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By R. T. Hukki, A. M. Gaudin

Previous work on the principles of comminution has shown: (I) that the surface produced is proportional to work input (Rittinger law,1a-3); (2) that there is regularity to the weight distribution of the fragments according to size.4-10 In this paper it is brought out that the surface on the fragments is distributed in definite and simple relation to size. The experimental work has involved: I. Construction of an apparatus capable of measuring the surface of mineral fragments independently of the chemical composition of the fragments and independently of the site of the surface; 2. Refining the methods available for measurement of particle size; 3. Designing and building a crusher capable of operating on very small quantities of mineral, if necessary on single crystals, and in such fashion as to minimize handling losses of material. Complete experiments have been carried out with massive quartz and individual quartz crystals. partial experiments, lacking surface measurements, have been made with glass spheres, galena, sphalerite, fluo-rite, salt and coal. Introduction The existence of regularity in weight distribution with size was noted many years ago, especially by A. 0. Gates;' the subject was also studied in detail by one of us.6 In the latter paper it was shown that rocks can be divided into two classes: homogeneous rocks, which show no preferential breaking, and heterogeneous rocks, which show preferential breaking at the grain size of the rock. It was shown, furthermore, that the fragments obtained by rupturing a homogeneous rock occur (in the fine range) in such abundance as to permit the writing of a relatively simple equation to relate the weight retained on a screen to the screen opening. With screens of which the openings are in constant ratio, the weight retained, w, is related to the screen size x by the equation w = Cxm [I] In this equation C and m are experimental constants. A plot of weight retained against particle size is a straight line of slope m if the scales for x and w are both logarithmic. In the fine range, the slopes of the size-distribution graphs plotted according to the method described above vary within a limited range. An inspection of a number of size-distribution data by various experimenters indicates that the slope very seldom exceeds 1.0, but is usually greater than 0.7. More recently, schuhmann8 proposed a method of charting that has so many advantages of its own that it has been used primarily in this work. For fine particles Schuhmann has found that the data are represented by the equation (x)m k [2]

Jan 1, 1947

By A. M. Gaudin, R. T. Hukki

Previous work on the principles of comminution has shown: (I) that the surface produced is proportional to work input (Rittinger law,1a-3); (2) that there is regularity to the weight distribution of the fragments according to size.4-10 In this paper it is brought out that the surface on the fragments is distributed in definite and simple relation to size. The experimental work has involved: I. Construction of an apparatus capable of measuring the surface of mineral fragments independently of the chemical composition of the fragments and independently of the site of the surface; 2. Refining the methods available for measurement of particle size; 3. Designing and building a crusher capable of operating on very small quantities of mineral, if necessary on single crystals, and in such fashion as to minimize handling losses of material. Complete experiments have been carried out with massive quartz and individual quartz crystals. partial experiments, lacking surface measurements, have been made with glass spheres, galena, sphalerite, fluo-rite, salt and coal. Introduction The existence of regularity in weight distribution with size was noted many years ago, especially by A. 0. Gates;' the subject was also studied in detail by one of us.6 In the latter paper it was shown that rocks can be divided into two classes: homogeneous rocks, which show no preferential breaking, and heterogeneous rocks, which show preferential breaking at the grain size of the rock. It was shown, furthermore, that the fragments obtained by rupturing a homogeneous rock occur (in the fine range) in such abundance as to permit the writing of a relatively simple equation to relate the weight retained on a screen to the screen opening. With screens of which the openings are in constant ratio, the weight retained, w, is related to the screen size x by the equation w = Cxm [I] In this equation C and m are experimental constants. A plot of weight retained against particle size is a straight line of slope m if the scales for x and w are both logarithmic. In the fine range, the slopes of the size-distribution graphs plotted according to the method described above vary within a limited range. An inspection of a number of size-distribution data by various experimenters indicates that the slope very seldom exceeds 1.0, but is usually greater than 0.7. More recently, schuhmann8 proposed a method of charting that has so many advantages of its own that it has been used primarily in this work. For fine particles Schuhmann has found that the data are represented by the equation (x)m k [2]

Jan 1, 1947

By J. O. Nelson, C. J. Altstetter

Single crystals of hcp cobalt, 3 mm in diameter and up to 35 cm long, were grown using an electron-beam, zone-melting technique. The martensitic-phase transformation was studied in single-crystalline and polycrystalline specimens by making length-change measurements as a function of temperature under various elastic compressive stresses. Upon thermal cycling, single-crystalline or polycrystalline specimens repeatedly transformed almost entirely on the same variant of close-packed plane provided the maximum temperature did not exceed 600°C. Cycling to 1000°C resulted in transformation on more than one {111} variant. This behavior is termed multivariance. The multivariant transformation occurred very rapidly at an M, temperature 2° to 6°C lower than the M, of a transformation which would result in a single-crystal product. Elastic compressive stresses (up to 253 g per sq mm) tended to lower the A, and raise the M, temperatures, decreasing the width of the temperature vs dilatation hysteresis loop. The transformation habit plane and transformation shear direction of an as-grown single crystal were not grossly affected by elastic compressi?ie stress. This was evidenced by similar dilatations on the temperature us dilatation loops joy specimens with and without compressive stress. A dislocation mechanism is proposed to explain the observed results. IT has been shown that, on heating, cobalt transforms martensitically from the hcp to the fcc phase.' The transformation habit plane is (0001)hcp || (lll)fcc and the transformation shear direction is (1010)hcp || (112)fcc. The transformation involves a shear of 1g°28', which may be achieved by a shearing of a/6(112) of every two planes with respect to the plane beneath, thus changing the ABABAB stacking of hcp to the ABCABC stacking of fcc. Associated with the phase change is a 0.3 x 10"3 contraction in the habit plane and a 4.2 X 10"3 expansion perpendicular to the habit plane resulting in a 3.6 x X volume increase on heating.' On cooling, an identical volume decrease takes place. The temperature at which the fcc phase begins to form on heating (A,) is reported as 430°C, and the temperature at which the hcp phase begins to form on cooling from an elevated temperature (A&) is reported as 390oC1,3 Consequently, temperature vs dilatation plots have the form of a hysteresis loop. If heating or cooling is reversed during a transformation, a smaller hysteresis loop results. Upon heating, the transformation is always complete; whereas, fcc is often retained at room temperature as a metastable phase entrapped in the polycrystal-line hexagonal matrix.1,4,5 Two obstacles in the theory of the allotropic-phase transformation of cobalt have been: 1) a detailed knowledge of the product nucleus, and 2) a plausible method of propagation of the transformation. Bilby,8 christian, 7 and seeger 8,9 have suggested a "pole mechanism" as a means of propagation of partiai dislocations from plane to plane. A pole dislocation and a Shockley partial come together at a node. The a/6(112) Shockley partial rotates about the pole dislocation effecting the transformation shear. The pole dislocation must have a 2a/3(111) screw component which causes extension of the transformed region by two atomic planes with each full rotation of the Shockley partial. Bollmannl0 suggested, on the other hand, that transformation propagation occurs due to the stress fields of intersecting (111)-type stacking faults. As faults intersect, a stress distribution is set up about their intersection which is in turn reduced by the emergence of another fault on the second nearest plane. This process continues with the final result of a complete phase transformation. In view of the similarities between deformation and transformation in cobalt, the effect of stress on the transformation would, hopefully, yield valuable information concerning nucleation and propagation. In the present work single-crystalline and polycrystalline specimen length changes were measured as a function of temperature at various compressive loads. PROCEDURE Several orientations of single crystals of hcp cobalt in lengths up to 25 cm were grown by electron-beam floating zone melting from 99.95 and 99.999 pct, 3-mm-diam cobalt rod as supplied by Johnson

Jan 1, 1964

By Paul A. Farrar, Sanford Adler

The Tz-Zr system was reinvestigated using both metallographic and X-ray diffraction techniques. It mas found that titanium and zirconium are soluble in all proportions in both the a and 0 phases. The minimum in the transformation was found at 50 at. pct and 535°C. THE Ti-Zr system has previously been the subject of several investigations.1-6 A study by Hayes et al.5 using magnesium-reduced titanium and zirconium melted in graphite crucibles indicated that the system was a continuous series of solid solutions in both a and 0 phases with a minimum at approximately 545°C and 65 pct* Zr. These conclusions were substantiated by the work of Duwez4 as well as by the limited data of Craighead et al.,3 Fast,2 and deBoer.1 However, a more recent investigation of the titanium-rich region by Ence and Margolin6 indicated that the solubility of zirconium in a, titanium at 500°C is approximately 22 pct with the a + 0 field extending to approximately 47 pct Zr. Therefore in order to resolve this discrepancy the following investigation was initiated. EXPERIMENTAL PROCEDURES The alloys used in this investigation were prepared as 20- to 30-g buttons by nonconsumable electrode melting in a helium atmosphere. The starting materials were Bureau of Mines titanium BHN 71 and Foot Mineral iodide crystal bar zirconium. The titanium was premelted before the alloys were prepared to avoid excessive weight losses in the final melting. The compositions of the alloys prepared were as follows: Ti-12.0, 22.2, 29.0, 39.6, 50.0, 58.0, 72.4, 83.5. and 90.8 pct Zr. Prior to heat treatment the alloys were cold-worked 10 to 20 pct, stopping at the first signs of cracking. Specimens for heat treatment were wrapped in molybdenum sheet and annealed in argon-filled quartz capsules for the following times and temperatures: 750°C-40 days, 675°C-61 days, 600°C—109 days, 575°C-112 days, 550°C-112 days, 525°C—127 days, and 450°C —153 days. Quenching was accomplished by breaking the capsules in an iced-brine solution. The standard techniques used for polishing the specimens involved belt grinding, grinding on emery paper, polishing electrolytically, and etching with Remington "A" etch7 or "R" etch 8 Debye-Scherrer X-ray powder photograms were obtained for a number of samples using a 114.6-mm camera and CuK, radiation. Exposure times were from 19 to 23 hr. The powder samples were obtained by filing to 270 mesh size. After filing the samples were wrapped in molybdenum foil capsuled in quartz and reannealed at the temperature of original heat treatments; following the heat treatment the samples were quenched into iced brine without breaking the capsules. RESULTS AND CONCLUSIONS On the basis of the microstructural examinations of the heat-treated samples and of the X-ray diffraction data, the Ti-Zr system shown in Fig. 1 was constructed. The data indicate that a, and 0 titanium form a complete series of solid solutions with a, and ß zirconium. The minimum was found to occur at 65 pct (50 at. pct) Zr and 535°C, in excellent agreement with the earlier investigations,1-5 see Fig. 2. Typical microstructures are shown in Figs. 3 to 7. Figs. 3, 4, and 5 show the 22.2, 39.6, and 50.0 pct Zr alloys after heat treatment at 675°C for 61 days with the 22.2 pct Zr showing equiaxed a, and the 39.6 pct Zr alloy a + transformed ß, while the 50 pct Zr alloy shows only transformed B. Figs. 6 and 7 show the 29.0 and 39.6 pct Zr alloys after heat treatment for 109 days at 600°C. The 29 pct Zr alloy has an equiaxed a structure while the 39.6 pct alloy has a partially recrystallized a+ß structure. X-ray diffraction data obtained from the 50 pct Zr alloys after heat treatment at 525° and 450°C as well as from the as-cold-rolled material showed only those lineos which couid be indexed a: a titanium, good agreement with the previously published values. 2,4,5,9 Chemical analysis* of the 50 pct Zr alloy

Jan 1, 1967

By H. A. MEGRAW

THE meeting of the A. I. M. E. at Wilkes-Barre, Pa., Sept. 12 to 15, inclusive, celebrated the fiftieth anniversary of the Institute. It was at Wilkes-Barre, in 1871, that the foundation was laid for the great institution that now includes in its roster the greatest names. in mining engineering in every civilized country of the world. The founders of the Institute, with rare prescience, established a common ground upon which all mining engineers, whatever particular branch they might consider most pertinent, could stand securely, assured of a deep-seated interest from their brethren similarly minded in other localities. So wise and clear was the vision of the founders that every engineer connected with mining has found it beneficial, not to say indispensable, to maintain his connection with the Institute and to increase his technical enthusiasm through the medium of the valuable technical publications. The little coterie of 1871 has grown to a strong body of more than 10,000 members in 1921, reflecting the glory of the founders in the record of the accomplishments written on the pages of the fifty years of the

Jan 1, 1921

By C. P. Kempter, H. L. Brown

Recently Chang determined heat content values of tantalum monocarbide and tungsten monocarbide from 325" to985°Kand 326" to 912"K, respectively, and, using other published data, made certain solid-state calculations for these two compounds. Chang expressed his Cp values in units of cal per "g-atom alloy" OK. We consider this poor usage since l) tantalum monocarbide and tungsten monocarbide are not alloys, and 2) an atom of an alloy does not exist. However, one may convert his values to units of cal per mole OK by merely doubling them. For TaC he calculated a Nernst-Lindemann parameter of 9.07 x lo-' "g-atom per cal". We have refined the calculation of this parameter and have arrived at a much lower value. Rather than approximating the true coefficient of volume expansion, a,, as three times the true coefficient of linear expansion, a, we calculated u, from the TaCo.99, lattice expansion data of Fries and Wahman.38 At 25°C a, = 14.3 x 10s per OC. The molar volume was calculated to be 13.32 cu cm per mole at 25°C. From the lattice compression data of Champion and Drickamer~' for "TaC,.,," we determined the room-temperature compressibility to be 3.5 x 10-l3 sq cm per dyne by plotting l/Vo (aV/ap) vs applied pressure. (Since the lowest pressure at which Champion and Drickamer reported a relative volume was 20 kbars, one may calculate an approximate compressibility only. Chang calculated a compressibility of 3.175 x 10-l3 sq cm per dyne from the same data.) We also used twice Chang's value of Cp = 4.38 cal per "g-atom alloy" OK for the molar heat capacity at 25°C. From these four values we calculated a Nernst-Lindemann parameter of 5.8 x 10-l4 mole per erg or 2.4 x lo- ' mole per cal, and a Cdil value of 2.3 x 10' ergs per mole OK. In the case of tungsten monocarbide no isothermal compressibility has been reported; however, one may calculate an approximate Nernst-Lindemann parameter by using the adiabatic compressibility reported by Brown, Armstrong, and Kempter." Using the WC lattice expansion data of Mauer and Bolz~l we calculated a, to be 12., x l0-' per OC. The molar volume was calculated to be 12.5 cu cm per mole. We used twice Chang's value of Cp = 4.18 cal per "g-atom alloy" OK for the molar heat capacity at 25°C. From these four values we calculated an approximate Nernst-Lindemann parameter of 2 x lo-' mole per cal, which is much

Jan 1, 1969

By Walter R. Hibbard, Harold Margolin

The effect of ten ternary additions on the aging of a Cu-Ag alloy was measured by X ray, microstructure and hardness. A supersaturated copper-rich transition structure was found. The effect of the ternary element was related to differences between transition and precipitate lattice parameters and analogies with solution and strain hardening. IN addition to the prerequisite of diminishing solid solubility with falling temperature, the theory of coherency hardening1 proposes that the principal source of hardening during precipitation is strain caused by coherency between the matrix and precipitate. For a given system greater coherency hardening would result from lengthening the period of coherent growth and/or increasing the number of nuclei, other things remaining equal. However, the hardness change during aging is a function of a number of phenomena in addition to coherency hardening, such as dispersion hardening, loss of coherency, solute depletion, matrix recovery or recrystal-lization, coalescence, and their relative time sequences. The present investigation was undertaken to study the effect of ternary additions on the age-hardening of Cu-Ag alloy. For this purpose a series of alloys were made containing as ternary constituents Mg, Al, Si, P, Mn, Ni, Zn, As, In, and Sb. These elements were added to a master 5 wt pct Ag in Cu alloy in such amounts as to obtain alloys listed in Table II containing the following approximate atomic percentages: 96 pct Cu, 3 pct Ag, 1 pct ternary addition. A 97 atomic pct Cu, 3 atomic pct Ag alloy was used as a comparison standard. There have been numerous investigations of age-hardening in Cu-Ag alloys2-lo but few of ternary Cu-Ag alloys. Pfister and Weist" found that 1 wt pct Ni reduced the solubility of Ag in Cu above 600 °C and that the rate of precipitation was slower than in polycrystalline Cu-Ag alloys of similar silver content. More recently Hodge, Jaffee, Dunleavy, and Ogden12 investigated the effect of ternary additions of Mg, Li, P, Cd, Zn, Zr and Be on strength properties of Cu-Ag alloys. Mg, Cd, and P were found to increase strength in the aged and cold-worked condition. Experimental Procedure Charges weighing 7.5 lb were melted in a closed carbon crucible under a reducing atmosphere* of nitrogen and hydrogen. A Durville-type casting procedure with a hot-top arrangement was used to obtain a sound casting, 2x2x43/4 in. Prior to rolling and annealing of the ingots, a trial solution anneal of rolled sections of the hot-top portions indicated that at 780°C melting was avoided except for the Cu-Ag-Sb alloy. This alloy could not be produced as a single phase within the limits of temperature control. i 3" to 5oC, since melting occurred at 64O °C, and below this temperature precipitation was

Jan 1, 1952

By K. Tangri, B. Swaroop

Simultaneous measurements of lattice (elastic) strain by X-ray line shift method and total strain with an electrical strain gage have been carried out on polycrystalli,ne nickel with the help of a specially designed tensometer attachment for the X-ray dif-fractometer. During the initial stages of deformation, the rate of increase in lattice strain closely follows the total strain until the plastic strain sets in. From then onwards, the two strains deviate from each other and with further increase in afiplied stress the rate of increase of lattice strain eventually decreases. Depending upon the mode of unloading, both compressive and tensile strains have been observed in nickel deformed up to 0.29 pct strain. These results have been explained on the basis of the effects of clustering of dislocations and also the production and behavior of point defects during loading and unloading, respectively. POLYCRYSTALS deformed plastically in a uniaxial tension test show residual lattice strains (hereafter referred to as RLS), which broaden the X-ray line profiles and shift their peak positions.''4 It is known that uniform straining of a crystal lattice (macrostrain) produced movement of ddfraction line peaks, whereas nonuniform straining (microstrain) causes line broadening.= Though the nature and origin of RLS in deformed metals is not yet clearly understood, these are believed to be due to the presence of some form of a locked-up stress system. Several possible detailed interpretations6'" of the stress system have been proposed by various workers and common to all these interpretations is the assumption that different parts of the aggregate have different tensile yield stresses; e.g., that a part A yields under a lower applied stress than a part B. Therefore, during the deformation process, the elastic strain in A will be less than that in B, and, after completion of deformation, B will tend to contract further than A but will be prevented from doing so by the restraining influence of A. Thus, when equilibrium is reached, A will be in compression while B is in tension. Although there is general agreement on the correctness of this argument, controversy still exists as to the exact nature of the parts A and B in a deformed metal. In an alternative approach to the creation of parts A and B, many other investigators have assumed that the RLS observed in unloaded specimens are in some way connected with the lack of proportionality between lattice strain and applied stress in the region above the yield stress." cullity13 has prepared a schematic summary of the results of previous workers, mainly Smith and Wood,2'11 which suggests that, above the elastic limit, the lattice strain may increase less rapidly with respect to strain, or may even decrease with increase in applied stress. If the applied stress is then decreased, the lattice strain would decrease along a line parallel to the loading line in the elastic region and thus produce a compressive residual lattice strain after unloading. At equilibrium, to balance these compressive stresses? there would have to be regions under tensile stress which may well be the grain boundaries or the substructure walls formed during deformation. The present investigation was undertaken to gain a better understanding of the nature and origin of RLS and also to experimentally verify the salient features of this hypothesis. EXPERIMENTAL Stress and strain determinations were made with a specially constructed tensometer attachment for the X-ray diffractometer, Fig. 1: which permits the following measurements simultaneously on a sheet specimen under uniaxial tension at various stress levels during loading and unloading: a) lattice strains, E=. in a direction perpendicular to the direction of pulling (x direction) from shifts in X-ray line peak positions; b) the total strain, ex, in the direction of pulling. with the help of an electrical strain gage affixed to the back of the specimen directly below the area irradiated by X-rays: and c) the applied stress, with the help of a load cell which consisted of a calibrated stainless-steel sample of dimensions identical to those of the specimen under investigation, and to which it was coupled. Because of its high stacking fault energy.I4 nickel

Jan 1, 1970

By Robert H. Richards, Richard W. Lodge

A great deal of speculation, as well as actual experiment, has been devoted to ascertaining the changes in the materials (luring their descent in an iron blast-furnace, affecting (1) the chemical constitution, (2) the mechanical condition, and (3) the arrangement of the materials. With a view to throw some light upon the third question, we constructed a model and tried experiments which are here described. Our model is a vertical section of a furnace, with the lines of the Edgar Thomson furnace D of 1885 for the use of which we arc indebted to Mr. Gayley. The model is 40 inches high, and made to scale (1/2 inch equals 1 foot), and the horizontal section of the space through which the charge falls at any point in the descent is 11/2 in. x d, d being the diameter of the furnace at that place. We are unable to say just where the idea of making this model came from ; perhaps, partly from The Principles of the Manufacture of Iron, and Steel, 1884, I. Lowthian Bell, p. 124 ; partly, also, from

Jan 1, 1888

By Seymour G. Epstein

Using a modified capillary-reservoir technique, electromigration of dilute solutions of silver in liquid bismuth has been measured with relatively good precision. The effects of experiment duration, temperature. current density, and silver concentration have been investigated. Chemical diffusion coefficients of silver in liquid bismuth were also measured at temperatures ranging from 300°to 600°C. The effective valence of silver in bismuth was calculated as a function of temperature from a comparison of electric mobilities and diffusion coefficients. In an alloy containing 1 wt pct Ag, the electric mobility of silver increased from 1.65 x X sq cm per v-sec at 300°C to 2.38 x 10-4at 600°C; the diffusion coefficient in-creased from 3.0 to 17.5 x 10-5 sq cm per sec over the same temperature range. Calculated values of effective valence decreased from 0.28 at 300°C to 0.10 at 600°c. ALTHOUGH there has been considerable progress in the theoretical treatment of electron-transport properties in liquid metals, the mechanisms of mass-transport phenomena in liquid metals are still not clearly understood. This is especially true for the case of electro migration, alternatively termed elec-trotransport or electrodiffusion, which is mass transport induced by an applied electric field. A thorough knowledge of the mechanisms governing electromigration will considerably aid in understanding the electronic state of an impurity atom in a liquid metal. Electromigration has been long observed and studied in liquid metals and alloys. However, no satisfactory theory to explain the observed effects has been developed. The disparity in the present theoretical treatments, summarized by Verhoeven,1 has been attributed to the difficulty in describing the momentum transfer between electrons and ions and to the lack of precise measurements in liquid metals, especially at elevated temperatures. Prior to the last decade most of the electromigration studies were qualitative, in that only the direction of migration of alloy constituents was determined with any degree of reliability. These results have been summarized by schwarz,2 who was able to measure the electric mobility of several elements in mercury. More recently electromigration in liquid metals has been measured by a variety of techniques, with a varying degree of success. Mangelsdorf3,4 made precise measurements on dilute amalgams at room temperature, using a technique relating changes in composition to changes in alloy resistivity, but was unable to make measurements at elevated temperatures. Using a modification of this technique, Verhoeven and Hucke5 measured electromigration and resistivities in liquid Bi-Sn alloys. However, the resistivity technique is not sensitive to small composition changes and is impractical for very dilute alloys. Verhoeven and Hucke6 also measured electromigration of several solutes in liquid bismuth by adapting the capillary-reservoir method for determining diffusion coefficients in liquids. The reported precision of these measurements was poor, however, primarily due to the large uncertainties in the chemical analyses to determine concentration changes. Belashchenko7 has summarized the recent Russian investigations of electromigration, many of which, however, are of questionable accuracy. The present study was initiated to develop an experimental technique which would be both versatile and sufficiently sensitive to yield precise measurements of electromigration of solutes in dilute metal alloys at elevated temperatures. Using this technique, a comprehensive study of silver in liquid bismuth was made to determine the effects of experimental variables on the apparent electric mobilities. Chemical diffusion coefficients of silver in liquid bismuth were also measured over the same temperature range for comparison with the electromigration data. EXPERIMENTAL TECHNIQUE Electromigration Measurements. Electromigration of silver in liquid bismuth was measured by the capillary-reservoir technique, similar to that used by Verhoeven and Hucke,6 but modified to yield more

Jan 1, 1967

By R. W. Newcomb

THE constancy of calibration, and to a great extent the life, of a thermoelement is dependent on the suitability of the primary protecting tube in which the wires are mounted, particularly when used at high temperatures. An ideal thermocouple protecting tube would be com-posed of materials that would not contaminate the thermoelement wires contained in it-one that would remain absolutely gas-tight ,it all temperatures of usage, that will not be attacked by gases, or other surrounding agencies, that is not destroyed by heat, that withstands sudden and extreme temperature changes, that affords a high degree of mechanical protection and does not deform at high temperatures, that is a good heat conductor and obtainable in small diameters so as to keep down lag factors. It has not yet been possible to produce tubes of any known mate-rials that will meet all of these conditions. In selecting protecting tubes, therefore, one should be chosen the characteristics of which best fit it to the particular conditions of usage. Frequently conditions are such that two tubes have to be used, a primary gas-tight protecting tube inside of a secondary protecting tube, because certain agencies will attack the primary gas-tight tube unless it is guarded by the outside tube.

Jan 9, 1919

By R. M. Asimow

Both smith1 and wells2 have shown that the dif-fusivity of carbon in austenite increases rapidly with increasing carbon concentration. Smith has shown, in addition, that part but not all of this increase can be attributed to the concentration dependence of the activity coefficient of carbon in austenite. From the work of Eshelby', it is known that, because of the image displacements, there is a uniform dilatation of the material in a body containing random centers of dilatation. It is thus tempting to explain the enhanced diffusivity as resulting from this apparent negative pressure caused by the interstitial carbon atoms.* That is, the activation free energy for diffusion is not directly a function of concentration if we consider that the alloy is subjected to a concentration-dependent pressure. To proceed with a quantitative solution, it is necessary to determine the activation volume AV for the diffusion process. An exact calculation of AV is quite a difficult problem and does not appear to have been solved as yet. A simpler procedure is to use the semiempirical, macroscopic theory of seyes' which relates the activation free energy AG to AV. Keyes has shown that for many types of diffusion processes the following relationship is valid Where p is the Gruneisen constant and x the compressibility. This relationship is based on the assumption that AG can be identified with strain-energy terms. In general there will also be contributions to AG due to a change in the energy of the valence electrons of the metal; thus the relation must be considered largely empirical. Surprisingly, for self-diffusion where it is well-known that the electronic contribution is quite important,' the Keyes relation works quite well for many systems. For interstitial diffusion where it might be expected that the relationship is on a firmer theoretical basis, the limited experimental data available is not in particularly good agreement as can be seen from Table I. However, it must be remembered that besides the uncertain basis of the Keyes formula there is considerable uncertainty in some of the experimental values of AV. The only real justification for using the Keyes formula in the present analysis is that it gives a result which satisfactorily solves the problem at hand and, further, there are no more reliable procedures for calculating AV available. The coefficient 3 in Eq. [I] is determined such that the room-temperature value for x is to be used. The activation entropy AS is estimated as 8.95 x 10"3 kcal per OK mole using the values in Table I1 and the Zener" relation AS = PAHIT, where p is a dimensionless thermal coefficient of Young's modulus which is to be evaluated at low values of T/T,, aH is the activation enthalpy, and T, is the melting temperature of the alloy. The resulting value of AG at 1000°C is 25.6 kcal per mole. The Gruneisen constant (p = 3cup/XC,), where p is the density, is evaluated from the room-temperature data in Table I1 after calculating C, from the relation. A value of p = 8.32 g per cu cm based on the value of a. in Table I is used. The result is C, = 5.0 x lo6 erg per g, H = 2.32, and AV = 3.41 cu cm per mole at 1000°C and infinite carbon dilution. It is assumed that the activation volume is not a function of carbon concentration. The theory could be refined to consider AV a function of concentration, but due to the uncertainties in the parameters there seems little justification for this. Carbon dissolved in austenite forms a nonideal solid solution, so that in writing an equation for. the diffusivity of carbon it is necessary to take into account the change in activity coefficient with concentration. The resulting equation is16

Jan 1, 1964

By M. Metzger, J. Intrater

IN the large number of important studies on high-purity aluminum (e.g., recrystallization and grain growth, creep, internal friction), it does not seem to have been generally recognized that the iron content, despite its very low figure, has a strong influence on a number of properties. In part, its influence is due to the very low solubility of the Fe-A1 6 phase. For aluminum of about 99.99 pct purity, the iron content may be 0.001 to 0.004 pct. For values in this range, a second phase will be present below 410" to 480 °C. This was determined by extrapolation of a log solubility vs inverse temperature plot of the solid solubility data of Edgar.' One consequence is the inhibition of grain coarsening below the solubility limit. This is shown in Table I, which gives, for three iron contents, the annealing temperature required for the absence of grains smaller than 1/2 mm average diameter together with the minimum temperature for the presence of some grains larger than 2 mm diameter. The specimens were 1/4x 1 1/2-in. strips cut from hard-rolled 1/16-in. sheet supplied by the Aluminum Co. of America.

Jan 1, 1954

By C. W. Crispell

The four nomograms presented in this article were designed to simplify and make more rapid the calculations connected with the compression and transmission of air. The formulae involved are rather complicated, but the graphic solutions are simple; their use requires an ability to follow explicit directions and to interpolate values on a logarithmic sca1e. † For the sake of convenience, the nomograms will be divided into two classes, and the purpose and accuracy of each will be discussed. Power foR CompREssion It is frequently desirable to determine the horsepower necessary to compress a given amount of free air from atmospheric pressure to a certain final pressure. The nomograms in Fig. 1 and 2 present a rapid method of calculating the horsepower required to compress 1 cu. ft. of free air per minute by single or two-stage compression. The general formula for the horsepower required to compress air adiabatically is: S X 144 PVn [(P')n-1/sn -1 (1) where: P = absolute atmospheric pressure at compressor, in pounds per square inch. P' = final absolute pressure of compressed air, -in pounds per square inch. V = volume of free air compressed per minute, in cubic feet. S = number of stages. n = exponent of the compression curve.

Jan 1, 1918

By C. W. Crispell

THE four nomograms presented in this article were designed to simplify and make more, rapid the calculations connected with the compression and transmission of air. The formulae involved are rather complicated, but the graphic solutions are simple; their use requires an ability to follow explicit directions and to interpolate values on a logarithmic scale. ? For the sake of convenience, the nomograms will be divided into two classes, and the purpose and accuracy of each will be discussed. Compression It is frequently desirable to determine the horsepower necessary to compress a given amount of free air from atmospheric pressure to a certain final pressure. The nomograms in Figs. 1 and 2 present a rapid method of calculating the horsepower required to compress 1 cu. ft. of free air per minute by single or two-stage compression. The general formula for the horsepower required to compress air adiabatically is: HP = S X 144/33,000 PVn/(n-1) [(P'/P) n-1/Sn -1] (1) where: P = absolute atmospheric pressure at compressor, in pounds per square inch. P' = final absolute pressure of compressed air, in pounds per square inch. V = volume of free air compressed per minute, in cubic feet. S = number of stages. n = exponent of the compression curve.

Jan 6, 1917

By H. L. Luo

SYSTEMATIC investigations of the Fe-Ga system have been reported only very recently."' The maximum solid solubility of gallium in a-Fe is nearly 50 at. pet at 900°C. However, from Ref. 1, it was not evident that the a-Fe solid solution could be retained successfully beyond 17.38 at. pet Ga by solid-state quenching. The present investigation reports the retention of a-Fe solid solution at 50 at. pet Ga by quenching from the liquid. An ordered phase of CsC1-type B2) structure was observed between 34 - 50 at. pet Ga. Since it was considered very probable that the CsCl structure would occur at high temperatures, alloy filings were also quenched by the conventional quenching technique. In addition to the CsCl phase, a second ordered phase of BiF3-type (DO3) structure was found in the range 25 - 30 at. pet Ga. Alloys were prepared from elements of 99.99 pet purity or better, induction-melted in alumina crucibles under hydrogen. After reweighing, the alloy ingots were cast into wires under argon. From the weight losses and the reproducibility of the lattice parameters, compositions were estimated to be within ± 0.3 at. pet. The techniques of quenching from the liquid state were reported before.3-5 Prior to quenching, a small section of cast alloy wire (30 - 50 mg) was melted in an alumina insert under an argon flow. The quenched specimens were in the form of flakes, typically 1 sq mm in area. For solid-state quenching, alloy filings passing 200 mesh were sealed under a reduced helium atmosphere in a thin-bottom silica tube. After heating for -30 min at the desired temperature in a vertical furnace, the sealed tube was rapidly dropped into ice water so that the thin bottom of the tube broke on impact. The quenched alloy filings were always ferromagnetic and could be collected by a magnet. X-ray diffraction patterns were taken with iron-filtered cobalt radiation in a 114.6-mm-diam Debye-Scherrer camera. High-angle lines were always resolved and spacings were computed relative to ? (CoKa1) = 1.78890Å. Lattice parameters were obtained from extrapolation against the Nelson-Riley function. The variation of lattice parameter with composition is shown in Fig. 1, together with the data of Dasarathy and Hume-Rothery.1 Uncertainties in the present measurements are within the dimensions of the symbols or indicated by error bars. X-ray diffraction lines indicative of CsC1-type ordering could be clearly identified for alloys of 34 - 50 at. pet Ga quenched from the liquid and alloys of 35 - 41 at. pet Ga quenched from -975°C. Within experimental error, no difference in

Jan 1, 1968

By R. F. Mehl, R. F. Bunshah

A fast amplifier technique has been developed for the measurement of the rate of propagation of martensite in an Fe-29.5 pct Ni alloy. The time of formation of one plate of martensite is 3x10 sec and the rate of propagation is 3300 ft per sec approximately. IT has been known for some time that the plate-like structural unit of martensite forms from austenite with great rapidity. Wiester1 and Hane-mann, Hofmann, and Wiester took motion-pictures of the transformation as it occurs in a 1.65 pct C steel; they demonstrated that a single plate formed fully in the time interval between successive frames, viz., 1/20 sec, thus setting an upper limit. Forster and Scheil,3 using an Fe-Ni alloy with 29 pct Ni, recorded the sonic characteristics of the process electrically, upon an oscillograph, setting the upper time limit at 0.002 sec. Forster and Scheil,~ measuring the change in electrical resistance in the same alloy upon a cardiograph, set a limit of 0.02 sec. Forster and Scheil5 later, employing the same alloy, improved their technique, reporting an upper limit of 7.10 sec. In studying signals of such short duration, it is an important question whether the frequency response of the electrical system used is high enough compared to frequency of the pulse measured, or, put differently, whether the system is able to reproduce without distortion the signal arising, in this case, from the formation of a single martensite plate. Forster and Scheil (referring only to their last paper) obtained signals of a frequency of 30 kilocycles (hereinafter kc); this was about the frequency response of the equipment used; thus, if the signal had a frequency higher than 30 kc, it would still appear as a signal of frequency 30 kc. All of these results thus provided upper limits only. Recent developments in electronics have made available equipment with very high frequency response, very high sweep-speeds, high gain, etc. The electrical characteristics of such equipment, used in the present study, are given in Table I. Such equipment offers obvious attraction in the study of the rate of propagation of a martensite structural unit—and perhaps of other structural alterations proceeding at a very high rate. This paper reports an attempt to develop a technique employing such equipment to measure the time of propagation of a martensite structural unit and the variation of this with temperature, with the mode of formation—athermal and isothermal—in both polycrystalline and single-crystal samples; and from such measurements to obtain the rate of propagation. As will be seen, the results obtained are useful theoretically. Materials All data presented here are for an Fe-Ni alloy of the following analysis: 29.5 pct Ni, 0.027 pct C, 0.135 pct Mn, 0.094 pct Si, balance Fe. There were several reasons for choosing this alloy: 1—it is substantially the one used by previous investigators; 2—it exhibits both the athermala and the isothermal' mode of formation of martensite, both studied in detail by Machlin and Cohen; 3—the subzero temperatures of transformation in this alloy are experimentally very convenient; 4—it exhibits the "burst phenomenon";" 5—the change in electrical resistance upon the formation of martensite, a decrease, is great, approximately 50 pct.' The polycrystalline specimens were in the form of wires of 0.025 in. diameter; the single crystals were 1x1/4x1/4 in. Experimental Methods Electrical Apparatus: Fig. 1 is a schematic drawing of the electrical circuit used. The principle used in these measurements is the same as that used by Forster and Scheil." A small direct current, about 1 to 2 amp, is passed through the sample. When a martensite plate forms, the resistance of the sample changes and a high frequency signal is generated. This signal is picked up by the probes attached to the sample, fed into the bank of amplifiers and thence to the vertical deflection plates of a cathode-ray oscilloscope. The signal itself triggers the oscilloscope trace which flashes across the tube face and is photographed by means of a 35 mm movie camera at the end of a light-tight hood. The camera has no shutter. As soon as the signal flashes

Jan 1, 1954

By H. D. Outmans

The author applies the theory of hydrodynamic stability to fluid flow in porous media and concludes that the displacement of miscible liquids is stable if the stability coefficient, as defined by Eq. 19.2 or Eq. 27.0, is positive. The conclusion is invalid, however, since it is based on a faulty argument. To demonstrate this, the reader is referred to Eqs. 4.1 through 4.5 of the paper which describe, in differential form, the first-order disturbances c, u, v, w and p. In these same equations, cx, cz, gl, g3 and are functions of the stable concentration c. This concentration c is known and depends on x, z and t (the author assumes cy = 0). It follows that cx, cz, gl, g3 and µ are also functions of x, z and t. With this in mind, we turn to Eqs. 8.1 through 8.5 which were derived from Eqs. 4.1 through 4.5 by substituting Eq. 6.0. The significance of this substitution is that the author thereby limits the solutions of Eqs. 4.1 through 4.5 to equations of the form of Eq. 6.0. Eqs. 8.1 through 8.5 represent an infinite linear system with five unknowns: c, u, v, w and p. The coefficients cx, cz, gl, g3 and µ in this system are known at each point and at each instant; the coefficients containing derivatives of f are unknown. If this infinite linear system in c, u, v, w and p is to have a nontrivial solution, then it is indeed necessary (as the author states) that the determinant of the coefficient matrix of Eqs. 8.1 through 8.5, i.e., ( A 1, be equal to zero. This condition, however, is not sufficient. A non-trivial solution exists if, and only if, the rank of the coefficient matrix of the entire infinite system is smaller than five. In other words. all minors of order five must vanish and only if all the coefficients in Eqs. 8.1 through 8.5 are constant is this equivalent to the condition |A| =0. Constant coefficients means that gl, g3 and µ, for instance, are constant; and, since they depend on c it follows that c must be constant. We conclude that the condition I A I = 0, on which the author bases his calculations, is necessary and sufficient for a nontrivial solution only if the concentration c is constant. In other words, the author does not investigate the stability of a miscible displacement but, rather, only the stability of the flow of a homogeneous liquid. Using the initial condition and the fact that the coefficients are constant, we find

By Robert F. Mehl

Jan 1, 1944

By Robert F. Mehl

Jan 1, 1944