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By B. Ramaswami, U. F. Kocks, B. Chalmers

This paper describes the tempetrature, solute (gold), and orientalion dependence of the plastic rleforlirnlion of silver single crystals. The virgin flow stress, To, and its temperatutre dependence incrense with increase in solute concentration. el decreases with decrease in temperature below room teiirperature and with increase in solute coucentralion. The dependence of 011 on temperature arid solute sontenl is due to the dependence of Ts on the two variables. An increase in ts, due to either the temperature or the solute conlent, results in a decrease of e11 in crystals of single-slip orientation and an increase of 011 in crystals of' (100) find (111) orientation. is orientation-dependent and at all the temperatures and in all the materials studied. The Leveling off of the engineering stress-strain curve in crystals of (100) 07-ientotion at a stress tl, is associated with extensive cross slib. The temperature and strain -rate dependence of tl are similar to those of indicating that a rate process is the cause 01 this phenomenon. The plastic deformation of silrer crystals of (110) orientation is multiple to that of crystals of single-slip orientation. THE work hardening of fcc crystals has been the subject of intensive investigations in the past 15 years. The effect of orientation, deformation temperature, solutes, second phase or precipitates, strain rate, etc., has been studied in a number of fcc metals.'-5 In spite of the considerable amount of work reported on the dependence of work hardening on the orientation, temperature, and solute concentration, certain aspects of the plastic deformation of fcc crystals have not been clarified. For instance, with the exception of a few investigations,6-8 where crystals of multiple-slip orientations have been studied, almost all the studies have been on crystals of single-slip orientations. Hence, a major portion of this study has been devoted to the dependence of plastic deformation on the multiplicity of slip systems and the enhanced possibility of dislocation interactions resulting from such multiplicity. Further, the abnormally low rate of work hardening observed at large strains at certain temperatures in crystals of the (100) orienta-tion 6-8has not been explained satisfactorily. It is the aim of this study to clarify this aspect of the orientation and temperature dependence of the plastic deformation of fcc single crystals. The work-hardening characteristics of single crystals of aluminum of ( 110) orientation have been studied at room temperatur "'12 and above." They have not been studied at temperatures where the virgin flow stress is dependent on temperature or where, in Seeger's terminology is important. The work hardening of single crystals of (110) orientation is of interest for another reason. As shown in Table I, the dislocation reactions that are possible in the (110) orientation are similar in certain respects to those that are possible in the (100) orientation. Hence, the deformation of single crystals of silver of (110) orientation was studied in the temperature range 100° to 900°K at intervals of 200°K. The effect of solute concentration on the plastic deformation of fcc single crystals of single-slip orientation has been studied by several investiaators.> In all of these investigations—with the exception of Ref. 20—single crystals of identical orientation have not been used, with the result that the orientation dependence of plastic deformation is superimposed on the effect of the solute. In addition, the effect of the solute on the work-hardening characteristics of single crystals of multiple-slip orientations has not been studied by the previous

Jan 1, 1965

By L. W. Davies

A problem often encountered is the provision of materials which have impurity contents below a certain specified level. This problem is in some cases solved by making use of the segregation of the impurity with respect to the liquid and solid states of the material: an ingot of the material is subjected to directional solidification and the ends of the ingot. which are richer in solutes which respectively raise and lower the melting point of the solvent, are removed. An important extension of this process is the zone-refining process invented by Pfann,' in which molten zones are passed successively along the length of an ingot and displace solutes towards the ends. Pfann's process is particularly appropriate in cases for which the segregation coefficient k does not differ greatly from unity, or when the impurity content must be kept extremely low (=10-6 atom fraction); it is widely used, particularly in the purification of materials for use in semiconductor electronic devices. It is the purpose of this paper to investigate theoretically the efficiency of the above refining processes; that is! we determine the most economic method of attaining a given yield of solvent of specified purity, taking into account the variables of the process. One variable of interest is the effective value of the segregation coefficient. which depends on the rate of movement of the liquid-solid interface and on the degree of stirring in the liquid; in addition to this, in the zone-refining process we are also interested in the choice of zone length for most efficient operation. A mathematical determination is made here of the lengths of successive molten zones which give, for an initially uniform distribution, the most efficient removal of a solute of arbitrary distribution coefficient. In order to be able to give a quantitative treatment of efficiency, we first define figures of merit applicable to a given distribution of solute. FIGURE OF MERIT Let an ingot of length L contain a distribution y(x) of solute: we confine our discussion to mono-tonic distributions, in order to avoid inconsistencies in the subsequent analysis. The first moments of the distribution about the origin and x = L are respectively L F = hy{x)dx [I] G = f(L -x)y(x)dx = YoL2-F, [21 where yoL is the total amount of solute present. We shall see that the quantities F and G are useful figures of merit for a discussion of the efficiency of zone-refining processes. In the first place, it is

Jan 1, 1960

By J. T. McGrath, R. C. A. Thurston

Poly crystalline specimens of copper, and copper with various additions of zinc, were tested in plane-bending fatigue. In tests performed at a constant stress, the fatigue life of copper increased slightly with the addition of up to fifteen per cent zinc. There was a sharp increase in fatigue life as further additions of zinc of up to 35 pct were made. Surface observations showed that the coarse slip bands that are characteristic of fatigue became narrower as the concentration of zinc increased. The rate of crack propagation also decreased with increasing zinc content. It is suggested that the fatigue behavior is controlled by cross slip processes. CROSS slip occurs when dislocations move from one primary slip plane to another along a connecting or cross slip plane. The primary and cross slip planes have a common slip direction. Wide stacking faults, having low energy, tend to make cross slip more difficult. According to recent theories, the ability of a material to cross slip is important to the formation and propagation of fatigue cracks. McEvily and Machlin2 have examined this concept experimentally by fatiguing single crys tals of lithium fluoride, sodium chloride, silver chloride, and KRS-5.* The latter two materials ex- hibit easy cross slip, while the former two do not. Normal rapid fatigue failure was obtained in the silver chloride and KRS-5 specimens, whereas it was much more difficult to achieve in sodium chloride and lithium fluoride crystals. Furthermore, numerous slip band extrusions and intrusions were found in silver chloride and KRS-5 crystals, whereas only one isolated extrusion was found in lithium fluoride and none was found in sodium chloride. McEvily and Machlin also consider that there is no clear-cut demarcation between crack initiation and propagation. The intrusion-extrusion process, which initiates crack formation, continues ahead of the cracks to allow propagation of these cracks along slip bands. The process of cross slip is therefore important not only to crack initiation, but also to crack propagation. Holden4 postulates that fatigue crack growth is dependent upon cross slip and thus upon stacking-fault energy. Using an X-ray microbeam technique, he found a cyclic subgrain structure in fatigued aluminum and a-iron. Holden suggests that micro-cracks develop in the densely-packed sub-boundaries ahead of the main crack front, and when sufficiently numerous join up to promote crack growth. The ease with which a subgrain structure could form would depend upon the ability of the dislocations to cross slip, and thus upon the stacking-fault energy. Hence in aluminum, which has a high stack-ing-fault energy and in which cross slip is easy, Holden found that the relative rate of fatigue crack propagation was considerably greater than in stainless steel, a low stacking-fault energy material. It has been shown by a number of investigators that the probability of forming deformation stacking faults in copper increases as zinc is added.5-7 Cross slip should, therefore, become more difficult as the zinc concentration is increased. In order to check the validity of the foregoing theories, it was decided to test copper and copper with various additions of zinc in plane bending fatigue, and determine to what extent their fatigue properties are dependent upon their ability to cross slip. EXPERIMENTAL PROCEDURE Fatigue tests were carried out on polycrystalline OFHC copper and various copper-zinc alloys with 5, 15, 20, 30, and 35 wt pct Zn. The Cu-Zn alloys were obtained commercially in sheet form. Test specimens, as shown in Fig. 1, were machined from sheet that had been reduced to an approximate grain size of 0.040 mm, the heat-treatment procedure being similar to that of Feltham anc copley.8

Jan 1, 1963

By A. A. Bauer, F. A. Rough, G. H. Beatty

AS a result of recent studies, the constitution of the zirconium-uranium system has been fairly well defined. A diagram for the system is shown in Fig. 1. However, both oxygen and nitrogen are known1-3 to have a pronounced effect on the limits of both ß- and e -phase regions. It has been shown that small amounts of oxygen severely constrict the compositional limits of these phase regions in the ternary zirconium-uranium-oxygen system. A previously published tentative diagram shown in Fig. 2 illustrates the ß-phase constriction resulting from oxygen additions. Generally, iodide zirconium has been used in constitutional studies of zirconium-uranium alloys. While this is the highest purity material available, cast iodide zirconium-uranium alloys will generally average from 200 to 300 ppm 0 and from 50 to 60 ppm N. Thus, while the constitution of the zirconium-uranium system is fairly well defined, it must be realized that this definition applies to alloys containing in the vicinity of 250 ppm 0 and 50 ppm N. The present investigation was undertaken to accurately determine the boundary between the ß-plus-P and ß phases at a single temperature in the binary zirconium-uranium system by quantitatively

Jan 1, 1959

By H. I. Aaronson

The nucleation of pearlite at proeutectoid ferrite is inhibited, to an increasing extent, at the following locations: At twin boundary-nucleated ferrite, between closely spaced ferrite sideplates, and at intragranular plates. These effects are discussed in terms of the influence of transformation strain energies and of the interfacial free energy of austen-ite:ferrite boundaries on the rate of pearlite nucleation. The growth of pearlite into the interiors of austenite grains from the region of the grain boundaries is markedly restricted when low reaction temperatures and large austenite grain sizes permit the development of interlocking networks of intragranular ferrite plates. PREVIOUS investigators have made extensive studies of the interactions which occur between the proeutectoid ferrite and the pearlite reactions from the viewpoint of the mechanisms through which pearlite interferes with the nucleation and growth of proeutectoid ferrite.1-3 In the present investigation, the processes through which proeutectoid ferrite (hereafter termed simply "ferrite") can reduce the rate of formation of pearlite have been explored in some detail. A steel with a relatively low carbon content, in which the ferrite reaction can compete successfully with the pearlite reaction over a wide range of reaction temperature, and exceptionally coarse-grained specimens, which further emphasize the role of the ferrite reaction, have been employed for most of this work. A brief examination also has been made, however, of the effects of smaller austenite grain sizes upon these processes. Experimental Procedure The steel employed had the following composition: 0.29 pet C, 0.76 pet Mn, 0.25 pet si, 0,007 pet S, and 0.005 pct P. This alloy was homogenized for 48 hr at 1250°C. The investigation was performed

Jan 1, 1959

By Nicholas J. Grant, Ulf Kalling, John Chipman

D. E. Babcock (Republic Steel Corp., Youngstown, Ohio)—I would like to know what evidence you have to prove the MnO was pure MnO. I would also like to know whether you might not explain it on the basis of a temperature reversion; and, was it due to the oxidizing power of MnO? N. J. Grant (authors' reply)—Briefly, we have no proof that pure MnO was used. The manganese oxide was added as chemically pure MnO,. MnO is assumed as the oxide in the reacted slag following standard molecular slag theories, especially under the reducing conditions of these experiments. The noted sulphur reversion cannot by any means be explained on the basis of a temperature reversion since the temperature effect is shown in this paper to be very small. Until a more logical explanation can be offered, backed I hope by some experimental proof, we propose to explain this sulphur reversion as stated in the paper, namely, that it is due to the oxidizing effect of the added manganese oxide. Member—How did the oxygen in the slag give you a reversion of sulphur? What was the mechanism there?

Jan 1, 1952

By William L. Lennemann

Chemistry of uranium with respect to its hydrometallurgical recovery from carnotite ores was investigated and well defined during the radium boom period between 1900 and 1920. Since that time, methods used to extract uranium from its ores have remained basically either acid leaching or sodium carbonate leaching. Until about 1950, the only practical methods known for achieving a better than 75 pct U2O3 concentrate from the leach liquors involved fundamental chemical techniques for either purifying a solution prior to the uranium precipitation, or refining a crude uranium concentrate that was produced by neutralizing a pregnant mill liquor.

Jun 1, 1956

By C. L. Meyers, J. L. Lytton, T. E. Tietz

The recovery of tensile flow stress of 99.995 pct A1 under conditions of elastic strain and plastic creep straining was investigated using a fractional recovery parameter. Tensile straining was conducted at room temperature to a true strain of 0.10, and recovery treatments were made under stress in the temperature range from 80° to 198°C. Whereas elastic strains had no appreciable influence on flow-stress recovery, plastic creep straining was found to accelerate the recovery process. Although higher creep stresses gave greater recovery for a given time and temperature, it was found that lower stresses produced greater recovevy at equal ALTHOUGH many studies have been made to date on the recovery of metals from the cold-worked creep strains above about 0.005. This effect was attributed to the coarser, and therefore weaker, substructure developed during creep at the lower stresses. The activation energy for recovery during creep straining at 2075 psi between 160" and 198°C was found to be 25,000 cal per mole. This value was not significantly greater than the value previously obtained for no-load recovery. The activation energy for creep at 2075 psi between 160" and 198°C was 34,000 cal per mole, a value significantly greater than that for recovery under the same conditions. state, little is known concerning some important aspects of recovery behavior. One such area is the effect concurrent strain has on the recovery process. Since metals in structural applications at high temperatures are under stress, the possible effects of the resulting elastic and plastic strain on recovery may be of significant importance.

Jan 1, 1962

By Frank Firmstone

In the summer of 1842 my father, William Firmstone, was engaged by Charles Jackson, Jr., of Boston, to examine the conditions in the Lehigh valley as a site for blast-furnaces using anthracite for fuel. In consequence of his report, he was further engaged by Mr. Jackson to build a furnace for him and his partners on the Lehigh canal, 2 miles above the mouth of the river at Easton. Work was begun in the fall of 1842, and the first furnace blown-in in 1844. The history of the works, therefore, from 1844 to 1887, when my own connection with them ceased, covers only four years less than the whole period of the rise, culmination, and commencement of the decline in the smelting of iron with anthracite in America, the beginning of which, in a commercial sense, may be put in 1839.' Although this paper, as the title indicates, is concerned almost exclusively with the furnaces at Glendon, still what was done there was more or less influenced by current opinion in the district, and even reflects, to some extent, the changes in opinion and practice with mineral fuel the world over. No. 1 Furnace was built of red brick, on four piers, had three tuyeres and fore-hearth and tymp, as was universal with furnaces using mineral fuel until the introduction of Lurmann's cinder-tuyere. The dimensions and profile are shown in Figs. 1 and 2. The first hearth (Fig. 1) was of sandstone; all after were of fire-brick (Fig. 2). The profile was no doubt derived directly from Gibbons's furnace,2 for it appears from W. Firmstone's note-books that in October, 1840, he visited " Gibbons' new furnaces building at Corbyn Hall," and I have an old drawing,

Jan 1, 1910

By W. Mostowitsch, H. O. Hofman

The mineral gypsum, CaSO4 + 2 H2O, has been used for many years as a sulphurizing and basic flux in several smelting-operations. Thus, in smelting oxide nickel-ore in the blastfurnace, it is commonly added to the charge to furnish the sulphur necessary for collecting the metal in a matte, and a base for slagging the siliceous gangue. In the concentration of lead-copper matte in the reverberatory furnace it has been used for years at Preiberg, Saxony,1 for a similar purpose, and for producing at the same time a copper-matte with less than 0.15 per cent. of Fe. The latest use gypsum has been put to is in the blast-roasting process of Carmichael-Bradford.2 The term " blast-roasting," given by A. S. Dwight3 to the Dwight-Lloyd method of roasting and agglomerating: is a happy generic term which covers the ground better than the " lime-roasting " of Ingalls5 or the " pot-roasting " of Austin: in that it leaves the operation independent of the character of the flux and the form of apparatus, and retains the characteristic feature of this class of processes—namely, that of using forced draft. In the Carmichael-Bradford process the dehydrated material, mixed with galena-concentrate, acts as a diluent and a flux. The process differs in this from the Huntington-Heberlein7 and the Savelsberg8 processes, in both of which limestone is used.

Jan 1, 1909

By H. Landsberg

The curriculum presented here is an outgrowth of discussions by the Committee on Geophysics Courses of the A.I.M.E. in previous years. It had to be a compromise between the desires voiced by employers of geophysicists, professional geophysicists and the possibilities at an average college. There one has to face the questions of the available teaching staff, the inertia of administrators and teachers set in their ways, and the red tape involved in modernizing antiquated curricula. It is, of course, not ideal to have colleges and universities lag Io years behind the times. Rather, instead of being prodded by industry, they should be ahead of industrial needs. There should also be a certain amount of leeway for the student in any college curriculum. All these points had to be considered in drawing up a curriculum, which, instead of being narrowly termed "geology" or "geophysics" was rather called "earth science." It gives the student a chance to specialize in one of the various branches represented by teachers on the faculty of The Pennsylvania State College, giving as options Geology (with subdivisions of Mineralogy and Paleontology), Geophysics, Geography, and Meteorology. Table iA represents the option of geophysics in the curriculum that envisages that a student may want to make his career in any of the fields encompassed by the American Geophysical Union or in geoexploration. This is, of course, only the start of an education that in most cases will have to be followed by graduate work for complete professional training. The outlined curriculum is definitely of an engineering type and is identical for all of the four options mentioned for the first two years. Specialization will start in the junior year but even thereafter the branches are kept as closely allied as feasible in order to permit a student to change from one tO the other (e.g., because of a different aspect in the mployment situation) with a minimum of additional work. Table IB shows the geophysics option according to subject matter, indicating the considerable amount of work in the fundamentals of mathematics, physics and chemistry with a liberal number of geology courses, and some engineering. The courses in the field of geophysics are limited—just two lecture courses as a general introduction and one field course, to permit the student a visualization of the correlation between mathematically analyzed physical data and the geological realities. Thesis work is considered essential to teach the student, while he is still in college, some things S. F. Kelly has mentioned as desirable: (I) following of instructions for somewhat independent work; (2) organizing of material, and (3) producing a readable report. This, together with the personal contact with the advising faculty member, will help in forming a student's personality. The seminar course attempts to get the student into the habit of reading current literature, so that he can keep abreast of the times.

Jan 1, 1946

By H. Landsberg

The curriculum presented here is an outgrowth of discussions by the Committee on Geophysics Courses of the A.I.M.E. in previous years. It had to be a compromise between the desires voiced by employers of geophysicists, professional geophysicists and the possibilities at an average college. There one has to face the questions of the available teaching staff, the inertia of administrators and teachers set in their ways, and the red tape involved in modernizing antiquated curricula. It is, of course, not ideal to have colleges and universities lag Io years behind the times. Rather, instead of being prodded by industry, they should be ahead of industrial needs. There should also be a certain amount of leeway for the student in any college curriculum. All these points had to be considered in drawing up a curriculum, which, instead of being narrowly termed "geology" or "geophysics" was rather called "earth science." It gives the student a chance to specialize in one of the various branches represented by teachers on the faculty of The Pennsylvania State College, giving as options Geology (with subdivisions of Mineralogy and Paleontology), Geophysics, Geography, and Meteorology. Table iA represents the option of geophysics in the curriculum that envisages that a student may want to make his career in any of the fields encompassed by the American Geophysical Union or in geoexploration. This is, of course, only the start of an education that in most cases will have to be followed by graduate work for complete professional training. The outlined curriculum is definitely of an engineering type and is identical for all of the four options mentioned for the first two years. Specialization will start in the junior year but even thereafter the branches are kept as closely allied as feasible in order to permit a student to change from one tO the other (e.g., because of a different aspect in the mployment situation) with a minimum of additional work. Table IB shows the geophysics option according to subject matter, indicating the considerable amount of work in the fundamentals of mathematics, physics and chemistry with a liberal number of geology courses, and some engineering. The courses in the field of geophysics are limited—just two lecture courses as a general introduction and one field course, to permit the student a visualization of the correlation between mathematically analyzed physical data and the geological realities. Thesis work is considered essential to teach the student, while he is still in college, some things S. F. Kelly has mentioned as desirable: (I) following of instructions for somewhat independent work; (2) organizing of material, and (3) producing a readable report. This, together with the personal contact with the advising faculty member, will help in forming a student's personality. The seminar course attempts to get the student into the habit of reading current literature, so that he can keep abreast of the times.

Jan 1, 1946

By H. Landsberg

THE curriculum presented here is an outgrowth of discussions by the Committee on Geophysics Courses of the A.I.M.E. in previous years. It had to be a compromise between the desires voiced by employers of geophysicists, professional geophysicists and the possibilities at an average college. There one has to face the questions of the available teaching staff, the inertia of administrators and teachers set in their ways, and the red tape involved in modernizing antiquated curricula. It is, of course, not ideal to have colleges and universities lag 10 years behind the times. Rather, instead of being prodded by industry, -they should be ahead of industrial needs. There should also be a certain amount of leeway for the student in any college curriculum. All these points had to be considered in drawing up a curriculum, which, instead of being narrowly termed "geology" or "geophysics" was rather called "earth science." It gives the student a chance to specialize in one of the various branches represented by teachers on the faculty of The Pennsylvania State College, giving as options Geology (with subdivisions of Mineralogy and Paleontology), Geophysics, Geography, and Meteorology. Table IA. represents the option of geophysics in the curriculum that envisages that a student may want to make his career in any of the fields encompassed by the American Geophysical Union or in geoexploration. This is, of course, only the start of an education that in most cases will have to be followed by graduate work for complete professional training. The outlined curriculum is definitely of an engineering type and is identical for all of the four options mentioned for the first two years. Specialization will start in the junior year but even thereafter the branches are kept as closely allied as feasible in order to permit a student to change from one to the other (e.g., because of a different aspect in the employment situation) with a minimum of additional work. Table IB shows the geophysics option according to subject matter, indicating the considerable amount of work in the fundamentals of mathematics, physics and chemistry with a liberal number of geology courses, and some engineering. The courses in the field of geophysics are limited-just two lecture courses as a general introduction and one field course, to permit the student a visualization of the correlation between mathematically analyzed physical data and the geological realities. Thesis work is considered essential to teach the student, while he is still in college, some things S. F. Kelly has mentioned as desirable: (I) following of instructions for somewhat independent work; (2) organizing of material, and (3) producing a readable report. This, together with the personal contact with the advising faculty member, will help in forming a student's personality. The seminar course attempts to get the student into the habit of reading current literature, so that he can keep abreast of the times.

Jan 1, 1941

President MRS. HARRISON SOUDER Smith Paramus Road Ridgewood, N. J. First Vice-president MRS. ROBERT HURSH 10 Kilburn Road Belmont, Mass. Second Vice-president MRS. ERLING L. JORGENSEN 95 Knollwood Rd. Short Hills, N. .1. Third Vice-president MRS. PERCY E. BARBOUR 1R(; Riverside Drive New York, N. Y. Fourth Vice-president MRS. C. B. MURRAY 2040 Stearns Rd. Cleveland, Ohio

Jan 1, 1938

By Noel Stearn

OF THE many instruments devised for the measurement of magnetic anomalies, the ordinary dip needle, by virtue of its superior simplicity of construction, facility of manipulation, and definiteness of interpretation, seems to merit serious attention as the instrument most readily applicable to the detection of magnetic anomalies of the higher order of magnitude. , In spite of the fact that it has been used for many years for the discovery of iron ore in Europe and in the Lake Superior region of America, its capabilities as a geological instrument have not yet been thoroughly plumbed. The Wisconsin Geological Survey, under Dr. W. 0. Hotchkiss, E. F. Bean, and H. R. Aldrich, has been most thorough in developing the technique of the instrument, and the results it has obtained have aroused a general interest in a more widespread use of geomagnetics as an exploration method and the dip needle as a geological instrument. The simplicity of the instrument is an especial advantage, as it can be used by anyone, regardless of his technical training; but to insure useful results not only is a knowledge of the background of geomagnetics necessary but also an understanding of the principles of the instrument itself.

Jan 1, 1928

By L. W. Davies

A problem often encountered is the provision of materials which have impurity contents below a certain specified level. This problem is in some cases solved by making use of the segregation of the impurity with respect to the liquid and solid states of the material: an ingot of the material is subjected to directional solidification and the ends of the ingot. which are richer in solutes which respectively raise and lower the melting point of the solvent, are removed. An important extension of this process is the zone-refining process invented by pfann,' in which molten zones are passed successively along the length of an ingot and displace solutes towards the ends. Pfann's process is particularly appropriate in cases for which the segregation coefficient k does not differ greatly from unity, or when the impurity content must be kept extremely low (-=,6 atom fraction); it is widely used, particularly in the purification of materials for use in semiconductor electronic devices. It is the purpose of this paper to investigate theoretically the efficiency of the above refining processes; that is! we determine the most economic method of attaining a given yield of solvent of specified purity, taking into account the variables of the process. One variable of interest is the effective value of the segregation coefficient. which depends on the rate of movement of the liquid-solid interface and on the degree of stirring in the liquid; in addition to this, in the zone-refining process we are also interested in the choice of zone length for most efficient operation. A mathematical determination is made here of the lengths of successive molten zones which give, for an initially uniform distribution, the most efficient removal of a solute of arbitrary distribution coefficient. In order to be able to give a quantitative treatment of efficiency, we first define figures of merit applicable to a given distribution of solute. FIGURE OF MERIT Let an ingot of length L contain a distribution y(x) of solute: we confine our discussion to mono-tonic distributions, in order to avoid inconsistencies in the subsequent analysis. The first moments of the distribution about the origin and x = L are respectively L F = hy{x)dx [I] G = f(L -x)y(x)dx = YoL2-F, [21 where yoL is the total amount of solute present. We shall see that the quantities F and G are useful figures of merit for a discussion of the efficiency of zone-refining processes. In the first place, it is

Jan 1, 1960

By K. L. Young

The general energy equation, including change in kinetic energy, was solved by numerical integration and used to evaluate simplifying assumptions and application practices over a wide range of conditions. When extreme conditions were encountered, sizable errors were caused by large integration intervals, application of Simpson's rule and neglecting change in kinetic energy. A maximum error of only 1.31 percent was caused by assuming temperature and compressibility constants at their average value. It was discovered that a discontinuity can develop in the integral for the injection case. This discontinuity indicates a point of zero pressure change and is an inflection point in the pressure traverse. INTRODUCTION When a pressure in a gas well is to be calculated, one of the first decisions is to select a method of calculation. In many instances, this selection becomes a problem because the literature, at best, provides an evaluation of any method for only a limited range of conditions. Once a method has been selected, a question often arises as to the size of the calculation interval which should be used. The question regarding calculation interval arises because an analytic solution is not obtainable and approximate solutions must be used. This paper presents an evaluation of major assumptions and application practices of probably the two most widely used methods for calculating steady-state single-phase gas well pressures. The two methods are Cullender and Smith1-" (numerical integration), and average temperature and com-pressibility. The Cullender-Smith method assumes that change in kinetic energy is negligible and is normally applied in two steps with a Simpson's rule correcton. The average temperature and compressibility method, in addition to neglecting kinetic energy change, asumes that temperature and compressibility are constant at their average values. This method is normally applied for wellhead shut-in pressures of less than 2,000 psi, and in one step. Computer programs were written to compute bottom-hole pressure with and without the assumptions, using various approaches. Values of input parameters investigated are shown in Table 1. Flow rate was limited to a maximum of 5,000 and 10,000 Mcf/D for tubing sizes of 1.610 and 1.995 in. ID, respectively. Flow rate was also limited to 10,000 Mcf/D for a tubing size of 2.441 in. ID when wellhead flowing pressure was 100 psia. These limitations were imposed on flow rate so as not to exceed sonic velocity. The z factor routine available necessitated limiting bottom-hole temperature to 240F and wellhead pressure to 3,000 psia. Pressures were compared on the basis of percent deviation from the trapezoidal integration of Eq. l or 2 at 100-ft intervals. A preliminary investigation indicated that a 1,000-ft interval solution would differ from a 50-ft interval solution by less than 0.25 percent; therefore, the 100-ft interval was chosen for a base. For the purpose of comparison, deviations less than 1 percent were considered insignificant. where 111.1 qeC2/d p = kinetic energy term. Eqs. 1 and 2 can be evaluated numerically at specific depths using the trapezoidal rule as shown by Cullender and Smith. If change in kinetic energy is neglected and temperature and compressibility are assumed constant at their average values, Eq. 1 can be integrated to give the average temperature and compressibility equation,

WASHINGTON, D. C. HERBERT C. HOOVER, Chairman H: FOSTER BAIN, Vice-chairman DAVID WHITE, Vice-chairman HARVEY S. MUDD, Secretary-Treasurer, Room 2114, Dept. of Interior Bldg. J. F. CALLBREATH HENNEN JENNINGS E. W. PARKER T. T. READ An inspiring meeting of the Washington, D. C., Section was held at the Cafeteria of the Interior Building on Friday evening, Dec. 6, 1918. One-hundred and thirty-five members and guests attended, and Vice-chairman H. Foster Bain presided. The Committee on Nominations reported: for Chairman, Herbert Hoover; for Vice-chairmen, Frederick G. Cottrell, and F. L. Ransome;

Jan 1, 1919

By M. G., Corson

1. In addition to the alloys of copper with iron previously found by Hanson and Ford to show an increase in the concentration of the alpha range with increase in temperature the following binary and ternary systems have been found by the author to exhibit: the same feature: (a) Copper-chromium. (b) Copper-cobalt. (c) Copper-silicon. (d) Copper-nickel-silicon and its pseudo-binary section Cu-Ni2Si (formula of compound definitely established). (e) Copper-cobalt-silicon and its pseudo-binary section Cu-Co2Si (formula of compound established with some probability but not as definitely as for Ni2Si). (f) Copper-chromium-silicon; formation of a compound definitely established (compare Figs. 1 and 2). The formula of this compound may be either Cr2Si or Cr3Si. (g) Copper-iron-silicon; presence of a phase containing both iron and silicon established in an indirect way only. No definite microconstituents observed. 2. RANGES OF SOLID SOLUBILITY (percentage at various tempera¬tures). (a) For copper-chromium: 0.8 at 1000° C.; 0.5 at 900° C.; 0.25 at 800° C.; 0.05 to 0.1 at 500° C. (b) For copper-cobalt: 3.4 at 1000'C.; 2.4 at 900'C.; 1.7 at 800'C.; 0.9 at 600°C.; 0.35 at room temperature. (c) For copper-silicon (Fig. 3) : 6.8 ± 0.1. per cent. at 800° C.; 3 per cent. at 400° C. and probably below 2 per cent. at room temperature if sufficiently long annealed. (d) For copper-cobalt silicide: 3.3 at 1000° C.; 2.4 at 900° C.; 1.6 at 800° C.; 0.7 at 600° C.; 0.3 at 300° C. (e) For copper-nickel silicide (Fig. 4): 8.2 at 1000° C.; 5.5 at 900° C.; 3.6 at 800° C.; 1.6 at 600° C.; 0.7 at 300° C.

Jan 1, 1927

By C. R. Masson, M. L. Pearce

The nitrogen contents of seven specimens of iron and steel were determined by the three methods. Good agreement won generally observed between the results of the isotope -dilution and Kjeldahl determinations, tltzts establishing the reliability of the isotope -dilutzon technique. For some specimens, the vacuum-fusion values at 1650 °C were lower than the corresponding Kjeldahl values by up to 0.0015 pct absolute. These differences were eliminated for a specimen of "pure" iron by performing the vacuum-fusion analyses at 2100 ° to 2240 °C. The reason for this relatively high temperature required m the vaczium-fusion analyses is discussed. ThE determination of nitrogen in iron and steel has been the subject of numerous investigations and a concise review of the extensive literature in this field has recently appeared.' Two methods of analysis are most commonly employed, the vacuum -fusion and the chemical or Kjeldahl method. Except in special cases where the presence of certain alloying elements may present difficulties, both methods are generally regarded as applicable, although the vacuum-fusion method is more sensitive and is often preferred for samples of very low-nitrogen content. The method of isotope dilution, first employed for the determination of gases in metals by Kirshenbaum and Grosse,2 has recently been applied to the determination of nitrogen in iron and steel.3,4 The method is attractive in that it does not require the quantitative extraction of gas from the metal specimen. Staley and Svec3 modified the standard Kjeldahlpro-cedure by introducing, along with the steel sample, a measured amount of ammonium sulfate enriched in the isotope 15N. The nitrogen content was obtained by measuring the isotopic ratio 15N/14N in the resultant solution. The technique involved the distillation of nitrogen as ammonia from alkaline solution and subsequent oxidation of NH4+ in the distillate to gaseous nitrogen. The results for iron and steel samples of commercial origin were often in reasonable agreement with values quoted by the suppliers, although occasional marked discrepancies were observed, particularly with the results of vacuum-fusion analyses. Preliminary work in this laboratory4 on the determination of nitrogen by isotope-dilution in the gas phase yielded results for three samples which were significantly higher than the values obtained by vacuum-fusion. The present paper describes an extension of this work to a wider variety of samples. Analytical results by the Kjeldahl method are also reported. EXPERIMENTAL The technique employed for the isotope-dilution determinations was similar to that described elsewhere.4 Several minor modifications were made to the apparatus. These included the use of molybdenum instead of platinum-rhodium suspending wires when crucibles were degassed at temperatures above 1600°C. The circulatory system used previously for converting CO to CO2 was replaced by a single chamber, the walls of which were cooled directly in liquid nitrogen. Temperatures were measured with an optical pyrometer which had been recently calibrated and, as in the previous study, were minimum values obtained by sighting on the center bottom of the crucible. Temperatures obtained by sighting on the interior walls were always higher by 100' to 130°C with the design of crucible employed. Flat-bottomed crucibles exhibited an even larger temperature difference. To check the efficiency with which crucibles were degassed in the isotope-dilution apparatus, several experiments were done in the vacuum-fusion apparatus, suitably modified4 for isotope-dilution studies. Faster pumping speeds and higher degassing temperatures were possible, the latter due to the use of a generator with a higher power output (10 Kva at 398 kc per sec). In these experiments the combustion of CO was omitted and a correction4 was made for the contribution of CO to the ion current at m/e 28, used in determining the isotopic ratio R = l5NP4N. This correction did not seriously influence the re-

Jan 1, 1962