do show in an unusual way a direct connection between "secondary" (nonortho-gonal or oblique) slip and strain hardening in these materials. Specifically, a correlation has been found between two independently measured properties, first the latent hardening of oblique (110)(1i0) slip systems as measured by direct stress activation of these systems, and second the stress-strain behavior at small strains. From prior work, it was known that in most cubi-cally oriented rock-salt structure crystals, two orthogonal slip systems operate and exclude the other equally stressed pair, oblique to the first pair.7'8 This observation apparently indicates that a significant interference exists between slip on oblique (110) planes and a relatively small interference between orthogonal (110) planes. The present experiments were begun with the intent of obtaining a quantitative measure of this difference by means of a study of latent hardening in these crystals. I) EXPERIMENTAL METHODS The experiments were basically of two types, first the determination of stress-strain curves by compression along a single (100) axis, and second the measurement of latent hardening by compressive prestrain along one cube axis followed by the determination of the yield stress in a second (latent) cube direction. All tests were done at room temperature in an Instron machine by compression between lapped, parallel steel faces. Three specimen shapes were used. For long crystals (nominal dimensions, 1/8 in. square by 1/2 in. long) the ends were lubricated with an oil-graphite mixture. Superior results with short crystals (about 1/8 in. cube) were obtained using 0.003-in. teflon film.' Thin crystals (1/4 in. square by 3/32 in.) were used for latent-hardening measurements and similar results were obtained with either lubricant. Test specimens were cleaved from Harshaw single crystals which had been irradiated to a dose of lo8 roentgen using a cobalt-60 source. The irradiation raises the yield stress and tends to prevent plastic deformation during sample preparation.10 Prior to testing, the irradiation hardening was removed by an anneal at 400°C. Ideal compression specimens have flat, parallel faces. In short specimens particularly, satisfactory results demand a close approximation to this ideal. In the present work, cleaved surfaces were often used directly as compression faces. The degree of success using this method depends on two factors: 1) the smoothness of cleavage faces, and 2) the extent to which the crystal is deformed or crushed by the chisel during the cutting of a long crystal into short pieces. Unfortunately, only one material of those studied, LiF, was completely satisfactory. NaF, NaC1, KC1, and KBr behaved less well so that

Jan 1, 1964

By William Hilliard

IN any manufacturing business, it is of vital importance that the management should know the exact cost of the units of production. Without such knowledge, a company can sell blindly in the open market, obtaining the best prices it can in competition with other firms, and manage perhaps to continue in business for a time; but at any moment, and especially in a period of falling prices, such a firm is at a loss to know exactly at what point it can sell at a profit and exactly how much it is losing per unit if it sells below that point. Furthermore, it is necessary not simply to know the exact total cost per unit, but to know definitely all the different-factors which enter into that cost. A firm manufacturing pocket knives had been doing a profitable business for many years when it began to earn smaller and smaller profits, until there was scarcely any profit at all being realized. Being unable to determine exactly what its future policy should be, it called in experts who studied the past records carefully and followed out for a period a better cost, system. Investigation then showed that on several different kinds of knives in common use, a small profit per unit was being made. On a number of special kinds of knives, of which the firm was very proud, it had been forced to cut prices under the pressure of outside competition and had believed that a small profit per unit was still being made on that product, while a detailed cost analysis showed that a loss was being incurred on each knife of that kind produced. It then became clear that the company must either give up the special line and concentrate wholly on the cheaper knives and extend their sales to territory not yet developed; or expand its plant and produce more of the higher grade knives and thus lower the cost per unit enough to make money on the higher grade knives also, if conditions warranted such expansion. Investigation revealed that the market for large quantities of the high-grade -knives was decidedly uncertain and that the most promising move would be to manufacture only the less expensive knives on a larger scale. That plan was carried out and the concern began again to make a better profit.

Jan 1, 1932

By P. D. S. St. Pierre

IN recent years the use of high sulphur fuels and charges in steelmaking has necessitated rapid methods of slag control in order to insure the production of high quality steel. Several systems of control have been discussed in the literature, and of these the method described by Philbrook, Jolly, and Henry' has received the most attention recently. In their process the hydrogen ion concentration of an aqueous slag suspension is determined under controlled, but arbitrary conditions. The basicity of the slag may then be derived from a previously established pH-V ratio curve. Thus, by measuring the pH, some indication of the V ratio is gained, from which significant properties of the slag may be deduced. Philbrook et al. made no claims as to the theoretical justification of their treatment, but simply offered it as a rapid means of slag control. Encouraging results caused others to study the method and publish their findings.2-5 Although there was fair agreement on the efficacy of the method, no common parameter was evolved against which pH readings could be plotted. The results of the various determinations were related to such V ratios as CaO/SiO2 and CaO/ SiO2 + P2O5 by some,'-3 while others" plotted against "excess lime." Rivet,' however, found a simple proportionality between the hydrogen ion concentration and the sulphur content of the molten steel beneath the slag. Since slag control in North American practice is largely directed toward the efficient removal of sulphur from steel, Rivet's approach to the problem had the advantage of connecting directly a property of the slag with the impurity being removed. In view of the diversity of parameters used it seemed probable that some fundamental point was being overlooked in seeking a relationship. Examination of the literature revealed that much emphasis had been laid on experimental detail but scant attention paid to the fundamental aspects of the hydrolysis of the aqueous slag suspension. Consequently the present investigation was undertaken with the object of rectifying this deficiency and deriving, if possible, a parameter of general application. Petrographic studies on several matured Canadian open-hearth steel slags have shown that their major constituents are dicalcium and tricalcium silicates set in a complex matrix of iron oxides and ferrites. These phases are shown in Figs. 1 and 2. Free lime is frequently encountered in slags, but is not an equilibrium phase since on continued heating it dissolves forming silicates or ferrites. Thus, it appeared that a study of the hydrolysis of the major phases in steel slags would be profitable. The experimental technique used in the present work was a modification of that described by the other workers.'- Electrical conductivity measurements were also made on the suspensions, since Smith et al." had claimed advantages for this method in their paper on slag control. Experimental Procedure The compounds studied in this investigation were prepared in the laboratory by heating purified oxides

Jan 1, 1954

By AIME AIME

SHORTLY after he started his professional career, the subject of this sketch acquired the sobriquet "Moose" Allen. At the time he was engaged in geological exploration it1 the Canadian wilds. The nickname was given .him because of the wide, straight trail that he broke with unusual speed when going through the bush. Like a moose he was strong, energetic, and determined. To a considerable degree, Rolland Craten Allen today displays the same characteristics in larger affairs-business, civic, and professional. It is his habit to study a problem thoroughly, to decide u11on the best course of action, and then to pursue that course with vigor and

Jan 1, 1936

By W. E. Keck

THE flotative properties of the principal minerals in Michigan's potential iron ores have been investigated to develop methods of bene-ficiation for the ores. One of these minerals, magnetite, is of considerable importance as a source of iron. Study of its flotation was similar to that of hematite1, another iron mineral in these potential ores. The present research consisted essentially of: (1) a survey of the literature on mag-netite flotation, (2) the preparation of pure magnetite, (3) the develop-ment of laboratory procedure and (4) flotation experimentation. Literature an Magnetite Flotation.-For the purpose of this discussion, the results of previous work on the flotation of magnetite can be sum-marized as follows. The mineral has been floated with pine oil2, and it has also been separated from synthetic mixtures with silicates by the use of the same reagent2. Magnetite and apatite in iron-ore slimes have been separated by flotation of apatite with sodium palmitate3. These data were utilized in the present investigation. Preparation of Magnetite.-The pure mineral was prepared from the magnetic-separator concentrate of an iron ore (obtained from the Wither-bee Sherman Corporation, Port Henry, N. Y.). This concentrate was slowly comminuted with laboratory rolls and pulverizer to pass 65 mesh and was then tabled several times. Tabling yielded a relatively coarse magnetite concentrate, tailing and slimes. The two latter materials were rejected insofar as the present work is concerned, and treatment of the magnetite (table concentrate) was continued by separating it into -65 + 200 and -200-mesh sizes. Separation of the sizes was made by first dry screening and then wet screening. The -200-mesh material was rejected to eliminate possible introduction of error into flotation

Jan 1, 1937

Discussion of the paper of CLARENCE A. WRIGHT, presented at the St. Louis meeting, October, 1917, and printed in Bulletin No. 130, October, 1917, pp. 1565 to 1591. H. A. WHEELER, St. Louis, Mo.-This paper by Mr. Wright is one of the most thorough and exhaustive studies that has been made of the milling practice in the Joplin district. Mr. Wright spent about two years there, in behalf of the U. S. Bureau of Mines and the Missouri Geological Survey, and this paper, which is the result of his work, will, repay careful reading by any student of ore dressing and is invaluable to an operator in that district.

Jan 1, 1918

By AIME AIME

WILLIAM BAYARD HEROY, Director of the Institute since 1935 and Vice-President for the past year, has been active in both geological and engineering circles of the petroleum industry for many years. "Bill," as he is generally called, was born in New York City in 1883, and graduated from the department of geology at Syracuse University in 1909 with a Ph.B. degree. Immediately he joined the U. S. Geological Survey, where he established an enviable record during the next eleven years. While with the Survey he acted variously as chairman, chief, and advisory engineer for a variety of Governmental bodies, many concerned with power.

Jan 1, 1939

By P. C. J. Gallagher

A number of recmt determinations for the ratio of extrinsic to intrinsic stacking fault energy in fcc solid solutions are examined. Some of these arise from incomplete analyses which can yield only approxi?nate values for the ratio. Reliable results, on the other hand, obtained using extrinsic-intrinsic fault pairs, show that the extrinsic and intrinsic fault energies are essentially equal in several materials. There is some reason to believe that this finding is of general applicability to fcc elements and alloys. A wide range of values has been obtained for the relative magnitudes of the extrinsic and intrinsic stacking fault energies (yext and yint, respectively) in recently published studies in a variety of materials. In contrast, Hirth and Lothe' using a central force model have shown that out to tenth nearest-neighbor interactions the perturbation in energy caused by both types of fault is the same. Although the model used is not completely valid in metals, there is nevertheless some indication that marked variations of yext/nnt should not be observed from one material to another. In early work in Cu-A1, Cu-Ge, Ni-Co, and stainless steel all the deformation faults observed in the electron microscope were found to be intrinsic in nature, which led to an attitude that the extrinsic fault energy must be considerably greater than the intrinsic. Extrinsic faulting arising from deformation has, however, more recently been directly observed in Au-4.8 at. pct n;~ Ag-6 at. pct Sn and Ag-8 at. pct sn; Ag-7.5 at. pct In and Ag-11.8 at. pct 1n;"' pure silwer and Ag-0.5 at. pct ~n;' and Cu-22 at. pct Zn, Cu-30 at. pct Zn, and Cu-7.5 at. pct ~1.l' Multilayer loops containing extrinsic faulting have also been observed in quenched aluminum." While peak asymmetries in X-ray faulting probability studies were generally attributed to the presence of twins,Lelel2 has recently reinterpreted earlier X-ray data in Ag-Sb alloysU in terms of the presence of extrinsic faulting. The determinations of yeXt/yint made from the above studies are shown in Table I, with a brief description of the techniques employed. A number of the methods utilized are deficient in one or more respects, and the reliability of the values listed will be discussed. ~ele'~ recognizes that his approximate determinations of yext/yint assumes equal numbers of extrin-sically and intrinsically faulted dislocations. It is well-known, however, that such an assumption is not at all justified since extrinsic faulting has but rarely been observed in samples studied in the electron microscope. The only conclusion that should be drawn from the X-ray results at present is that the total intrinsic scattering cross section (i.e., the product of the width of the intrinsically faulted dislocations with their density) is approximately ten times greater than for extrinsic faulting in these particular samples. An important point is that the relative magnitudes of the energies cannot be inferred from results of this type, unless the intrinsic and extrinsic faults form with equal ease. One must recognize that, although a formation barrier may restrict the amount of extrinsic faulting which occurs, this in no way implies that the extrinsic and intrinsic energies should be different. It is unlikely that a worthwhile estimate of the relative densities of extrinsically and intrinsically faulted dislocations can be made at the high deformations present in X-ray samples. ~oretto,'~ from a statistical argument applied to the nonobservation of extrinsically faulted tetrahedra out of a large sample, concluded that yeXt/yint could not be less than -4.5. However, the present author feels that a high-energy formation barrier as just supposed also explains this finding satisfactorily and that no conclusion can possibly be drawn concerning the actual extrinsic stacking fault energy. The same argument also serves to explain the fact that extrinsic faulting has been relatively little observed in the electron microscope. Extrinsic-intrinsic node pairs and isolated extrinsic nodes were first reported by Loretto~ and subsequently by Ives and Ruff,' Gallaher,' and Gallagher and Wash-burn.' Ives and Ruff' found a wide spread in the ratio of extrinsically to intrinsically faulted area in the node pairs they observed, and drew the very tentative conclusion that yeXt/yint 2 2. They recognized that a straightforward comparison of the size of the faulted areas could provide no more than a qualitative result without a theoretical analysis of the dislocation geometry associated with extrinsic faulting. A theoretical

Jan 1, 1969

By Freeman Bishop

The House Ways and Means Committee recently heard a bitter dispute over whether gasoline with lead is a worse pollutant than gasoline without lead. The lead industry is also squarely in the middle of this dispute for obvious reasons. Lead used in gasoline amounts to 270,000 tpy, or more than 254 of the annual total mined in the U.S. Few industries can face the loss of such a market without wondering how they are to stay in business. The lead industry picked up unexpected support in this dispute, however, when the AFL-CIO stepped up with outright opposition to the President's proposal to tax lead in gasoline.

Jan 1, 1970

By M. B. Kasen

eralized strain equation appear quite different they are really identical. This identity can be shown in a simple mathematical rearrangement. Referring to Eq. [I], the substitution of ln(1 +?E) for ? (where ?E is the engineering strain) yields: a =s8- (s8?so)e?1/?c) ln(1 +s8??E) [4] or s =s8?(s8?so)(l +?E)-1 [5] Replacing (1 + cE) with its equivalent, (l/lo): s=s8?(s8?so)l/€c [6] Adding and subtracting the quantity (s8 - so) yields: s=s8?(s8?so)+ (s8-so) l-(^)l/£c [7] = s0+(s8?so)ri-(^0)1/^l [8] Letting n = 1/?c it follows that: This equation will be seen to be identical to the generalized strain expression in Eq. [3], the coefficients a and b being equal to so and (s8?so)/?c or n(s8?so), respectively. Confirmation of the relationship noted above was provided by fitting experimental stress-strain data5 for 304 stainless steel (total strain from 0.072 to 1.15) at room temperature at a true total strain rate of 4 x 10-3 sec-1 to Eqs. [I] and [3]. In this study nonlinear regression analyses were used to evaluate the equation constants. The results of this evaluation are presented in Table I. When these constants are used in Eqs. [I] and [3] the curves obtained are coincident. It will also be noted that the value of n is equal to YE,, the value of a is equal to so, and the value of b is equal to (s8 - so)/Ec. These equalities are illustrated in Table I where the Voce constants in parentheses were calculated from a, b, and n values. Excellent agreement is seen to exist. It is concluded, therefore, that the Voce equation is, indeed, identical to the linear expression involving generalized strain. In applying the generalized strain concept to stress-strain data, it has been noted3 that data within what was termed the transition region (first few points in the plastic flow region) must be excluded from the analysis in order to obtain the linearity in Eq. [3]. A similar exclusion applies in the use of the Voce equation since an expression which would describe the strain-hardening region would usually be found to be not too effective in the elastic-plastic fillet2 which connects the elastic line to the strain-hardening region. These considerations further substantiate that Eqs. [I] and [3] do indeed describe identical behavior. Note added in proof. Since this manuscript was submitted for publication, correspondence with Professor S. R. Davies, University of Edinburgh, (of Ref. 3) indicated that his associates have also confirmed the identity between the Voce equation and the generalized strain concept. It is sometimes desirable to obtain a small grain size in super-purity metals. Unfortunately, the absence of impurities, the low recrystallization temperatures, and the low activation energies for boundary motion result in rapid growth of relatively few grains when conventional recrystallization practices are used. For example, Arajs et al.1 were unable to obtain a mean grain diameter less than about 0.4 mm in iron containing 38 at. ppm of impurity. The <1 at. ppm purity range in many modern superpurity metals results in yet larger limiting grain sizes. It is the purpose of this communication to describe a technique by which mean grain diameters as small as 30 µ have been produced in aluminum having an impurity content < 0.5 at. ppm. The technique should be applicable to superpurity metals other than aluminum and has potential applications to grain refinement of commercial alloys. The necessary and sufficient requirements for production of a small grain size are as follows: a) a large number of potential nucleating sites must be created randomly within the cold worked material, b) sufficient thermal energy must be provided at a rate that will simultaneously activate a large fraction of the potential nuclei, and c) the grain growth must be stopped shortly after grain impingement.&apos; A high density of potential grain nuclei may be cre-

Jan 1, 1970

By C. W. Merrill

Minerals research by the U.S. Bureau of Mines embraces the mining and metallurgical problems of some 80 metals and nonmetals excluding the mineral fuels. It requires the energies and talents of about 1400 persons, almost half of whom are professionally trained in the physical sciences or engineering. Of approximately $13 million appropriated to the Bureau for minerals programs in Fiscal Year 1962, 76% has been allotted to technologic research and 24% to resources examination and appraisal. In addition, almost $2 million will be made available to the Bureau for minerals research from other Government sources and from private organizations that wish to utilize Bureau experience and capabilities in cooperative studies.

Jan 11, 1961

By Robert J. Morris, John N. Butler

A series of organic collectors has been developed which successfully float synthetic secondary uranium minerals, such as autunite, carnotite, and torbernite. Recoveries up to 97 pct have been obtained. With cleaning of rougher concentrates, ratios of concentration as high as 15:l are possible on head assays of 0.10 to 0.50 pct U308. Additions of certain base metal salts aid in recovery and materially in- crease the rate of flotation and selectivity of the collectors for the synthetic minerals. Flotation tests on natural uranium minerals have not yet equaled results obtained on the synthetics, although these collectors do give better results than conventional collectors for nonsulfide minerals.

Oct 1, 1956

By B. M. Larsen

ATTEMPTING to review the fundamental aspects of segregation in steel ingots of all types in a paper of reasonable length, we encounter two difficulties: (I) the fact that a large number of different physical and chemical effects are involved, and (2) rather incomplete and confusing evidence on certain aspects of detail and mechanism in the freezing process in which the segregation effect is involved. The best solution seemed to be to link together most of the underlying factors into a simplified theoretical picture that appears to the writer to explain most of the observed data, in the hope that this will serve as a reasonably good target for discussion and criticism. Segregation effects, especially in steel ingots or castings, are often divided into " microscopic " and " macroscopic," depending on whether the variations in concentration of solutes? or dissolved elements in the iron occur as: (I) a periodic variation over the small distances between the nuclei and the surfaces of the primary grains, or (2) as a larger scale effect involving concentration gradients over distances of the order of several inches, more or less. The reason for this somewhat artificial division is, of course, that it is only the macroscopic scale effect that has much practical importance. About the only effect of practical importance that results from microscopic segregation is the banded structure often left in rolled sections, and even this is relatively harmless in most cases. However, the causes of microscopic segregation also underly the larger scale effect, so we must first consider matters such as the formation and growth of crystal nuclei, selective freezing and diffusion, and others that are fundamental to all segregation effects. UNDERCOOLING AND NUCLEI FORMATION It is probable that although the degree of undercooling is small in iron, as in metals in general, a certain amount of it takes place, and also that the number of crystal nuclei increases very rapidly with increased undercooling below the liquidus tempera¬ture. In practical terms this means that the nuclei number increases very rapidly with increased cooling or freezing rate, thus being dependent on the rate of heat flow out from the zone of crystallization. TEMPERATURE GRADIENTS AND HEAT DISSIPATION DURING FREEZING Each pound of steel evolves about 100 B.t.u. when freezing. In addition to this, the temperature gradient in the solidified portion (required to dissipate the heat as freezing progresses into the axis) necessitates a loss of heat required to cool the solid metal below its freezing range, which is equivalent to an amount of not so much less in magnitude. In a 5-ton ingot, the total would include about one million B.t.u. for freezing alone and about 0.4 to 0.5 million B.t.u. for the gradient, up to the end of the freezing period: Thus the rate of freezing depends primarily on the rate of heat dissipation. In the ordinary ingot shapes, the axial rate of growth of the solid

Jan 1, 1944

By J. Serra, M. Turpin, R. Alberny

A new method is proposed to obtain automatically an unbiased estimate of the interdendritic spacing A. It is shown that the structure can be built by a random distribution of a rectangular basic unit. The usual definition of the interdendritic spacing yields a value 1 which, coupled with A, gives the shape of the basic rectangular unit. A study of the relationship between dendrite arm spacing and solidification rate was conducted as a part of a research program on dendritic solidification. For any comparison between theory and experiments to be meaningful, it is necessary to measure reproducible and clearly defined spacings. Fig. 1 shows clearly that even in a fairly simple structure such measurements are difficult. if we compare photos (a) and (b), we can hardly assess which one shows the larger spacing. Moreover, the quantity to be measured can be defined in several ways. On a small scale, dendrites seem to be distributed in a very regular and ordered way. However, on a larger scale, this regularity no longer exists. The usual way to measure spacings is to pick up some rows of dendrite stalks; such measurements are obviously biased since less orderly regions are not taken into account. A more objective method is to section the picture with randomly oriented straight lines and average the measured interdendritic spacings. The purpose of this paper is to show that such measurements, which can be conducted automatically, yield objective and reproducible results which are directly related to characteristic features of the dendritic structure. I) THEORETICAL ANALYSIS 1-1) Mathematical Morphology and Function of Co-variance. Matheronl and Serra2 enlarced- the definition and geometrical meaning of the notion of covariance to encompass problems in mathematical morphology. A brief review of part of their theory can be stated as follows. Let A&apos; be an isolated particle, and let us consider a group of two scanning points h is the vector joinlng these points, h its modulus, and a its direction. Let us also define a boolean function, k(x), whose value is 1 if x lies inside the particle and 0 if it 1s outside. The total number of events in which both points are inside A&apos; IS the covariance Ii&apos;,(h): is the measure of the intersection of A&apos; with the particle ALh obtained by translating A&apos; of -h Obviously K,(O) is the volume of the particle A&apos;, or its area if A&apos; is a two-dimensional body. The average value of K,(h), when the direction of a vector h of constant modulus is rotated, is: An important property of the covariance is illustrated on Fig. 2: if the shape of a particle shows some regularity along a direction a, K,(h) generally presents a maximum. We now consider a group A, made of many particles A&apos; distributed in space; then k(x) is taken as the realization of a stationary random f~nction.~ The volume fraction (or fraction of area if the problem is two-dimensional) occupied by A equals the average value q of k(x): meaning "average value of"). We also replace

Jan 1, 1970