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By John Wulff, Richard P. Seelig

The importance of the pressing operation in the forming of articles by powder metallurgy depends to a great extent on the type of product to be made. While in some few cases the pressing is merely a means of compacting loose powder particles into a solid mass preliminary to a sintering treatment, in most applications it constitutes a molding operation with the purpose of shaping the raw material in powder form into a certain predetermined, accurately defined part not altered in shape by subsequent sintering. In still other cases, no pressing at all but sintering in molds gives useful articles. A limited number of products are made by the simultaneous application of pressure and heat. The factors that control the product of the pressing operation are raw material, lubricant, type, size and shape of die and compact, magnitude and time of application of pressure, as well as temperature of pressing. All such factors need to be controlled; yet, depending on the function of the pressing operation, greater emphasis may be placed on processing factors other than the pressing operation. In any complete discussion of pressing, subsequent sintering cannot be disregarded. For the sake of brevity, the present paper has been limited to the mechanics of pressing and only occasionally refers to sintering. For the same reason, hot-pressing has been omitted as beyond the scope of this paper In any survey of the literature on the pressing of metal powders, the 1938 paper of Balshinl on the theory of the process of pressing deserves mention. The first attempts at an interpretation of pressing phenomena were made by Balshin' and RakovskL2 The experimental results of both are of great interest. Since the experimental results are not described, the work was repeated, using our own interpretation of the possible techniques, and is reported in the following pages. The basic theory of Balshin,' based on a hydro-dynamic analogy, however, leads to hut another way of plotting density and pres- , sure against height of a pressed compact. Since it does not give any new insight into the phenomena, nor account for the influence of side-wall friction, a discussion of the theory has been omitted from this paper. Density Gradients in Compacts The process of pressing metal powders in a die (disregarding for this consideration the powder filling and ejection operations) may be divided into three phases: (I) packing, (2) elastic and plastic deformation, (3) cold-working with or without fragmentation. It must be emphasized that these three steps do not follow each other in sequence; on the contrary, in practice

Jan 1, 1946

By John Wulff, Richard P. Seelig

The importance of the pressing operation in the forming of articles by powder metallurgy depends to a great extent on the type of product to be made. While in some few cases the pressing is merely a means of compacting loose powder particles into a solid mass preliminary to a sintering treatment, in most applications it constitutes a molding operation with the purpose of shaping the raw material in powder form into a certain predetermined, accurately defined part not altered in shape by subsequent sintering. In still other cases, no pressing at all but sintering in molds gives useful articles. A limited number of products are made by the simultaneous application of pressure and heat. The factors that control the product of the pressing operation are raw material, lubricant, type, size and shape of die and compact, magnitude and time of application of pressure, as well as temperature of pressing. All such factors need to be controlled; yet, depending on the function of the pressing operation, greater emphasis may be placed on processing factors other than the pressing operation. In any complete discussion of pressing, subsequent sintering cannot be disregarded. For the sake of brevity, the present paper has been limited to the mechanics of pressing and only occasionally refers to sintering. For the same reason, hot-pressing has been omitted as beyond the scope of this paper In any survey of the literature on the pressing of metal powders, the 1938 paper of Balshinl on the theory of the process of pressing deserves mention. The first attempts at an interpretation of pressing phenomena were made by Balshin' and RakovskL2 The experimental results of both are of great interest. Since the experimental results are not described, the work was repeated, using our own interpretation of the possible techniques, and is reported in the following pages. The basic theory of Balshin,' based on a hydro-dynamic analogy, however, leads to hut another way of plotting density and pres- , sure against height of a pressed compact. Since it does not give any new insight into the phenomena, nor account for the influence of side-wall friction, a discussion of the theory has been omitted from this paper. Density Gradients in Compacts The process of pressing metal powders in a die (disregarding for this consideration the powder filling and ejection operations) may be divided into three phases: (I) packing, (2) elastic and plastic deformation, (3) cold-working with or without fragmentation. It must be emphasized that these three steps do not follow each other in sequence; on the contrary, in practice

Jan 1, 1946

The income of the Institute is derived from dues, subscriptions to MINING AND METALLURGY and sale of publications. These sources are fortunately supplemented by the interest from invested funds now amounting to over $500,000, a considerable portion constituting endowments for especial purposes. Aside from the medal funds the principal endowments are the James Douglas Fund for support of the Library, the Rocky Mountain Fund and the Seeley W. Mudd Memorial Fund. The income from the two last named is available for the support of research and a variety of other purposes. It is allocated by the Board of Directors upon recommendation of standing committees in each case. An active effort is being made to increase the endowments of the Institute, it being felt that unusual opportunities exist for research and public and professional service through the organization.

Jan 1, 1936

By Douglas R. Piteau

Douglas R. Piteau (Engineering Geologist, De Beers Corp., Kimberley, South Africa; Presently Consulting Specialist at Nchanga Mine Open Pit, Chingola, Zambia)-Mr. Lutton is to be commeneded on his analyses and presentation of such practical data which can be used for predicting a preliminary optimum slope angle in rock. It appears that he assumes all slopes analyzed to be straight. Although there are overriding factors which affect the general slope configuration, such as structural discontinuities, ground water, and other environmental factors such as weathering conditions, regional stress, etc.,8 the affects of plan geometry under certain conditions also can be of outstanding importance. In investigation of natural slopes, for example, the effects of plan geometry are not entirely appreciated and it is in this respect that discussion is given. Experience in southern Africa has shown that the overall geometry of surface openings in rock, particularly those with dimensions of the order of 1500 ft or less, i.e., where radii of curvature of the slopes are less than, say, 700± ft, must be considered in rational slope-stability analyses. That is, the slope angle is not only a function of slope height, strength of the mass, and geometry of structural discontinuities, but also is dependent upon the plan geometry of the local slopes and the plan shape of opening. Technically speaking, adequate analysis of the slope must be three-dimensional, the third dimension being that of overall plan configuration and the analysis must incorporate its subsequent effects. However, current theories of slope stability all deal with the slope as a two-dimensional problem, i.e., a slice of unit length of an infinitely long slope is considered for a condition of plane strain. In this the tacit assumption is made that the plan radii of the crest and toe of the slope are infinite and no attention is given to the plan geometry of the slope. Clearly this is not the condition encountered in practice, particularly in open pit mining where excavations, relatively speaking, can be small and where these radii of curvature accordingly can have important affects on the slope stability. This is illustrated by the analyses of Piteau and Jennings 9 of the natural slopes which had developed around pipes of four diamond mines in the semiarid Kimberley area of South Africa. Although these slopes consist of dolerite overlying shale, the values of the slope angles of all the pits were corrected for a height of slope of 320 ft assuming that no dolerite occurred. This brought the data onto a comparable basis. These data were analyzed statistically and a clear empirical relationship, as is shown [in Fig. 4], is seen to have formed between angle of slope and curvature of slope, i.e., the angles of slope are greatest where the radii of curvature are least. Also, it can be seen that the slope of each line is different, indicating that the plan shape of the open pits also are significant, the curve being steepest for the open pits which are more circular in shape in contrast to those which are more elongated. The effect of slope curvature on the average angle of slope for the two extreme radii of 200 ft and 1000 ft for all four open pits is 39.5° and 27.3°, respectively. Hence, the concave curvature effect represents an average increase in slope angle of 12.2° from the essentially straight slope. In quantitative terms in Mr. Lutton's Fig. 2, this represents displacing the curve for a 320-ft pit from the second curve from the bottom (i.e., shale in subtropical climate) to that of the third from the bottom (i.e., quartzite in temperate environment).

Jan 1, 1972

By John T. Awald

The Bradshaw Mountains of west-central Arizona cover an area of 1600 square miles and contain numerous old mines and prospects. The area has been geochemically sampled on a reconnaissance basis to relate mineralized areas to regional structure and rock types. Copper analyses of stream sediments have been classified and contoured to show the distribution of low and high backgrounds and low, intermediate, and highly anomalous areas. Contoured results are compared to geology and known mines. Several prospecting areas are indicated.

Jan 1, 1972

By Walter R. Hibbard

BACKOFEN' reported recently that "the deformation texture of cold-drawn OFHC copper wire, after a reduction in area of 97.3 pct, may still be described as a composite of [lll.] and [loo] directions aligned parallel to the wire axis." In the introduction, he indicated that this was in contrast to the work of Hibbard,' who reported a single [111] texture after a reduction of 96.4 pct. Unfortunately Backofen stated that this was a reduction in area when actually it was a reduction in diameter, as is clearly stated in the reference. Moreover, the results of Backofen are in complete agreement with the results of Hibbard. Backofen's 97.3 pct reduction in area is an 83.3 pct reduction in diameter, after which he foundadouble [ll11 and[l001texture with the former predominating. Similarly, Hibbard; after an 86 pct reduction in diameter found a double [Ill] and [I001 texture with the former predom- inating. Hibbard, however, when he drew the wire further to 96.4 pct reduction in diameter, found primarily a single [Ill1 texture as illustrated by Fig. 2 of ref. 3. Here also, Hibbard- reported evidences of the [loo] recrystallization texture found by Backofen. It might also be pointed out that Backofen not only drew his wire 97.3 pct reduction in area but also etched them over 99 pct reduction in area from 0.125 to 0.01 in. diam. Hibbard's wires were drawn directly to size. In summary, the deformation texture of cold-drawn copper wire still may be described as primarily a single Clll] texture after a sufficient amount of drawing, such as 96.4 pct reduction in diameter." a

Jan 1, 1952

By V. H. Wilhelm

The year 1936 was a prosperous one for the oil industry in California. Increases in crude prices were posted in February and March. Re-establishment of voluntary curtailment in February was a factor in holding production at an efficient level throughout the year. Reduction of storage was effected through adherence to curtailment measures, aided by greater demand and smaller average well completions. During the first six years of voluntary curtailment, allotments were increased during the summer season and reduced during the winter season. This year, good results were obtained through a revised system of allocation, by which the California monthly quota was held constant at approximately 540,000 bbl. per day. After a 7-month period of practically unrestricted production (ending in January 1936), numerous operators found that curtailment was still necessary, as California and export market,s were not yet capable of absorbing the state's potential production, which was estimated to be in the neighborhood of 850,000 bbl. per day. Therefore, in February California operators again placed themselves under voluntary curtailment; with the result that state production dropped from around 700,000 bbl. per day in January to a low of 565,000 bbl. per day in April, and increased gradually to around 585,000 bbl. per day for December. Drilling activity during the year increased about 10 per cent over that of the preceding year, although the resultant production per well decreased. Field Discoveries As a result of a very active wildcatting campaign in California, aided by better interpretation of geophysical data, five new oil fields and two new gas fields were discovered. Oil Fields Greeley Field, Kern County.—The Standard Oil Co. added to its list of djscoveries by drilling and completing its K.C.L. No. 11-1 well at a

Jan 1, 1937

By James G. Crawford

Correlation Of water with its reservoir zone or formation has been one of the applications of oil-field water analysis of greatest direct value to the petroleum engineer. The water in each producing zone tends to have diagnostic characteristics by which it can be distinguished from every other water above or below that zone in that immediate vicinity. Representative analyses of oil-field waters from producing oil and gas fields in the Rocky Mountain region are included, and the diagnostic characteristics are discussed briefly. It is concluded that the generally dilute nature of Rocky Mountain oilfield waters is a result of dilution by meteoric waters, and that there is no relationship between presence or absence of commercial oil and the character of water in a structure. Introduction The study of waters associated With oil and gas began more than 50 years ago and has been well recognized by operators, engineers, and geologists for about 30 years. It appears unnecessary at this time to recite the history of oil-field water analysis; suffice to say that it has proved its worth many times to the production engineer suddenly confronted with water problems in producing oil and gas wells. Chemists and geologists have studied the possible origin of these waters and as Yet the subject is unsolved in many important phases. There are both local and regional problems connected with the explanation of concentrations and character- istics peculiar to each field, each subsurface zone and each province. Criteria useful in postulating the Occurrence of oil Or gas in One province completely fail when applied to another, and data carefully prepared and analyzed from one field may be actually misleading when applied to another. Correlation of water with its reservoir zone or formation has been one of the applications of oil-field water analysis of greatest direct value to the engineer. The concentrations and characteristics of the waters are essential to the engineers and geologists making interpretations of electric logs in this region. The behavior of water under conditions of reservoir temperature and pressure is dependent to a great degree upon its concentration and characteristics, and thus important to the reservoir engineer. With the advent of secondary recovery methods in the Rocky Mountain region the characteristics and treatment of water will become increasingly important. Premises upon which Correlation Is Based A brief review of the geochemical history of oil-field waters will suffice to present the premises upon which correlations of the waters are based. Sedimentary rocks which are now stratified were first sediments in seas, lakes and streams. These sediments were filled interstitially with connate water. With burial the sediments were compressed arid consolidated, integrated and indurated into bed rock and much of the connate water was dispelled. Following the formation of bed rock the strata were sub-

Jan 1, 1949

By D. Foster Hewett

The scope of this paper is the description of two districts in Peru in which deposits of vanadium have been found, and the consideration of much laboratory-work that I and others have done to determine the nature of these deposits. It is with regret that I present some of the data in a state of evident incompletion, particularly the analyses of a few of the minerals, which leaves some doubt as to whether the true nature of the migerals is understood. I make no apology, however, since in this case, as in many others referring to ore-deposits, conclusive opinions cannot be stated until a great amount of work has been done, and the deposit has been thoroughly exploited. I believe that the data and the tentative conclusions here presented indicate a unique and interesting condition which may assist others in work along similar lines; arid further, what is of more practical importance, stimulate a search for a metal which, though long considered rare, is probably so merely because proper care has not been taken to recognize it. An excellent bibliography on the occurrence of vanadium in nature is given by I?. W. Clarke in his paper, Data of Geochemistry;' and in the preparation of this paper 1 have consulted many of the references contained in the Bibliography of the Chemistry of Vanadium, by M. Moisan.2 A brief review of the subject having special reference to the metallurgy of vanadium is contained in the small book by P. Nicolardot.3 One of these vanadium-deposits has already been briefly. 1 Bulletin No. 330, U. S. Geological Survey (1908). 2 Chimie Minerale, vol. iii. (1905). 3 Le Vanadium (1905).

Jan 1, 1910

By E. T. Hunter

Surrounded by the 13,000-ft high peaks of the San Juan Mountains in southwestern Colo., the town of Silverton is the site of the extensive development operations initiated 20 months ago by Standard Metals Corp. Appropriately termed the Silverton Project, Standard's operation has now passed the half-way point in its program to reopen two mines that were once sizeable producers of copper, lead, and zinc ores.

Jan 1, 1961

By S. C. Suboleski, C. B. Manula

In a high risk venture such as mining where capital is committed and contracts are signed on a minimum of information, decisions are based primarily on production forecasts derived through consideration of such factors as management-labor relations, mining practice, variations in physical conditions, and the equipment applied. Among these factors, the physical conditions offer the least opportunity for control, and, due to the wide range of mining conditions experienced, little effort has been made to develop objective methods for measuring their effects on mine output. This paper's aim is to demonstrate a method for assessing these relationships that can be applied under a wide range of conditions both in new mines and in working sections where there is a need to determine the impact of proposed operational modifications. Using empirical data from active underground mines, a mathematical model was developed to derive a set of regression equations for predicting production as a function of mining conditions.

Jan 1, 1982

By H. D. Kessler, F. A. Crossley, J. J. Rausch

The titanium-rich corner of the system Ti-AI-V has been studied to determine the phase relationships in the temperature interval 600° to 1200°C. Metallographic examination of long time isothermally annealed specimens was the principal method of investigation. TWENTY-SIX alloys in the region 1 to 22 pct A1 and 2 to 11 pct V, and the temperature range 600° to 1200°C, were studied as part of a program on phase relationships and transformation processes of titanium alloy systems. Experimental Procedure Preparation of Alloys—Materials used in the preparation of alloys were high purity Bureau of Mines sponge titanium (103 Bhn), 99.7 pct pure V chips obtained from the Electro Metallurgical Div., union Carbide and Carbon carp., and 99.71 pet pure A1 in the form of granulated shot from Aluminum cO. Of The alloy ingots, weighing l5 g, were melted in a nonconsumable tungsten electrode arc furnace un-

Jan 1, 1957

By N. K. Chen, C. H. Mathewson

Recrystallization of aluminum single crystals after plastic extension is carefully studied in relation to the structure of the deformed matrix. The shapes of the new grains are analyzed with regard to slip planes and to the presence or absence of deformation bands. A mechanism by which the orientations of the grains are related to the parent lattice is described. EXPERIMENTS previously reported&apos; have been extended to develop some of the characteristics of the new crystals which are formed on annealing axially strained crystals whose deformational characteristics had been documented with special care. Thus, the presence of deformation bands affects the growth contours of the crystals, some of the strained crystals produced single crystals anew, and some, polycrystals, on annealing, while others merely "recovered" or "polygonalized" after the 600°C annealing treatment generally adopted in these tests. In the matter of orientational relationships between new crystals and the strained matrix, the present experiments have added little to previous experience, which had demonstrated great variety in the range of orientations encountered and no simple theory or correlation. For example, there has been ample evidence for the predominance in various face-centered cubic metals of a favored orientational relationship; viz., a rotation of 30° to 40° around a <1ll> axis, between grains growing in a matrix with a strong single orientation texture and the matrix itself.&apos;-&apos; This reorientation has been interpreted by various investigators in support of both the "oriented nucleation" and the "oriented growth" hypothesis. In the case of axially extended single crystals of aluminum, no general relationship, such as the one stated above, can be used to correlate the orientations of the recrystallized grains with that of the original crystal. Thus, Carpenter and Elama and Burgers and Basart7 were content to assume that the orientational relationships so developed were random in nature. Mathewson, however, in the Campbell Lecture of 1943 "rgued on the basis of <112> slip that a complex strain, chiefly characterized by rotation around a variable axis in the slip plane combined with a principal rotation around the pole of the slip plane, could be responsible for such devious relationships. Nevertheless, owing to the limited data now available dealing with orientational relationships between new grains and the single crystals strained in tension from which they have recrystallized, no adequate examination of the above generalization could be made. Here, there is the disturbing preliminary condition that any desired orientational relationship may be expressed by means of two rotations about mutually perpendicular axes, so the process lacks a certain critical flavor and any successful choice of axes meeting certain theoretical requirements could be replaced by another differently selected pair. With this reservation clearly in mind the process of double rotations, as previously indicated, was used to relate the orientations of the single crystals which grew out of the strained single crystalline matrix and was construed as certain evidence in favor of the theory of incongruent shearing action proposed by Mathewsons as a necessary element in the (111) slip process with close-packed metals. There is here

Jan 1, 1953

By M. A. Olade

Biotite, magnetite and quartz feldspar separates from rocks around porphyry copper deposits in the Highland Valley have been analyzed for copper, zinc and other related trace and major elements. Results show high copper concentrations in mineral samples close to mineralization, with a strong positive correlation with whole-rock copper contents. Zinc, on the other hand, shows no cleat-cut systematic relationship to mineralization, although there is a subtle decrease in the dues obtained for anomalous biotite samples. Manganese, cobalt and nickel in biotites show similar patterns as zinc. Using a sulfide-selective leach, it is show that the enhanced copper dues in mineral samples proximate to mineralization can be accounted for by the presence of minute inclusions of sulfides. In contrast zinc seems to occur in isomorphous substitution for femic elements, in a form that is leachable by hydrothermal activity. Results also show that copper content of biotite has a positive correlation with the modal proportion of biotites and their iron contents, whereas a negative relationship with manganese is apparent Geochemical contrast for copper between background and anomaly is not better in mineral fractions than whole rocks, consequently the use of minerals as sampling media shows no obvious advantage for mineral exploration purposes in the Highland Valley district.

Jan 9, 1979

By J. H. Swisher

HIGH-temperature anneals in wet hydrogen are widely used in research as a technique for decarburiz-ing Fe-C alloys. This technique is also used commercially in processing low-carbon steels for magnetic applications. The results of some calculations to be presented show that for temperatures up to 1100°C there is a critical temperature for maximizing the decarburization rate of alloys containing about 0.1 pct C. The low-temperature portion of the iron side of the Fe-C phase diagram1 is reproduced in Fig. 1. Preliminary calculations show that the critical temperature is between 727" and 905°C. In this range, the alloy contains two phases during heat treatment, ferrite and austenite. Decarburization therefore occurs by a process termed "diffusion accompanied by a phase change".&apos; For intermediate stages of decarburization, the carbon concentration profile in a flat plate is shown in Fig. 2. The carbon content increases linearly from zero at the surface to a value, cB , at the two-phase boundary. cB is known from the phase diagram, see Fig. 1. At the interface where x = 5, the carbon content increases to ci, the initial concentration in the alloy. smith3 has derived an equation which describes the rate of movement of the boundary. With a rearrange-

Jan 1, 1969

By AIME AIME

HENRY YONGE WALKER is one of Canada&apos;s numerous gifts to the American mining and metallurgical industry, having been born it1 New Brunswick 59 years ago. At eighteen he came to the United States and has since been continuously identified with what are known as the Guggenheim interests. His first position was in the capacity of clerk at the Philadelphia Smelting & Refining Co. plant of M. Guggenheim Sons at Pueblo, Colo. In 1905 he was transferred to the plant of the American Smelting & Refining Co. at Everett, Wash., as assistant manager, two years later going to the Tacoma plant in the same capacity though with added

Jan 1, 1938

By G. R. Rubly, H. J. Steele

LOCATION AND HISTORY THE San Manuel property is in townships 8S and 9S, range 16E, Gila and Salt River Base and Meridan, State of Arizona. This area is in the Old Hat mining district, southern Pinal County, and is about 3;2 miles southwest of the town of Mammoth on the San Pedro River and one mile south of the Mammoth mine at Tiger, Arizona. The property consists of over 150 contiguous lode claims. The Old Hat district was prospected prior to the Civil War, but there was little or no production until 1881.1 The chief producers have been the Mammoth and Mohawk mines, now consolidated and operating as the St. Anthony Mining and Development Co., Ltd. Production to 1936 was $5,200,000, of which 83 pet was gold.2 Since 1940 the production has been chiefly lead and zinc, and some molybdenum and vanadium. There are a few small properties in the vicinity that have produced very minor tonnages of copper ore. In the San Manuel group there are claims which have been held continuously from 1906 to the present time, and at least two churn-drill holes were put down on or near the outcrop in 1917. No logs for these holes are available, but it is assumed that the grade of copper encountered was not sufficient to encourage further exploration. A small amount of ore has been shipped from open cuts on the San Manuel outcrop area, but there is no record of the tonnage or grade. It is estimated that not more than 5o tons were mined. These cuts, plus a few shallow shafts and some short adits indicate limited and unenthusiastic prospecting at San Manuel. In 1942, through the efforts of James M. Douglas, R. B. Giffin, Victor Erickson, and Henry W. Nichols, owners of the San Manuel group, the Reconstruction Finance Corporation and War Production Board authorized the United States Geological Survey to investigate the property, and by their recommendation, the United States Bureau of Mines was authorized to put down a limited number of churn-drill holes. The Bureau of Mines carried on drilling from November 1943 to February 1945. Seventeen holes were drilled, varying from 305 to 1990 ft in depth. The property was brought to the attention of Magma Copper Co. in June I944 and an option agreement was made with the owners. Subsequently, a group of claims lying north of the original group and held by the Apex Lead Vanadium Mining Corp., and a group to the east held by the Quarelli family, were optioned. A drilling program was laid out to conform to the Bureau of Mines pattern, and drilling started in December 1944. San Manuel Copper Corp. was incorporated September 1945, and has carried on the exploration program to the present time. GEOLOGY General The mineralized outcrop, chief copper mineral of which is chrysocolla, is a tri-

Jan 1, 1947

By E. A. Beck

(New York Meeting. February, 1913.) For a number of years many attempts have been made to use thermit in order to do away with piping in ingots. Some of these attempts were successful, while others did not give the expected results. Nearly every plant had its own method of using the thermit, and no special care was taken to study, the results or to find the causes for lack of success. Formerly the principle of the process was to decrease the piping by introducing a can filled with thermit, attached to an iron rod, into the head of the ingot directly after it bad been poured. In this case the thermit reaction took place in the upper part of the ingot, and it was thought that through the heat produced the head would keep liquid longer and piping thus be reduced. In other words, the aim was to keep the head of the ingot open by making use of the heat of the thermit reaction, which would thereby give the gases in the steel sufficient time to escape. This result can be attained by the application of a large enough quantity of thermit, but it would not be economical in general practice, and could only be used for high-grade material. Many steel-makers abroad and in this country have had this experience. The Th. Goldschmidt A. G., Germany, has, therefore, made a special study of this question with the co-operation of a well-known steel company, and has worked out a new method for. the application of thermit for this purpose. The results obtained have been most satisfactory and reliable, and this- process is now used in Germany on a large scale in many prominent steel-works.

Jan 4, 1913

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

By P. S. Katval

It is interesting to note that an attempt has been made to rationalize the effect of prestrain on the strength of Hastelloy X-280 after various aging treatments. However, two points raised by the authors seem to be somewhat unclear. 1) Concerning their Fig. l(a), the authors state: "Extensive dislocation networks are still in evidence. The 24-hr aging at 1500°F and the 15-min soak at 1350°F did not eliminate the dislocations introduced by the 20 pct cold reduction." This is, of course, to be expected since complete "elimination" of dislocations would require recrystallization which does not occur at 1500°F in Hastelloy X. However, recovery

Jan 1, 1969