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By Henry P. Ehrlinger, James C. Bradbury

Tripoli is a naturally occurring, very finely divided form of silica found chiefly in some midwestern and southeastern states and used commercially as fillers and abrasives. Definitions Tripoli is a microcrystalline, finely particulate, more or less friable form of silica that appears to be the product of leaching of siliceous limestone or calcareous chert. The term was originally applied to a deposit near Seneca, Mo., that resembled material of that name found near Tripoli in North Africa (Hovey, 1894). The two deposits were subsequently found to have different physical characteristics -the North African tripoli, now called tripolite, is a diatomite, composed of the siliceous skeletons of microscopic marine plants called diatoms, and the Missouri tripoli contains no diatom remains; the term tripoli, however, continued to be used for the Missouri material and is now applied in a general way to most silica deposits similar to it in characteristics and geologic origin. In commercial trade tripoli is commonly understood to designate material from the Missouri-Oklahoma field; silica from southern Illinois, the other major producing area, is referred to commercially as amorphous silica. Each term, however, may be used commercially for material, regardless of place of origin, that has the characteristics or uses commonly ascribed to the material from one or the other major producing area. For example, in the commodity price listings, Engineering and Mining Journal routinely lists under Tripoli, prices "f.0.b. Elco, III." and "f.0.b. Seneca, Mo., and Rogers, Ark.," and under Silica, amorphous, prices "f .o.b. Ill.," and "f .o.b. Dierks, Ark." Amorphous silica, the commercial designation given to southern Illinois tripoli, is, like the term tripoli, a misnomer. Mineralogically, the southern Illinois deposits are composed of microcrystalline quartz, and no amorphous material has been detected during X-ray and scanning electron microscope investigations (Leamnson, Thomas, and Ehrlinger, 1969; Thomas et al., 1970). Soft silica is another term that has been applied to Illinois and Tennessee tripoli, presumably to distinguish it from the more compact Missouri material. It has also been used in the ceramic trade to distinguish tripoli from "hard" silica, or silica flour, produced by pulverizing silica sand (Heinz, 1937). Rottenstone, produced commercially in Pennsylvania, is similar to tripoli in that a major constituent is finely particulate silica, and its uses are much the same as those of tripoli- as abrasives and fillers. The origin of rottenstone also is similar to that of tripoli-decomposition of a siliceous sedimentary rock. The parent rock is defined as a siliceous limestone (Gary, McAfee, and Wolf, 1972; Thrush, 1968) or as shale (personal communication). Heinz (1937) quotes a brief statement describ-

Jan 1, 1975

INTRODUCTION AND SCOPE This chapter is intended as a brief review of the mathematics of compound interest and of the meaning of time equivalent money. In order to make valid economic evaluations of various investment alternatives, it is important that they be analyzed on an equivalent basis, taking into account the time value of money. Compound interest has been said to be one of the eighth wonders of the world. Certainly compound interest is a fact of life in today's economy. Whenever we deal with money over time-investments, earnings, savings, loans, etc.-we are immediately confronted with the principles and effects of compound interest. In such an environment it is necessary to be able to determine time value equivalence of various sums of money received or paid at different dates. It follows that all future payments or series of payments that would repay a present sum with interest at a stated rate can be said to be equivalent with each other. Equivalence, then, is a function of the interest rate. MATHEMATICS OF COMPOUND INTEREST FACTORS In order to develop mathematical formulas for various time value equivalence of compound interest we will use symbol designations: P is Present or principal sum of money; usually refers to value at time zero. F is a single sum of money at some designated future date. R is The amount of each payment in a uniform series of equal payments made at the end of each period. n is Number of interest compounding periods (may represent annual, semiannual, quarterly, or even daily periods). i is the period compound interest rate. Figure 20-1 illustrates the increase of princi-

Jan 1, 1980

By John L. Watson

A conceptual model (MAGSEP) is described to simulate the beneficiation characteristics of a drum magnetic separator in terms of the probability of an individual grain being recovered in the magnetic concentrate. This probability is determined as a function of particle magnetic composition and magnetic field strength and is modified by particle size and the separator operating conditions. The model predicts the size, magnetic grade and distributions of magnetic and gangue minerals in the concentrate and tailings produced by the drum separator. The configuration of the magnetic concentration circuit may be altered to permit single or double drum units in parallel or series operation. The characteristics of the feed material, in terms of a magnetic parameter, are essential in permitting the determination of individual grain recovery probabilities upon which the model is based. Thus the model requires input data relating to the distribution of composite grains in terms of magnetic grade and particle size. To illustrate the use of the conceptual model an example is given for the beneficiation of New Zealand iron sands.

Jan 1, 1984

By J. S. Miller

This paper describes the method of mining a steeply pitching anthracite seam on a heavy pitch in the Orchard vein in No. 1 Tunnel of the Lehigh Coal and Navigation Co. The Orchard vein in the Neaquehoning district has a thickness of about 15 ft. on the level of the gangway, which is sufficient thickness for the gangway to be driven full width in coal. Above the gangway, the vein becomes thinner and near the surface is about 8 it. thick. The coal is of good hard quality and carries a fairly good roof. The pitch of the vein is between 65" and 70". Usually the breast-and-pillar method has been employed in the mining of the steeply pitching veins in this section. This method produced good results as far as the mining of the breast was concerned but the recovery of the pillar was difficult as to full extraction and expensive as regards costs. To recover these pillars after the breasts were driven, three methods were commonly employed; they were known as the pillar-breast method, pillar-skipping method, and pillar-chute method. The pillar-breast method consisted in putting a battery in one corner of the pillar (Fig. I), coupling the manways A and B of the two adjacent breasts for two or three lengths ahead of the working face of the pillar being cut, and working the pillar as a breast. This method was used by the more skilled miners of the earlier days but has practically been abandoned. A slight variation of this method is used to some extent. In this case, the pillars are left wider than ordinarily and of sufficient width for the full-width breast to be driven in and a small pillar left on each side of the pillar breast between it and the regular breasts. With the completion of the "pillar breast," the ribs are drilled full of holes, loaded, and fired. In the pillar-skipping method (Fig. 2), the middle breast of three is not driven through and is drawn empty while the outside and inside breasts are kept full. At the corners of the two pillars standing, batteries are put in and a skip of the two pillars started; the coal in the two pillars is blasted over into the empty breast. A small pillar is kept along the

Jan 1, 1925

By Walter Hull Aldridge

Much has been said about the foreseeable exhaustion of known mineral reserves-particularly in the United States. It is claimed that we are about to become a have-not nation insofar as certain essential minerals are concerned; and in this respect our position is often contrasted with that of the world as a whole, largely because we have drawn so heavily on our domestic resources during the last fifty years. As a matter of fact, the difference is not great if one takes a reasonably long-term view of the situation. No one denies that nature endowed the United States richer in mineral resources than any other equal area. It is granted that we have skimmed the cream of many kinds of minerals; but in a free international trade in minerals it would not be many decades before the richer deposits-at least the deposits easy of discovery throughout the world would be depleted to much the same degree as those in the United States today. For it is a fact that the problem of satisfying the needs of our industrial society for minerals is fundamentally worldwide in scope. The singular and significant attribute to all minerals is that there is but a single crop. Forests can be grown, but mineral deposits can be replaced only by finding new ones. Thus, one of the vital tasks of the mining engineer, the petroleum engineer, and the geologist is to find these new mineral resources. Another task is to devise means and methods for the exploitation of, at costs that are economic, low-grade deposits and those deeply buried in the crust of the earth. The first need, however, is to find the deposits in the ground. If the assumptions of those who today fear an early exhaustion of all deposits are valid, the outlook for continued material and social progress is gloomy indeed. I take a more optimistic view, for it is my belief that vast new sources of needed minerals will have come to light before our known resources are gone. The real question is whether the outside layer of the crust of the earth that is accessible to engineers contains adequate mineral deposits; and whether engineers can find those deposits. The answer must be based on geologic science, geologic fact, and mining history. Every continent, and almost every country, has yielded minerals of industrial utility in substantial quantity. Mineral deposits are widespread. Geologists know the conditions that were favorable to the occurrence of ores and the types of rocks in which various kinds of ores may ordinarily be found. They know that such rocks occur over broad regions of the earth's surface. They also know that in large areas rocks that are potential carriers of ores are covered and concealed by material of entirely different character. Such cover may consist of lava flows, layers of volcanic ash, or beds of material washed down from the surrounding mountains. Sometimes those covers are thick, sometimes relatively thin. But men well-qualified to pass judgment are sure that concealed deposits, large in number and in size, exist close enough to the surface to make exploitation practical. Only by actual penetration of the surface can this contention be proved, but to conclude otherwise would be to ignore the laws of probability and to deny the over-all consistency of nature. The task of probing the crust of the earth to determine the location of these deposits, and to obtain some notion of their size and quality, poses serious problems. However, they should not be beyond human solution. Much more research must be done in analyzing and explaining the laws of ore deposition. New tools, in the shape of techniques and methods and of mechanical and electrical devices and instruments, must be developed. But no reasonable person can doubt that these objectives will be achieved. As the need becomes increasingly pressing, scientists and engineers will supply the imagination and the ingenuity that will provide the solution. The time and effort thus far devoted to the development of methods for locating hidden ore bodies have been pitifully meager. Energetic investigation of the subject of applied geophysics is essential to the success of the mineral industry, and I have no hesitation in predicting that effective techniques will be found and successfully applied. Twenty-five years ago the petroleum industry

Jan 3, 1950

By Eugene C. Robertson

INTRODUCTION A direct proportionality between the observed displacement of a fault and its thickness of breccia and gouge has been proposed recently (Robertson, in press). To validate this finding, an explanation of the mechanics of continuous breccia formation is needed and is offered in this paper. A summary of evidence for the finding will show why an explanation is needed. The correlation between fault displacement [d] and accompanying breccia- plus-gouge thickness [t] seems to be linear and reasonably well established over 6 orders of magnitude, with a range in [d] from 1 mm to 1 km, on a trend of [d/t]= 100, shown in Figure 1. Most of the points are for faults observed underground in mines. The [d] – [t] relation is limited to normal and reverse faults, that have a flat to steep dip and a displacement less than 5 km. It is not applied to large strike-slip and low-angle overthrust faults, whose displacements and breccia thicknesses are widely variable and uncertain. Undisplaced jointed rock is not included in the thickness measurement. A complete description of sources and analysis of the data is given in Robertson (in press). One would intuitively expect that continued movement on a fault would grind up the previously formed breccia and gouge and not produce any more, but the evidence (Fig. 1) indicates otherwise. A physical model to explain continuous formation of gouge and breccia from the wall rocks can be obtained from laboratory experiments on friction.

Jan 1, 1982

By Ernest Darby

WHEN bronze is melted in open-flame furnaces a considerable amount of slag is formed during the melting operation. This slag may be incidental to the melting practice or it may be formed intentionally by slag-forming constituents added to the furnace charge to provide a covering for the melted metal. When this slag is removed from the furnace, it contains, in addition to the free metal carried with it by the skimming operation, a considerable amount of metal as oxide either combined or mechanically mixed with it. By the usual crushing and washing methods this metallic oxide generally goes to the tailings pile, so diluted by other foundry waste that its recovery is economically impossible. If this furnace slag is not mixed with other foundry waste, practically all of the metal oxide as well as the free metal may be recovered by some form of smelting operation. The first side of the problem to be considered is the amount of slag produced. It may not be true that the majority of foundries have no record of the amount of slag made, but it is certainly true that a very great many either have no record or pay little attention to it. Usually the collection of furnace slag for one normal week's run will be sufficient to determine the advisability of its being handled in a different manner from the crushing and concentrating generally employed. If a large representative sample of the accumulation is crushed and concentrated and the recovery compared with the results of a careful assay, it will be found that a large percentage of the total metal content was lost in the washing process. The percentage of loss will be greater than the metallic oxide content, as some free metal in extremely fine particles always is carried away in grains of slag. From such a comparison, it may be determined whether or not the slag should be melted, sold or treated as before. An example of an actual test of this kind is given below.

Jan 1, 1928

By Ernest Darby

WHEN bronze is melted in open-flame furnaces a considerable amount of slag is formed during the melting operation. This slag may be incidental to the melting practice or it may be formed intentionally by slag-forming constituents added to the furnace charge to provide a covering for the melted metal. When this slag is removed from the furnace, it contains, in addition to the free metal carried with it by the skimming operation, a considerable amount of metal as oxide either combined or mechanically mixed with it. By the usual crushing and washing methods this metallic oxide generally goes to the tailings pile, so diluted by other foundry waste that its recovery is economically impossible. If this furnace slag is not mixed with other foundry waste, practically all of the metal oxide as well as the free metal may be recovered by some form of smelting operation. The first side of the problem to be considered is the amount of slag produced. It may not be true that the majority of foundries have no record of the amount of slag made, but it is certainly true that a very great many either have no record or pay little attention to it. Usually the collection of furnace slag for one normal week's run will be sufficient to determine the advisability of its being handled in a different manner from the crushing and concentrating generally employed. If a large representative sample of the accumulation is crushed and concentrated and the recovery compared with the results of a careful assay, it will be found that a large percentage of the total metal content was lost in the washing process. The percentage of loss will be greater than the metallic oxide content, as some free metal in extremely fine particles always is carried away in grains of slag: From such a comparison, it may be determined whether or not the slag should be melted, sold or treated as before. An example of an actual test of this kind is given below.

Jan 1, 1928

By Roshan B. Bhappu

Selenium is found most frequently as an accessory mineral in the ores of lead, copper, and nickel, and is recoverable as a byproduct in the treatment of many of the ores of these metals. The geographic distribution of the selenium industry closely follows that of electrolytic copper, with the United States and Canada producing approximately 75% of the total output of the non-communist world. This situation is problem number one for selenium-its dependence upon the electrolytic refining of copper- for this byproduct source is not sufficiently flexible to permit a normal supply-demand balance. Furthermore, selenium has become a strategic material in short supply. Thus, new sources are being sought by both government and private interests. Although considerable attention has been given to this effort during the last few years, hardly any research has been published concerning the recovery of small amounts of selenium present in low-grade deposits. In such ores the metal occurs as native selenium or as selenides of iron, copper, silver, lead, and bismuth. In recent years, some native selenium (in both the gray and red form) and selenides, especially iron selenide (ferroselite), reportedly have been found in the sandstones of the Morrison formation near Grants. New Mexico. Similar occurrences have been reported in the Hagan coal basin, in Sandoval County, New Mexico. Samples from New Mexico ores have contained from a trace amount to as high as 0.425% Se. Some of the samples from uranium mines in the Grants area represent mixed ore and mill feed fur uranium reduction plants. In such cases, the selenium usually is reported as an impurity and is lost in the tailings. At present, no attempt is made to recover this waste metal.

Jan 8, 1962

By C. S. Smith, L. W. Kempf, C. S. Taylor

The thermal conductivity of aluminum alloys is of considerable industrial importance. This is particularly true in such applications as internal-combustion engines where one of the principal reasons for the use of these alloys is their relatively higher thermal conductivity. In spite of this, relatively few data are available on this property of aluminum alloys. The reason is quite apparent to anyone concerned with the experimental determination of coefficients of thermal conductivity. This determination, in theory so simple, is extraordinarily difficult if any high degree of precision is desired. Fortunately, some .knowledge of the relationship between thermal and electrical conductivity has permitted the use of the latter physical property in deducing the relative approximate values of the thermal conductivities of metals. This fundamental relationship, first enunciated by Wiedemann and Franz' as applying to metallic elements and later shown by Lorenz2 to be applicable to alloys within a single metallic system, has been of service in the industrial application of metals. The electrical conductivity of metals is easily determined with a high degree of precision. It is, therefore, quite desirable that the relationship between electrical and thermal characteristics be determined with the greatest possible precision. This paper presents data on the electrical and thermal conductivities of a number of aluminum alloys of industrial importance. Literature on Thermal Conductivity of Aluminum Alloys Masumoto3 determined the electrical and thermal conductivities of 18 aluminum alloys. His results indicated a relatively constant relationship between thermal and electrical conductivity.

Jan 1, 1937

By B. L. Averbach, M. Cohen

THE PROBLEM MANY hardened steels contain significant quantities of retained austenite even in cases where the carbon and alloy contents are low. In fact austenite has been detected in plain carbon steels containing as little as 0.50 pct carbon.1 Although the austenite may not be visible metallographically it causes definite dilatometric and magnetic effects during subsequent tempering or subatmospheric cooling.1,2,3 Therefore if the reactions which hardened steels undergo during later treatment are to be understood in quantitative fashion it is most essential to have some kind of absolute analysis for the austenite content in hardened steels. Once this analysis has been made, the austenite transformations can be followed precisely by observing such sensitive phenomena as changes in length or in magnetization but the latter techniques can only determine differences in the amount of retained austenite and usually an independent method must be found to put these differences on an absolute basis. In certain instances the microscope can be used advantageously to determine the percentage of retained austenite. The quenched sample is tempered to "darken" the martensite with minimum decomposition of the coexisting austenite, and then is polished and etched in the usual fashion. If the austenite is clearly distinguishable from the tempered martensite and other possible constituents its volume percentage can be measured quantitatively by point counting or lineal analysis.4 Such microscopic methods, however, depend on the etch being sufficiently discriminatory. In fairly coarse structures, if the austenite content is greater than 10-15 pct, there is probably little smearing of the etch, and point counting or lineal analysis seems to be quite accurate. On the other hand if the structure is difficult to resolve, as in commercially treated fine-grained steels which contain less than 10-15 pct retained austenite, the latter may be completely obliterated by the dark etching martensite or it may appear disproportionately low as the interfaces between the two constituents become difficult to distinguish. Another disadvantage of the metallographic method is the need for "darkening" the martensite and hence the determination cannot be applied to as-hardened steels. The required tempering may spoil the structure for other tests or may even remove a small part of the austenite which is being sought. X ray methods hold more promise for covering the range under 15 pct retained austenite. Although austenite and martensite in the hardened steel may be chemically identical, their crystal structures and lattice parameters differ, and the intensity of an austenite diffraction line is some continuous function of the percentage of re-

Jan 1, 1948

By M. A. Meyers, P. P. Meyers

The analysis of the phenomena involved in determining the compressive strength of iron-ore agglomerates leads to the identification of important parameters. It is shown mathematically that the pellet rupture strength is proportional to the cross-sectional area. Fracture is initiated at the center of the pellets by the tensile stresses developed by the compressive loads normally to the compressive axis. The variation in strength between individual pellets of identical composition and subjected to identical treatments u due to internal voids of varying sixes that act as stress-concentration sites. Two novel testing procedures are proposed. The first consults of testing the pellets between two plates having three steel spheres each. This configuration simulates much better the environment actually encountered by the pellets. The second procedure consists of a thick-walled cylinder in which a piston penetrates; a large group of pellets is tested simultaneously, as the stress versus strain plot is being recorded. This latter test presents vacant advantages over the conventional testing procedure; the main one is that one single test is sufficient to characterize the mechanical response of the pellets.

Jan 1, 1984

Secondary minerals are the result of a process of concentration and enrichment and are commonly richer than the primary minerals of the same deposit. Secondary ores that contain abundant sulphides are commonly distinguishable in the field from primary ores; this distinction is more difficult with ores that carry a small quantity only of sulphide minerals, and microscopical examination of the ore in thin section is advisable in all doubtful cases. It is frequently difficult, and in some cases impossible, to determine the primary or secondary character of quartzose gold ores. The safest guide is the presence or absence of gaseous or fluid inclusions in association with the ore minerals; such primary association coupled with a lack of traces of oxidation is indicative of primary origin. Any ore that carries traces of oxidation, such as iron stains, endritic oxides of manganese, kaolin and so forth must be considered to have been acted upon by surface agencies, and secondary enrichment must be suspected. Further examination, however, may indicate that the contained value is primary, and, therefore, persistent in its vertical distribution. The manner of occurrence of secondary minerals is frequently characteristic; secondary minerals, being due to the action of surface waters, are commonly found in cracks through earlier minerals, or as crusts lining vugs or surrounding nucleal masses, or in general, in some distribution later than and not conforming to the arrangement of the primary minerals. Secondary sulphides are often found as soft black pulverulent masses or coatings, although they frequently occur well crystallized or as

Jan 1, 1932

By C Gunther

Secondary minerals are the result of a process of concentration and enrichment and are commonly richer than the primary minerals of the same deposit. Secondary ores that contain abundant sulphides are commonly dibtinguishable in the field from primary ores; this distinction is more difficult with ores that carry a small quantity only of sulphide minerals, and microscopical examination of the ore in thin section is advisable in all doubtful cases. It is frequently difficult, and in some cases impossible, to determine the primary or secondary character of quartzose gold ores. The safest guide is the presence or absence of gaseous or fluid inclusions in association with the ore minerals; such primary association coupled with a lack of traces of oxidation is indicative of primary origin. Any ore that carries traces of oxidation, such as iron stains, dendritic oxides of manganese, kaolin and so forth must be considered to have been acted upon by surface agencies, and secondary enrichment must be suspected. Further examination, however, may indicate that the contained value is primary, and, therefore, persistent in its vertical distribution. The manner of occurrence of secondary minerals is frequently characteristic; secondary minerals, being due to the action of surface waters, are commonly found in cracks through earlier minerals, or as crusts lining vugs or surrounding nucleal masses, or in general, in some distribution later than and not conforming to the arrangement of the primary minerals. Secondary sulphides are often found as soft black pulverulent masses or coatings, although they frequently occur well crystallized or as

Jan 1, 1932

By Teder R. I., M. M. Protodyakonov

In order to find an empirical relation between a quantity F and (m) independent variables or factors, each of which take (n) different values or levels, it is necessary to conduct nm different experiments (all possible combinations of the factors), each of which has to be repeated a few times (usually five) due to the scattering of the data. The total number of such experiments is very large, thus for example, when m = 4 and n = 5, it is equal to 5.54 = 3125; and very rarely is it possible to conduct such a number of experiments. Various possible methods of planning partial experiments are illustrated in Fig. 1. Each method shows a large combinative square consisting of five columns and five rows of middle squares, each of which, in turn, is further divided into five columns and five rows of cells. Such a partition corresponds to a plan of an experiment with four factors, each of which takes five different levels. The blackened cells indicate the combination of factors in a partial experiment. The total number of experiments is reduced on the basis of the following considerations: a) The effect of only a few levels of some factors is studied (Fig. la). Such an investigation gives no information on the effect of some factors, therefore it cannot be accepted as satisfactory; b) By reducing the number of levels of each factor; in such a case it is not possible to obtain an empirical relationship, but only whether some factors have an effect. This is evidently inadequate;

Jan 1, 1971

By E. R. Morgan

A series of manganese-rich ferromagnetic alloys has been studied. The alloys are based upon an interstitial solution of carbon in manganese. In each of the systems investigated, the ferromagnetic phase was found to be face-centered-cubic in structure. This magnetic phase is based upon the composition (Mn, X)4C; where X is a metallic element which has both a positive size factor with respect to manganese and a high positive valence. Typical elements of this type are aluminum, indium, and tin. Preliminary magnetic measurements indicate that the effective magnetic moment of manganese in the alloys is at least 1.0 Bohr magneton per atom. It is emphasized that the critical atomic separation beyond which ferromagnetism can occur will be governed by the electronic configuration of the manganese atoms. Lattice parameter measurements show that the ferromagnetic condition in the present alloys is associated with an increased atomic separation of only 3 to 6 pct compared with a hypothetical face-centered-cubic lattice of pure manganese. MANGANESE which is paramagnetic and not ferromagnetic in the pure state can become ferromagnetic if suitably alloyed. Under favorable conditions manganese can have an effective ferromagnetic moment of the order of 3.41,2 or even 4.0 compared with a moment of 2.2 Bohr magnetons for iron. The incidence of ferromagnetism is believed to be controlled by the degree of atomic separation.4,5 This is consistent with the fact that the atomic separation, when considered in terms of the ratio of the atomic diameter R to the diameter r of the 3d-shell, is larger in the ferromagnetic metals. The values of R/r calculated by Slater,' for metals of the iron group are given in Table I, and Slater has suggested that the critical ratio of R/r is 1.5. Consideration of the criterion of atomic separation alone would suggest that there are three classes of possible ferromagnetic manganese alloys: 1— Ordered structures, of either solution or compound types, such that manganese atoms are not near neighbors; 2—Structures in which the separation of near-neighbor manganese atoms is sufficiently increased by the presence of suitable solute atoms; and 3—Dilute solutions of manganese. Typical ferro- magnetic alloys of types 1 and 2 are the Heusler alloys and Mn4N, respectively. There are no recognized ferromagnetic alloys of type 3. In view of the proximity of the ratio R/r for manganese to the critical ratio of 1.5, the present work was concentrated on manganese-rich alloys rather than on ferromagnetic alloys of low manganese content, several examples of which are already known. Calculation of the distance of closest approach of manganese atoms in each of its allotropic forms, Table 11, indicates that the high temperature ? phase provides the most suitable basis for ferromagnetic alloys of high manganese content. However the high temperature forms of pure manganese cannot be retained on quenching, although a face-centered-tetragonal form apparently can be produced by electrodeposition. Since the critical separation which must be exceeded in order to obtain ferromagnetism is dependent upon the number of electrons in the d-shell, no exact critical value of R/r can be assumed. Not only will this separation vary from one pure metal to another, but it will also vary with the valency of the given type of atom when it is in an alloy. Raynor8 has shown that metals of the iron group probably

Jan 1, 1955

By M. Cohen, B. L. Averbach

Many hardened steels contain significant quantities of retained austenite even in cases where the carbon and alloy contents are low. In fact austenite has been detected in plain carbon steels containing as little as 0.50 pct carbon.1 Although the austenite may not be visible metallographically it causes definite dilatometric and magnetic effects during subsequent tempering or sub-atmospheric coo1ing.l,2,3 Therefore if the reactions which hardened steels undergo during later treatment are to be understood in quantitative fashion it is most essential to have some kind of absolute analysis for the austenite content in hardened steels. Once this analysis has been made, the austenite transformations can be followed precisely by observing such sensitive phenomena as changes in length or in magnetization but the latter techniques can only determine differences in the amount of retained austenite and usually an independent method must be found to put these differences on an absolute basis. In certain instances the microscope can be used advantageously to determine the percentage of retained austenite. The quenched sample is tempered to "darken" the martensite with minimum decomposition of the coexisting austenite, and then is polished and etched in the usual fashion. If the austenite is clearly distinguishable from the tempered martensite and other possible constituents its volume percentage can be measured quantitatively by point counting or lineal analysis.4 Such microscopic methods, however, depend on the etch being sufficiently discriminatory. In fairly coarse structures, if the austenite content is greater than 10-15 pct, there is probably little smearing of the etch, and point counting or lineal analysis seems to be quite accurate. On the other hand if the structure is difficult to resolve, as in commercially treated fine-grained . steels which contain less than 10-15 pct retained austenite, the latter may be completely obliterated by the dark etching martensite or it may appear disproportionately low as the interfaces between the two constituents become difficult to distinguish. Another disadvantage of the metallographic method is the need for "darkening" the martensite and hence the determination cannot be applied to as-hardened steels. The required tempering may spoil the structure for other tests or may even remove a small part of the austenite which is being sought. X ray methods hold more promise for covering the range under 15 pct retained austenite. Although austenite and martensite in the hardened steel may be chemically identical, their crystal structures and lattice parameters differ, and the intensity of an austenite diffraction line is some continuous function of the percentage of re-

Jan 1, 1949

By B. L. Averbach, M. Cohen

Many hardened steels contain significant quantities of retained austenite even in cases where the carbon and alloy contents are low. In fact austenite has been detected in plain carbon steels containing as little as 0.50 pct carbon.1 Although the austenite may not be visible metallographically it causes definite dilatometric and magnetic effects during subsequent tempering or sub-atmospheric coo1ing.l,2,3 Therefore if the reactions which hardened steels undergo during later treatment are to be understood in quantitative fashion it is most essential to have some kind of absolute analysis for the austenite content in hardened steels. Once this analysis has been made, the austenite transformations can be followed precisely by observing such sensitive phenomena as changes in length or in magnetization but the latter techniques can only determine differences in the amount of retained austenite and usually an independent method must be found to put these differences on an absolute basis. In certain instances the microscope can be used advantageously to determine the percentage of retained austenite. The quenched sample is tempered to "darken" the martensite with minimum decomposition of the coexisting austenite, and then is polished and etched in the usual fashion. If the austenite is clearly distinguishable from the tempered martensite and other possible constituents its volume percentage can be measured quantitatively by point counting or lineal analysis.4 Such microscopic methods, however, depend on the etch being sufficiently discriminatory. In fairly coarse structures, if the austenite content is greater than 10-15 pct, there is probably little smearing of the etch, and point counting or lineal analysis seems to be quite accurate. On the other hand if the structure is difficult to resolve, as in commercially treated fine-grained . steels which contain less than 10-15 pct retained austenite, the latter may be completely obliterated by the dark etching martensite or it may appear disproportionately low as the interfaces between the two constituents become difficult to distinguish. Another disadvantage of the metallographic method is the need for "darkening" the martensite and hence the determination cannot be applied to as-hardened steels. The required tempering may spoil the structure for other tests or may even remove a small part of the austenite which is being sought. X ray methods hold more promise for covering the range under 15 pct retained austenite. Although austenite and martensite in the hardened steel may be chemically identical, their crystal structures and lattice parameters differ, and the intensity of an austenite diffraction line is some continuous function of the percentage of re-

Jan 1, 1949

By Chester A. Fulton

APATITE, the most abundant crystalline phosphate mineral, is found in igneous rocks and probably is the primary origin of all other phosphates, whether mineral or organic. Its chemical formula may be expressed as Ca5(Cl,F) (PO4) 3. The chlorine may be replaced almost entirely by the fluorine. It is found in large or small hexagonal prisms, usually of a vitreous luster and a green or red color, but also violet, white, or yellow. It is found largely as an accessory mineral in granitoid rocks. Its hardness is 4.5 to 5 and its specific gravity is about 3.2. There are many other phosphate minerals-for instance, amblygonite, autonite, collophane, lazulite, monazite, pyromorphite, torbenite, triphylite, turquoise, vivanite, wavellite-with base elements of calcium, magnesium, iron, aluminum, manganese, lead, cerium, lanthanum, lithium, or several of these in combination and with various amounts of water of crystallization. However, these phosphate minerals have but little value save as specimens for mineral collections, the exception perhaps being turquoise. While large deposits of igneous apatite are mined today for the production of fertilizers and chemicals, more than 90 pct of the world phosphate production is derived from secondary apatites, called phosphorites. These calcium (and magnesium, aluminum, and iron) phosphates have been formed in the alteration of sediments by solutions containing phosphoric acid. Such solutions have come from the weathering or leaching of igneous rocks containing apatite, bone deposits of prehistoric animals and marine life, or guano deposits (excreta of birds). These phosphorites are mostly alterations of phosphatic limestones that took place slowly over many years. Whether it is apatite or phosphorite that is being produced, it is known in the trade as "phosphate rock." The sedimentary phosphate deposits are of marine origin. Some, as laid down, were rich in phosphate or have become so by subsequent subaqueous action and have not been further enriched since emergence from the sea. Some were originally phosphatic limestones or marls from which calcium carbonate was dissolved away by waters containing carbon dioxide, in which calcium carbonate is much more soluble than

Jan 1, 1949

By Peter I. Brooker

Elementary estimation methods in which blocks are assigned values according to a geometrical area of influence concept are investigated for a tabular deposit. This quantitative assessment of the estimation technique is made using Matheron's geostatistics which allows the variance of the error between actual block values and estimated values to be found once the semi-variogram is known. For the deposit in question it is shown that the elementary technique makes poor use of the available information. There is a 20% relative error associated with it, whereas by using the optimal technique of kriging this can be reduced to 9%. An infill drilling program, which might have been suggested on area of influence results, would reduce the estimation variance only marginally over that of the current campaign; the relative error being lowered to 6%. Thus the geostatistical analysis shows this would be an unnecessary expense. The accuracy of an earlier drilling stage is also studied and it is shown that with the information available at the earlier stage block values could have been known with a relative error of 13%. Drilling could have stopped then if this were reckoned a tolerable error level. These results are all obtained for blocks whose size is dictated by the mining engineer and is set at the current grid size. In the area of influence approach smaller blocks are considered as the grid becomes finer and a study of the accuracy of area of influence estimates and kriged estimates for differing block sizes is presented. Between drilling stages more information from which the semi- variogram is calculated becomes available. The sensitivity of the estimation to changes in the semi-variogram parameters between earlier and current drilling programs is investigated.

Jan 1, 1977