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Jan 1, 1949

Jan 1, 1949

Jan 1, 1949

Jan 1, 1949

Jan 1, 1949

By Cyril Stanley Smith

Jan 1, 1949

By W. R. Hibbard

Although extensive pole figure studies have been reported by Brick1 and others2,3 showing preferred orientations in rolled and annealed 70-30 alpha brass, and by Hermann and Sachs4 in 70-30 alpha brass cups, comparatively little information has been published on textures in drawn 70-30 alpha brass tubes. Crampton5 reported a (110) , [111] texture in drawn brass tubes based on selected individual X ray photograms following the method of Norton and Hiller,6 but the extent and ease of developing this texture and the annealing texture have not been reported and pole figures of these structures were not found in the literature. The present investigation was further stimulated by the possible influence of textures on the mercury stress-corrosion cracking of brass tubes. According to Snoek,7 iron-nickel alloy sheet with a strong cubic texture was more resistant to corrosion than a randomly oriented sheet. Crampton5 reported that single crystals of 70-30 alpha brass drawn into tubes did not crack after 24 hr in a standard mer-curous nitrate test. Edmunds12 found that single crystals of 70-30 alpha brass did not crack in a standard mercurous nitrate test but did crack when subjected to ammoniacal vapor. Wasserman11 reported a similar failure of a single crystal of brass in ammonia. A tube with a strong texture might approach single crystal behavior and tend to resist mercury cracking if the differences in orientation between adjacent grains were sufficiently slight. Preparation OF Specimens Crampton's5 tubes drawn 28 pct reduction in area developed a slight degree of preferred orientation while in tubes drawn 48 pct it was more marked. Based on this information, in order to obtain specimens with markedly different degrees of preferred orientation but with the same final draw, two sets of 70-30 alpha brass tubes were made following the mill schedules shown in Table I. The final draw involved a large reduction in outside diameter, and a ratio of reduction in area to reduction in outside diameter similar to that reported by Crampton,5, 10 to cause mercury cracking of brass tubes. The brass contained 71.31 pct copper, 0.01 pct lead, 0.01 pct iron and zinc by difference. Determination of Pole Figures A 6-in. length from each tube was rotated rapidly by an electric stirrer in 25 pct nitric acid until the gauge was reduced to 0.003-0.005 in. The tubes were carefully cut longitudinally and the walls gently flattened. They were further etched in 25 pet nitric acid to 0.0015 in. thickness and (111) pole figures were determined using copper K-alpha radiation in the manner described by Brick.' The three general types of pole figures

Jan 1, 1949

By W. R. Hibbard

The term lineage was first introduced by Buergerl to denote dendritic branches, grown from a crystal nucleus during solidification from the liquid, with imper- fections in alignment of the order of 10 : to 10-4 cm. These imperfections are associated with distortions of the dendrites caused by the subsequent solidification of the inter-dendritic filling and are illustrated in Fig I. Buerger etched zinc single crystals made by the Bridgman3 method to develop this dendritic pattern and show lineage microscopically. Since maximum crystal growth in face-centered cubic metals occurs along the [IT] directions,2 lineage would appear in copper as small deviations of dendritic branches from these directions. Elam4 and others5"8 reported etching effects resulting from coring along the cube face traces of various copper alloy crystals. These traces were used by Samans8 to orient single crystals. Williamson9 noted a "lined structure (in alpha brass single crystals) consisting of an ordered arrangement of etch pits" which were probably traces of {IOO} planes but somewhat uncertain because they were never straight (that is, apparently lineage). Greningerl1 described the distortion and multiplicity of Laue spots in back reflection X ray photograms of copper single crystals showing lineage. The present investigation -includes metal-lographic, X ray, and property studies of lineage in large grain and single crystal specimens of copper. Preparation of Specimens specilnens 10 in. long 35 1/2 in. diam of oxygen-free copper (o.F.H.c.) (99.985 pet) were' melted vertically in graphite crucibles under an atmosphere of commercial nitrogen purified through a gas train including sulfuric acid, potassium chloride, magnesium chiorate, hot copper chips and phosphorus pentoxide. After a temperature of 1200°C had been maintained for 1/2 hr, the furnace was turned off and the specimens cooled at a rate of about 150°c an hour' This method of direct solidification was used by Greningerlo to produce single crystals with marked lineage and in this investigation produced a fair yield of single crystal specimens in

Jan 1, 1949

By Harold Margolin, W. R. Hibbard, R. W. Fenn, H. P. Moore

Deformation lines, also called etch markings or strain markings, are non-effaceable lines developed in individual grains by etching a metal specimen which has been cold worked sufficiently to cause atomic non-conformity or slight orientation differences within the grains. Etching occurs more rapidly at these lines of high chemical reactivity to produce a result similar to that revealing grain boundaries. Wider etching effects forming bands have been found. They are believed to be bands of deformation lines which form areas of measurably different orientation from the crystal matrix. The crystallite rotations causing these bands have been shown by Barrett2 to contribute to deformation textures. Although deformation lines have been observed in many metals, the amount of deformation requireti for their appearance has been established only in general terms. Mathewson and Phillips3 observed the first appearance of deformation lines in cold-rolled alpha brass at about 20 pct reduction in thickness using the standard ammonium hydroxide hydrogen peroxide etchant. Price and Davidson4 noted defor- mation lines in common high brass after 26.5 pct reduction by cold rolling using the same etchant. Johnson6 observed dark thick forklike lines in 99.99 pct pure copper reduced 31.8 pct. Adcock6 observed deformation lines in 80-20 copper-nickel alloy rolled 50 pct. Samans7 found no deformation lines in alpha brass single crystals cold rolled 9.5 pct but they did appear after 25 pct reduction using ammonium hydroxide and hydrogen peroxide etchant. Barrett and Levenson8 observed deformation bands in drawn polycrystalline iron at very small reductions in area and noted that their initial appearance perhaps depends on grain size and other conditions. They reported deformation bands in a single crystal of iron reduced 6 pct by drawing. Brickg noted that deformation lines in 70-30 brass apparently associated with I I I I ) planes appeared after reductions of from 20-50 pct by cold rolling. Brick and Williamson10 noted that in single crystals of 70-30 alpha brass "as in polycrystalline brass, no deformation markings appeared until reductions exceeded 20 pct." Cook and Richards" reported that in Copper cold rolled less than about 50 Pet few strain markings were apparent but for higher reductions many strain markings appeared transverse to the rolled direction. In a review article Brick and Phillips12 noted that previous studies had not shown deformation lines in cold rolled alpha brass below 20 pet reduction and added that 4

Jan 1, 1949

By C. H. Mathewson, W. R. Hibbard, Robert Maddin

A satisfactory mathematical relationship between shear, elongation and change of orientation in the axial straining of a single crystalline rod or wire may be based on a simple model in which blocks, representing glide lamellae, glide over one another and rotate so as to maintain the original fixed position of the axis as the wire elongates.' Obviously such a model gives no information concerning strain-hardening or the atomic adjustments at the sliding surfaces and their influence on the internal structure of the blocks. Moreover such an operation could be conducted with rigid blocks only by using self-aligning grips or a flexible attachment which would permit the adjacent blocks to freely assume their changing orientations. There are many unsolved problems (see Andrade2) concerning the manner in which nature departs from the simple model in permitting the essentials of slip, rotation and elongation to occur along with strain-hardening and the appearance of glide lamellae of various dimensions and special characteristics, not fully appreciated at the present time. This paper describes part of an extensive investigation on the development and characteristics of glide ellipses in single crystalline alpha brass rods and is especially concerned with the observation of cross-slip in crystals oriented wholly within the range of slip on a single system according to the generalizations first presented by Taylor and Elam in 1923.³ Experimental Procedure Half-inch rods of alpha brass (nominally 70 pet Cu, 30 pet Zn)* were converted into single crystals by melting and gradual solidification in a graphite mold according to the Bridgman method.4 In order to remove any coring, the crystals were homogenized at 800°C for 16 hr and tested by etching with a 50 pet nitric acid solution. The back-reflection Laue technique as described by Greninger6 was used for determining the orientations of the crystals. Standard stereographic operations were employed to locate the specimen axis in a triangle of the Taylor and Elam3 projection so that the slip plane and direction could be predicted. The lineage structure reported by Buer-ger6 was present in the crystals used in this investigation. However, only crystals were used in which the internal differences in orientation did not exceed two degrees. Very little is known concerning the effect of the presence of a lineage structure on the detailed mechanism of plastic deformation.

Jan 1, 1949

By C. S. Barrett, J. E. Burke

The fine lines shown in Fig I are typical of markings that ma): be detected after polishing and etching deformed specimens of alpha brass and other alloys. Although they have long been the subject of discussion by metallurgists their nature is still uncertain and the names that have been applied: to them, such as deformation line4 or strain markinas, indicate this uncertainky. In this paper which repotts the results of a furthcr investigatinn of their nature, they will be called strain mxrkings. Introduction Mathewson and Phillips1 described strain markinps in 1 916 and concluded that they appear only after 20 pet deformation. They objected to the markings being called slip tines believing this term should be sewrved for surface markings protluced by plastic deformntion. In 1921. vogel² described similar striations which appeared after polishing and etching the roughly ground surface of numerous alloys. He reported that the markings were crystallo-graphic in nature, and since they resemble Seumann hands in iron, at least superficially, he assumed them to be mechanical twins. In 1928, Matherwson reported work by Phillips which indicated that the lines were more readily produced by impact than by slow deformation and that in many cases the twins inside recrystallized grains were parallel to strain markings in the original deformed grains. This was taken as cvirlence that the markings coalesce into anncaling twins. and hence that they themselves are mechanical twins. Many attempts have been made to demonstrate directly that the markings are mechanical twins. In 1934, Samans described the results of X ray studies of two defomed crystals of alpha brass. Evidence was obtained which could be interpreted to indicate that the strain markings arc mechanical twins, and this remains the only direct evidence to this effect. Several other attempts to obtain similar evidence by X ray diffraction have failed5.8.7 although in no Ease was the original method of Samans employed. An

Jan 1, 1949

By W. R. Hibbard, Ming-Kao Yen

Various rationalizations of preferred orientations in cold worked polycrystalline metals have been based on the operation of at least two three2 five, an indefinite number, and all,6 slip systems of the type occurring in single crystals. Pickus and Mathewson3 suggested that the cold rolling texture in face-centered cubic metals could be rationalized on the basis of two or more operating slip directions symmetrically disposed about the direction of flow in such a manner that the resolved shear stress factor is equal for all operating slip systems and lattice rotations cancel each other. The importance of the direction of flow, the necessity for the operation of slip systems capable of producing the required changes in external dimensions, the maintenance of a common surface between adjacent grains and a symmetrical arrangement of the operating slip systems in order to produce an end orientation which is stable under additional deformation lead to the following rationalization of textures based on the type of slip systems operative in single crystals. The rationalization is intended to explain why certain orientations are suitable for deformational flow without a change in orientation and thus are stable end orientations or ideal texture orientations. It does not attempt to explain how the grains of a randomly oriented polycrystalline aggregate will reach this orientation. The rationalization is based on the following four postulates: 1. The ideal textures for polycrystalline aggregates are the result of reorientations of individual crystals toward the same stable end orientation at which no further reorientation will occur even during additional deformation. Since, in simple slip, the relative orientations of the stress axis and the active slip system determine the change in orientation during slip, it is considered that the orientation of the stress axis with respect to the ideal texture determines what slip systems must be active to retain the stable end orientation. Therefore the stable end orientation should be a symmetrical one around the stress axis with respect to the active slip systems such that lattice rotations resulting from slip will cancel each other and prevent a resultant change in orientation. (Rotational symmetry only—not translation, inversion, nor others—is considered here.) Thus a metal under a pure stress should develop a texture consisting of one or more of the crystallographically symmetrical directions, <100>, <110> or <111> for cubic metals or <0001>, <1010> or <1120> for hexagonal close-packed metals, parallel to the stress axis. 2. Since the active slip direction is the direction of glide during simple slip and thus the direction of maximum shear movement, in the ideal texture the active slip

Jan 1, 1949

By Y. G. Shiau, J. E. Burke

Several attempts have been made to account for the fact that grains in a fully recrystallized metal will coarsen on annealmg. Two fundamentally different hypotheses have been advanced, with several variations of each. One school considers that the cause of grain growth is the surface energy of the grain boundary. The theory of Jeffriesl that grain size and grain size contrast control growth is an example. The second school considers the primary cause to be a difference in the lattice energy on either side of the grain boundary. The more perfect grains are considered to grow at the expense of their less perfect neighbors, with a decrease in free energy, and a consequent increase in the stability of the system. Burgers2 presents the case for the strain or lattice imperfection theory of grain growth quite completely. The latter theory is attractive, since there is no doubt that differences in lattice energy or lattice perfection can cause grain boundary migration. A recrystallization nucleus grows for this reason as was beautifully demonstrated by van Arkel and Ploos van Amstel.³ Although it is generally stated that grain growth does not precede recrystallization, several workers4-5 have shown that small strains may induce a single crystal in an aggregate to grow, or at least may cause some grain boundary migration. The origin and nature of the imperfections that are considered to be responsible for normal grain growth have never been clearly described, but it is generally agreed that they are a consequence of the difficulty of atomic reorientation in the solid state, and that they do not seriously differ from the type of imperfection that can be introduced by mechanical deformation. An object of the present work was to determine whether the introduction of mechanical deformation would cause grain growth in a specimen which would not otherwise show it under the conditions used. It was also planned to determine the effect of such deformation on the rate of growth in a specimen which would show growth in the unstrained condition. Recently Maddigan and Blank6 have indicated that slightly strained specimens of alpha brass can undergo considerable growth prior to recrystallization if annealed at low temperatures. French7 has reported that at deformations less than 17 pet it is very difficult to detect the beginning of recrystallization in the same material. It was therefore planned to broaden this work to include a complete study of the microscopic behavior of alpha brass under condition~ of temperature, time, grain size and deformation such that recrystallization would not occur or would occur to only a Small extent. Experimental Procedure The brass was prepared by melting cathode copper and commercially pure zinc

Jan 1, 1949

By Paul A. Beck, John Towers, W. D. Manly

Recent work on grain growth in high purity aluminum and in a solid solution type alloy of aluminum and magnesium1 showed that the isothermal increase of the average grain diameter D with time follows the equation D = K(tg + A)2 Eq 1 Here tg is that portion of the total annealing time 1, which is available for grain growth, that is the annealing time less the time necessary for complete recrystallization. The parameters A and n depend only on the temperature. A has the dimension of time, and is usually of the same order of magnitude as the time for recrystallization: R. In some instances R may be substituted for A in Eq I. This is the case for example at long periods of annealing or at high temperatures, where both A and R become small in comparison with t. In such instances Eq I is simplified to D = K, tn Eq 2 For high purity aluminum the exponent n increases in the ratio of about I to 5 in. the temperature range of 350&apos; to 6w°C. 70-30 brass has been long known to exhibit grain growth of the continuous type, such as occurs in pure metals. For this reason, it was of interest to determine whether grain growth in brass also follows Eq I and 2 as it does in aluminum. Isotherma1 grain growth data for 70-30 brass were published in recent years by R. S. French2 and by H. L. Walker.&apos; Fig I shows a log D vs. log t plot of French&apos;s data, together with the 500, 600 and 700°C data by Walker for 42.8 pct reduction by rolling. In such a log D vs. log t plot Eq 2 corresponds to a straight line with a slope of n. As seen in Fig I, the data of French and the 600°C data of Walker can be represented by straight lines. However, the 500 and 7c0°C data of Walker give curved lines and the average slope of his 500°C line is very different from the slope of the line representing French&apos;s data for the same temperature. Furthermore the curvature of the 700°C line suggests a tendency for grain growth to stop after 8 hr. If confirmed, this would constitute a definite deviation from Eq 2, not explainable on the basis of the specimen thickness effect found in high purity aluminum.&apos; Walker&apos;s specimens were 0.125 in., or 3.18 mm thick, while the deviation occurs at a grain size of approximately 0.4 mm. A further point of divergence arose recently, when J. E. Burke suggested4 on the basis of Walker&apos;s data, that, instead of Eq 2, grain growth in 70-30 brass follows the equation D - D, = K . tgn Eq 3 Here D, is the grain size as recrystallized at the temperature in question. Although it was possible to show5 that, for pure aluminum, for which isothermal grain growth has been carefully investigated, Eq 3 is incompatible with the experimental facts, the situation remained somewhat obscure with respect to 70-30 brass. In view of the discrepancies between the published data on brass from different

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&apos;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 L. S. Darken

It has been known for sometime that in an ionic lattice, such as that of Ag,S or FeO, the migration velocity of the anion may differ markedly from that of the cation, the cation being usually the more mobile. It has been shown, for example, that during the formation of silver sulphide tarnish on silver, the tarnish layer grows principally by the motion of silver cations through an essentially stationary silver sulphide lattice. Similarly, the growth of wüstite scale on iron proceeds principally by motion of iron ions, this being accomplished with the aid of vacant iron lattice sites into which the iron may readily move. Likewise investigations of solid solutions of various salts show that there is usually considerable difference in the mobility of the different cations. Measurements of the mobility of various metals in liquid mercury indicate that the various metals move at different rates relative to the mercury. In view of the foregoing it seems reasonable to suppose that when any single phase solution is acted upon by a field, the atoms of different elements respond in different ways; in particular, that the force arising from a particular concentration gradient in a binary alloy would cause the atoms of one component to move with a drift velocity which is in general different from that of the atoms of the other component. The recent experiments of Smigelskas and Kirkendall&apos; support this viewpoint, since they found, in essence, that during diffusion in alpha brass zinc moves appreciably faster than copper. This was evidenced by the relative motion of inert molybdenum wires. Such a phenomenon is incompatible with the place interchange theory of diffdsion proposed by several authors, most recently by Bir-chenall and Mehl.2 This theory has, however, also been questioned3v4 for other reasons, principally because of the high energy required for direct atomic interchange. The rather large difference between self-diffusivity, as determined by tracer technique, and mutual diffusivity, as determined with the aid of another element at low concentration, might also be interpreted as favoring the above idea; however. Birchenall and Mehl have pointed out that there is another possible interpretation of this difference; this is discussed later. A rather interesting and pertinent observation was made by Schwartz, who noticed that tungsten lamp filaments, heated by direct current, commonly fail by necking down in the region at the temperature gradient near the positive end, with a concomitant swelling at the corresponding position near the negative end. He introduces considerable auxiliary evidence to show that this phenomenon is occasioned by the motion of tungsten cations which migrate in the high temperature region from the positive end toward the negative end. The mechanism of this migration is not clearly understood. If, however, this experimental evidence be accepted, we are forced to conclude that alloying elements in the tungsten may migrate by the same or a Similar mechanism, whatever it may be, at a greater Or lesser rate, thus giving rise

Jan 1, 1949

By B. L. Seegmiller

Regular entry trusses are used in headgates, tailgates, roadways and intensely-faulted areas. These trusses have proven to give the required support and maintain roof stability even under major abutment loading conditions for both the re-treating and advancing longwalls. Areas previously requiring steel arches have been eliminated. A special Continuous Entry Truss? provides permanent support to adjacent tunnel/crosscut zone for more than 300 feet in each tunnel. The continuous nature of the tensioned truss allows sup-port forces to be placed on the roof in not just the two-dimensions of regular trusses, but in a full three-dimensions. A newly developed Roktruss? provides support in an arched 30-foot high rock zone. The Roktruss? allows truss support concepts to be used in an opening with a curved roof.

Jan 1, 1989

By Otto Schumacher

Shortcut methods are commonly employed for estimating mining costs for prefeasibility studies. Most of these methods, however, are suitable for earliest stage studies or for internal discussion purposes only. The experts at InfoMine?s CostMine division recommend that any cost estimate completed for purposes of significant decisionmaking or for compliance with Canada?s NI 43-101 requirements be completed using a determinative itemized method. The same basic principles apply for an early stage, intermediate stage, or advanced stage estimate. The only difference is in the level of detail and effort employed. ? Based on the results of a completed resource estimate, an itemized cost estimate begins with development of a conceptual mine plan. Using a surface mine as an example, four elements are crucial no matter what level of study is initiated. Basic geometry of the ore deposit and waste material, with a determination of the expected ratio of waste to ore, a reasonable pit slope angle, possibly requiring the completion of geotechnical studies to predict the waste-to-ore ratio with certainty. ? Determination of the assumed ore and waste production rates. ? Locations of all ore stockpiles and waste dumps. ? Segmental haulage distances and gradients for ore and waste.

Oct 1, 2013

By George A. Morrison

THE Columbia Chemical Division of the Pittsburgh Plate Glass Co. is at Barberton, Ohio, 35 miles south of Cleveland. For many years large tonnages of limestone have been brought to the Barberton plant from distant points. The stone is here burnt in vertical kilns, the resultant product then hydrated and the hydrated lime used in chemical processing. To eliminate the expense of these shipments, the company decided to investigate a limestone bed known to exist on company property at Barberton, where the stone is used. The bed lay at a depth of more than 2000 ft. and was known locally as the "Deep Lime." Chemical analyses of sludge from churn-drill holes made some years ago proved that the limestone was of sufficient purity to warrant diamond-drill exploration. Four diamond-drill holes were put down at well-spaced intervals, to represent fairly an area of four miles by one mile. Cores logged as to chemical and physical conditions were found to compare closely, and to corroborate the earlier evidence that the limestone was of superior quality for chemical use. A plant of 300 tons per hour was subsequently decided upon. SITE The yard at the chemical plant was already so congested that location of the projected mine within its area could not be considered. Eventually a site was selected 2 miles northwest of the plant, near the main line of the Erie Railroad. Here 412 acres were owned outright by the company and stone rights were obtained on 250 additional acres. This location required a transportation line of nearly 2 miles (8800 ft.), crossing two major highways, and to avoid interruption of deliveries to the plant, overpasses were planned. GEOLOGY The limestone in the immediate vicinity lies about 2200 ft. below the surface. Geologists* identify this stone as Delaware of Devonian age. It is overlain by 18 ft. of unconsolidated (sand and gravel), 100 ft. of water-bearing sandstone, and finally 2080 ft. of shale into which sandstone in thin layers is interbedded. The contact of shale and limestone is abrupt, flat-lying and very pronounced. Berea sandstone, often found at 520 ft., is absent, but Euclid sandstone was encountered, together with a seepage of oil and a small amount of methane gas. The limestone bed itself is 345 ft. thick, and overlies 200 ft. of gypsum. The lower part becomes dolomitic as it approaches the gypsum. A detailed study of the drill cores indicates that the upper 50 ft, are highest in lime and reasonably low in silica. The physical make-up shows several separating cherty layers. These occur at definite horizons and cause distinct partings, which become horizontal planes of

Jan 1, 1943

By J. C. Fisher, J. H. Hollomon, David Turnbull

Understanding of the diffusion problem has recently been furthered by the analysis of Birchenall and Meh1.l They pursued the problem of the variation of the diffusion coefficient with composition for non-ideal solid solutions. Their analysis follows the tradition of Wagner,l Jost, Dehlinger, and Darken & who assumed the net flux of diffusing material to be proportional to the gradient of a quantity related to free energy. The basic assumption in Birchenall and Mehl&apos;s formulation of the problem is that the net flux of diffusing material is proportional to a thermodynamic activity gradient. To estimate the applicability of the derived relations, they corrected the diffusion coefficients of carbon in austenite by utilizing Smith&apos;s6 activity data for carbon, and the diffusion coefficients for zinc in copper with activity data computed from the vapor pressure measurements of Har-greaves.&apos; The corrected coefficients for carbon were virtually independent of carbon concentration. For the diffusion of zinc in copper a moderate variation of diffusion coefficient with concentration remained after the correction. The problem of diffusion can be formulated in another way than that used by Birchenall and Mehl. The method is that of chemical rate theory and has been used by Eyring and his coworkers8,9 as well as by Eyring and Zwolinskilo in a discussion to Birchenall and Mehl&apos;s paper. As yet the method has not been applied to substitu-tional solid solutions. On the basis of their assumptions, Eyring and Zwolinski derived a relation between the diffusion coefficient and activity that is identical with that of Dehlinger and Darken but which does not correct for the variation of the diffusion coefficient with concentration as well as does the relation derived by Birchenall and Mehl. It was thought that the theory of diffusion would be more complete if the inconsistency between the two analyses could be rationalized and if diffusion in substitu-tional alloys were analyzed on the basis of the concepts of the chemical rate theory. Chemical Rate Theory According to the theory of absolute reaction ratess the reaction +..... +X, Eq I is viewed as taking place in two steps. First the reactants A1, A², . . . A; combine to form an activated complex M with which they are in equilibrium: A1 + A1+ . . . + A=M. Eq 2 Second the activated complex decomposes to give the products XI, XZ, . . . Xi: M?X, + X²+ . . . +Xi Eq g It has been showns that the number of activated complexes decomposing per unit volume per unit time is given by the expressiont kT -h CM † The transmission coefficient has been taken as unity.

Jan 1, 1949