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By William H. Emmons

Discussion of the paper of William H. Emmons, presented at the Canal Zone meeting, November, 1910, and printed in Bulletin No. 46, October, 1910, pp. 767 to S37. CHARLES R,. KEYES, Des Moines, Ia. (communication to the Secretary*) :-It is not in a spirit of criticism that I offer a supplemental suggestion or two on the subjects covered by this valuable and highly instructive memoir. There are two points which, in my opinion, should have received greater emphasis in Mr. Emmons's excellent paper. One is the fundamental role played by the chlorides under certain conditions in ore-formation. The other is the possible establishment of geographic relationships among the four phenomena of (1) excessive chloridic content of mine-waters; (2) the abundance of chloridic compounds of the precious metals ; (3) the presence of. manganese oxides; and (4) the diminishing importance, in ore-genesis, of the metallic sulphates. Although Mr. Emmons's notes refer to gold alone, it may be pertinently asked whether the same principles do not hold good for silver and copper also, since these metals form, together with gold, a distinct and well-known chemical group. That the reactions involved apply equally well to the other two metals mentioned, is shown by a number of recent observations and discussions. Chloridic ores of silver are, as I have lately endeavored to show, mainly worked in. arid or desert regions only ; and the great deposits of disseminated copper-ores are similarly characteristic of such regions, in which both classes doubtless owe their formation to the abundance of saline materials derived from desert dusts, and to the .plentiful and almost universal presence of manganese oxide. Under these climatic conditions, silver is somewhat more abundantly deposited than copper and gold, because its chloride is so much * Received Nov. 11, 1910.

Jun 1, 1911

By Paul R. Cook

The ore deposit of the Buckhorn Mines Co., Buckhorn, Nev., is peculiar in being a shallow kaolinized mass of material with basalt walls, and having apparently no direct connection with any of the usual gold-bearing rocks. The average ore contains 16 per cent. water of hydration, and the cyaniding of this hydrous clayey material offered unusual difficulties as compared with an average Nevada quartz ore. The orebody was thoroughly developed; then the mill was built according to the latest cyanide practice, with such changes as were thought to be demanded by the peculiar nature of this ore. Upon starting the mill, the ore proved more difficult to handle than had been anticipated. It is hoped that an account of how these difficulties were met may prove of interest to anyone having a clayey ore to handle and to the profession in general. Geology The Buckhorn orebody lies along a north and south fault plane of perhaps 1,000 ft. dislocation, that can be traced for miles; but the only other known mineralization consists of similar ore in the Murphy mine, a mile farther north. The east or hanging wall is hard and smooth, being a typical fault plane. The best ore is along this wall, gradually grading down toward the west until at 30 to 60 ft. it is too low-grade to mine. The country rock on the west consists of alternating layers of hard and soft basalt and basalt scoria, pitching toward the mine. One of these basalt layers on the hillside a little above the mine is marked, for 3 or 4 miles in length, by a line of springs which seep out along it. Perhaps the meeting of the surface drainage, passing down these basalt layers, with the fault-plane solutions explains the formation of the Buckhorn orebody.

Jan 1, 1917

By W. A. Clark

The production of sand in an oil well increases operating costs because of abnormal wear in subsurface equipment, the necessity for frequent cleanouts, and the need for a means of disposing of the sand. Moreover, removal of sand from the zone can bring about the creation of cavities from which bodies of formation, sand or shale, may slough into the hole, endangering the shutoff, impeding production or collapsing the liner. The procedure known as gravel packing is attracting attention as a means of controlling these factors and contributing to the productive life of a well. That gravel packing is now substantially beyond the preliminary stage on the Pacific Coast is reflected in the 191,000 bbl. of oil produced monthly by the 66 gravel-packed wells in 11 different producing sectors. Reasons fob Gravel Packing Gravel packing, if properly carried out, can be expected to provide the following benefits: 1. Prevent the movement of sand and thus eliminate sand production and sand fills, and prevent the formation of cavities. 2. Provide a practical, relatively inexpensive, large-diameter hole, which will provide well-known theoretical advantages. 3. Support the walls of the hole by completely filling the space between the liner and the formation, regardless of its irregularities, and afford a support for liners. 4. Provide for more efficient pumping operations in wells by: (a) possibly utilizing the gravel as a gas trap in pumping gaseous fluids, (b) allowing deep submergence of the pump into the oil zone. In a conventional well—that is, where the liner is set in an open hole-. even though perforation sizes are chosen according to known rules based on analysis of sand grains from samples from the zone, there is likely to be some production of sand. This may be due to the miscalculation of

Jan 1, 1940

By W. A. Clark

The production of sand in an oil well increases operating costs because of abnormal wear in subsurface equipment, the necessity for frequent cleanouts, and the need for a means of disposing of the sand. Moreover, removal of sand from the zone can bring about the creation of cavities from which bodies of formation, sand or shale, may slough into the hole, endangering the shutoff, impeding production or collapsing the liner. The procedure known as gravel packing is attracting attention as a means of controlling these factors and contributing to the productive life of a well. That gravel packing is now substantially beyond the preliminary stage on the Pacific Coast is reflected in the 191,000 bbl. of oil produced monthly by the 66 gravel-packed wells in 11 different producing sectors. Reasons fob Gravel Packing Gravel packing, if properly carried out, can be expected to provide the following benefits: 1. Prevent the movement of sand and thus eliminate sand production and sand fills, and prevent the formation of cavities. 2. Provide a practical, relatively inexpensive, large-diameter hole, which will provide well-known theoretical advantages. 3. Support the walls of the hole by completely filling the space between the liner and the formation, regardless of its irregularities, and afford a support for liners. 4. Provide for more efficient pumping operations in wells by: (a) possibly utilizing the gravel as a gas trap in pumping gaseous fluids, (b) allowing deep submergence of the pump into the oil zone. In a conventional well—that is, where the liner is set in an open hole-. even though perforation sizes are chosen according to known rules based on analysis of sand grains from samples from the zone, there is likely to be some production of sand. This may be due to the miscalculation of

Jan 1, 1940

By Peter Hood

Data on worldwide geophysical activity in mining exploration programs is collected annually by the Geophysical Activity Committee of the Society of Exploration Geophysicists as part of a continuing service to the industry. The data is obtained by sending out questionnaires to all organizations (which are) known to be carrying out mining geophysical work; the organizations canvassed include mining companies, contractors, government departments and universities. The questionnaire is divided into three sections, namely ground methods, airborne methods and research. In 1968, 515 questionnaires were circulated throughout the non-Communist world and 283 replies were received which is a 55% return. A 67% return was received from the U. S. organizations surveyed so the statistics quoted in this report for the United States are reasonably reliable. This report is published in condensed form, but with emphasis on the United States statistics, with the permission of the Society of Exploration Geophysicists. It was presented at the 39th Annual International Meeting of the SEG in Calgary, Alberta, on September 15, 1969. Worldwide utilization of mining geophysical methods reached a new high in 1968 with total expenditures of United States $41.4 million, compared lo $32.3 million in 1967, representing a 28%, increase. The expenditure distribution by area and type of activity is shown in the graph on page 64. In terms of money spent, ground geophysical surveys accounted for 49% of the total, airborne survey's 36% and research 15%. The percentage of the money spent on ground geophysical surveys fell by approximately 7% from 1967, that for airborne surveys, increased by 5%, and for research the amount increased by 2%. Industry accounted for 79°1% of the total monies spent on mining geophysical activity in the world in 1968 and governments and universities 21 o%.

Jan 1, 1970

By Dorsey Hager

THE information given in the accompanying table is submitted as evidence confirming the application of the anticlinal theory and the value of geology in the Kansas and Oklahoma oil fields. The term anticline has been used to define a particular type of arched fold. The anticlinal theory of oil accumulation should, however, be broadened to include any structural fold of an arched type even if not a distinct anticline. A terrace may very properly come under the heading of the anticlinal theory of accumulation, as the folding is closely related to that of the anticline; in fact, in many cases is an arrested anticline, though not completely closed in all directions. Stratigraphic forms due to lensing or irregular cementation of the sands certainly cannot be considered to fall within the anticlinal theory, though the laws of accumulation may be similar. A dome is similar to an anticline and belongs to the same class. A dome is broader in proportion to its length than an anticline. Many anticlines undulate along their axes to form domes. The anticlinal theory in this discussion will then be applied to anticlines, domes and terraces. In the following list, the writer has tabulated the main oil fields of Oklahoma, and a few recently discovered fields in Kansas. The fields discovered within the past 4 years are listed with the date of their discovery. Under "How found," the writer puts "Wildcat" where a geologist has not been employed, "Geology" where it has been used, and "?" where there is doubt. In some places the geologists have claimed pools that may rightly belong to them, but their claims have been questioned, so that they belong in an unsettled category.

Jan 2, 1917

Charles R. Eeyes, Des Moines, Ia. (con~munication to the Secretary*):—It is not in a spirit of criticism that I offer a supplemental suggestion or two on the subjects covered by this valuable and highly instructive memoir. There are two points which, in my opinion, should have received greater emphasis in Mr. Emmons's excellent paper. One is the fundamental r6le played by the chlorides under certain conditions in ore-formation. The other is the possible establishment of geographic relationships among the four pheilomena of (1) excessive chlo-ridic content of mine-waters; (2) the abundance of chloridic compounds of the precious metals; (3) the presence of man-gancse oxides; and (4) the diminishing importance, in ore-genesis, of the metallic sulphates. Although Mr. Emmons's notes refer to gold alone, it may be pertinently asked whether the same principles do not hold good for silver and copper also, since these metals form, together with gold, a distinct and well-known chemical group. That the reactions involved apply equally well to the other two metals mentioned, is sbown by a number of recent observations and discussions. Chloridic ores of silver are, as I have lately endeavored to show, mainly worked in arid or desert regions only; and the great deposits of disseminated copper-ores are similarly characteristic of such regions, in which both classes doubtless owe their formation to the abundance of saline materials derived from desert dusts, and to the plentiful and almost universal presence of manganese oxide. Under these climatic conditions, silver is somewhat more abundantly deposited than copper and gold, because its chloride is so much less soluble. During volcanic emanations, the metallic chlorides perform at all times distinct functions; when these are

Jan 1, 1912

By M. C. Flemings, R. Mehrabian

In a recent series of papers,1-3 it was shown that a variety of apparently different types of macrosegrega-tion result from the same basic mechanism, the inter-dendritic flow of solute rich liquid to feed solidification and thermal contractions. The important parameter governing sign and extent of segregation was shown to be (v.?T)/ where v is interdendritic flow velocity, ?T is temperature gradient, and E is rate of temperature change. It was proposed in one of the previous papers that the "negative cone of segregation" often found at the base of large ingots results from the large value of (v. VT)/E expected to pertain there. The reason why this parameter is expected to be large in that location is the high flow velocity to be expected there, as discussed earlier,' and as shown schematically in Fig. 1. In this note, two experiments are summarized which are intended as laboratory simulations of the inter-dendritic flow behavior sketched in Fig. 1 and, therefore, of the "negative cone of segregation". Experimental procedures employed are as described in the the earlier work.3 Alloy cast was nominally Al-4.5 pct Cu. Fig. 2 shows one of these ingots, a "prism" ingot, 6 cm high by 12 cm wide by 10 cm long, unidirectionally solidified from a water cooled base. In this ingot, in-terdendritic flow velocity increases near the upper portion of the ingot because of the gradually decreasing ingot cross-section. Calculations were presented earlier of the negative segregation to be expected in this type of ingot,' and results presented in Figs. 2 and 3 agree closely with those of earlier calculations. A more direct (although less easily calculable) simulation of the "negative cone of segregation" is the

Jan 1, 1970

By W. L. Penberthy, H. J. Ramey

Experimental work on the combustion oil recovery process has consisted of both laboratory and field studies. Although field experiments are the ultimate test of any oil recovery process, they are costly, time consuming and difficult to analyze quantitatively. Laboratory combustion tube experiments can be opertzted far more rapidly and cheaply, but are subject to scaling and interpretation problems. This paper points out some important design problems, operational criteria and considerations in2portunt to interpretation of results. An analytical hcut model of movement of a burning front axiully along a cylinder with heat loss through an annular insulation was developed. The result was used to identify steady-state temperatrrre distributions both ahead of and behind the burning front, with and without heat loss. Results indicate potential operating limitations on the minimum burning front rielocity (or air flux) which may be used for any given combustion tube. Results also enable estimating the effective thermal diffusivity and over-all heat loss from experimental data and thickness of the brnning zone. Resu lts of operation of a combustion tube constructed recently verify this preliminary theory in the region immediately ahead of and behind the burning front surprisinRly well. INTRODUCTION Many field and laboratory studies of the forward combustion oil recovery process have been conducted since the early publications of Kuhn and Kochl and Grant and Szasz2 in 1953 and 1954. In view of the complex and costly nature of this type of investigation, it is not surprising that no complete theory of the nature of the forward combustion Drocess is yet available. However, gross effects are understood well enough that reasonable design procedures are available for planning field operations. Nelson and McNeil 3,4 have published two comprehensive papers concerning design procedures. One major consideration in planning field operations is the fuel concentration at the burning front. Fuel concentration controls air requirements — an important cost factor in forward combustion. Although fuel concentration can be estimated from field test results by various methods, results are subject to great uncertainty in view of natural limitations on experimental observations. Nelson and hlcNeil4 recommend that fuel concentration be determined from laboratory combustion tube studies. Fuel concentration is only one of many important factors which can be studied by combustion tube experimentation. An obvious goal of imporrance must be development of a comprehensive theory of the forward combustion process. If a theory of this process can be established which matches controlled laboratory experimentation, it should be possible to apply this theory to field operating conditions with some confidence. Laboratory combustion tube studies have already yielded important information concerning the combustion process. However, details concerning the design, construction and operation of combustion tubes are rare. Combustion tubes used by various investigators vary in size, length and mode of operation. Therefore, one purpose of this paper is to present considerations important to design, construction and operation of a combustion tube. In regard to previous combustion tube studies, attention is called to Refs. 1 through 9. These references describe a wide variety of equipment types and present a great deal of pertinent experimental data. In general, combustion tubes usually consist of thin-walled stainless steel tubes containing an oil sand pack mounted within a pressure jacket. Provisions have often been made to heat the tube ex tern a lly by separately controlled heaters to reduce heat losses. This step usually permits operation at low air fluxes (air rate per square foot burning front surface) similar to those encountered in field operations. Burning is usually conducted from the air inlet end of the tube to the outflow end. The tube orientation used has been vertical or horizontal. For vertical tubes, burning has been conducted vertically downwards. As a result of laboratory studies, many of the

Jan 1, 1967

By J. H. Scaff, H. C. Theurer, E. E. Schumacher

The microwave region of the radio spectrum was effectively utilized in radar designs during the recent war and it has become of increasing interest in the field of communications. Work in this field has led to an important use for silicon—that of the point contact rectifiers†1 in the frequency converter of microwave (radar or radio) receivers—and has stimulated considerable interest in the electrical properties and preparation of silicon and its alloys. Silicon is an electronic semiconductor. Its conductivity at room temperature results principally from the presence of certain impurities. While for metals an increase in impurity content increases the resistivity, for semiconductors such as silicon the opposite occurs and, in general, the addition of impurities lowers the resistivity. Silicon materials may be classified into one of two groups depending upon the manner in which the impurities contribute to electrical properties. These have been termed for convenience p-type or n-type. P-type silicon develops a very large positive thermal emf against metals, has a Hall coefficient of positive sign and a low resistance direction in point contact rectification with the silicon positive with respect to the point. N-type silicon, on the other hand, develops a negative thermal emf against metals, has a Hall coefficient of negative sign and a low resistance direction in rectification with the silicon negative with respect to the point. Impurities which produce n-type silicon are called donors inasmuch as these elements contribute to electrical conductivity by donating electrons to an unfilled energy band in the silicon. On the other hand, elements which produce p-type silicon are known as acceptors as these impurities contribute to the electrical conductivity by accepting electrons from a filled energy band permitting what is known as conductivity by "holes" in which the sign of the carriers appears to be positive. A general treatment of the mechanism of conduction in semiconductors from the viewpoint of modern band theory has been given recently by Pearson,2 by Becker, Green and Pearson,3 and by Torrey and Whitmer.4 In this investigation boron and aluminum have been found to be acceptors, and phosphorus, arsenic, and antimony to be donors in silicon. Data on the effect of boron and phosphorus on the electrical properties, when present singly and in combination, have been acquired. These data are discussed in the present paper. Raw Materials Used and Methods for Adding Seeond Constituents Silicon from two sources was used in this work and these will be referred to as A and B respectively. Silicon A is a material of high purity supplied by the Electro Metallurgical Co. It is prepared by chemical purification of "commercial" silicon obtained from the arc furnace reduction of SiO2. It contains 99.8 pct silicon, minimum, with small amounts of calcium, iron, aluminum, boron, and phosphorus as the principal impurities. This material was extensively employed in these studies as well as in the commercial preparation of rectifier materials. Silicon B is a material of high purity from the du-Pont Co. It is prepared by a pyrolytic reduction of Sicl4 and is free of analytically detectable amounts of boron and phosphorus. Its use permitted study of the effect of boron and phosphorus individually on the properties. This material contains, however, spec-troscopic traees of a number of metals, some of which affect electrical and rectification properties. Typical analyses for the two grades of silicon are given in Table 1. To make controlled additions of boron to the charge it was necessary to employ a low boron content master alloy since the quantity of boron to be added was usually only a few thousandths of one percent. The alloy containing nominally one percent boron was prepared by melting chemically pure boron with silicon A using the melting techniques for 320 g silicon

Jan 1, 1950

By Charles R. Holmes

MORE than 70 igneous pipes and dikes are known to occur in Cambrian sediments throughout an approximately circular area of about 75 sq miles in southwestern Ste. Genevieve County and southeastern St. Francois County, Mo., across the southern portion of the Farmington anticline, which is outlined in fig. 1. From evidence obtained from fossil fragments taken from some of the in-trusive~, and from the similarity in composition of the more basic intrusives to those of known age in surrounding states, these pipes and dikes are believed to be at least post-Devonian and probably Cretaceous in age. As first postulated by Rust,' these intrusives are believed to represent explosion tubes, or diatremes, punched through great thicknesses of solid rock by gaseous pressure. The particular intrusive studied is located about 1 mile north of the small town of Avon at an elevation of 880 ft in the EVz SEy4 NEY4 of see. 2, T. 35N, R. 7E. Outcrop is through the Bonneterre dolomite in two separated exposures. The larger outcrop extends east and west for about 50 ft along a tributary in a small ravine (fig. 2). The smaller exposure occurs as a few scattered patches over an area 20 ft square about 100 ft to the north. The area between the exposures is covered, but scattered patches of the Bonneterre dolomite outcrop throughout the area surrounding the diatreme. Where exposed, contact relations show the surrounding dolomite to be shattered and metamorphosed to a fine-grained rock for a distance of 15 to 20 ft from the intrusive. The igneous rock occurs as a dark greenish-gray porphyry near the center of the diatreme and as a fine-grained, greenish-gray material containing lapilli and metamorphosed fragments of dolomite near the contact with the country rock. The most abundant original mineral of the porphyritic rock is olivine now largely serpentinized as the result of extensive hydrothermal alteration at time of emplacement. The most common constituent of the fine-grained rock, which occurs near the border of the intrusive, is calcite. Mica is a common constituent of both types of rock, occurring as tufts or flakes. Magnetite makes up about 2 pct of the diatreme and occurs as small irregular grains or streaks of tiny grains. Singewald and Milton' have termed the rock of this body an "augite-free alnoite." Susceptibility measurements of pulverized specimens were made from selected samples taken from both the diatreme and the surrounding country rock. The susceptibility of the Bonneterre dolomite was found to be less than 40xlO-6 cgs (centimeter-gram-second) units and that of the metamorphosed contact dolomite less than 200x10-6 cgs. Measurements of individual samples of the igneous rock showed a wide variation in susceptibility between limits of 1000x10-6 cgs to 8000x10-6 cgs, with the maximum difference occuring in samples taken only a few feet apart. The maximum value was exhibited by a highly weathered sample taken from the northern outcrop, while minimum susceptibility was determined from a partially weathered sample taken only a few feet away. These extremes are believed to represent small local concentrations of stringers and grains of magnetite crystals in the igneous rock. A detailed magnetic survey of the horizontal and vertical components of the earth's magnetic field was made over the diatreme area. Stations were occupied at 20-ft intervals as shown by the grid on fig. 2. When greater detail was desired, intervening stations were also occupied. The field instruments were supplied by the Department of Geophysics, St. Louis University. The magnetometers are the Schmidt balance type constructed by the Ruska Instrument Co. These instruments are temperature compensated and have a standard sensitivity of 10 gamma. Calibration of the instruments

Jan 1, 1951

By S. T. Wlodek, John Wulff

Dense, adherent, and ductile coatings of chromium can be applied to Molybdenum by selectively freezing out the chromium solute from a supersaturated copper-or tin-rich liquid alloy. The successful exploitation of this technique depends on the control of variables common to any freezing process. Under the most favorable combimtion of supersaturation, nucleation, and mass-transfey, coatings as thick as 0.004 in. can be obtained. In exploratory experiments it was found that a coating of chromium may be applied to molybdenum by immersing the molybdenum body in a supercooled copper-chromium or tin-chromium melt and selectively freezing out the contained chromium onto the molybdenum body. Supercooling of the liquid metal plating bath can be achieved by cooling, or the maintenance of thermal or concentration gradients in the melt. The technique is similar to conventional dip-plating procedures where the sample is immersed in a molten bath of the pure plating medium, except that in these studies, the plating medium consisted of a dilute solution of chromium in liquid tin or copper. The success of this method requires that the base material to be plated be isomorphous with the coating and insoluble in the plating bath. In addition, the plating bath, while having an appreciable solubility for the coating component, must have negligible solid solubility in the solid plate. Such relationships exist in the molybdenum-chromium, chromium-tin, and chromium-copper systems. Liquid tin and copper are satisfactory as the plating solvent, because although chromium is appreciably soluble in both of these liquid metals, solid inter-solubility is almost negligible, and no compound formation occurs. The same relationships exist between molybdenum and copper or tin except that the solubility of molybdenum in liquid tin or copper is insignificant. It is this combination of solubility relationships, as well as the completely isomorphous nature of the molybdenum-chromium system, which allows the formation of a chromium coating on molybdenum by the selective freezing mechanism. Since the main deterrent to the widespread use of molybdenum for high-temperature structural applications is its poor oxidation resistance, the formation of a dense and ductile chromium coating on molybdenum may well be of commercial significance. In addition, the basic principle of coating formation by selective freezing should be applicable to other metallic or even nonmetallic systems. The precipitation of the solute from a liquid metallic solution, for the formation of a protective coating, has not been previously considered in the literature. Frequently, however, a similar phenomenon has been described in the corrosion of metallic heat exchangers by liquid metals1 wherein temperature gradients in the liquid metal heat-transfer medium result in the formation of layers or deposits of metallic residue2 in the cooler portions of the system. Impregnating techniques using liquid baths have been tried as a plating process. Semchyshen and Barr, for instance, have successfully diffused chromium into molybdenum by immersing the molybdenum specimen in a liquid tin-chromium or copper-chromium alloy. This simple holding technique fails to produce a layer of pure chromium and requires prolonged immersion to allow for the diffusion-activated enrichment of the molybdenum. During the course of this investigation, most of the phase relations published for the copper-chromium4 and molybdenum-chromium4 systems, were found reliable. It was necessary, however, to investigate the solubilities of chromium and molybdenum in liquid tin as well as the solubility of molybdenum in liquid copper. These determinations were made by a simpie weight loss technique on materials of the same purity as used in the plating studies. The results of these solubility studies are given in Tables I and I1 and indicate that although the solubility of molybdenum in liquid

Jan 1, 1961

By Charles R. Holmes

MORE than 70 igneous pipes and dikes are known to occur in Cambrian sediments throughout an approximately circular area of about 75 sq miles in southwestern Ste. Genevieve County and southeastern St. Francois County, Mo., across the southern portion of the Farmington anticline, which is outlined in fig. 1. From evidence obtained from fossil fragments taken from some of the in-trusive~, and from the similarity in composition of the more basic intrusives to those of known age in surrounding states, these pipes and dikes are believed to be at least post-Devonian and probably Cretaceous in age. As first postulated by Rust,' these intrusives are believed to represent explosion tubes, or diatremes, punched through great thicknesses of solid rock by gaseous pressure. The particular intrusive studied is located about 1 mile north of the small town of Avon at an elevation of 880 ft in the EVz SEy4 NEY4 of see. 2, T. 35N, R. 7E. Outcrop is through the Bonneterre dolomite in two separated exposures. The larger outcrop extends east and west for about 50 ft along a tributary in a small ravine (fig. 2). The smaller exposure occurs as a few scattered patches over an area 20 ft square about 100 ft to the north. The area between the exposures is covered, but scattered patches of the Bonneterre dolomite outcrop throughout the area surrounding the diatreme. Where exposed, contact relations show the surrounding dolomite to be shattered and metamorphosed to a fine-grained rock for a distance of 15 to 20 ft from the intrusive. The igneous rock occurs as a dark greenish-gray porphyry near the center of the diatreme and as a fine-grained, greenish-gray material containing lapilli and metamorphosed fragments of dolomite near the contact with the country rock. The most abundant original mineral of the porphyritic rock is olivine now largely serpentinized as the result of extensive hydrothermal alteration at time of emplacement. The most common constituent of the fine-grained rock, which occurs near the border of the intrusive, is calcite. Mica is a common constituent of both types of rock, occurring as tufts or flakes. Magnetite makes up about 2 pct of the diatreme and occurs as small irregular grains or streaks of tiny grains. Singewald and Milton' have termed the rock of this body an "augite-free alnoite." Susceptibility measurements of pulverized specimens were made from selected samples taken from both the diatreme and the surrounding country rock. The susceptibility of the Bonneterre dolomite was found to be less than 40xlO-6 cgs (centimeter-gram-second) units and that of the metamorphosed contact dolomite less than 200x10-6 cgs. Measurements of individual samples of the igneous rock showed a wide variation in susceptibility between limits of 1000x10-6 cgs to 8000x10-6 cgs, with the maximum difference occuring in samples taken only a few feet apart. The maximum value was exhibited by a highly weathered sample taken from the northern outcrop, while minimum susceptibility was determined from a partially weathered sample taken only a few feet away. These extremes are believed to represent small local concentrations of stringers and grains of magnetite crystals in the igneous rock. A detailed magnetic survey of the horizontal and vertical components of the earth's magnetic field was made over the diatreme area. Stations were occupied at 20-ft intervals as shown by the grid on fig. 2. When greater detail was desired, intervening stations were also occupied. The field instruments were supplied by the Department of Geophysics, St. Louis University. The magnetometers are the Schmidt balance type constructed by the Ruska Instrument Co. These instruments are temperature compensated and have a standard sensitivity of 10 gamma. Calibration of the instruments

Jan 1, 1951

By R. E. Ogilvie, N. L. Peterson

Diffi-lsion measurements were conducted at all compositims in the bcc solid solution of the U-Nb system employing incremental couples at composition intemals of 10 at. pct. Diffusion coefficients were determined by the Matano method from concentration gradients obtained with the electron-probe microanalyzer. The activation energy for inter-diffi-lsion as a function of compositim shows three distinct regions: 1) 80 to 100 pct U.6= 30 kcal per mole; 2) 20 to 80 pct U, $ - 70 kcal per mole; 3) Oto 20 pet U, Q = i40 kcal per mole. The frequency factor, fi0 and the activation energy $ were found to be roughly related by the following equation: log Do ^9.7 X IO-5Q -6,6. The Kirkendall marker movement indicates that DU is larger than DNb between 16 and 100 pct U and DNb is larger than DU from 0 to 4 pct U. FOR practical as well as fundamental reasons, the rates of diffusion in alloys are of considerable consequence. Most solid-state reactions are largely dependent upon the diffusion of atoms through the lattice structure and along grain boundaries. The high-temperature strength and reasonable nuclear properties of niobium have prompted its use as a reactor material in contact with uranium fuel. Hence, diffusion data for the U-Nb system are of considerable importance. In the previous diffusion study1 on the U-Nb system using pure element couples, reliable data were obtained only in the range of 0 to 10 at. pct Nb due to the large variance of the diffusion coefficient with composition. Also, a large Kirkendall effect and considerable porosity in the uranium-rich areas of the specimen were reported, which suggests that the true diffusion coefficients are somewhat larger. The purpose of the present study was to obtain reliable diffusion coefficients at all compositions using incremental diffusion couples with intervals of 10 at. pct. In view of the abnormal self-diffusion be- havior of y uranium2-4 and some other bcc transition elements,&apos;-&apos; it was felt that a comparison of the interdiffusion coefficients in the bcc U-Nb system with those of Reynolds et al.9 for the fcc gold-nickel system might shed some light on the diffusion mechanism involved. Both systems have similar phase diagrams, in that complete solid solubility exists above a miscibility gap. EXPERIMENTAL PROCEDURE The uranium used in this investigation was obtained through the courtesy of Argonne National Laboratory. An analysis of this material detected only Si-30, A1-7, C-6, N < 10 and 0-18 ppm. The niobium was electron-beam melted material obtained from Stauffer-Temescal. The gaseous impurities were less than 50 ppm, and the spec troc hemical analysis showed Ta-500 and W-200 ppm. U-Nb alloys were prepared at composition intervals of 10 at. pct by melting the appropriate amounts of the pure elements in an arc furnace. The buttons were inverted and remelted 6 times to assure complete mixing. The buttons were then wrapped in molybdenum foil, canned in Zircaloy-2 or stainless steel, and hot rolled 30 pct reduction in thickness at temperatures between 850" and 1100°C. Alloys with 10, 20, 30, 40, and 90 at. pct Nb rolled quite easily under these conditions, but the 50, 60, 70, and 80 pct alloys remained brittle. After melting and rolling (when possible), the alloys were annealed for 24 hr at a temperature within 100°C of their melting point in a dynamic vacuum of better than 4 x 10-8 mm Hg. These treatments produced alloys which were homogeneous on a 1 p scale within the detectability limits of the electron probe. During fabrication, the alloys picked up as much as 100 ppm Mo and 100 ppm Zr. Other elements checked for but not found were Co, Cr, Fe, Mn, Ni, and Ti. The grain size of the annealed samples ranged from 3 mm for the uranium-rich alloys to 0.3 mm for the niobium-rich alloys. This permitted measurements of the concentration gradients in the diffusion samples without crossing more than one or two grains, thereby eliminating any grain boundary effects. The specimens were bonded by theU&apos;picture frame" technique as reported by Kittel.10 Specimens of composition b)U + (100 - x)Nb were sandwiched between two specimens of composition (x + 10)U + (90 - x)Nb after they were ground flat and parallel

Jan 1, 1963

By I. R. Kramer

Studies of the effect of size of the specimen on the change of slopes of Stages I and 11 by surface removal showed that the change of Stage I was independent of size with respect to the polishing rate; however, the change in the slope of Stage 11 with polishing rate increased directly in proportion to the surface area. The removal of the surface during the test affected the plastic deformation characteristics of gold, aluminum, and zinc single crystals and polycrystalline aluminum. The apparent activation energy of aluminum was found to be decreased markedly by removing the surface during the deformation process. In previous papers1-3 it was shown that the surface played an important role in the plastic deformation of metals. By removing the surface layers of a crystal of aluminum by electrolytic polishing during tensile deformation, it was found that the slopes of Stages I, II, and III were decreased and the extents of Stages I and II were increased when the rate of metal removal was increased. By removing a sufficient amount of the surface layer after a specimen had been deformed into the Stage I region, upon reloading, the flow stress was the same as the original critical resolved shear stress and the extent of Stage I was the same as if the specimen had not been deformed previously. The slope of Stage I was decreased 50 pct and that of Stage 11 decreased 25 pct when the rate of metal removal was 50 X 10"5 ipm. These data show that in Stage I the work hardening is controlled almost entirely by the surface conditions, while in Stages 11 and III both surface conditions and internal obstacles to dislocation motion are important. It appears that during the egress of dislocations from the crystal, a fraction of them becomes stuck or trapped in the surface regions and a layer of a high dislocation concentration is formed. This layer would not only impede the motion of dislocations, but would provide a barrier against which dislocations may pile up. In this case, there will be a stress, opposite to that of the applied stress, imposed on the dislocation source and dislocations moving in the region beyond this layer. It has been found convenient to refer to this layer as a "debris" layer. The "debris" layer may be similar to the dislocation tangle observed by thin-film electron microscope techniques.4 Reported in this paper are the results of studies on the effects of removing the surface during plastic deformation on aluminum crystals of various sizes. The effects of the surface on the yield point behavior of gold and high-purity aluminum crystals as well as the creep behavior were also determined. The effects of surface removal on polycrystalline aluminum (1100-0 and 7075-T6) are also reported. EXPERIMENTAL PROCEDURE For those portions of the investigation involving creep and tensile specimens, single crystals, having a 3-in. gage length and a nominal 1/8-in. sq cross section, were prepared by a modified Bridgman technique using a multiple-cavity graphite mold. The single crystals were prepared from materials which had initial purities of 99.997, 99.999, 99.999, and 99.999 pct for Al, Cu, Zn, and Au, respectively. The aluminum specimens for the size effect studies were prepared through the use of a three-tier mold in which crystals having a cross section of 1/8, 1/4, and 1/2 in. were grown from a common seed. The mold design was arranged so that one 1/2-in. crystal, two 1/4-in. crystals, and four 1/8-in, crystals of the same orientation could be cast. With this technique, it was possible to obtain only one set of crystals with the same orientation. Because of this limitation, it was not possible to determine both the changes of extent and slope of the various stages since a large number of crystals of the same orientation would have been required. Instead, only the change of slope as a function of the rate of metal removal was studied by abruptly altering the current density of the electrolytic polishing bath at various strains within the regions of Stages I and 11. The experimental techniques used for the tensile studies were essentially the same as those used previously.1,3 The specimens were deformed in a 200-lb Instron tensile machine, usually at a rate of 10-5 sec-5. A methyl alcohol-nitric acid solution was used as the polishing bath for aluminum. The temperature was maintained constant within ±0.l°C by means of a water bath. The tensile machine was

Jan 1, 1963

By A. M. Gaudin

Activation of sphalerite with silver ions results from the exchange of two Ag ions for one Zn ion in the sphalerite lattice. The exchange is proportional to the logarithm of time and proceeds until either of the reactants is consumed. Sodium cyanide prevents the activation of sphalerite by controlling the ratio [Zn++]/[Ag+]&apos; in solution. If sphalerite has already been activated with excess silver, cyanide ions can deactivate sphalerite provided oxygen is present. SOLUBLE: silver salts are effective activators for flotation of sphalerite with potassium ethyl xan-thate as collector.* Since sphalerite takes up large quantities of silver ions rapidly,2-4 investigation of this system appeared fruitful for studying the mechanism of sphalerite activation and deactivation. Experimental data presented here comprise studies of the mechanism and rates of activation and deactivation of sphalerite with silver and cyanide ions. A 20-lb sample of sphalerite from Ottawa County, Oklahoma, was handpicked, crushed, screened, hy-drosized to produce a 65/100-mesh fraction, and purified by electrostatic separation. The sphalerite was then leached with benzene and absolute ethyl alcohol to remove possible organic contaminants and with 0.1 M NaCN to remove any copper that might have been picked up during screening. The benzene had been specially purified by grinding with fine sphalerite for 12 hr to remove trace impurities that might have had a specific affinity for sphalerite. Ii&apos;inally, the mineral was washed, dried in flowing nitrogen, and stored in large ground-glass stoppered weighing bottles under a small nitrogen pressure. The specific surface of two samples from the 65/100-mesh sphalerite stock, measured by krypton gas adsorption," was 420 cm2 per g. Compared with spheres of the same size and specific gravity, the prepared mineral had five times as much surface. Results of a wet chemical analysis and of a spectro-graphic study are given in Table I. Manganese, nickel, tin, indium, thallium, cobalt, and magnesium were not detected spectrographically. All solutions were preparid by -adding reagent-grade chemicals to conductivitv water. which had been previously saturated with the desired gases. Nitrogen and oxygen were purified, but no attempt was made to purify the laboratory air. Radioanalysis was carried out with prepurified Ag110 tracer obtained from the Oak Ridge National Laboratory. The complete decay scheme for Ae is complex. Its primary emissions are 0.09 and 0.55 mev ß rays and 1.48 mev y raysB and its half-life is believed to be 270 days. In preparation of solutions of AgNO3, the amount of Ag110 added was negligible compared to that of the inert silver. Abstraction of silver from solution by sphalerite was measured after agitation of 1.5 g sphalerite with 20 ml of solution in 50-ml pyrex flasks. All sample preparations were carried out in a dry box so that the proper atmosphere could be maintained. After the mineral had been agitated in the silver nitrate solution, an aliquot of the solution and a sample of the wet mineral were transferred to separate counting vials and weighed. The solid sample was dried and re-weighed and the activity in both vials measured by means of a scintillation counter. With scintillation counting it is possible to count y radiation from the solid and liquid, a distinct advantage over the older ß-ray counting techdiques.4 All measurements of silver activity were made using a sodium-iodide well-type scintillation counter. The amount of zinc in solution was measured colorimet-rically by the monocolor method of Sandell.7 Activation Studies Exchange Between Zinc Ions and Silver Ions During Activation: The increase of Zn++ in solution during activation with Ag+ is shown in Table 11. These data indicate a replacement of one Zn++ by two Ag+. Analysis of a separate two-month agitation test indicated that the replacement of Zn++ by Ag+ was, as expected, in the molar ratio of 2.0.

Jan 1, 1958

By W. L. Phillips

Single crystals of aluminum, brass, and copper oriented for (100) and (110) slip were extended at 25°, 400°, and 600°C in simple shear. Aluminum specimens oriented for nonoctahedral slip began to shear at a higher critical resolved shear stress than specimens oriented for octahedral slip. Parabolic stress-strain curves were obtained from zero strain. The initial rate of parabolic hardening was lower for specimens sheared on the (100) plane in a close-packed direction <110>, than for specimens sheared in a nonclose-packed direction <100>. metallographic evidence, however, showed that all slip traces could be explained in terms of (111) <100> slip. All attempts to cause nonoctahedral slip in copper and 70-30 a-brass single crystals were unsuccessful. Instead of shearing, the crystals bent, allowing {111} type planes to come into action. NONOCTAHEDRAL slip in aluminum has been reported under three different conditions: first, as the main mode of slip in tension experiments at elevated temperatures;&apos;-&apos; second, as the main mode of slip in direct shear experiments at room temperat~re; and third, as a minor mode of deformation, i.e., as cross-slip, in tension, shear, and bicrystal experiments at room and elevated temperatures."-l2 However, as far as the author knows, nonoctahedral slip has not been reported in either copper or 70-30 a-brass. The present study was undertaken to determine whether nonoctahedral slip could be obtained in aluminum, brass, or copper at room or elevated temperatures when the shear stress was approximately constant over the cross-section, a maximum at the center, or a maximum at the surface. EXPERIMENTAL PROCEDURE A detailed description of the crystal preparation and shearing apparatus has been given previo~sly. Cylindrical crystals 1/2 in. in diam and 8 in. long were grown from the melt in a temperature-gradient furnace. The aluminum contained 0.001 pct Zn, 0.001 pct S, and 0.001 pct Fe; the 70-30 brass contained 0.015 pct Pb, 0.001 pct Fe, 0.01 pct Ni, 0.02 pct Sn, and 0.005 pct Se; the copper was certified OFHC of 99.98 pct purity. All samples were electropolished prior to testing. The shear apparatus was a modified Bausch type. The strain sensitivity was 4 x lob4 Load was applied by clamping the rods attached to the shear plates in an Instron tensile machine. The rate of loading was 0.02 in. per min. In all cases a 1/8-in. gage length was used. For the tests performed at 400° and 600°C the shear plates, collars, and rods were made of stainless steel. These elevated-temperature tests were performed in an argon atmosphere. A) Aluminum at Room Temperature. Values of a and ß for the various slip planes and slip directions investigated are shown in Table I where a is the complement of the angle between the specimen axis and the slip direction, and ß is the angle between the specimen axis and the normal to the shear plane. The shear stress is a function of a (assuming ß - 0);10 when a is less than 27 deg, the shear stress on the slip plane for which the specimen is oriented has a maximum at the center of the crystal; at a = 27 deg the shear stress is constant across the slip plane; for a greater than 27 deg the shear stress is a minimum at the center. Fig. 1 shows the stress-strain curves for specimens cut from crystals 1, 2, and 5, which were sheared on the (010) plane in the [loll direction at room temperature. These three crystals have shear-stress distributions corresponding to the three dif-

Jan 1, 1962

By Takashi Katsura, Avnulf Muan

Equilibrium relations in the system FeO-Fe2O3 Cr2O3 have been determined at 1300°C at oxygen pressures ranging from that of air (0.21 atm) to 1.5 x 10-11 atm. The following oxide phases have stable equilibrium existence under these conditions : a sesquioxide solid solution with corundum-type structure (approximate composition Fe2O3-Cr2O3); a ternary solid solution with spinel-type structure (approximate composition FeO Fe2O3-FeO Cr2O3) and a ternary wüstite solid solution with periclase-type structure and compositions approaching FeO. The metal phase occurring in equilibrium with oxide phase(s) at the lowest oxygen pressures used in the present investigation is almost pure iron. The extent of solid-solution areas and the location of oxygen isobars have been determined. ThE system Fe-Cr-O has attracted a great deal of interest among metallurgists as well as ceramists and geochemists. Metallurgists have studied the system because of its importance in deoxidation equilibria, ceramists because of its importance in basic brick technology, and geochemists because of its importance for an understanding of natural chromite deposits. Chen and chipman1 investigated the Cr-O equilibrium in liquid iron at 1595°C in atmospheres of known oxygen pressures (controlled H2O/H2 ratios). The main purpose of their work was to determine the stability range of the iron-chromite phase. Hilty et al.2 studied oxide phases in equilibrium with liquid Fe-Cr alloys at 1550°, 1600°, and 1650°C. They reported the existence of two previously unknown oxide phases, one a distorted spinel with composition intermediate between FeO Cr203 and Cr3O4, the other Cr3O4 with tetragonal structure. They also sketched diagrams showing the inferred liqui-dus surface and the inferred 1600°C isothermal section for the system Fe-Cr-O. Koch et al3 studied oxide inclusions in Fe-Cr alloys and also observed the distorted spinel phase reported by Hilty et al. Richards and white4 as well as Woodhouse and White5 investigated spinel-sesquioxide equilibria in the system Fe-Cr-O in air in the temperature range of 1420" to 1650°C, and Muan and Somiya6 delineated approximate phase relations in the system in air from 1400" to 2050°C. The present study was carried out at a constant temperature of 1300° C and at oxygen pressures ranging from 0.21 atm (air) to 1.5 x 10-11 atm. The chosen temperature is high enough to permit equilibrium to be attained within a reasonable period of time within most composition areas of the system, and still low enough to permit use of experimental methods which give highly accurate and reliable results. These methods are described in detail in the following. I) EXPERIMENTAL METHODS 1) General Procedures. Two different experimental methods were used in the present investigation: quenching and thermogravimetry. In the quenching method, oxide samples were heated at chosen temperature and chosen oxygen pressure until equilibrium was attained among gas and condensed phases. The samples were then quenched rapidly to room temperature and the phases present determined by X-ray and microscopic examination. Total compositions were determined by chemical analysis after quenching. In the thermogravimetric method, pellets of oxide mixtures were suspended by a thin platinum wire from one beam of an analytical balance, and the weight changes were recorded as a function of oxygen pressure at constant temperature. The data thus obtained were used to locate oxygen isobars. The courses of the latter curves reflect changes in phase assemblages and serve to supplement the observations made by the quenching technique. 2) Materials. Analytical-grade Fe2O3 and Cr2O3 were used as starting materials. Each oxide was first heated separately in air at 1000°C for several hours. Mixtures of desired ratios of the two oxides were then prepared. Each mixture was finely ground and mixed, and heated at 1250" to 1300°C in air for 2 hr, ground and mixed again and heated at the same temperature for 5 to 24 hr, depending on the Cr2O3 content of the mixture. A homogeneous sesquioxide solid solution between the two end members resulted from this treatment. A Part of some of the sesquioxide samples thus prepared was heated for 2 to 3 hr at 1300°C and oxygen pressures of 10-7 or 1.5 x 10-11 atm. Reduced samples (either iron chromite

Jan 1, 1964

By A. Steiner, K. L. Komarek

Activities of aluminum in solid Ni-A1 alloys have been determined between 20 and 60 at. pet Al and 1200" and 1400°K by an isopiestic method in which nickel specimens, heated in a temperature gradient, are equilibrated with aluminum vabor in a closed all-alumina system. The activity of aluminum shows a strong negative deviation from Raoult&apos;s law at low concentrations but increases by three orders of magnitude within the ß(NiAl) phase. The partial molar enthalpy and entropy of mixing are negative. Using Wagner and Schottky&apos;s theory of ordered compounds, a degree of disorder of 4 x 10 -4 for NiAl and 1.25 X 10-2 for FeAl has been calculated THE Ni-A1 system has been studied by a great number of investigators, and the results, as far as the phase diagram is concerned, have been compiled by Hansen.1 The phase boundaries from 0 to 50 at. pet Ni are well-established. At higher nickel contents the boundaries are still in dispute and an additional phase, A12Ni3, has been reported.&apos; The phase diagram is dominated by a very stable high-melting compound, NiA1, with a relatively wide range of homogeneity. Heats of formation of solid alloys have been determined calorimetrically by Oelsen and Middel3 from 20 to 95 at. pet Ni and by Kubaschewski4 from 25 to 80 at. pet Ni. According to the most recent compilation5 no other thermodynamic investigations have been reported for the Ni-A1 system. Due to the corrosive nature and the low vapor pressure of aluminum, a method has been employed for determining activities of aluminum which was previously developed for the Fe-A1 system.= Nickel specimens, heated in a closed evacuated alumina system in a temperature gradient, were equilibrated with aluminum vapor from a source within the system kept at constant temperature. After complete equilibration the specimens were analyzed and activities calculated from the known vapor pressure of aluminum. APPARATUS AND EXPERIMENTAL PROCEDURE Materials. The nickel specimens were made from wafers of electrolytic nickel (International Nickel Corp.) of 99.99 pet purity which were rolled to a 0.001-in.-thick foil by Driver-Harris Co. and to a 0.005-in.-thick sheet in our laboratory. The aluminum (Aluminum Corp. of America) had a purity of 99.99+ pct. The alumina tubes and crucibles were made of impervious recrystallized alumina with an alumina content of 99.7 pet (Triangle RR, Mor-ganite Inc.). Experimental Procedure. Annular specimens were punched from the sheet, the punching burrs removed, and the specimens degreased in carbon tetrachloride and acetone and weighed on a micro-balance to within an accuracy of ±0.01 mg. The specimens were positioned with alumina spacers along an alumina tube, and the positions measured. Aluminum metal was machined into cylindrical shape, and placed into an alumina crucible. The tube with the specimens was then inserted into a hole drilled into the aluminum metal. An alumina tube with its closed end at the top was slipped over the specimens so that its lower end fitted snugly into the alumina crucible. The assembled reaction tube was inserted into a mullite tube with a water-cooled brass head which had an opening for a quartz thermocouple protection tube and a metal-to-glass connection to a conventional vacuum system. A Pt-Pt 10 pet Rh thermocouple could be raised and lowered in the quartz tube which was placed along the outside of the alumina reaction tube. The mullite tube was heated by two separately controlled resistance-tube furnaces so that in the experimental temperature range an over-all temperature gradient of approximately 150o to 250°C could be imposed on the reaction tube. The position of the mullite tube was adjusted so that the surface of the aluminum metal was always at the temperature minimum. The reaction tube was thoroughly evacuated before and during slowly heating the assembly up to the melting point of aluminum. A pressure of less than 2 µ (Hg) was maintained during an experiment. Once the aluminum had melted, it isolated the contents of the alumina tube from the surroundings. Several times during an experiment the temperature gradient was carefully measured. An experiment lasted from 3 to 6 weeks and it was terminated by air cooling the evacuated mullite tube. For further details of the experimental procedure the paper on the Fe-A1 system6 should be consulted.

Jan 1, 1964

By R. T. DeHoff, F. N. Rhines

The problem of determining the number of particles of a phase distributed randomly in unit volume c an opaque matrix from measurements made on random plane sections is closely investigated. A formalized derivation for the general case is presented. Applications of this formal result are made to specific types of aggregates dispersed in a matrix; circles, particles with flat circular ends, cylinders, and constant shape aggregates of ellipsoids of revolution. Quantitative measurements of the average geometric properties of these aggregates are developed. In 1953 R L. ullman&apos; developed a technique for determining, from measurements made on random plane sections, the number per unit volume, Nv, of particles imbedded in an opaque matrix. Using meas urements previously developed for volume fraction, vV,&apos; and surface area per unit volume, .SV,= he was able to determine average volume, average surface area, and average dimensions of particles, independent of size distribution, for spheres and circular disks,&apos; as well as for uniformly sized cylinders of any axial ratio.4 The technique is mathematically rigorous for the cases studied. Recent studies of this problem have yielded rigorous solutions for the general case of cylinders, permitting evaluation of NV independent of size distribution and with all axial ratios intermixed. Generalization to shapes having flat, circular ends has been deduced. A solution has also been obtained for the ellipsoid of revolution, independent of size distribution, but requiring a constant axial ratio in the generating ellipses. In the following derivations, as in Fullman&apos;s work, it is assumed that the problem is purely a combination of geometry and probability theory,that is,eithe the particles to be measured are imbedded randomly in the matrix, or a sufficient number of random plane sections are taken to make the sample representative. A relationship exists between the number of par- ticles of a given size and shape that may be situated in unit volume (Ny) and the number of intersections a random plane can be expected to make with these particles (Na). It is the purpose of the following section to derive this relationship. The probability of Intersecting Convex Bodies. Consider a convex, closed surface, that is, one for which no two surface normals point in the same direction, situated at some arbitrary position and orientation in a cube of material that is one unit long at each edge. It is not necessary to assume that this surface is symmetrical. Let planes be constructed in the cube parallel to the top face and at random distances from it. Those planes which lie between the two planes which are just tangent to the top and bottom of the surface will intersect it. The probability that a plane will intersect the body may be defined as the limit of the fraction of planes that lie between the two tangent planes as the total number of planes constructed becomes infinite. This fraction, in the limit, is equal to the distance between the two tangent planes, DV, divided by the total length over which planes are constructed, which has been taken as unity. If the body is now rotated to a new orientation, applying the same argument, the probability of intersection is again numerically equal to the distance between tangent planes. Let DV ($, 0) be defined as the distance between tangent planes of a convex body as a function of orientation, Fig. 1. The probability, Pr, of intersecting the body with a randomly oriented and randomly positioned plane, is then equal to the average value of DV (0, $) over all possible orientations. It may be easily shown that for a system of spherical coordinates the probability of finding an orientation between Q and Q + de, $ and $ + d$ is (1/4n) sin $ dB d$, so that This relationship may be applied to each body in an aggregate of convex bodies. In particular, if the bodies in an aggregate are classified according to size and shape, and the ithsuch class is considered, Eq. 111 may be applied to this entire class, the probability of intersecting any body in this class being

Jan 1, 1962