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By G. A. Guess

THIS investigation was started with the idea of determining whether copper-nickel mattes might not have a lower flowing temperature than copper mattes, and thus perhaps aid in accounting for the difficulty so far experienced in attempts at pyritically smelting copper-nickel ores. We have used the term flowing temperature to avoid confusion with the usual melting temperature. The idea at first was that there might be a greater viscosity range in the one matte than in the other. In the early experiments it was in our minds to determine the relative fluidity of the mattes at a given temperature. Looking to this end we tried pouring equal quantities of matte at the same temperature down an inclined graphite slab, and comparing the distances traveled. Results from such experiments were not satisfactory. We next tried pouring equal quantities at the same temperature through a drilled hole in an Acheson graphite crucible, timing the flow with a stop watch, the whole operation being carried out in the muffle. The flowing temperatures of the mattes tried in this way appeared to be about the same, and there was no marked difference in their fluidity when well fused. Oxidation gave some trouble. These experiments finally led to the adoption of the following apparatus which we thought at the time was wholly original with us, but which we have since found was described by W. McA. Johnson.' The tray used was a slab of graphite 8 in. long, 2 in. wide and ¼ in. thick. It had six holes, into each of which sat a cup of Acheson graphite. Centrally in the bottom of each cup was a vertically drilled hole 3/16 in. in diameter and ½ in. long. The mattes to be tested were put into the cups, in a solid piece. The cups were covered with inverted Battersea "A" cups. The tray was put into the muffle of a gas-fired furnace. Supports on .each end held the tray about 2 in. from the floor of the muffle. Udder

Jan 6, 1916

By P. Bouéry

This account of a contrivance which has been found serviceable in practice may be of interest to engineers, and especially to those engaged in hydraulic mining. In that process, one feature which seems at first sight to possess little significance, is highly important in its effects—namely, the regular supply of water to the " giants." The chief condition of this regularity is an even flow in the pipe-line from the penstock to the nozzle.' This, of course, requires that the penstock be kept full. Any considerable surplus of water, overflowing at the penstock, is a simple waste, unless it be otherwise utilized in the sluices. At all events, it does not affect the delivery of the nozzles. But a deficiency at the penstock may admit air into the pipe; and this may produce hydraulic recoil, injuring the line by incessant vibrations, giving rise to leaks, and even to blow-outs, and (when a partial vacuum exists at the time of the fracture) the collapse of the pipe. An accident of this sort in our main pipe-line, occasioned partly by a settling of the ground and partly by the presence of air in the pipe, led to the employment of the device here described. The line referred to is made of 30-in. pipe, successively reduced to 18 and 15 in. in diameter, for the supply of two giants. By reason of the causes above mentioned, the 30-in. pipe burst more than 1,400 ft. from the penstock, and, despite the air-valve, the 30-in. pipe was collapsed to such a degree that one length of it, next to the penstock, was squeezed together and positively swallowed by the main pipe, through which it traveled for 750 ft., piercing through a short elbow on the way. This remarkable result was undoubtedly the effect of the vacuum suddenly produced when the pipe burst.

Jan 1, 1907

By Ken-ichi Hirano, B. L. Averbach, Morris Cohen, N. Ujiiye

The influence of plastic deformation in compression on the self-diffisivity of a iron has been measured in the temperature range of 742º to 885°C. The diffusivity is enhanced in proportion to the strain rate, but this dependence decreases with increasing temperature. The magnitude of the strain is relatively unimportant in this connection. Strain rates from 0 to -2 x 10-3 sec-1 were investigated, with a corresponding increase in diffusivity up to 3 x 103 times. The results are analyzed in terms of vacancy diffusion and the excess vacancies introduced during dejornzntion. It is concluded that grain boundaries are the main vacancy sinks in polycrystalline iron and that the vacancy lifetime is therefore dependent on the grain size. A typical vacancy lifetime at 800°C with a nzean grain-boundary intercept of 0.3 cm is of the order of 1 sec. LATTICE imperfections are considered to be the dominant mechanism of diffusion in close-packed crystals. Vacant lattice sites are usually the most important defect, but the enhancement of diffusion along grain boundaries and other short-circuiting paths has been well documented. Inasmuch as plastic straining produces a variety of defects, it would be expected that the application of stresses sufficient to cause plastic flow during a diffusion run might result in an increase in the self-diffusivity. Enhanced self-diffusion in a iron under compressive creep has been observed by Buffington and Cohen' and subsequent coworkers.2 Lee and Maddin3,4 have also found an enhancement in the self-diffusivity of silver single crystals undergoing torsional deformation. On the other hand, Darby, Tomizuka, and Balluffi5 have not observed any significant diffusion increase in single crystals of silver deformed either in tension or in compression, although the results in this case may have been affected by the occurrence of recrystallization. With poly crystalline silver, however, Forestieri and Girifalco6 have found en- hanced diffusion during compressive creep. A small decrease in the self-diffusivity of zinc single crystals under compressive loading has been reported,7 but the applied stresses in these experiments were too low to cause appreciable plastic deformation. For the cases in which enhanced diffusion has been found, a number of common effects have been noted. Usually, the ratio of the diffusivity during straining, Ds, to the diffusivity in the unstrained condition, D,, varies linearly with the strain rate, and does not seem to be a function of the plastic strain, at least up to ? = 0.2. Values of Ds/Du of the order of 100 have been reported'-4 but the enhancement decreases with increasing diffusion temperature. The activation energy for diffusion decreases markedly with increasing strain rate and approaches a level of roughly one-half the unstrained value. Most of the current explanations of these observations assume that excess vacancies are generated by the deformation, but rather large concentrations of excess vacancies and/or long lifetimes are required by these theories.',',',' Since the original work on iron, there has been an important improvement in the compressive-loading technique.2 The early data were also analyzed without taking into account the motion of the coordinate system in the specimens undergoing plastic deformation. This problem has now been solved by a number of investigators (see Refs. 11, 12, and the appendix of the present paper). Consequently, the strain-diffusion runs on iron for the Ds measurements were repeated and extended over wider ranges of temperature and strain rate. In addition, the original diffusivity data9 on the unstrained iron have been corrected for the divergence of the beam in the counting system and new data points have been added, resulting in somewhat different values for the self-diffusi-vities in a iron.10 The new values for Du are used in this paper. A comparison of Ds and Du confirms the large enhancement in the self-diffusivity of iron during compressive creep, as previously reported.',2

Jan 1, 1963

By R. E. Reed-Hill, W. H. Hartt

The "(3034) " twin lamellae in magnesium have been reexamined using electron microscope replicas. The double twinning sequence (1011)- (1012) for these lamellae has been reconfirmed. Evidence is presented showing that the irrational habit of these twins is probably the direct result of a need to accommodate the second-order twinning shear. This accommodation vesults in both an external shear in the matrix and an internal shear in the lamella. A model is presented which accounts for the experimental obseruations. HCP metals are generally characterized by strong textures in which the basal planes of the grains tend to be aligned parallel to the rolling direction in sheet or plate and to the axis of wires and rods. Since these directions are normally those in which finished products may be subjected to uniaxial tensile stress, these textures effectively place the crystals of magnesium objects in orientations unfavorable to both basal slip and {1012) twinning, the easily activated deformation systems of this metal. However, when magnesium crystals are deformed near room temperature by a tensile stress nearly parallel to the basal plane, another mode of deformation can occur.',2 This is _a double twin which forms first by twinning on {loll), followed by retwinning on (1012). The resulting twin lamellae are of considerable interest. First, they can be responsible for "brittle fracture''; when a tensile stress axis lies in the basal plane, because the reoriented crystal structure of a lamella is well-aligned for slip while the parent crystal is not. Extensive internal deformation may thus occur while the matrix is still almost undeformed. This deformation can produce a ductile rupture running the length of the twin.3 Complete failure of the specimen may then oc-cure by the spreading of cracks from one twin lamella to another, or by the movement of a crack into a grain boundary and then along grain boundaries. Since the the volume fraction of these doubly twinned elements is normally very small, the fracture may be classed as brittle, although the fracture mechanism is, of itself, essentially ductile. It is quite probable that the ductility transition, normally observed4 in magnesium at or slightly Obove room temperature, is closely associated with these second-order twins. The detailed relationship of these twins to fracture in single crystals will be the topic of another paper. The present paper is concerned with a second important aspect: the irrational habit of these double twins that falls close to {3034), or approximately 7 deg away from the primary (10il) twin habit. There is good reason to believe that this habit results directly

Jan 1, 1968

By G. R. Fitterer

Trends in slag composition in acid open hearth practice, particularly the variation in iron and manganese oxides during refining, are reviewed. A procedure which is currently being used to control the refining reactions is described and partially explained through slag phase diagram considerations. In addition, the ionic nature of these slags is considered and it is proposed that silica combines with the oxide ion and forms a series of complex silicate ions. The effect of basic oxides such as FeO, MnO, and CaO is apparently additive in furnishing the oxide ion for this purpose. IT is now possible to control192 the refining of steel in an acid open hearth furnace to a surprising degree. This control has been brought about through the knowledge and use of several facts and tests. These are: 1—A planned charge analysis based on a knowledge of the type of fuel, the bath depth, etc. 2—Knowledge and control of rate of fuel input as well as its method of atomization, if any. 3—Determination of the slag fluidity. 4—Bath temperatures (use of the Pt-Pt-Rh thermocouple). 5—Periodic determination of carbon content (use of the Carb-analyzer or Carbometer). Through the use of these control methods, a heat may be made to "melt-in" with or without residual manganese and silicon. The rate of refining or carbon elimination may be controlled accurately, and the desired tapping (or "go-ahead") carbon may be approached at a rapid or slow rate according to preference and type of steel being made. Thus operating time may be predetermined and greatly reduced. Further, all of the refining can be done without any ore or other oxidizing additions, and the heat may be brought to the desired tapping temperature simultaneously with the attainment of the desired carbon analysis. This control procedure is being used in most acid plants in the United States today and has been de- scribed.', ' Although the slag metal relations are sufficiently well known to control the heat as stated, yet it is possible to account for only about two-thirds' of the 0, which must have been used for the elimination of the carbon and other metalloids. Phase diagram studies' of the slags, slag weights, the metal particle theory,' ore additions, limestone additions, etc., may all be taken into consideration; yet, the mechanism of oxidation and source of all the oxygen remain to be explained. This paper reviews some of the principles upon which the control methods were based and proposes other possibilities regarding the unexplained phenomena. Old and New Acid Open Hearth Practice Some of the recent statements in the literature regarding acid open hearth operation are based on old heat data which are not typical of modern American practice. These old heat logs have been responsible for many misconceptions regarding the acid hearth practice and represent heats which do not coincide with modern methods. In recent years, American practice has been altered materially and these changes will be briefly described. Modern American Practice: A typical log of a modern American acid open hearth heat' is shown in Fig. 1 which indicates that the refining time was only two hours, during which the carbon was eliminated rapidly and the bath temperature increased at a fast rate. The manganese and silicon contents of the metal were essentially eliminated and their oxides had become constituent parts of the slag at the "melt-down" period. During the course of the heat, the MnO content of the slag remained practi-

Jan 1, 1954

By Lester Guttman

The connection between short-range order and thermodynamic activities in binary solid solutions has been pointed out by Birchenall1 who calculated approximate values of the energy of interaction of Zn and Cu and of the degree of short-range order in alpha-brass at one composition and two temperatures. The purpose of this note is to call attention to a somewhat more accurate theory than that used by Birchenall and to extend the calculations to a wider range of temperatures and compositions as a means of testing its applicability. This is an example of the well-known general method of comparing measured thermodynamic functions of a system with those calculated from a microscopic model by means of statistical mechanics. In this case, mathematical approximations must be used which make difficult any decision about the validity of the model. Birchenall's statistical method resembles closely that calletl by Fowler and Guggenheim2 the "quasi-chemical" method which has been shown to lead in certain cases to results identical with those obtained by the method of Bethe.3 The quasi-chemical method has been extended by Takagi4 to give general formulas for the free energy of binary solid solutions based on several lattices at all compositions and temperatures. Specifically, he treats the four systems typified by: I. ß—brass; 2. a— brass; 3. AuCus; 4. AuCu. When the temperature is so high that no long-range order exists, these formulas reduce to the same form for all lattice types, namely: F - FO = (E - EO) - T(S - S°) = ½N(c — x)(2vAB — vAa - Vbb) + M1/2KTzN[x log x + 2(c - x) log (c - X) + (I - 26 + X) log (1 - 2c + x)] -kT(z - I)N[c log c+(I-c) log (I -c)] Eq 1 Here the symbols have the following meanings: F—Helmholtz free energy E—nergy 5—ntropy k—the gas constant per molecule z—coordination number, (e.g. I2 in a-brass). N—total number of atoms c—atomic fraction of A Vaa, vbb, vab—nergy per bond of the corresponding bonds log means log, throughout The superscript ° denotes the thermodynamic fuliction in the standard state, which has been chosen to be pure A or B with the same crystal structure as the solid solution. The quantity x is the ratio of the number of A-A bonds to the total number and for minimum F satisfies the equilibrium condition Vaa + Vbb — 2Vab _ (c — x)2 kT l0g x(i - 2C + x The free energy may also be written in terms of /La and B, the chemical potentials or partial free energies per alom:

Jan 1, 1949

By Lester Guttman

The connection between short-range order and thermodynamic activities in binary solid solutions has been pointed out by Birchenall1 who calculated approximate values of the energy of interaction of Zn and Cu and of the degree of short-range order in alpha-brass at one composition and two temperatures. The purpose of this note is to call attention to a somewhat more accurate theory than that used by Birchenall and to extend the calculations to a wider range of temperatures and compositions as a means of testing its applicability. This is an example of the well-known general method of comparing measured thermodynamic functions of a system with those calculated from a microscopic model by means of statistical mechanics. In this case, mathematical approximations must be used which make difficult any decision about the validity of the model. Birchenall's statistical method resembles closely that calletl by Fowler and Guggenheim2 the "quasi-chemical" method which has been shown to lead in certain cases to results identical with those obtained by the method of Bethe.3 The quasi-chemical method has been extended by Takagi4 to give general formulas for the free energy of binary solid solutions based on several lattices at all compositions and temperatures. Specifically, he treats the four systems typified by: I. ß—brass; 2. a— brass; 3. AuCus; 4. AuCu. When the temperature is so high that no long-range order exists, these formulas reduce to the same form for all lattice types, namely: F - FO = (E - EO) - T(S - S°) = ½N(c — x)(2vAB — vAa - Vbb) + M1/2KTzN[x log x + 2(c - x) log (c - X) + (I - 26 + X) log (1 - 2c + x)] -kT(z - I)N[c log c+(I-c) log (I -c)] Eq 1 Here the symbols have the following meanings: F—Helmholtz free energy E—nergy 5—ntropy k—the gas constant per molecule z—coordination number, (e.g. I2 in a-brass). N—total number of atoms c—atomic fraction of A Vaa, vbb, vab—nergy per bond of the corresponding bonds log means log, throughout The superscript ° denotes the thermodynamic fuliction in the standard state, which has been chosen to be pure A or B with the same crystal structure as the solid solution. The quantity x is the ratio of the number of A-A bonds to the total number and for minimum F satisfies the equilibrium condition Vaa + Vbb — 2Vab _ (c — x)2 kT l0g x(i - 2C + x The free energy may also be written in terms of /La and B, the chemical potentials or partial free energies per alom:

Jan 1, 1949

By William M. Bowron

In the hope that a brief description of the conditions that are favorable or unfavorable to success in the practical treatment of titaniferous ores in the blast-furnace may not be without interest to the members of the Institute, the present paper is submitted. The class of ores of which I speak may be described as magnetites, with a gangue of siliceous matter, in which a portion of the silica is replaced by titanic acid. Professor Dana, in his System of Mineralogy, gives a long list of representative analyses of titanic iron ore in which the percentage of titanic acid varies from 59 down to 34. If the percentage is below the latter figure, the ore is no longer recognized as a "titanic ore;" although, according to my experience, titanic acid is present, in small quantities, in almost all ores. In the methods followed in ordinary analysis it is usually included with the "insoluble matter," unless special search is made for it. In the ores usually regarded as "titanic "the proportion of titanic acid frequently assumes quasi definite percentages, such as from 4 to 5, 8 to 9,12 to 13, and so on, in an ascending scale to those higher percentages that do not at present concern us. The proportions quoted characterize large masses of ore that are now accessible to market and are lying idle only on account of the titanic stigma. My experience with titanic acid in the furnace began in England, fourteen years ago, with my being employed as chemist by the manager of the Norwegian Titanic Iron Company, which was at that time smelting, without mixture, ilmenite from Norway in a furnace 16' X 50'. The process, regarded as a process, was a perfect success; but the enormous quantity of fuel required, the small quantity of iron in the ore, and the cost and uncertainty of importation militated seriously against its commercial success, and a few years saw the attempt abandoned. The metallurgy being successful, an at-

Jan 1, 1883

By James K. Stanley

WHEN a plastically deformed metal is heated to a certain temperature, it undergoes a complete change in microstructure, the consequence of which is a marked alteration of mechanical properties such as hardness, strength and ductility. This change in microstructure occurs by recrystallization and is a process involving the formation and growth of strain-free nuclei in the deformed matrix. These nuclei continue to form with time and grow until a new grain structure replaces the cold-worked structure. The formation of the nuclei in the deformed sheet of 1 per cent silicon ferrite is illustrated in Fig. 1. If a recrystallization is conducted isothermally, a measurement of the fraction of the matrix recrystallized plotted against time leads to an isothermal recrystallization curve, first established in 1942.1 Such recrystallization curves are shown in Fig. 4. These curves show that the recrystallization of a cold-worked metal is best considered as a rate process rather than a time independent process such as is suggested by the improperly named and misleading recrystallization diagrams involving deformation, temperature, and grain size. 2-5 Any study of the rate of recrystallization resolves itself into a study of the component rates of nucleation and growth. The previous paper' provided an account of the determination of the rates of nucleation; N, the number of nuclei formed per unit time per unit of unrecrystallized area, and growth, G, the radial growth in unit time, in the recrystallization of silicon ferrite (1 per cent Si). A method was developed to furnish experimental data for evaluating the effect of the recrystallization variables on N and G. The mathematical analysis for the derivation of the isothermal recrystallization curve was developed for a two-dimensional case (in thin sheets where the diameter of the recrystallized grain is greater than the sheet thickness). The present paper is a continuation of the study of recrystallization of 1 per cent silicon ferrite begun in 1942.1 In this work the effect of the factors deformation, temperature, grain size, composition, and recovery is studied with respect to the rates of nucleation and growth. At the same time it is shown how the cooperation of N and G affects the isothermal recrystallization curve. The study of these variables on N and G has a definite bearing on the mechanism of recrystallization and should lay a foundation for a rational theory on the subject. PROCEDURE The procedure used in these experiments was essentially the same as that described previously but in certain details some changes were made in the interests of speed. With few exceptions, the procedure is the same for the study of all the variables. Where the procedure is different from standard manipulations attention is called to this fact.

Jan 1, 1945

By Charles M. Rolker

It is now three years ago that I wrote a paper on the fire which broke out in October, 1880, at the Chrysolite mine, Leadville, Col orado, of which I was at that time manager. The paper was read by title at the Harrisburg meeting in 1881, and was accompanied by plans and sections fully illustrating it. It was written to invite a general discussion of the course pursued in the management of that fire, since the various fragmentary and sometimes prejudiced or inaccurate newspaper accounts were not suitable to base judg ment on. The paper I offered, gave the facts as they appeared in the contemporaneous record which I had kept. At that time, a dif ference of opinion had arisen with an adjoining mine, as to possible damages entailed through the fire; and a law suit was talked of. In view of these circumstances, the President of the Chrysolite Company advised a temporary withdrawal of my paper. Somewhat later, I withdrew it entirely, because of the unlooked-for delay in * arranging the controversy referred to. It. has now, indeed, been amicably settled; but the lapse of time has deprived the matter of much of its immediate professional interest. To the urgent request of some of the members, that I should, at least, give a description of the fire- and gas-proof bulkheads employed, I yield with some hesitation, since I lay no claim whatsoever to orig inality in these devices, and therefore question the value of such a paper. The fire originated by accident, in the Chrysolite, a mine comprising extensive and more or less irregular workings, containing immense quantities of timbering, but partially packed with waste rock or earth. This class of mines is numerously represented at

Jan 1, 1885

By Julian Kennedy Edgar

THINKING that it may prove of interest to the Institute, I have prepared a short account of the blowing in and subsequent working of the "A" furnace of the Edgar Thomson Steel Works. This furnace was built for the purpose of making spiegel, but has been started and is now running on Bessemer iron. The shape and size of the furnace are shown in the accompanying drawing. It will be seen that the section is formed of lines making very small angles with each other. In fact, an arc of a circle can be drawn, from the top to the tuyeres, which will nowhere deviate more than two inches from the lines given. In building, also, great pains were taken to gradually round the angles, so that the most careful observer, standing in the crucible and looking upward, could not tell at what points the slopes changed. It will also be seen that the widest part of the furnace is almost exactly midway between the bottom and the stock line, The flattest slope is maintained for 20 feet above the crucible, and is about 1 s inch to the foot from the perpendicular. The furnace is lined with small brick throughout, and has six tuyeres four inches in diameter, which project seven inches inside of crucible. There are three Siemens-Cowper-Cochrane stoves, each 15 feet in diameter by 50 feet high. Blast is furnished by an upright engine with 32-inch steam cylinder, 84-inch air cylinder, and 48-inch stroke. The steam cylinder has balanced poppet valves, working horizontally. The steam valves are worked by a Porter link-movement in order to obtain a variable cut-off. The exhaust valves are worked by a separate eccentric. It is intended to attach a governor to the cut-off, but at present it is set by hand. The steam cylinder is

Jan 1, 1880

By Julian Kennedy

THINKING that it may prove of interest to the Institute, 1 have prepared a short; account of the blowing in and subsequent working of the "A" furnace of the Edgar Thomson Steel Works. This furnace was built for the purpose of making spiegel, but has been started and is now running on Bessemer iron. The shape and size of the furnace are shown in the accompanying drawing. It will be seen that the section is formed of lines making very small angles with each other. In fact, an arc of a circle can be drawn, from the top to the tuyeres, which will nowhere deviate more than two inches from the lines given. In building, also, great pains were taken to gradually round the angles, so that the most careful observer, standing in the crucible and looking upward, could not tell at what points the slopes changed. It will also be seen that the widest part of the furnace is almost exactly midway between the bottom and the stock line. The flattest slope is maintained for 20 feet above the crucible, and is about 18 inch to the foot from the perpendicular. The furnace is lined with small brick throughout, and has six tuyeres four inches in diameter, which project seven inches inside of crucible. There are three Siemens-Cowper-Cochrane stoves, each 15 feet in diameter by 50 feet high. Blast is furnished by an upright engine with 32-inch steam cylinder, 84-inch air cylinder, and 48-inch stroke. The steam cylinder has balanced poppet valves, working horizontally. The steam valves are worked by a Porter link-movement in order to obtain a variable cut-off. The exhaust valves are worked by a separate eccentric. It is intended to attach a governor to the cut-off, but at present it is set by hand. The steam cylinder is

Jan 1, 1880

By Kenneth Seaver

Discussion of the paper of KENNETH SEAVER, presented at the San Francisco meeting, September, 1915 and at the New York meeting, February, 1916, and printed in Bulletin No. 105, September, 1915, pp. 1913 to 1927. WILLIAM HUTTON BLAUVELT, Syracuse, N. Y.-I think that Professor Richards' statement regarding the reason for the failure of the Bethlehem ovens was due to a misconception on his part. Silica bricks were not used because the ovens were built under German design and management and it has not been the practice in Europe to use silica brick nor has it been necessary, on account of their lower heats and slower coking time as compared with the present American practice. J. W. RICHARDS, So. Bethlehem, Pa.-While acting as Chairman at the San Francisco meeting, in introducing this paper of Mr. Seaver, I made some remarks in discussion referring to unsuitable brick having been used in a coke plant at So. Bethlehem, Pa., and being the principal cause of the failure of these ovens. This statement having come to the attention of the Didier-March Co. of Perth Amboy, N. J., who furnished the firebrick used in the construction in the original ovens referred to, at the Lehigh Coke Works, near So. Bethlehem, Pa., their. manager, Geo. A. Balz has corresponded with me, and wishes to have placed on record a general denial of the statement referred to. As a matter of justice to the manufacturers of the firebrick, it is but right that their statement should be given as much publicity as my statement which has been objected to, and I take pleasure in placing upon record the statement of Mr. Balz, general manager for Didier-March Co., extracted from a letter to me dated Jan. 14, as follows: "The

Jan 5, 1916

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

Jan 1, 1980

By P. Greenfield, P. A. Beck

The phase is a hard and extremely brittle material with a tetragonal crystal structure, containing 30 atoms per unit cell' It occurs in many binary and ternary alloys of the transition elements. The existence of twelve a phases has been reported in binary alloys of metals from the group vanadium, chromium, molybdenum, and tungsten with metals from the group manganese, iron, cobalt, and nickel. It is a characteristic fact that the composition of the o- phases in the various binary systems is not the same. Rather, there is a gradual shift in composition, for instance in the series of chromium a phases, approximately as follows: CrMn,, FeCr, Cr3Co,. In recent years several ideas have been put forward to account for this variability of composition. SullyZ proposed that a was a type of electron compound, characterized by 1.7 electrons per atom in excess of the number required to fill the Pauling atomic orbitals. These excess electrons were supposed to just fill the first Brillouin zone of the u structure. However, later work indicated that the phase is ferromagnetic at low temperatures, so that a- is unlikely to be a full zone compound.~ Another proposal,* which is also based on the structure of the transition elements advanced by Pauling, and in fact leads to essentially the same a compositions as Sully's theory, suggests that the u phase is characterized by a constant number of electron vacancies per atom. The electron vacancy numbers N,. used were originally the same as those in the Pauling theory, but were later modified empirically vn order to bring about better agreement with data for the p phase in certain ternary systems. For alloys, N,, was calculated on the assumption of simple additivity from the electron vacancy numbers of the components, as follows: N,. = 4.66 (Mo + Cr + V) + 3.2 (Mn) + 2.2 (Fe) + 1.71 (Co) + 1.6 (Ni). On this basis a reasonably constant value of N, = 3.4 was obtained for all of the binary u phases and a fairly constant value of N,, = 3.1 for the various p phases. More recently, Bloom and Granta pointed out that a similar correlation with the total number of 3d and 4s electrons per atom is also fairly well fulfilled and concluded that no reference need be made to the Pauling theory. This proposal does not lead to the same binary a compositions as the one described above, so that the relative merits of the two proposals may be determined on the basis of direct comparison with experimental composition data. The purpose of the present paper is to provide such a comparison. Since the experimental data for the composition ranges of several of the known u phases were rather incomplete, it was decided to carry out new experimental determinations for many of the binary systems. Experimental Procedure The alloys were prepared by induction melting in recrystallized alumina crucibles, either in vacuum or in helium atmospheres. Some aluminum was picked up from the crucibles in the alloys of high vanadium content, but this was minimized by keeping the alloys in the molten state for as short a time as possible. The maximum aluminum impurity was 0.13 wt pct by chemical analysis, in an alloy containing over 50 wt pct V. In general, the as-melted compositions agreed accurately with those obtained by chemical analysis. In the case of manganese, however, losses inevitably occurred; consequently all manganese alloys were analyzed. Specimens of all alloys were annealed at temperatures ranging from 1000" to 1300°C in an atmosphere of purified 92 pct helium and 8 pct hydrogen mixture. All manganese alloys were sealed in quartz tubes under vacuum before annealing. The specimens were held at temperature for between four and eight days before being quenched into cold water. Alloys were prepared for microscopic examination by mechanical polishing, usually followed by electrolytic etching. X-ray diffraction specimens were prepared by crushing the homogenized alloys, and by reanneal-ing the obtained powders in evacuated quartz tubes for a few hours at the temperature of the lump anneal. X-ray diffraction patterns were made with unfiltered chromium radiation, using an asymmetrical focusing camera of high dispersion. Using microscopic and X-ray techniques jointly, the accuracy

Jan 1, 1955

By Frank Foote, E. R. Jette

In recent years the constitution of the high-silver aluminum-silver alloys has been extensively investigated. Hansenl has reviewed the literature to 1935. More recently, Obinata and Hagiya,2 Hofmann and Volk,3 Taziri4 and Tishchenko5 have confirmed the general features of the phase diagram in the region around 25 atomic per cent aluminum. In this paper we present the results of high-precision measurements of lattice constants of the silver-rich alpha solid solution in the homogeneous range and the neighboring two-phase regions. These results are used to establish the nature of the solid solution, the identity of directly measured densities with those calculated from lattice constants and the homogeneity limits of the alpha solid solution with respect to three different neighboring phases. A study of the earlier investigations indicated that the last two subjects in particular required new and accurate data. Experimental Procedure Preparation of the Alloys.—The alloys were made from high-purity silver and aluminum. The silver was "Proof Silver," 99.999 per cent pure, supplied by the U. S. Metals Refining Co. The aluminum was 99.97 per cent pure (contained Si, 0.009 per cent; Fe, 0.0016 per cent; Cu, 0.004 per cent) and was supplied by the Aluminum Company of America. The lattice constants of these two materials have been reported by Jette and Foote.6 Weighed amounts of the two metals were placed in alundum crucibles and melted in vacuo in a high-frequency induction furnace. The melts were allowed to cool in the crucible, the ingots thus obtained weighed about 10 grams. These ingots were then filed clean, hamered, again cleaned and given a homogenizing anneal in vacuo of from 6 to 15 days at temperatures ranging from 500" to 695°C. The ingots were air-cooled from the annealing temperature. Lattice-constant Measurements.—Carefully prepared filings for X-ray analysis were sealed into evacuated quartz or Pyrex tubes and annealed for various periods of time at suitable temperatures. The furnaces used were vertical, rapid-quenching furnaces, the samples being quenched by crushing the sample tube under water by means of a heavy plunger. The general X-ray technique has been previously described6 The cameras were of the symmetrical, back-reflection, focussing type. Ka, radiation from a cobait-nickel alloy target was used. The wave-length values were taken from the second edition of Siegbaum's book.7 A correction for the index of refraction was applied and the lattice constants were calculated by the method of Cohen.8, 6 The lattice constants were calculated to a common temperature of 25°C., using the value of the linear expansion coefficient of pure silver as 18.9 X 10-6. Presumably the expansion coefficient for

Jan 1, 1941

By Frank Foote, E. R. Jette

In recent years the constitution of the high-silver aluminum-silver alloys has been extensively investigated. Hansenl has reviewed the literature to 1935. More recently, Obinata and Hagiya,2 Hofmann and Volk,3 Taziri4 and Tishchenko5 have confirmed the general features of the phase diagram in the region around 25 atomic per cent aluminum. In this paper we present the results of high-precision measurements of lattice constants of the silver-rich alpha solid solution in the homogeneous range and the neighboring two-phase regions. These results are used to establish the nature of the solid solution, the identity of directly measured densities with those calculated from lattice constants and the homogeneity limits of the alpha solid solution with respect to three different neighboring phases. A study of the earlier investigations indicated that the last two subjects in particular required new and accurate data. Experimental Procedure Preparation of the Alloys.—The alloys were made from high-purity silver and aluminum. The silver was "Proof Silver," 99.999 per cent pure, supplied by the U. S. Metals Refining Co. The aluminum was 99.97 per cent pure (contained Si, 0.009 per cent; Fe, 0.0016 per cent; Cu, 0.004 per cent) and was supplied by the Aluminum Company of America. The lattice constants of these two materials have been reported by Jette and Foote.6 Weighed amounts of the two metals were placed in alundum crucibles and melted in vacuo in a high-frequency induction furnace. The melts were allowed to cool in the crucible, the ingots thus obtained weighed about 10 grams. These ingots were then filed clean, hamered, again cleaned and given a homogenizing anneal in vacuo of from 6 to 15 days at temperatures ranging from 500" to 695°C. The ingots were air-cooled from the annealing temperature. Lattice-constant Measurements.—Carefully prepared filings for X-ray analysis were sealed into evacuated quartz or Pyrex tubes and annealed for various periods of time at suitable temperatures. The furnaces used were vertical, rapid-quenching furnaces, the samples being quenched by crushing the sample tube under water by means of a heavy plunger. The general X-ray technique has been previously described6 The cameras were of the symmetrical, back-reflection, focussing type. Ka, radiation from a cobait-nickel alloy target was used. The wave-length values were taken from the second edition of Siegbaum's book.7 A correction for the index of refraction was applied and the lattice constants were calculated by the method of Cohen.8, 6 The lattice constants were calculated to a common temperature of 25°C., using the value of the linear expansion coefficient of pure silver as 18.9 X 10-6. Presumably the expansion coefficient for

Jan 1, 1941

By J. W. Ristori, V. R. Garfias, R. V. Whetshel

During the past eight years, in trying to estimate world consumption of petroleum and related products, the authors have been unable to account for all the supplies available in any one year. There has remained at all times a balance, which at first was thought to represent almost entirely additions to stocks in foreign countries. But as this discrepancy continued year after year-over 148,000,000 bbl. in 1937—it became unreasonable to conclude that corresponding additional foreign storage capacity was continuously being made available. It became therefore clear that the balance in question was due to other causes than to additions to stocks. Last year Mr. A. G. White, Chief Economist of the Petroleum Economics Division of the United States Bureau of Mines, pointed out to one of the authors that an unknown and important factor in consumption of petroleum and related products is to be found in the requirements for military purposes in foreign countries. This paper is the result of Mr. White's timely suggestion. There are no reliable data available either on the storage capacity, and therefore oil stocks, or on the petroleum consumption for military purposes in foreign countries. This information is so closely related to national defense that its divulgation is forbidden. One can therefore but surmise as to these facilities and needs in line with the relative strength of the military land, air and sea forces of the various countries. The authors have assumed many of the component factors that go to make the tables herein presented, such as fuel consumption of fighting ships in relation to tonnage and horsepower, gasoline consumption of air fleets in relation to number of planes, and the consumption of petroleum products by mechanized armies; but in making these assumptions they have availed themselves of the advice and counsel of those whose wide experience in these questions make their views authoritative. The opportunities for error in an estimate of this nature are obvious and ever present; to illustrate: The air fleets in Spain no doubt consumed

Jan 1, 1938

By Eckley B. Coxe

I wish to call the attention of the Institute to a peculiar variety of anthracite which occurs in the Buck Mountain vein at our collieries at Drifton, and in the same and other veins in different localities in the anthracite coal-fields. It is known among the workmen as iron-gray or cast-iron. It has a dull, greasy appearance, as if a piece of ordinary anthracite had been rubbed with a dirty and greasy rag and allowed to dry. It was formerly considered a very impure coal containing a high percentage of ash, and was picked out of the coal and thrown away. But the following analysis of it and of its ash, made by Mr. J. Blodget Britton, of Philadelphia, shows that such is not the case, the percentage of ash not being much higher than that of the ordinary anthracites as they are prepared for market. ANALYSIS OF COAL. Water,.........4.36 Fixed carbon, by difference,.. 84.90 Volatile combustible matter,. . 3 48 Ash,..........7.26 100.00 The carbon proved to some extent to be of the nature of graphite, and slowly combustible. ANALYSIS OF ASH. Silica,.........25.66 Sulphur,........ .17 Alumina,........27.03 Phosphoric acid,.......21 Ferric oxide,.......42.83 Alkali, undetermined matter and Lime,.........1.56 loss,.........60 Magnesia,........1.83 Manganous oxide,......11 100.00 We recently collected a quantity of the substance and made a fire with it, in an ordinary stove, which was kept up several days. We found that it burned with intense heat, and apparently as freely as our other coal does. Mr. Britton is probably right in his view, that the difference in appearance is not due to impurities in the coal, but to the fact that the carbon is in a more or less graphitic form, as many of the standard coals are no purer. I bring this before the Institute as I know that a large quantity of this valuable fuel is thrown away every year, on account of its supposed impurities.

Jan 1, 1879

By Thomas D. West

A short time ago, I had occasion to cast iron plates 1 in. thick, direct from metal containing Si, 0.51; 8, 0.045; Mn, 0.75; and P, 0.094 per cent. Much to my astonishment, I found that there was no trouble in planing them; whereas, if cupolaimetal of like composition had been used,*the planing would have been a difficult operation. I have often noticed a greater fluidity or " life " in furnace-metal, as compared with the cupola-product. Iron can be seen flowing down the furnace-runners from 50 to 100 ft., and reaching the last pig-bed in satisfactory condition, while cupola-metal might have solidified before it had flowed so far. I have seen Bessemer iron, which, on account of its low phosphorus-content, does not have the " life " of ordinary foundry-iron, held in a 30-ton ladle for nearly an hour and a half; and after skimming off the coke-dust, it still had to be cooled off' considerably before being cast. As a general proposition, it is known that the lower sulphur-content and the frequently higher temperature of direct-metal, compared with the same iron remelted in the cupola, has much to do with its greater life; yet some problems connected with this phenomenon seem to call for further study. For instance, furnace-metal containing more than 1 per cent. of silicon holds carbon, which is separated later as "kish." This separation does not take place to any great degree while the metal is very hot; but during its gradual cooling, at times, the kish is given off in such large quantities as to cover the ground from 20 to 30 ft. around the ladle. In making castings of direct-metal, especially with a high content of silicon, the separation of kish becomes an annoyance. Perhaps this throwing out of the excess of carbon makes the life of the metal shorter, after it has been remelted in a

Jan 1, 1905