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By P. A. Beck

In the course of work on grain growth in high purity aluminum a simple optical method was developed for detecting the presence or absence of preferred orientation in annealed specimens. The specimens were prepared by grinding, polishing and "deep etching." The etching reagent used for high purity aluminum has been described.* The resulting etch pits produced selective

Jan 1, 1949

By William T. Barrett, James E. Lawver, James L. Wright

One of the problems facing both the designer and the user of magnetic separators is the evaluation of the body forces acting on particles in the magnetic field of the separator. Perhaps the most elegant method of evaluating the body force associated with a drum-type magnetic separator is that recently suggested by W. F. Brown.' Brown measures the radial component of the field intensity 1/2 in. from the drum surface and fits a Fourier series in the angle about the drum axis (Fig. 1). Once the coefficients of the series are known, it is then possible to calculate the values of the radial and angular

Jan 1, 1971

By C. W. Spencer, K. A. Semlak, F. N. Rhines

IN an effort to obtain a better understanding of sintering in the presence of a liquid phase, it was decided to study the rate of capillary rise of a relatively low melting liquid metal in a higher melting metal powder compact. By assuming that the metal powder compact consists of a great number of parallel capillary tubes and that the flow of liquid

Jan 1, 1958

By Walter R. Hibbard, Harold Margolin

DURING preliminary tests on the aging of a Cu-plus 5 pct Ag alloy,' a specimen which had been overaged 24 hr at 550°C was annealed in a nitrogen-hydrogen atmosphere first for 2 hr and then for an additional 28 hr at 600°C. After each anneal the specimen was cooled to room temperature in about ½ hr and X-ray photograms were made. The first film, Fig. la, revealed two sets of copper-base lines, one intense and corresponding to the parameter at 550°C, the other fainter and shifted away from the beam, corresponding to the larger parameter at 600°C (see arrows). The 30-hr film, Fig. lb, revealed the same two sets of copper-base lines with a reversal of intensity. In neither case do the copper lines form a broad band which would be indicative of a range of compositions. This phenomenon is thus a "discontinuous" type of solution. A similar phenomenon was observed in a Ag-rich Cu-Ag alloy.' Finlay and Hibbard9 have suggested that directional rather than random solution of precipitate occurs in some alloys. Conceivably, for Cu-Ag alloys, the matrix-transition-precipitate precipitation sequence is reversible for the re-solution of the precipitate caused by rapidly raising the annealing temperature of an overaged specimen. A copper-base transition structure supersaturated with solute might be formed around the precipitate as it dissolves, thus obviating the necessity for a gradually changing solute composition of the matrix. The solute atoms then might be transferred rapidly and locally from the transition to the matrix phase in the proper amount and at the proper location to obtain directly the new ex- panded solid solution. The theory implies a minimum of diEusion of solute in the matrix (i.e., no significant range of matrix composition) and possibly suggests that the composition of the transition structure will vary with the conditions of re-solution. A transition copper phase found in aged Cu-Ag alloys1 might fulfill this function. Evidence regarding this suggestion could be obtained in Cu-Ag alloys by overaging a specimen until no trace of the expanded copper lattice is present and then subjecting the specimen to a retrogression treatment. Re-appearance of the transition copper phase would confirm the theory. Additional details could be secured by varying both aging and retrogression temperatures. References 'H. Margolin and W. R. Hibbard, Jr.: Effect of Ternary Additions on the Age Hardening of a Copper-Silver Alloy. Trans. AIME (1951) 191, p. 174; Journal of Metals (Feb. 1951) TP 3002E. 2 W. Ageew, M. Hansen, and G. Sachs: Decomposition and Changes in Properties of Super-saturated Silver-Copper Alloys. Ztsch. Physik (1930) 66, p. 350. 3W. L. Finlay and W. R. Hibbard, Jr.: Some Effects of Applied Stresses on Precipitation Phenomena. Trans. AIME (1949) 180, p. 255; Metals Technology (Sept.

Jan 1, 1952

By L. S. Richardson, N. J. Grant

REACTIONS of oxygen and nitrogen at low pressures with titanium have recently been studied by a number of investigators.1-3 Gulbransen and Andrew' noted that the reaction with nitrogen followed the parabolic rate law whereas the reaction with oxygen deviated slightly from this law in the temperature range 300° to 800°C. In the work reported here, commercial titanium (75 A) was used as the test material. Cylinders 2.5 in. long and 0.25 in. in diameter were machined from heavier bar stock. The test pieces were given a metallographic finish, immersed for 30 min in cold concentrated HC1, washed in water, then acetone, and dried with lint-free cloth. Reaction rates were determined in a modified Sieverts type apparatus by measuring the decrease in gas pressure of the reacting gas contained in a constant volume. The amount of gas added could be measured in a calibrated gas burette to an accuracy of 0.01 mm. During the course of a run the temperature never varied by more than 10°C and then only for brief moments. After placing the specimen in the furnace, the system was first evacuated for 12 hr at room temperature, and then flushed with purified argon five times, adsorbed gases being discharged during this period from the glass system with a high frequency spark coil. The flushing and discharging were repeated at 400°C. This rather involved procedure was found necessary after a number of trial runs indicated extraneous effects traceable to the system. Reaction periods up to 2 hr were used, at initial gas pressures of 0.2 to 0.5 atm. Experimental Results Fig. 1 shows the decrease in oxygen pressure for tests at 0.5 atm at various temperatures as a function of the square root of the time. Deviations from linearity are minor and the parabolic rate law is obeyed. Fig. 2 shows the same plot for the nitrogen reaction. A definite deviation from linearity is noted; however, it is probable that the higher initial rates are caused by the presence of small amounts of oxygen contamination, the initial faster rate changing to the slower rate after about 5 to 10 min. Calculations of the rate constants were made on the basis of the latter portion of the curves. The parabolic rate law constants calculated from these curves are shown for oxygen and nitrogen in Fig. 3. In spite of some scatter the average curves are quite definite. Changes in gas pressure of the order of 20 pct did not result in a measurable change in the rate law constants. The activation energy for the oxygen reaction was calculated to be 47,400 cal per mol (above 700°C), which is not in agreement with the value quoted by Gulbransen and Andrew' for lower temperatures, their value being 26,000 cal below 600°C. The activation energy for the nitrogen reaction was calculated to be 45,400 cal per mol above about

Jan 1, 1955

By A. W. Demmler

RECENTLY, Chaudron,&apos; Montariol,2 and their co-workers published the results of their studies on zone-refined aluminum. They found their material to be capable of recrystallization at —50°C, but gave no data as to the percentage reduction or time required. Their material was found to be practically non-work hardening at room temperature, but after 96 pct cold work at a low temperature and storage in liquid nitrogen it was found to recrystallize to coarse grains in less than 3 hr at 20°C. Recently, a study was made of the room temperature recrystallization characteristics of zone-melted aluminum. An ingot 14 in. in length, with a 3hx3 in. cross section, was made in an extremely high purity graphite boat under an atmosphere of dried commercial argon. It was made by first passing the molten zone along the ingot of 99.99+ pct A1 15 times. At this point, the most impure 3 in. (the end toward which the eutectic forming impurities migrated) were replaced with more of the original starting material, and 15 more traverses were made. Each traverse of the zone along the ingot required approximately 3 hr. Three ingots were prepared in this identical fashion and the chemical analyses were made spec-trographically on two of these ingots, rather than on the one used in this investigation. The analyses were made at 1 in. intervals along the ingot, in duplicate. Over the purest 5 in. of the ingot, which were most important in this investigation, there was found an average composition of <0.00004 pct Cu, <0.0003 pct Fe, <0.0001 pct Si, and <0.0001 pct Mg. In addition, the following elements were not detected spectrographically even in the more impure end of the bar: manganese, zinc, nickel, chromium, titanium, vanadium, lead, tin, boron, beryllium, bismuth, gallium, zirconium, cadmium, antimony, cobalt, and molybdenum. The original ingot was given several cold reductions, with intermediate anneals in order to refine the grains. Owing to the extreme length resulting and the ease of deforming the material plastically, it was cut into eight equal lengths and identified as shown in Fig. 1, with the highest numbered section at the purer end (that enriched with peritectic formers). Section 6 was used in the exploratory work and was found to be of exceptionally high purity, giving more rapid rates of room temperature re crystallization than any previous aluminum studied at the Alcoa Research Laboratories. This fact suggested that the entire midsection of the ingot might be of very high purity. Accordingly, section 4 was chosen for the next study. A portion of it was rolled to cold reductions of 10, 25, 40, 60, 75, and 90 pct at room temperature, and the re-crystallization of each specimen was followed by X-ray pinhole transmission photographs. The other portion received the same treatment, except that both the specimens and the rolls were maintained at 160°F in the process of rolling. The latter ortion was retarded in its recrystallization as compared to the former, probably due to the stress relief effect of the warm rolling. Both of these portions of the fourth section were found to recrystallize at a considerably slower rate than did the sixth section.

Jan 1, 1957

By G. Bassi

RECENTLY Wallbaum¹ found that copper wires with different degrees of deformation up to 98.7 pct area reduction recrystallize giving a [112] texture, while deformation over 98.7 pct gives either a [l00] texture at low temperatures or a [1ll] texture at high temperatures. Furthermore it was found that the recrystallization temperature as a function of deformation up to 98.7 pct decreases as expected, but increases over that deformation. Wallbaum concluded that the different textures have different recrystallization temperatures. The [112] texture has the lowest and [Ill] the highest. At the same time Bassi² found that for high deformation (over 99 pct area reduction) and for an annealing temperature of 400°C, the [l00] texture first forms and with prolonged annealing time the [12] texture appears through grain growth. This secondary texture does not appear if the wire is annealed at 1000°C before the deformation. From these two papers it might be concluded that the [I12] texture can appear either as a primary or as a secondary texture after annealing. The texture formed in a special case depends on the previous history of the wire. Probably the texture of the wire prior to the last deformation is important. To investigate this, wires were produced by adequate deformation and annealing to give a [l00], a [112], and a [lll] texture. The wires then were given a series of different deformations and were annealed at various temperatures, after which the textures were studied. Experimental Work The copper used was electrolytic tough-pitch (Cu 99.90 pct and 0, 0.04 pct). Three wires with the different initial textures were made in the following way: The [l00] and [112] by drawing a 16 mm rod to 1 mm and annealing it 16 hr at 200°C and 2 hr

Jan 1, 1953

By D. H. Davis, I. Fatt

Oil bearing rocks, usually found at depths of 2,000 to 10,000 it, are elastically deformed by overburden pressure. Although the change in porosity with pressure in a number of example rock.: has been shown to be small, it was thought that overburden pressure might have a significant effect on permeability. This note presents results of an investigation to determine the magnitude of the change in permeabilty with pressure. In routine core analysis permeabilities are measured on rock samples which are not under overburden pressure. If permeablity measured in this way differs from permeabilities measured under overburden pressure, a systematic error is introduced into well productivity calculations. The experiments described in this report were made to determine the magnitude of the change and thus to give an estimate of the error introduced into the calculations. The error introduced by the neglect of the change in permeability when overburden pressure is removed may account for part of the difference between well productivity calculated from core analysis and the actual well productivity. The results obtained in this investigation have only quali-tative significance because of the difficulty in reproducing in the laboratory the stress conditions on the rock buried in the earth. The assumption which is usually made is that the rocks in the earth are under a uniform pressure equal to the weight per unit area of the vertical overburden column from the rock in question to the surface of the earth less the pressure of the liquid in the pores of the rock. For an overburden consisting of sandstones and shales (of assumed average specific gravity of 2.3) and for a liquid pressure equal to the pressure in a salt water column (of specific gravity 1.0) reaching from the rock to the surface, the resulting net pressure on the rock is approximately 0.56 psi per ft of depth. EXPERIMENTAL METHOD Clean, dry sandstone core plugs one in. in diameter and about three in. long were mounted in a copper foil jacket as shown in Fig. 3 or molded in a Lucite jacket as shown in Fig. 4. All cores except those labeled "2" in Fig. 1 and "8" in Fig. 2 were measured in the copper foil jacket. Cores "2" and "8" were measured in the Lucite jacket. The jacketed core was placed in a high pressure hydraulic bomb in which the liquid pressure outside the jacket could be raised to 15,000 psi. Flow lines from the core were brought out of the bomb through special fittings in the bomh head and connected to a laboratory type gas permeameter. Measurements were made with nitrogen gas; the maximum mean gas pressure in the core was 16.1 psia. RESULTS The specific permeability of sandstone decreases with in. crease in overburden pressure. Most of the decrease takes place over the range of zero to 3,000 psi overburden pressure. If the net pressure on the rock is assumed to be 0.56 psi per ft of depth as discussed above, 3,000 psi of overburden pressure is equivalent to about 5,000 ft of overburden. At 3,000 psi overburden pressure, the permeability of the eight sandstone core samples tested ranged from 59 to 89 per cent of the permeability without overburden pressure. Figs. 1 and 2 show the permeability reduction as a function of overburden pressure. The permeability of the eight cores without overburden pressure ranged from 4.35 md to 632 md; these permeabilities are listed in Figs. 1 and 2. REFERENCES 1. Carpenter and Spencer: "Measurements of Compressibility of Consolidated Oil Bearing Sands," U. S. Bureau of Mines, R.I. 3450, (1940). * * *

Jan 1, 1952

By N. J. Grant, D. S. Bloom

N recent reports, Sully&apos; and Beck and coworkers&apos; I have advanced hypotheses concerning the formation of the phase. Both of these hypotheses are based on Pauling&apos;s theories of the electronic configuration of the elements of the first transition group. Sully considered that the number of electrons which can be absorbed in filling electron "holes" is the factor which determines whether or not the structure can form. Beck suggested that the presence of a certain concentration of electron "holes" is the controlling value. It can be shown that a similar criterion can be developed without making reference to Pauling&apos;s theories. Table I shows the elements of the first transition group and the incidence of the a structure in the binary systems of these elements according to the data presently available. Also appended is the number of electrons considered to exist in the 3d-4s levels of these elements. If the atomic percentages for the phase are listed as shown in Table 11, and if the number of electrons in the 3d-4s levels per atom is calculated for the a boundary values, the results are as shown in the last column. It can be seen that the numerical values are all in the vicinity of 7 electrons per atom. This is true also for the ternary Cr-Mo-Ni IT phase, which occurs in a system in which none of the binary compositions are known to develop the phase. In the Fe-Mo binary, the high temperature a phase, which occurs at a composition of 50 atomic pct of each element, also yields a ,;1 e of 7 electrons per atom. From inspection of Tables I and 11, it develops that any series of sequential numbers which is assigned to the elements under consideration will result in the numbers pertaining to a compositions grouping themselves around one specific number. It does not follow, however, that this random number necessarily has physical significance. Such a point has already been discussed by Hume-Rothery." One interesting point develops from this study, however, and that is the position of manganese with reference to the other elements and to the phase. In the system used here, the formation of phase is associated approximately with the value of 7 electrons per atom, which is also the number of electrons per atom that manganese has. Manganese, it will be recalled, exists in three different crystal forms, none of which are the usual, simpler metallic forms; on the other hand, elements just to the left of manganese (in Table I) generally have lower coordination-number structures (body-centered cubic) than do elements to the right of manganese (face-centered cubic). The contribution to a complex crystal structure by the interalloying of elements from opposite sides of manganese is significant in that the a phase is formed in binary systems including one element from each side of manganese, with manganese capable of participating with both sides. It is indeed an interesting coincidence that manganese, with 7 electrons per atom, solidifies in complex crystal forms, and that when alloys of the transition elements are made which have seven 3d-4s electrons per atom, they, too, tend to assume a complex crystal form. From the above, it might be deduced that the study of the a phase might be advanced by a critical examination of the element manganese and how its structure is affected by small additions of elements which change the 3d-4s electrons per atom number. The role of atom size would also be of interest in formation. References &apos; A. H. Sully: The Sigma Phase in Binary Alloys of the Transition Elements. Journal Inst. Metals (1951) 80, Part 4, p. 173. 2 S. Rideout, W. D. Manly, E. L. Kamen, B. S. Lement, and P. A. Beck: Intermediate Phases in Ternary Alloy Systems of Transition Elements. Trans. AIME (1951) 191, p. 872; Journal of Metals (October 1951). "W. Hume-Rothery, H. M. Irving, and R. J. P. Williams: The Valencies of the Transition Elements in the Metallic State. Proc. Royal Soc. (September 1951) 208A. p. 431.

Jan 1, 1954

By N. Brown, J. Washburn, E. R. Parker

MOST previous quantitative work on creep of single crystals has been concerned primarily with developing empirical equations for the creep curve. Although the equations used by Cottrell and Aytekin¹ and Tyndall² represented the data quite well, it was often necessary to use different values of the constants for different specimens even though they were apparently tested under identical conditions. In the course of previous work on the effect of surface coatings on creep of zinc single crystals," it was found that equal resolved shear stress frequently did not produce equal creep rates in different specimens. The work of Chalmers&apos; in the very

Jan 1, 1954

By E. S. Machlin

RECENTLY, there has been much activity in the field of nucleation of martensitic transformations.&apos;- One of the problems in this field is the calculation of the rate of nucleation (number of plates nucleated per unit untransformed volume per unit time) in terms of observable parameters. Two such observable parameters are the fraction of the length of a straight line which corresponds to the portion of the total length of the line that lies in the martensitic phase and the number of plates intersected by this straight line per unit length of line. Because of the necessity of a valid answer to this problem, the following investigation was undertaken. Although this problem has been treated in the past, a derivation of the relation between the volume and linear fractions of martensite will be described to illustrate the method used in the succeeding analyses. It is assumed that the martensitic plates are in the form of a right circular cylinder having a small height relative to the radius of the base. The volume fraction of martensite is then: fr = lXNl,hjAl [1] where f, is the volume fraction of martensite, and Nij is the number of plates per unit total volume having the area Ai and the height hi. The linear fraction of martensite is obtained as follows. For the plates having the particular area A, and height h,, the fraction sin 0 dB* will have their cylinder axes between the angles 0 and 0 + d0 to the straight line along which the linear fraction of mar-

Jan 1, 1953

By W. L. Freyberger

In a study of the kinetics of flotation of coal, employing a single-cell continuous flotation system, Jowett and Safvi1 pointed out that it was experimentally impossible to float all of the coal which could be floated in a batch tests. On the other hand, deBruyn and Modi, in a discussion of their paper, suggested that under certain conditions the recovery of floatable material from a similar one-cell continuous system would have been 100%.2 Both of these pairs of authors make the assumption that a state of perfect mixing exist in the flotation cell. This assumption, usually made by investigators studying flotation kinetics in a continuous system, has been confirmed experimentally on several occasions. The work is summarized by Arbiter and Harris.3 It is the purpose of this note to demonstrate that, for conditions of perfect mixing, one of two conditions exist: 1) the recovery of floatable material is 100%, and the flotation is infinitely fast, or 2) the recovery of floatable material must be less than 100%. This theorem can be proved simply in the following manner: 1) If recovery, R, of the floatable material is 100%, the concentration in the tailing must be zero. This follows from the definition of recovery as

Jan 1, 1964

By Norman Lamont

The evaluation of certain reser-voir properties, such as porosity and fluid saturation, from electrical well surveys has been widely accepted in petroleum engineering. Various investigators have established relationships between these properties and certain parameters which affect the response of the electrical log. Among these are the resistivities of the mud, its filtrate, and its filter cake. In 1949, Patnode1 established a relationship between the resistivities of the mud and filtrate. The well logging service companies have contributed relationships for the mud-mud cake resistivities2,3 These have been valuable since it was the practice to measure only resistivity of mud at the well site. During the mid-1940&apos;s the industry began drilling wells with oil-emulsion drilling fluids. These were conventional aqueous muds with a dispersed oil phase. Since 1950, oil-emulsion muds have been used on an increasing number of wells each year. However, the practice of measuring only the resistivity of the mud at the well site has continued, and the mud filtrate and mud cake resistivities have been determined by the above-mentioned relationships. Service companies are now equipped to measure all three resistivities at the well site. An investigation was conducted on the resistivities of oil-emulsion muds, mud filtrates, and mud cakes to determine if these values conformed to the relationships for aqueous muds. TYPES OF MUDS Fifty-one oil-emulsion mud samples were prepared in the laboratory following a standard manual&apos; published by a leading mud company. The diesel oil in the samples varied from 5 to 50 per cent, the majority of the samples being in the 10 per cent region. The basic aqueous mud types which were converted to oil-emulsion muds were commercial clay and bentonite muds, low pH and high pH, caustic-quebracho treated muds, and lime treated muds. The emulsions were stabilized by dispersed solids, lignins, lignosulfo-nates, sodium carboxymethyl cellulose, or sulfonated petrolatum. It is worthy of note that after a quiescent period of two weeks at room temperature all samples, regardless of emulsifying agent, remained stable. The make-up water for the muds was from the laboratory tap. Resistivities were varied by the addition of table salt to the water. A range of mud resistivities from 0.44 to 3.9 ohm-m was obtained in this way. Twenty-three field muds were tested. These covered the same range of mud types as did laboratory muds. Oil provinces of the Gulf Coast, South Texas, West Texas, Oklahoma, Montana, and Canada were represented. MUD TEST PROCEDURE Each mud was tested for density, viscosity, pH, and filter loss by standard testing techniques. The resistivity measurements were obtained with a Schlumberger EMT meter. This meter required small volumes of sample, e.g., 2 mm. Filtrate was obtained from a Standard Baroid fil-ter press at the end of a 30-minute test. The filter cake from the same test was used for cake resistivity measurements. Mud, filtrate, and cake samples were heated to 100" F in a constant temperature water bath prior to measurement of resistivities. RESULTS The relation between mud resistivity (Rm) and mud filtrate resistivity (Rmf) is shown in Fig. 1. The solid line represents an average for the data. The equation of this line is Rmf =0.876 (Rm) 1.075 . . (1) Arbitrary limits, indicated by the dashed curves, have been set. The majority of the data falls within these limits, but some points do lie outside the limits. The approximate equation Rmt = 0.88 Rm , . . . . (2) will give satisfactory results within these limits. The data on mud cake resistivity Rmc is shown in Fig. 2. The solid line is an average for the data. The equation for the line is Rmc = 1.306 (Rm)0.88 The dashed lines are arbitrary limits on the data. Within these limits, Eq. 3 may be simplified to Rmc = 1.31 Rm . . . . (4) DISCUSSION The limiting curves in Figs. 1 and 2 represent maximum deviations of ±25 per cent. Thus the use of the average curves can introduce considerable error. There is no substitute for accurate measurements of mud, mud cake, and mud filtrate resistivities at the well site. The mud sample tested should be representative of the mud opposite the formation being logged. The average mud filtrate resistivity curve of Fig. 1 is reproduced in Fig. 3 with two curves which have been published for clay-base aqueous muds2,3. The latter curves were determined from average values of a large number of drilling fluids. The three curves have essentially the same slope and the differences between them are from 7 to 22 per cent. Comparison is made only to illustrate the possibility of error

Jan 1, 1958

By R. W. Balluffi, B. H. Alexander

RELATIVE diffusion rates of copper and zinc in a brass have been measured in a vapor-solid type of couple with which the amounts of copper and zinc diffusing past inert Kirkendall markers can be obtained by means of a few simple experimental measurements. If inert markers are placed on the surface of copper which is then exposed to zinc vapor from a brass chips, the particles become buried due to outward diffusion of the copper, as shown in Fig. 1. A schematic diagram of such a couple after diffusion is shown in Fig. 2. Consideration of the diffusion flow of copper and zinc shows that the entire hatched area, including the cross-hatched area, is proportional to the amount of zinc diffused inward past the markers and that the smaller cross-hatched area is proportional to the amount of copper diffused outward past the markers. These areas are completely determined by the expansion of the couple, the depth of the buried particles below the surface, and the chemical composition at the specimen surface. As Darken1 has shown, the ratio of diffusivities of copper and zinc is then given by the ratio of these two areas. Polycrystalline copper and two copper single-crystals made by the Bridgman method were prepared in the form of 1.5 cm diam disks approximately 0.5 cm thick with faces plane and parallel. Tungsten particles approximately 0.001 cm in diam were bonded to the surface of each disk by heating 5 hr at 1060°C in vacuo. Each specimen was next

Jan 1, 1953

By K. P. Anderko

INVESTIGATIONS of the constitution of the system Mg-Ba were first made by Grube and Dietrich1 between 0 and 47 atomic pct Ba and then by Klemm and Dincke1acker" ver the whole composition range. Klemm and Dinckelacker corroborated intermediate phases of the approximate formulas Mg9Ba and Mg4Ba, and showed a third compound to have the formula Mg2Ba, rather than Mg5Ba, as suggested by Grube and Dietrich. Mg2Ba had been previously recognized by Hellner and Laves3 s a MgZn2 (C14) type structure. The main discrepancies between the results of Grube and Dietrich and those of Klemm and Dinckelacker exist, however, in the liquidus temperatures and solidification equilibria of alloys containing more than about 10 atomic pct Ba. The liquidus temperatures measured by Grube and Dietrich, and the outline of the liquidus of Klemm and Dinckelacker are plotted in Fig. 1 on an enlarged scale. Although there are strong reasons to prefer the results of Klemm and Dinckelacker, it was considered worthwhile to remeasure liquidus temperatures of some alloys in the controversial composition range. The alloys, made up from sublimed magnesium and 99.5 wt pct pure barium, were melted in an Armco-iron crucible in a dynamic argon atmosphere. Thermal analyses were taken using a Speedomax auto- matic recorder. Careful stirring during the solidification process was required in order to avoid segregation. After thermal analysis some of the cast alloys were chemically analyzed. The intended and analyzed compositions of the ten alloys prepared are listed in Table I. Since standard barium determinations cannot differentiate between barium present as element and as oxide, both the barium and magnesium contents of the alloys were analyzed. The fact that the sum of barium and magnesium was close to 100 pct in each case was taken as evidence that no excessive oxidation had occurred. The liquidus temperatures measured are listed in Table I and plotted in Fig. 1. As can be seen, they are in good agreement with the liquidus found by Klemm and Dinckelacker. This leaves no doubt that the thermal results of Grube and Dietrich above 10 atomic pct Ba are incorrect. This work was performed under the sponsorship of the Pitman-Dunn Laboratories of Frankford Arsenal, Philadelphia, Contract No. DA-11-022-ORD-1975. Sponsorship and permission to publish by this organization are gratefully acknowledged.

Jan 1, 1958

By F. C. Langenberg, R. W. Lindsay

COPPER sometimes is added to steel and cast iron as an alloying element to improve or impart specific properties. However, in some steels it exerts an impurity effect in impairing response to fabrication by hot working and deep drawing. The resid-

Jan 1, 1955

By H. C. Vacher, C. J. Newton

EXTENSIVE investigations in the field of residual strain measurement by X-ray diffraction have been made by Bollenrath, Hauk, and Osswald,1 by Smith and Wood,2&apos;3 by Greenough; by Rosenthal and Norton." and many others. Since X-ray strain measuremeits apply only to those crystals of the test body which are of the proper condition and orientation to diffract and since the residual strains revealed may be accompanied by either body or tex-tural stresses, there has been considerable disagreement among investigators with respect to the validity of conclusions in this field. Although the experi-mentors have employed a variety of loading schemes, surface preparations, and X-ray wave lengths, the observations almost invariably have been made only on the outer surfaces of the specimens. The present note is not to be construed as an exposition of a new method of stress analysis by X-ray strain measurements on sections but as a presentation of some results which point to interesting possibilities for further experiments with sections. The two test rods used in this study were of ingot iron annealed at 910°C. The initial length of the gage section was 2 in. and the diameter was 0.415 in. Cross-sections were cut from the ends of the annealed rods to provide strain-free material. The tensile rod was axially loaded the desired amount in a commercial testing machine. A 1 in. portion of the gage length was cut from the other rod and was subjected to compression in the same machine. Details of this plastic straining of each rod are given in the upper half of Table I. A half-cylinder piece about 1/4 in. long was obtained by making a short longitudinal plane cut containing the axis of the rod near the center of the gage length. From adjacent material a disk about 1/8 in. thick was cut to provide the cross-section specimen. Later another section was cut from this same region with an angle of 30" between the normal to its surface and the axis of the test rod. A cross-section and a longitudinal section were cut from the compression rod in a similar manner. All of these as well as the strain-free cross-sections were mounted in Bakelite and used as specimens for the following X-ray strain measurements. During the course of the study, it became apparent that the condition of the surface of a specimen was a highly critical factor. One of the annealed strain-free specimens as a control was subjected to about 24 hr of polishing with fine alumina, interrupted about every 2 hr for etching with 1 pct nital. Its lattice parameter was determined at intervals from measurements on back-reflection X-ray diffraction patterns, which were calibrated with diffraction from tungsten powder. The parameter gradually approached the value found in the literature for strain-free iron and remained there, within the limits of the experimental error. This determined a long polishing and etching procedure which was adopted for all the specimens and which gave X-ray results from the surfaces believed to be representative of each specimen as a whole. A large number of back-reflection patterns were made with cobalt and chromium radiation, all at normal incidence. Except for some preliminary stationary exposures made to monitor the removal of cold work from the surfaces, each exposure was made with the specimen slowly translating and the film slowly rotating. In appropriate cases a thin layer of a standard metal powder, tungsten with cobalt radiation and silver with chromium, was dusted over a film of vaseline on the surface of the specimen to serve to calibrate the X-ray patterns. After the preliminary work, four films were made,

Jan 1, 1956

By B. L. Averba

THE determination of retained austenite by X-ray diffraction uses the following relationship:"" Pa = constant . RVaA (8) [1] where: P is the diffracted power from phase a; R, the calculated intensity factor; A, the absorption correction; 8, the diffraction angle; and Va, the irradiated volume of phase a For a flat sample making a glancing angle + with the incident beam the absorption correction is calculated as: * 1 sin (28 - 4) A .= 1 [2] µ sin, (28 — 4) + sin 4 where µ is the linear absorption coefficient. Beu3 has proposed that the computed absorption correction be combined with the constant and that the experimental observation of the absorption correction used in the original method be eliminated. This procedure is permissible only if: 1—There is no preferred orientation in the sample, and 2—The geometric requirements have been met precisely. If these conditions are not met the validity of the determination is questionable. Unfortunately the necessary conditions must be tested experimentally for each determination, and this is done most easily by observing whether the apparent absorption has the form of Eq. 2. In practice it may be convenient to plot P/R vs the parameter sin (2? — )[sin (28 — +) + sin +] to obtain straight lines for the ap- parent absorption correction. Deviations from straight lines indicate either that the sample has not been positioned correctly or that the relative intensities are incorrect. Geiger counter spectrometer methods also have been used successfully for retained austenite determinations. In the usual spectrometer arrangement the sample makes equal angles with the incident and diffracted beams (8 = ); thus the absorption correction is simply 1/2µ and independent of 8. The retained austenite is then easily calculated from integrated intensity measurements on austenite and martensite lines. If the austenite content is not too low and if excessive fluorescence is not encountered it is possible to use filtered radiation and a recording spectrometer. The integrated intensities are then proportional to the areas of the diffraction peaks. For lower austenite contents the following technique was used: A bent quartz monochromator and a Geiger counter spectrometer are employed. The monochromatic radiation is focused on the front slit, and the counter slit is made broad enough to include the entire line. A series of readings are taken in the vicinity of the diffraction peak. The highest reading includes the diffraction line plus background. The background is obtained from the average of several readings on each side of the peak. The integrated intensity is obtained by subtraction. CrK, and FeKa have been used for such determinations. This technique has been found to be as sensitive and as accurate as the photographic methods. In the spectrometer methods the ratio austenite/ martensite may be obtained from readings on austenite and martensite lines and the application of Eq. 1. It is also possible to use external standards and to obtain the austenite contents from measurements on the austenite lines alone. The small correction for carbides then becomes unnecessary. The best standards are probably samples with known

Jan 1, 1954

By E. S. Machlin

THE function of this paper is to present certain results based on the fact that the strain energy arising from the solution of out-of-size solute atoms into the solid matrix is free energy and not internal energy, and that this strain energy is almost wholly shear strain energy as Zener1 pointed out. One natural consequence of this fact is an expression for the excess entropy of mixing due to the strain energy. Also, a derivation of the integral molar free energy of mixing partitioned to strain energy will be made using the model of Lawson2 and thermodynamics. This derivation has the advantage of showing in a simple way the assumptions involved in Lawson&apos;s treatment. The excess entropy of mixing partitioned to strain energy can be derived in two ways. The first way makes use of the fact that the strain energy is almost wholly in the form of shear strain energy. In this case, as Zener1 pointed out, the change in entropy due to the addition of shear strain energy is to a first approximation given by ?S/?? p,T = - ?lnµ/?T p,? Hence, the excess entropy of mixing partitioned to strain energy will be given by Sx ? = ?S/?? p,T Gx ? = - ?lnµ/?T p,? Gx ? where, Gx ? is the relative integral molar free en- ergy partitioned to strain energy; S is the entropy; is the shear strain energy; µ is the shear modulus; T is the absolute temperature; p is the pressure; and ? is the shear strain. Zener,1 as well as others, has pointed out that the shear strain energy stored in a compressible isotropic solid due to the insertion of an off-size incompres-sible sphere into a spherical hole in the solid, is approximately given by 2/3 µ/O (O°I - O)2 where a is the volume of spherical hole and no , is the volume of sphere. If we now consider the introduction of one mol of such spheres into an infinite volume of solid, then the relative partial molar free energy excess due to strain energy alone is GM ? = 2/3 µ/v (v ° 1 - v)2 where v is the molar volume of solvent and v°1, is the molar volume of pure solute type 1. Let us consider that these spheres are the two types of atoms in a binary solution, then there will be a similar relation for solute 2. The total relative integral molar free energy excess due to strain is then, to the approximations stated above GM ? = GM ? x1 + GM2 ? x2 = 2/3 µ/v [(v ° 1 - v)2 x1 + (v ° 1 - v)2 x2]. Lawson&apos;s relation for the strain energy can be de-

Jan 1, 1955

By C. G. Dunn, M. Sharp

HE orientations of 137 crystals of copper pro-T duced by secondary recrystallization in a cube texture matrix have recently been obtained. Although the crystals were not prepared for the purpose of determining a secondary recrystallization texture, the orientations obtained proved to be rather interesting, as they confirmed, in part, published results and also disclosed additional preferred orientations in the texture. The investigation of Dahl and Pawlek,&apos; Bowles and Boas,&apos; and Kronberg and Wilson3 showed respectively that the orientations of secondary grains growing in a cube texture matrix were related to those of the primary grains by a rotation of approximately 30" about [001], the rolling direction, by 30" about a <111> direction, and by either 22" or 38" about a <111> direction. Kronberg and Wilson also obtained a component of the texture similar to that of Dahl and Pawlek except the angle of rotation about [001] was 19". When the cube texture matrix was deformed a small amount, Kronberg and Wilson also obtained large grains on subsequent annealing corresponding to a rotation of 15" about the normal to the sheet, but these grains should not be classified as secondary recrystallization grains since they were produced subsequent to mechanical straining. The particular texture obtained, of course, depends on the composition of the copper and the processing schedule employed, since these factors markedly affect the primary recrystallization texture and the sharpness of any cube texture produced. In the present investigation, pieces of OFHC copper in the form of M in. round bars were cold forged to a thickness of about 0.40 in., annealed 1 hr at 350°C in an atmosphere of hydrogen, and cold rolled crosswise to a thickness of 0.200 in. These pieces were given a penultimate anneal of 1 hr at 350°C in hydrogen and a 90 pct cold-rolling reduction lengthwise to a thickness of 0.020 in. Indentations generally were put in one end of the as-cold-rolled strips to promote earlier formation of secondary grains.

Jan 1, 1953