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By F. Weinberg

The distribution of solute during the progressive solidification of dilute Sn-Ag alloys was determined in both solid and liquid as a jbnction of growth rate, rod diameter, temperature gradient, and solute concentration, using radioactive tracer techniques. The results indicated that partial mixing occurs in the liquid during freezing for most of the conditions investigated, approaching complete mixing for larger rod diameters (>2mm) and slow growth rates. Measured solute distributions were fitted to distribution functions based on diffusion controlled solute transport in the liquid state, by treating the normal solute diffusion constant and distribution coefficient as variable solute transport and segregation parameters. Values of these parameters were determined for the growth conditions investigated. Observations were made to determine whether mixing in the liquid was primarily due to volume changes in freezing or to differences in density between solute and solvent. The former effect was investigated using a selected Sn-Bi alloy as a solvent with zero volume change on fusion, and the density effect was studied using vertical solidifications of Sn-In and Sn-Ag alloys, systems having, respectively, very small and large differences in density between solute and solvent. The result indicate that mixing in the liquid cannot be primarily attributed to either volume changes or density differences. THE solute distribution in progressively solidified rods of dilute alloys, in which there is complete mixing in the liquid, is given by the expression1 where C, is the solute concentration in the solid at the point where the fraction g of the material has solidified, C, is the initial solute concentration and k is the equilibrium distribution coefficient. If it is assumed that there is no significant con-vective mixing in the liquid, then the solute distribution in the initial portion of a semi-infinite rod has been calculated to be2 where t is the time from the start of freezing and x1 is the distance in the liquid ahead of the solid-liquid interface at time t. Expressions [1] and [2] describe the limiting cases of solute distribution in the liquid, i.e., complete mixing, or no convective mixing; in practice it might be expected that the solute distribution would be somewhere between these two cases. pfann3 has suggested that Eq. [I] is applicable for partial mixing, as well as complete mixing, if an effective distribution coefficient k1 is used instead satisfactorily describes solute distributions in rods of magnesium, n-g, and b-sb6 alloys that were progressively solidified from the melt without mechanical mixing. The values of kl were observed to depend on the growth rate4-6 and the temperature gradient.6 The purpose of the present investigation was to measure solute distributions in both the solidified rods and the melt as a function of the solidification variables, and to determine to what extent the observed solute distributions could be described by the above theoretical expressions, keeping in mind that expressions [2] and [3] have been derived solely for the case of diffusion controlled solute transport in the liquid and are not theoretically applicable to

Jan 1, 1963

In 1934 the Southern Experiment Station of the U.S. Bureau of Mines in. cooperation with the University of Alabama began an investiga-tion of the availability of kyanite ores as a source of raw material for the manufacture of refractories. Under this program, gravity concentration and flotation tests have been made on two varieties of Georgia kyanite ore, mica schist and massive. Most of the attention has been directed to the mica schist ores, as they are more widely distributed and seem to offer greater economic possibilities than the massive ores. It is evident that the preparation of kyanite for use as a refractory material involves other considerations than the mere elimination of impurities. A concentration process that eliminates impurities satisfactorily may have to be followed by some additional treatment, since the final product must be of a coarse-ness and size ratio that will make it suitable for refractories manufacture. So far in the investigation at the Southern Experiment Station of the U.S. Bureau of Mines only the concentration problem has been considered, and this paper is intended as an interim report.

Jan 1, 1936

By M. Gensamer

THE PURPOSE OF THIS PAPER is to lay a foundation of elementary theory that might be useful in the discussions which it is hoped will be evoked during this Symposium. It is not my purpose to try to expound the details of the most complete theories as that would be impossible in the time at our disposal and, even if time were available, would probably be of less usefulness than a discussion of the principles underlying the advanced theoretical treatment. I shall try to discuss the fundamental bases for these advanced theories. There exists at the present time very much less need for a detailed description of complete theory than existed when this Symposium was being organized. The reason for this is that a series of papers by L. R. Underwood has been appearing in the magazine Sheet Metal Industries. It is understood that this series will he published soon in the form of a book. Dr. Underwood's articles are complete, critical and well written and it would be hopeless to try to do better in less space. The need, then, is for a brief treatment of basic theory. The objective of any theory of plastic forming- is to enable one to calculate the force and power requirements for the process, and where the deformation is not uniform, to calculate the distribution of strains- In the formed object. We need as the basis for the calculation the relationship between stress and strain in the metal, particularly for the combination of stresses imposed by the forming process. We need to know the stress-strain curve for some simple state of stress, and we need in addition some theory

Jan 1, 1948

By W. G. Pfann

The simultaneous segregation of two solutes during the directional solidification of an ingot is treated mathematically on the basis of simplifying assumptions. Expressions are derived for the difference in concentration of two solutes, and for the location and concentration gradient of a pn barrier formed in a semiconductor by the segregation of a donor and an acceptor. THE problem of normal segregation of a single solute during the freezing of an alloy has been treated mathematically by a number of investigators. Gulliver' showed that coring increases the quantity of eutectic above that to be expected at equilibrium, for a system having limited solid solubility and, on the basis of simplifying assumptions, calculated the fraction of eutectic to be expected. Scheuer2 expressed composition of solid solution in terms of a distribution coefficient and the fraction solidified and compared experiment with calculation for the systems A1-Cu, Al-Zn, Cu-Sn, Cu-Zn. Hayes and Chipman,3 in a detailed study of segregation in a low carbon, rimming steel ingot, calculated distribution coefficients for a number of solutes in iron, compared calculated and experimental segregation curves, and discussed the effects of process variables such as rate of solidification and stirring. In the present paper a mathematical analysis is made of the simultaneous segregation of two solutes during the orderly freezing of a solid solution system, with particular emphasis on the difference in solute concentrations. Although the analysis is quite general and can be applied to the segregation of minor elements in alloys, it is directed in particular at the solidification of a semiconductor containing a donor and an acceptor. Normal segregation has unique aspects in a semiconductor, because of the ways in which donors and acceptors affect the electrical properties. The difference between two solute concentrations becomes of importance, as does also the gradient of the difference where the difference goes through zero, this being the concentration gradient of excess carriers at a pn barrier. A primary object of this paper is to extend the mathematical treatment of segregation to include these newer aspects which are of particular significance for semiconductors. One property of interest is the electrical conduc- tivity, which arises from the presence of donors 'or acceptors in solid solution. The conductivity may be either n-type or p-type depending on whether donors or acceptors, respectively, are in atomic excess. For both germanium and silicon, elements of Group V of the Periodic System, such as P, As, and Sb, are donors and elements of Group 111, as B, Al, In, and Ga, are acceptors.4-6 If a donor or acceptor is present alone in solid solution, the conductivity is proportional to its concentration." If both a donor and an acceptor are present, then the conductivity is proportional to the difference in their atomic concentrations. If the donor and acceptor segregate at different rates then a pn barrier in certain circumstances may form at some point in the ingot. Accordingly, equations are derived and illustrated which express the effect of segregation on: 1—the concentration of a single solute with a discussion of the assumptions; 2—the difference between two solute concentrations and means for minimizing its variation in an ingot; and 3—the location and concentration gradient of a pn barrier. The analysis is applicable to processes in which the entire charge is melted and then progressively frozen from one end. The method in which an ingot is solidified in a crucible7 and that in which a solidifying rod is pulled from the melt8 both fall into this category. Segregation of One Solute If a cylinder of molten alloy is caused to freeze slowly from one end, a normal segregation of solutes will usually occur, producing a lengthwise concentration gradient in the ingot. Depending on whether a solute raises or lowers the melting point of the solvent, it will become concentrated in the first or last regions, respectively, to freeze. If it is assumed that freezing is such that there is no diffusion of solute in the solid, complete diffusion in the liquid, and that k, the distribution coefficient, defined as the ratio of solute concentration in the just-freezing solid to that in the liquid, is constant, then the

Jan 1, 1953

By C. O. Brawner

Simple, specific rules for achieving slope stability in open-pit mines are impossible to devise. Each pit has a different mining program and a different set of environmental conditions, and its final slope design must be based on an individual evaluation of the actual site. The overall philosophy of pit stability, however, is tending towards a limit design concept. Since slope angle has a great influence on the economics of most open-pit mines, efforts are being made to reduce the theoretical factor of safety for slope stability to very near 1.0. (Factor of safety is here defined as shear strength/shear stress on the most probable plane of failure.) Actually, where detailed, statistically significant testing has been done and a comprehensive ground control program is being instituted to warn of movement at an early stage, safety factors as low as 1.1 or 1.2 may be justified. The cost of the necessary procedures, however, is high. There are many factors that influence stability, but this article will be confined to three-rock structure, groundwater, and blasting.

Jan 8, 1969

By Orville R. Lyons

THE Russellton preparation plant of Republic Steel Corp., located north of Pittsburgh, Pa., prepares 395x0-in. Thick-Freeport coal by means of a 13-ft 6-in. diam Chance cone and 16 No. 7 Deister tables. The plant feed ranges between 370 and 410 tons per hr, of which approximately 31 pct is 1/4xO-in. size, and the plant reject ranges between 14 and 16 pct of the feed.

Jan 6, 1953

During the past year the Committee on Coal and Coke has been collecting data concerning various phases of the bituminous industry about which considerable misinformation has been circulated even, in some cases, through the coal trade papers. The data here presented have been compiled by various members, from the most authentic sources available and, where possible, cover the period 1913-1924. They will enable comparisons to be made within the industry, and of this and other industries, and will explain some of the differences between conditions existing now and in the prewar period. Capacity and Over-development The capacity of bituminous mines is frequently stated at figures ranging between 800,000,000 to 1,400,000,000 tons per year. Table 1 shows statistics for the industry, mainly from U. S. Geological Survey sources but partly from U. S. Coal Commission reports. Column 3 gives the mine capacity with equipment and labor as of given date, as estimated from the data published by the U. S. Geological Survey. This is calculated for each State by obtaining the total man days worked as reported by the operators (multiplying average men employed by total days worked at each mine) and dividing this figure into the total production, getting the production per man day; this figure times number of men employed times 308 (a theoretical full working year) equals estimated full-time capacity. Two major objections are made to this method—one that the total number of men employed is used, instead of the number actually working, and the other that the number of days used only deducts Sundays and five holidays. The first objection is answered by the fact that the same number of men is used in estimating capacity as is used in actual production, and while this number is always from 12 to 20 per cent. more than are actually working, this condition exists at all times, although it is worse at times of maximum output. Few coal men will agree with the conclusion that the use of 308 days is correct, as it is practically impossible to keep any mine working full time at the same daily rate of production as when it is working part time, and the opinion is

Jan 1, 1927

By G. E. McElroy

Changes in existing airway and fan-installation conditions offer the most common opportunities for effecting economical operation of mine-ventilating systems, but the largest possibilities for securing this result lie in the original design of the main airways for efficient service. Formulas, and charts for their graphical solution, are presented herewith for the determination of the elements of airways design when the conditions of service are known or may be roughly approximated. Although the analyses are made with particular reference to metal-mine airways, there is no essential difference between main airways in metal and coal mines, and the methods presented are applicable to both. Little attention is paid to designing airways for maximum economy in the ventilation of metal mines. Most of the openings used as main airways are originally designed and used for transportation and other operating purposes. Even where openings are made primarily for ventilation, the possibility of their future use for other operating purposes, or even custom alone, usually results in the selection of a size and shape similar to those of existing openings. Natural conditions, such as heavy ground, often seriously limit the size of opening that can be maintained without excessive expense; and various operating factors, such as velocity limitations on traveling roads, often dictate size requirements in excess of those required for economy in ventilation only. In metal mines the main airways are, as a rule, too small rather than too large for economic service, with the general result that the quantities in circulation are often less than the mine's proper requirements over long periods, even though excessive amounts of power are applied in an effort to remedy conditions. Increasing the area of an airway increases the cost for excavation and lining practically proportionately but at the same time affects a very rapid decrease in power requirements. The balancing of these two factors of the expense to give a minimum total yearly operating cost for ventilation is mainly a matter of proper original design of the main airways of the mine, since the large volumes handled through these parts of the system involve large power costs and thus present opportunities for effecting large savings through proper design. Many of the factors

Jan 1, 1932

The Library of the above-named Societies is open from 9 A.M. to 10 P.M. on a11 week-days, except holidays, from Sept. 1 to June 30, and from 9 A.M. to 6 P.M. during July and August. The Library contains about 55,000 volumes, including sets of technical periodicals and the publications of scientific and technical societies. Members of the Institute, with few exceptions, are forced to spend a portion of their time in localities isolated from sources of information. To these the Library can render valuable service through correspondence; letters requesting information will receive special attention. The Library is prepared to furnish references and copies of articles on mining and metallurgical subjects; to determine the existence of mining maps, and to furnish general information as to the geology and mineral resources of all countries. All communications should be made as definite as possible so that the information received may be what is desired and not include collateral matter which may not be of interest. The time spent in searching for such collateral matter will be saved, and the information will be sent more promptly and in more usable shape. The members of the Institute can be of service to the Library by for- warding copies of mining reports, maps privately issued, and similar material, which will be classified, indexed, and made available to other members. Suggestions for additions to the Library, either by purchase or personal solicitation as gifts, will be welcomed. It is hoped that members while in the city will use the Library freely, and assurance is given that most careful service will be rendered to them.

Jan 8, 1916

By P. W. Neurath, R. E. Waite

INFORMATION is available on the effect of stress on permeability, coercive force, and hysteresis for a variety of materials' but for the technically important grain-oriented 3 pct Si-Fe' the stress effects are not adequately covered in the literature; in addition, most of the stress data do not permit estimation of what would happen to the 60 cycle watt losses of the material under stress. Direct measurement of these effects therefore has been made and appears to be of considerable theoretical as well as practical interest. Losses were measured on the central 25 cm portion of 40~3~0.035 cm samples which could be stressed in a small tensile machine built for this purpose. Under tension the following effects, illustrated in the figures by a particular example, were observed: 1—"Unstrained" material of commercially acceptable loss level shows no change or a small increase in loss at low elastic stresses. For the sample shown in the figures, this is illustrated during the initial run, where a 7 pct increase is observed (Fig. 1). 2—There is no additional change in loss when the sample is further strained up to the elastic limit (Fig. 1). Within that limit the loss-stress curve is reversible. This is not illustrated in Fig. 1. 3—Even in the plastic range only small increases in loss are observed as long as the sample is kept under stress (Fig. 2, point N); often no increase can be observed (Fig. 1). 4—A large increase in watt losses is observed after removal of the stress subsequent to plastic deformation (Figs. 1 and 2). 5—All, or nearly all, of the foregoing increase in loss due to plastic deformation can be eliminated by a reapplication of tensile stress but returns upon removal of this stress. This is illustrated in the third run (Fig. 3). This run remains within the elastic limit and shows the reversibility of the stress-loss curve under this condition. These findings have been confirmed on large Samples (approximately 200~10~0.035 cm and larger) except that under 1 no initial increase in loss was ever observed on these. The accuracy of the watt loss measurements is of the order of 1 pct. Neither bending of the sample in the tensioning device nor a redistribution of flux along the width of the sample accounts for these results. They therefore must be explained on the basis of either a change in the domain configuration due to stress or a change in the domain wall mobility. Acknowledgment The assistance of Mr. Robert L. TenBroeck with the instrumentation is gratefully acknowledged.

Jan 1, 1956

By Norman B. Pilling

The technical difficulties hampering the metallographic analysis of silicon steels are chiefly the result of the extreme corrodibility of these alloys. The addition of silicon to iron in increasing quantities, up to about 6 per cent., rapidly increases the susceptibility of the alloy to chemical attack, not only in acid solution, but in water. This renders the preparation of metallographic sections very difficult, because of a non-selective attack upon the finely polished surface by the water used as a lubricant in polishing. This water attack masks the true structural details revealed by suitable etching reagents. It is thus necessary to use alcohol as a polishing lubricant in the last stages of preparation and to avoid all etching reagents having an aqueous base. A specific reagent for the identification of iron carbide in ferrous alloys, and the one hitherto used almost' exclusively by metallurgists, is an alkaline aqueous solution of sodium picrate, which stains this constituent selectively. Its application to silicon steels has not proved successful, as its distinctive selective action is more or less completely hidden by the general attack of the aqueous solvent on the silico-ferrite, greatly accentuated by the fact that this reagent must be used at its boiling temperature (105' C.). Thus, a powerful metallographic aid to the study of the higher silicon alloys, such as transformer steels, is lost. A new reagent has been developed for the purpose of overcoming this difficulty. It is with some hesitation that the list of etching reagents, already overburdened, is increased, but the properties of this new reagent are advantageous in several ways and a definite field for it may be found in the metallography of ferrous alloys. The reagent consists of a dilute solution of nitric acid and methyl alcohol in nitrobenzol. It is a great advantage to secure an anhydrous solution, as a tendency toward acidic etching has been traced to small amounts of water. A convenient method of preparation is to make an anhydrous stock solution of nitric acid in methyl alcohol in the proportion 20 per cent. acid by weight (12.5 per cent. by volume). The alcohol can

Jan 1, 1924

By Frank Firmstone

IT is often desirable to obtain one or more accurate horizontal sections of a blast furnace after blowing out. Wishing to do this, last April, in the case of No. 4 furnace at Glendon, which had worn in a very remarkable manner, the method described below was employed, with very good results. A scaffold was fixed in the furnace, and on it was placed a drawing- board, covered with paper, the top of which was made level at exactly the height at which the section was to he taken. (Fig. 8.) The centre of the furnace (which had previously been found, and marked on a plank across the top) was laid off on it by dropping a plumb-bob from above, and a strong needle was driven into the board in the centre. By means of a straight-edge and two plumb- bobs, the line passing through the centres of the front and back arches was also drawn on the board. A pencil was fastened to a light wooden straight-edge at a known

Jan 1, 1875

By Gordon E. Frantti

Under the auspices of the Geophysical Committee of Michigan College of Mining and Technology, an investigation was made in Michigan's Upper Peninsula to obtain geophysical data related to the regional subsurface geology in the area covered by Paleozoic sediments. The area surveyed includes that portion of the Upper Peninsula which lies between R18W to R26W and T41N and T49N, covering approximately 1300 square miles. On the index map, Fig. 1, it is represented by the cross-hatched zone west of Munising. Four of the five sites of detailed investigation are indicated by the letters A, B, C, and D. A detailed gravity and magnetic survey had previously been conducted by J. G. Wilson near Perkins, 8 miles north of Rapid River, on a local anomalous area. Results of his work, which showed a large positive magnetic anomaly associated with a gravity anomaly, aroused interest in the possible economic significance of the formations underlying the Paleozoic sediments in this part of the Upper Peninsula.

Jan 1, 1956

By C. Hertzler

The difference of means of milling characteristics by rock and ore type is tested in a statistical manner in the paper. The null hypothesis being tested is that the sample means of two different populations are equal. It is assumed that the null hypothesis is true when performing the test. Because of this, acceptance of this hypothesis leads to the conclusion that the sample means of the two different populations are equal (or there is no significant difference between the sample means), not that the samples come from the same population, as the author asserts. Rejection of the null hypothesis leads to the conclusion that the sample means of the two different populations are not equal. A P value for this test is reported in Table 2 and is incorrectly identified as the probability that the two samples came from different populations. Actually, what was recorded was 100(1 - p) where p is the usual p-value. The usual p-value measures, on a scale of zero to one, the extent to which the data agree with the null hypothesis. It is the probability of observi" a value of the test statistic (Z score) that is at least as contradictory to the null hypothesis as the one computed from the sample data (McClave and Dietrich 11, 1982). The author makes no mention of the fact that were these tests to be conducted together, the chances of determining that the null hypothesis is not true when it is really true are increased considerably (Snedecor and Cochran, 1980). This is a multiple comparisons problem and should be dealt with accordingly. The usual methods involve adjusting the level of the individual tests. Table 2 reports an incorrect 100(1 - p) value in the comparison of concentrate grades for other rock types with .30 to .69% Cu vs other rock types with .70 + % Cu; 86% should be 98.6%. Although the article can be criticized for poor data presentation and discussion of that data, the point the author makes regarding the use of these statistics in the ore reserve estimation process is well taken. It does not appear that inaccuracies in the statistical interpretations have hindered that usefulness.

Jan 1, 1985

By John Brownson

Ge-Si N-N heterodiodes hare been built recently which show promise as high-speed logic devices. Low-resistivity germanium is deposited on silicon substrates held at temperatures above the germanium melting point and an alloyed heterojunction formed. The diodes are fabricated from this material using conventional mesa techniques. Over-all device qualify has been greatly improved by the use of epitaxial silicon substrates, that is, a subsirale consisting of a film of thin, high -resistivity silicon on a thicker Piece of low-resistirily silicon crystal. A semimpirical device design equation has been devised which predicts switching performance fairly well within the range of resistivitics and geometries employed. Switching times 01 0.9 ns and PIV 's of —20 v are typical of the better 10-ma diodes. Switching times as low as 0.5 ns have been observed for 10-ma diodes and as low as 2.8 ns for 200-ma diodes. With further development it should be possible to improve switching speed by a factor of four. IN our laboratory, Ge-Si heterodiodes have been built recently which show promise as high-speed logic devices. The diodes have been built using a process reported in some detail in an earlier publication.' The process in short involves alloying a thin film of low-resistivity germanium into a silicon substrate. the germanium having been transported and deposited by the well-known Theuerer halide reduction process.2 This process contrasts with that reported earlier by Oldham who used an essentially conventional direct epitaxial deposition technique.3 Oldham's process, unlike ours, requires cleavage of the silicon sample inside the reactor furnace the instant prior to deposition. Our process has the advantage of yielding large-area macro-scopically plane heterojunctions. Heterodiodes in general have several interesting properties. Without attempting to summarize the theory of heterojunctions.4 two of these properties which have direct relevance should be mentioned. First, N-.V and P-P heterojunction diodes rectify alternating current. Provided that either the band gap or the electron affinity of the two materials is different (which in general is the case), electronic barriers will exist in the junction band structure. When the device is sufficiently forward-biased, the barriers shift so as to permit current flow, and when it is reverse-biased. the barriers block current flow. Second, for N-N and P-P heterodiodes. the foward-conduction process involves majority carriers only. Consequently. when such a device is turned off. there is no minority-carrier storage and hence the diodes switch on and off quite rapidly. As we have reported earlier. N-P and N-N Ge-Si heterodiodes have been built in this laboratory. As one would predict from theory, the N-P heterodiodes were rather slow in turning off while the N-N's were quite fast. Similarly, the turn-off time of the N-P's increased rapidly with forward current while that of the N-N's was independent of forward current. Both N-N's and N-P's were moderately photosensitive. Photocurrents resulting from normal room illumination were as high as 1 µa at 1 v for small-area devices. The most disappointing parameter of the early N-N devices was reverse leakage.' The reverse characteristic was invariably "soft" and leakage at only several volts reverse bias was intolerable. The reverse characteristic was greatly improved by using higher-resistivity silicon substrates. Leakage becomes large at voltages about one third of the avalanche voltage one would expect of a P-N homo-junction formed on silicon of the same resistivity. Thus leakage could be reduced to reasonable limits by using unconventionally high-resistivity silicon. Medium-power diodes formed on 30 ohm-cm substrates leaked typically 15 to 50 µa at 100 v reverse bias. The use of high-resistivity silicon substrate material, however, created a new problem. In order to have an acceptable forward-conductance characteristic. the area of the diodes had to be increased. With this increase in area, the capacitance increased. Switching time for N-N heterodiodes is essentially a linear function of capacitance. Thus when the resistivity was raised. so was the switching time. A SEMIEMPIRICAL HETERODIODE DESIGN EQUATION As a result of our experiments with a limited range of diode geometries and resistivities. a semi-

Jan 1, 1965

By W. R. Ingalls

THE present administration has made sincere and effective efforts to reduce the expense of the Federal Government, but it has reached a point beyond which it seems impossible, or anyway extraordi-narily difficult, to go. This is ascribable to the large part of the budget that is represented as war expense. There is no doubt that this spells high taxation for many years to come. Nevertheless, although a large part of the taxation will be attributable to the war, the paying out of the proceeds of that taxation by the government will not be war expense, except in minor part, as will be hereinafter made clear. It will be useful to explain the economic meaning of this situation, for it has bear-ings upon several open questions, such as a bonus to the ex-soldiers, the foreign debt accounts, etc. The expense of the war on the part of the American people was in the main paid concurrently with its prose-cution. This was necessary. Warfare is not conducted with money, but with materials and labor. Except for such previous production as was represented by stocks of goods, the requirements had to be supplied by coincident production. With the end of 1918 our war expense ceased, save for such production, e.g., of ships, that was allowed to run on unchecked, and the indemnities that had to be paid for cancelled contracts. When those matters have been settled we shall be done, barring one important thing. Of course, our war expense began to contract right after the armistice and shrunk rapidly with the demobilization of the troops in 1919. If we had not been able to obtain all needful material from our own sources and had been constrained to borrow it from foreign countries, incurring a foreign debt, we should have been in the quite different posi-tion of having to repay that material, or its equivalent, during subsequent years. The European countries had to come to us for such supplies. This outlines the fundamental difference between their present situations and ours. We were therefore compelled not only to furnish materials and man-power for our own warfare but also much for the Allies.

Jan 3, 1923

By W. C. Ellis, E. S. Greiner, M. E. Fine

C. H. Samans and W. R. Ham (Chicago, Ill., and Dix-field, Maine, respectively)-—For several years we have been studying transitions of this basic type in metals, alloys, glasses, etc. Usually, however, they are not so clearly marked as those which the authors have found, and hence are much more difficult to determine accurately. Since our studies indicate that most of them occur virtually unchanged (as far as temperature is concerned) regardless of the form in which the element appears, we believe that they are a characteristic of the atom. Specifically, we believe that there is an additional rotational degree of freedom possessed by the nucleus which has not been considered heretofore. This nuclear rotation is made up of several components, each related to the several quantum shells of electrons. In chromium there are four of these shells and hence four separate series of characteristic transition temperatures. The lowest temperature at which any transition occurs, based on the present state of our computations, is 125°K, 4° higher than the authors' value of 121°K. A convergence of this series, we believe, shows up at the higher temperature of 2085 °K, surprisingly close to the transformation temperature of 2103°K recently announced by N. J. Grant of M.I.T. for a body-centered to face-centered transformation in chromium. Likewise, our computations indicate a temperature of 311°K for the second transition temperature, reported by the authors as 310 °K. A convergence of this series, we believe, shows up at a higher temperature as the melting point at 2163°K. Although our work on these series must, in a sense, still be regarded as empirical, since we do not understand fully as yet just what the series mean, it is based on a reasonably firm picture. The individual constants, from which the various series are computed for each element, comes directly from the X-ray K absorption limit. Furthermore, the same basic method has accounted for transformation and melting temperatures in about 50 of the chemical elements, which is all we have tried thus far. In many cases the only known transformation is the melting point, but in others the occurrence of transformations or other transitions, equally as well marked as those of the authors, has been pointed out by others. These observations have assisted us greatly. Consequently we were very pleased to see the authors' excellent work in finding these two transitions in chromium. With these confirming data, our picture of this element is clarified considerably, so we expect that at least some of our work can be published in the near future. R. C. Ruder (E. I. du Pont de Nemours & Cu., Wilmington, Del.)—The authors' interpretation of these transitions in terms of 3d to 4s electronic structure transitions is most interesting. It would be interesting to have additional experimental evidence of such transitions from the temperature dependence of the Hall coefficient in the neighborhood of the property changes discussed in this paper. Simple theory15 suggests the Hall coefficient as a measure of the free electron (or s electron) concentration per unit volume. It has been shown that for paramagnetic'" and ferromagnetic1? metals the simple theory is in fact too simple. However, the existence of a discontinuity in the Hall coefficient would provide information which should aid both in our understanding of these transitions and the significance of the Hall coefficient in these metals. It was rather surprising that no significant paramagnetic effects were observed. In this connection the recent work of McGuire and Kriessman18 is cited. They measured the magnetic susceptibility of chromium from 20" to 1460 °C. They also observed no large change in the susceptibility although there might be a change in slope in the vicinity of the 40 °C transition. The existence of these 3d to 4s electronic transitions has been discussed in connection with the paramagnetic susceptibility behavior of nickel and nickel alloys.'"-" Assuming a correspondence principle between classical and quantum mechanical paramagnetic theory and using classical theory to calculate the effective Bohr magneton number from the Curie constant for substances obeying the Curie-Weiss law," it is found that the effective magneton number is a function of temperature. The process of calculation involves the inverse of the differential of the 1/x4 vs. temperature curve so that good and numerous data are necessary to obtain significant results. The data of Fallot23 show a discontinuous increase of about 12 pct in the effective magneton number between 850" and 900 oC, followed by a continuous increase up to the melting point. The data of Sucksmith and Pearce24 show a possible 8 pct increase. The older data of Terry25 and Weiss and Foex26 show a continuous increase. It is possible that small amounts of impurity atoms change these electronic transitions significantly. Fallot's23 data on a nickel alloy with 4.5 atomic pct Fe indicate that the discontinuity occurs around 1300 °C. Systematic investigation of the transition metals for transitions of this nature should provide information which would be very valuable for our understanding of these metals. The absence of antiferromagnetic structures in chromium has been shown by Shull27 using neutron diffraction techniques. M. E. Fine, E. S. Greiner, and W. C. Ellis (authors' reply)—The remarks by Drs. Samans and Ham are certainly very interesting, in particular those pertaining to the close agreement between the theoretically calculated values for transition temperatures in chromium and the experimental values reported by a number of investigators. This is a remarkable achievement and we shall look forward to a more detailed presentation of the method followed in their calculations. We do not believe that the transition in pure chromium near 40 °C remains temperature invariant with alloying, as was reported by Samans and Ham for a number of the substances that they studied. We have not done any work with alloys but base our belief on the results of earlier studies in which less pure chromium was included and considerably lower transition temperatures were observed. The transition tempera-

Jan 1, 1952

E. T. Turkdogan (British Iron & Steel Research Assoc., London, England)—I would like to suggest a different method for the treatment of the authors' data on the Si-0 equilibrium in liquid iron. Because the activity coefficient of silicon dissolved in iron is influenced by the concentration of silicon as well as that of oxygen, the equilibrium constant K2 of reaction 2 becomes a function of metal composition, and, as shown in Fig. 1, a plot of log KP1 at 1600°C against the weight percent of silicon gives a smooth curve. A similar curve is obtained when log Kzl is plotted against the oxygen content of iron. Before

Jan 1, 1955

By A. F. Melcher

The present paper is a progress report on an investigation of the physical factors of oil and gas and especially of their sands,' such as pore space, size of pores or permeability, retentivity, viscosity of the oil, temperature, pressure, thickness and area of the pay sand, water relations, and capillarity. The purpose is to determine as many of these physical factors as possible, and to ascertain the relations existing, directly or indirectly, between these physical factors and the production of oil and gas. As yet only pore space2 and size of grains of pay sands have been investigated, although an apparatus has been designed to determine the permeability of a sand to oil, water, or gas under definite drops of pressure between the entrance face and exit face of the sample. Messrs. E. W. Shaw, R. Van A. Mills, D. Dale Condit, G. B. Richardson, G. C. Matson, and C. H. Wegemann collected the samples upon which the physical determinations were made. Acknowledgment is made to my colleagues of the United States Geological Survey for many suggestions and criticisms; to Mr. Mills for the production data given of the oil wells from which some of the samples were collected; to Mr. A. W. McCoy of the Empire Gas and Fuel Co., Bartlesville, Okla., for many ideas. Determining Pore Space of Oil and Gas Sands In selecting a method for the determination of pore space, two objects were kept in mind: First, the method must not only be sufficiently

Jan 1, 1921

By Charles R. Stewart, William W. Owens

Reservoir performance predictions based on laboratory core test data assume that fluid flow is laminar for the laboratory test. A study has been made to determine the validity of this assumption for laboratory tests on various types of porosity found in producing limestone formation. Data are presented which show that turbulence and slippage can occur during laboratory tests on hetero-geneous-type porosity limestones, thus causing serious errors in measured single-phase permeabilities and two-phase relative permeability characteristics. In single-phase flow tests it is possible to eliminate turbulence and correct for slippage or to eliminate both factors by controlling test conditions. It is not always possible to control test conditions and thereby eliminate turbulence and slippage in two-phase .flow tests. A correction method is presented which can be used to calculate the true two-phase laminar flow relative permeability characteristic even though furbulence and slippage exist. .INTRODUCTION It is customary to make use of Darcy's law and modifications of this law, together with laboratory data on formation core samples to predict the performance of producing reservoirs. Such predictions are based on an assumption that fluid flow is in the laminar or streamline region for the laboratory test. It was the purpose of this inves- tigation to determine the extent to which turbulent flow may occur in laboratory fluid flow tests on hetero-geneous porosity limestones. Considering that turbulent flow conditions might exist in some laboratory fluid flow tests, additional emphasis was placed on the development of a method to correct for turbulence when laminar flow conditions could not be attained. FLUID FLOW CONCEPTS FOR POROUS MEDIA The Influence of Pore Geometry on Fluid Flow One of the more important factors influencing fluid flow in porous media is the geometry of the pore space which includes such characteristics of the pores as size, shape, distribution, roughness, uniformity, etc. In general, oil- and gas-producing formations can be divided into two broad types on the basis of pore geometry. One has been called sandstone-type porosity media, which is characterized by a small range in pore size, uniformity in shape of the pores, smooth pore surfaces and a regular and uniform distribution of pores. The other type has been called heterogeneous porosity media and is usually limited to the dolomites and limestones. This type is characterized by a wide variation in the size, shape, and distribution of the pores and rough, irregular pore surfaces. It is therefore apparent that conditions are much more favorable for turbulent flow* in heterogeneous-type porosity media than in sandstone-type porosity media. Interrelationship Between Turbulence and Gas Slippage In studying the problem of turbulent flow in laboratory tests on porous media, it is necessary to be aware of the interrelationship between slippage and turbulence for gas flow. As a result of slippage or the Klinken-berg effecta, apparent perrneabilities to gas are greater than the true value because there is no stationary layer of gas in contact with the walls of the flow channels. Gas slippage decreases as the mean free path of the gas molecules decreases. Since the mean free path of any gas decreases with increasing density, increases in static pressure result in lower apparent gas permeabilities. However, a reduction in gas permeability can also be due to turbulence. Therefore, in studying only turbulent flow in porous media, it is necessary to hold gas density, and slippage, constant or to reduce slippage to a negligible value by operating at high static pressures. Presentation of Laminar and Turbulent Flow Data A graphical relationship between permeability and a pseudo-Reynolds number, N,, will be used to show the two types of fluid flow, i.e., laminar and turbulent. The usual graphical method for such a description has been the use of friction factor-Reynolds number charts4. On such a logarithmic diagram, the laminar region appears as a straight line having a slope of 45 degrees. As the friction factor decreases and the Reynolds number increases, the turbulent region is reached and appears as a deviation from the 45-degree slope line. However, in petroleum engineering literature resistance of por-