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By M. C. Fuerstenau, A. M. Gaudin

A homogeneous suspension is viewed by X-rays. The radiation density seen, affords a measure of the extra absorption due to the solids contained. This radiation density, at a predetermined depth, varies with time. The chart of this relationship gives the desired determination. s it is frequently necessary to know the distribu-rt tion of particle sizes in various products used in industrial applications, a number of means have been devised for these determinations. Some of them include direct microscopic measurement, screening of product, extraction of samples from a settling slurry, air and liquid elutriation, adsorption of gases and liquids, and light absorption. The absorption of light as a means for particle size analysis has been known and employed for some time. X-ray absorption has not received the attention that light has enjoyed primarily because of the complex and costly instrumentation involved with X-rays. In 1954, Brown and Skrebowskil suggested the use of X-rays for this type of determination but did not supplement their suggestion with experiment. In 1958, the authors conducted size analysis experiments on suspensions of quartz with the Trans-viewer: an X-ray unit specifically adapted for sedimentation research, and Rossa conducted experiments in a similar manner in 1959 with a stable gamma emitter, AmZ4l, on suspensions of uranium oxide. To illustrate the applicability of X-ray absorption for analyzing particle size distributions, an essentially mono-energetic and well collimated X-ray beam was used as a source. The beam was made mono-energetic by placing a zirconium filter before the counting window together with feeding the pulses from the proportional counter into a reverter, a device capable of discriminating against pulses of various heights. The sketch in Fig. 1 shows the collimation arrangement in more detail. As shown, the X-ray beam was collimated by inserting a 3/8-in. ID pipe into one of the ports of the X-ray tube and further by two small steel plates with slits 3/32-in. wide and 1/2-in. long placed in front of the window of the Geiger-Mueller (G-M) tube. One of the plates was located 1/2 in. and the other 2 1/2 in. from the window of the counter; both plates were contained in an aluminum holder mounted on the box containing the G-M tube. This type and degree of collimation should eliminate any intensity due to scattered radiation; the transmitted intensity would then be solely a functior. of the absorption by the suspension at that level. Experimentally, homogeneous suspensions of finely ground quartz were prepared, Daxad (a sulfo-nated compound made from wood) was added as dis-persant, and the transmitted X-ray intensity measured as a function of time at a fixed depth in the suspension. In more detail, the experimental procedure involved the following: 1) measuring the transmitted X-ray intensity through the Daxad solution at a predetermined position or settling depth in the absence of solids, 2) placing a known amount of dry solids into the vessel and agitating thoroughly, 3) measuring the transmitted X-ray intensity at time zero (i.e., immediately upon cessation of stirring), and 4) measuring the transmitted X-ray intensity as a function of time (a 10-sec counting interval being chosen and counting being started 5 sec before the desired time). Since a linear relationship exists between percentage solid in a slurry and the logarithm of transmitted intensity for a homogeneous material, the cumu-

Jan 1, 1961

By C. E. Shoenfelt

There was a notable decrease in drilling operations in 1940 in all of the Rocky Mountain states except Montana, where the two large fields on the Canadian border, Cut Bank and Kevin-Sunburst, were espe-cially active. The expanding markets for Montana natural gas made necessary the more intensive development of such fields as Rowdoin, Cedar Creek and Devon. While there were no important oil and gas discoveries in 1940 in any of the Rocky Mountain states, a few small pools were opened, which may constitute separate areas but may prove with later development to be extensions of old fields. Some of the old fields were extended and deeper pay zones were discovered in others. These have given the areas greatly increased oil reserves and therefore are just as important as the discovery of new fields. The more important of the developments in 1940 are given, by states, in the following paragraphs. Colorado Hiawatha Field, Moffat County.—The Mountain Fuel Supply Co. began the development at Hiawatha of its oil reserves, which were discovered in about 1929, and late in the summer oil began moving from the field by truck to the shipping point at Rock Springs, Wyoming. The Hiawatha field of northwestern Moffat County was discovered in 1927 by the Sormir Petroleum Co., with the completion of No. r Florence Wilson for 4,5,000,000 cu. ft. of gas a day from a Wasatch sand lens at 2200 it. In later development of the field, oil showings were reported in several wells but no development of this resource was undertaken until 1940, when a test of the oil possibilities was started with the release in April of a location for No. 5-A Wilson on the S\W. SW. NW. of sec. 23-1zN-1ooW., on the east side of the field. The Well had an initial production of 327 bbl. of oil a day pumping from three Wasatch (Tertiary) sands between 2005 and 2540 ft. It was drilled to 2562 ft., where the 65/8-in. casing was cemented and gun-perforated at 2005 to 2125 ft., 2260 to 2335 ft. and 2513 to 2540 ft. At the end of the year, this well was averaging zoo bbl. of oil per day, pumping. Two other wells were drilled for oil on Hiawatha during the summer—one a small well of 60 bbl. per day and the other a small gas well. Powder Wash Field, Moffat County.—The development of the Powder Wash field in northwestern Colorado was resumed in 1940 by the Mountain Fuel Supply Co., with the release of a location for No. 2-A Musser in the CWL.NW.SE. of sec. 4-1rN-97W. The Powder Wash field was discovered in 1931 by the Mountain Fuel Supply Co. and the discovery well, No. I Musser, on C.NW. of sec. 5-IIN-97W., was completed at 2152 ft. in the Hiawatha member of the nonmarine Wasatch for-mation for an open flow of 34,000,000 cu. ft. of gas per day under a natural pressure of 685 lb. per sq. inch. Oil was discovered in the Powder Wash field on Nov. 26, 1936, in the company's No. I Carl Allen on the NE.SW.SE. of sec. 32-12N-97W. The oil production was

Jan 1, 1941

SEC. 1. The membership of the Institute shall comprise seven classes, namely: 1. Members; 2. Honorary Members; 3. Senior Members; 4. Associates; 5. Junior Members; 6. Rocky Mountain Members; 7. Junior Foreign Affiliates. All shall be equally entitled to the privileges of membership, excepting that no member of any class whose residence shall be outside of the United States of America, except those residing in Mexico and Canada, shall be entitled to vote. SEC. 2. Members: A person to be eligible for election or transfer into the class of Member must be at least 27 years of age and must have had at least six years' employ¬ment in the practice of engineering, mining, geology, metallurgy, or chemistry, during at least three years of which he must have held positions of responsibility in one or more of these fields. This shall not apply to Rocky Mountain members. SEC. 3. Honorary Members: Each candidate for Honorary Membership must be recommended by at least ten Members and must be elected by ballot at a meeting of the Board of Directors by the unanimous vote of the Directors present; provided, how¬ever, that the number of Honorary Members shall at no time exceed twenty. Such election shall automatically act as a transfer of such member from any other class of membership to which he may belong. SEC. 4. -Senior Members: The Directors may in their discretion place on the Honor Roll of Senior Members and transfer from any other class of membership other than Honorary Membership the name of any Member or Associate who has reached the age of seventy years and who has paid dues for thirty years, and for good reasons in special cases may vary the age or number of years. SEC. 5. Junior Members: A person to be eligible for election to the class of Junior Member must be qualified through education or experience to hold a subordinate position in engineering, mining, metallurgical, geological or chemical work. He shall be not more than 33 years of age at the time of election. SEC. 6. Associates: A person eligible for election or transfer into the class of Associate shall be one, who, in the opinion of the Committee on Admissions and the Board of Directors, is suitable for such election or transfer by reason of his interest in or connection with mining, geology, metallurgy, or chemistry. SEC. 7. Rocky Mountain Members: Membership in a special class of life member¬ships without annual or other dues and without right to receive the printed literature distributed to other members or the right and privilege of wearing the official badge of technical members, is given to all members of the Rocky Mountain Club at the time of consolidation. These special Rocky Mountain memberships shall be claimable by any member of the Rocky Mountain Club, not already a member of the Institute, availing himself of the privilege within ninety days after mailing of notice to him, by the Secretary of the Institute. SEC. 8. Junior Foreign Afliate: Upon appropriate action by the Board of Direc¬tors and with its approval, members in good standing of any technical society having its headquarters outside of the United States of America, Canada, or Mexico,

Jan 1, 1937

By Jack F. Harang, P. B. Leavenworth

Development during the year 1941 on the Texas Gulf Coast resulted in the dis covery of 27 new fields as compared to 26 fields for the year 1940. Drilling.—During the year, 1405 wells were drilled. Of this number, 1031 were completed as oil wells with 375,000 bbl. daily of new production; 50 were com pleted as gas wells and 324 were failures. The most active area was Jackson County, where 375 wells were drilled and 336 of them accounting for 190,000 bbl. daily of new production. Types of Fields.—Of the 2 7 new fields, 14 are considered to be oil fields, 8 are listed as gas-distillate fields and 5 as gas fields. This may be compared to 26 fields found in 1940, of which 14 were oil fields and 12 gas-distillate fields. Producing Sections.—Frio discoveries retained their predominant position by having 10 Frio fields discovered in comparison to 6 fields in the Wilcox, 4 in the Yegua, 5 in the Miocene and 2 in the Jackson. In the previous year 15 Frio fields were found, 4 in the Wilcox, 2 each in the Yegua, Cook Mountain and Miocene, and I in the Jackson. Production.—Production increased over 1940 approximately 10 per cent, being 113,726,893 bbl. for the year 1941 and 104,127,247 bbl. for 1940. The statistics in Tables I and 2 include distillate and condensate as oil production because no separate reports have been compiled. It is hoped that this separation may be possible some day, but as a great many fields produce both oil and distillate and these arc commingled in pipe lines, separation of statistics will be more difficult than for other areas. New Fields Big Hill, Jefferson County.—Stanolind Oil and Gas Company's No. I George D. Anderson was completed as a gas well from a Frio sand at 8705 to 8720 ft., on Dec. 24, 1941, after having been drilled to a depth of 9500 ft. Additional development is being carried on but it is not possible to evaluate this discovery at this time. Brushy Creek Field, Lavaca County.— Shell Oil Corporation's No. I D. G. McManus was completed as the discovery well in the Brushy Creek field on Oct. 29, 1941, from a Wilcox sand through perforations at 7225 to 7230 ft., making gas and 180 bbl. of 59° gravity distillate. This well was bottomed at 10,998 ft. in the Wilcox. No statement can be made at this time as to the importance of this discovery. Chenango Field, Brazoria County.—J. N. Rayzor et al. completed their No. I Sarah J. Christian through perforations at 8564 to 8572 ft. in a Frio sand, for 453 bbl. of 37.7° gravity oil, on Feb. 6, 1941, after having drilled to 9564 ft. Several wells were drilled in this area during the year but failed to establish important production. This is considered a minor discovery. Clodine Field, Fort Bend County.—Providence Oil Company's No. I Hatfield was the discovery well of the Clodine field, being completed through perforations at 7499 to 7502 ft. for 108 bbl. of 51.2° gravity distillate, on June 19, 1941. The well was bottomed at 8090 ft. Several wells

Jan 1, 1942

By W. D. Robertson, R. E. Reed-Hill

DEFORMATION of magnesium crystals in a direction parallel to the basal plane has a special significance as a result of the preferred orientation characteristic of cold worked and recrystallized polycrystalline magnesium sheet and extruded rod in which the basal plane tends to lie in or near the plane of the sheet or the axis of a rod. The principal objective of the present study is a determination of the modes of plastic deformation in magnesium single crystals in this orientation. Evidence for nonbasal slip in magnesium has been presented by a number of authors. Schmid and Was-serman&apos; indicated that pyramidal slip on {1011} < 1120> or {1012} <1120> could occur above 225°C. Bakarian and Mathewson2 stablished that the slip system {1011} <1120> operates at high temperatures and that 225°C was a lower limit for pyramidal slip. The latter authors also showed that the critical resolved shear stress for {1011} slip was 400 g per sq mm at 330°C, while that for basal slip was 66 g per sq mm at the same temperature. Thus, at 330°C basal slip should be expected for all orientations except those in which the stress axis lies almost in the basal plane. More recently Burke and Hibbard3 oserved pyramidal slip at 25°C, when the stress axis was 6" to the basal plane and 14" to a <1120> slip direction. The critical resolved shear stress for pyramidal slip was 52 g per sq mm, which is only slightly greater than their value for basal slip (46 g per sq mm). Chadhuri, Chang, and Grant4 have observed non-basal slip in creep tests with polycrystalline specimens in the temperature range 250" to 350°C. The observed slip bands, which were extremely irregular in appearance, can be explained in terms of cooperative slip on {1011} and (1010) planes which have a common slip direction. Prismatic (1070) slip in polycrystalline magnesium was observed by Hauser, Landon, and Dorn.5 It was found to occur at low temperatures (78" and 195°K) and it was accompanied by cross slip in which the cooperating plane was the basal plane. Since prismatic slip occurred only at regions of high stress concentrations, the critical resolved shear stress could not be determined. Experimental Procedure The present work was performed on crystal specimens which were all cut from the same large single crystal. The original cylindrical crystal, 0.5 x 7 in., was grown in a Bridgman type furnace in which the temperature gradient was moved past the stationary crystal in the manner described by Jillson6 and Burke.&apos; High purity magnesium was furnished by the Dow Chemical Co. with the following spectro-graphic analysis in weight percent: 0.003 pct Al, <0.01 pct Ca, 0,002 pct Cu, <0.001 pct Fe, 0.008 pct Mn, <0.001 pct Ni, <0.002 pct Pb, <0.01 pct Si, <0.001 pct Sn, and <0.01 pct Zn. The large crystal was cut into four cylindrical pieces about 1.5 in. long. A flat surface parallel to the basal plane was made by hand grinding with lubricated metallographic paper on one side of each cylinder. In order to prevent bending in subsequent cutting operations, the crystals were supported by

Jan 1, 1958

By C. B. Alcock, R. A. Oriani

Some simple models of solutions are described; these include the regular solution, the subregular solution, and the quasichemical model. The assunzption underlying these models, the physical signzficance thereof, and the experimental manifestations are discussed. Examples are presented from the fields of liquid and solid metallic solutions, liquid slags, mattes, liquid and solid ionic solutions, and mixed carbides to show under what conditions and for which systems these solution models are fair descriptions. The deviations of real solutions from the models are of theoretical interest. Some such deviations, both for dilute and for concentrated solutions, arc pointed out and their Physical sigtzzficance discussed. DURING the past half century there has been a gradual accumulation of thermodynamic data for systems of interest to the metallurgist. There remain many gaps in the data, however, and the metallurgist must often face the problem of estimation of thermodynamic quantities where measured values do not exist. One might hope that the experimental progress would be matched by theoretical advances which would make such estimations possible with a high degree of confidence. However, theoretical progress has been disappointingly slow even for the simplest kinds of solutions, and since the multicomponent systems in which the metallurgist is interested are very complex, one cannot expect theory to be of much help to the metallurgist. In this situation, therefore, it seems worthwhile to examine some simple models of solutions from two points of view: firstly, to see if such crude models represent the thermodynamic facts in as many types of solutions as possible sufficiently well for the needs of the metallurgist, and secondly to see what the deviations from such models show to be important for consideration by theorists. BOND ENERGY MODELS OF SOLUTIONS The simple models that we will examine from these points of view may be termed statistical models, in that they are concerned with the thermodynamic consequences of some simple assumptions about the energy of an assembly of atoms, molecules, or ions, and do not inquire into the physical basis of the interaction. The underlying assumption of these models is that the energy of an assembly of molecules (by which we include also atoms or ions) is given by the sum over all interaction energies of molecules taken two at a time; we will discuss only those models in which the pairwise interactions are restricted to those between nearest neighbors. Thus, in a pure substance of bond energy EAA, the internal energy (with respect to some specific reference state) will be expressed as NAA EAA where NAA is the number of nearest-neighbor pairs. A solution of molecules A and B will be characterized by NAA EAA + NBB EBB + NAB EAB where the Eij represent the bond energies of the nearest-neighbor i-j pairs. If one assumes that the EAA and EBB are the same in the pure components as in the solution, and that the coordination numbers in the two pure substances and in the solution are the same, then the energy of the solution with respect to the pure components (i.e., the energy of solution) is a function of the following linear combination of the bond energies: EAB - 1/2(EAA +EBB) = w. The thermodynamically ideal solution is defined as one in which the activity of each component is equal to the mole fraction of that component at all concentrations and all temperatures. It follows that

Jan 1, 1962

By P. B. Leavenworth, Jack F. Harang

Development during the year 1941 on the Texas Gulf Coast resulted in the dis covery of 27 new fields as compared to 26 fields for the year 1940. Drilling.—During the year, 1405 wells were drilled. Of this number, 1031 were completed as oil wells with 375,000 bbl. daily of new production; 50 were com pleted as gas wells and 324 were failures. The most active area was Jackson County, where 375 wells were drilled and 336 of them accounting for 190,000 bbl. daily of new production. Types of Fields.—Of the 2 7 new fields, 14 are considered to be oil fields, 8 are listed as gas-distillate fields and 5 as gas fields. This may be compared to 26 fields found in 1940, of which 14 were oil fields and 12 gas-distillate fields. Producing Sections.—Frio discoveries retained their predominant position by having 10 Frio fields discovered in comparison to 6 fields in the Wilcox, 4 in the Yegua, 5 in the Miocene and 2 in the Jackson. In the previous year 15 Frio fields were found, 4 in the Wilcox, 2 each in the Yegua, Cook Mountain and Miocene, and I in the Jackson. Production.—Production increased over 1940 approximately 10 per cent, being 113,726,893 bbl. for the year 1941 and 104,127,247 bbl. for 1940. The statistics in Tables I and 2 include distillate and condensate as oil production because no separate reports have been compiled. It is hoped that this separation may be possible some day, but as a great many fields produce both oil and distillate and these arc commingled in pipe lines, separation of statistics will be more difficult than for other areas. New Fields Big Hill, Jefferson County.—Stanolind Oil and Gas Company&apos;s No. I George D. Anderson was completed as a gas well from a Frio sand at 8705 to 8720 ft., on Dec. 24, 1941, after having been drilled to a depth of 9500 ft. Additional development is being carried on but it is not possible to evaluate this discovery at this time. Brushy Creek Field, Lavaca County.— Shell Oil Corporation&apos;s No. I D. G. McManus was completed as the discovery well in the Brushy Creek field on Oct. 29, 1941, from a Wilcox sand through perforations at 7225 to 7230 ft., making gas and 180 bbl. of 59° gravity distillate. This well was bottomed at 10,998 ft. in the Wilcox. No statement can be made at this time as to the importance of this discovery. Chenango Field, Brazoria County.—J. N. Rayzor et al. completed their No. I Sarah J. Christian through perforations at 8564 to 8572 ft. in a Frio sand, for 453 bbl. of 37.7° gravity oil, on Feb. 6, 1941, after having drilled to 9564 ft. Several wells were drilled in this area during the year but failed to establish important production. This is considered a minor discovery. Clodine Field, Fort Bend County.—Providence Oil Company&apos;s No. I Hatfield was the discovery well of the Clodine field, being completed through perforations at 7499 to 7502 ft. for 108 bbl. of 51.2° gravity distillate, on June 19, 1941. The well was bottomed at 8090 ft. Several wells

Jan 1, 1942

By C. H. Lee, R. Maddin

The diffusion rates of Ag110 in cylindrical single crystals of 99.99 pct pure silver, which were twisted to a total surface strain of 0.91 during the diffusion anneal at temperatures of 700°, 750°, and 800°C, were measured by sectioning and counting as a function of the strain rates. The ratio of the diffusivities while strain ing occurred (Ds) to those of the unstrained specimens varies linearly with the rate of twisting and attains values of near 100 for some of the rates used. The enhancement of diffusion by straining is inversely proportional to the temperature at which diffusion occurs. The activation energy for diffusion determined from the data plotted as a function of the rate of twisting decreases from 44,090 cal per mole for zero strain, to an asymptotic value of 21,000 cal per mole for the strain rates of 22 x it)"5 see-l. Qualitative explanation for the observations based on the generation of nonequilibrium number of defects by plastic deformation will be discussed. The initial research of Buffington and cohen1 on self-diffusion in a iron under compressive stresses contributed the first quantitative information concerning the effect of applied stresses on diffusion. These results were obtained from radioactive Fe55 plated on one of the horizontal surfaces and compressing the large-grained specimens while the diffusion-anneal was occurring. Enhancement of diffusion of a maximum of seventeen times was observed provided the strain was in the tertiary stage of creep and the rates of straining were at least as fast as rates used in the normal creep test. On the other hand, Darby, Tomizuka, and Balluffi,2 extending silver single crystals up to 30 pct elongation at rates of straining about equal to those used by Buffington and Cohen observed no effect. For the past two and a half years at the University of Pennsylvania, we have been investigating the effect or torsional strains on self-diffusion in silver single crystals. If enhancement is observed as has been reported1 a possible explanation may be based upon the generation of fairly large numbers of point defects and their role in the diffusion process. Hence, since torsion should produce an abundance3 of point defects, an increase in the diffusivity while the crystal is being twisted should easily be measured. EXPERIMENTAL PROCEDURE Our research uses single crystals of silver prepared from 99.99 Ag by the Bridgman method in a dynamic vacuum of less than 25 µ. As grown, they are about 25 cm long by 1.3 cm in diam. The crystals are cut into 7.5 cm lengths with a jeweler&apos;s saw and machined to the shape shown in Fig. 1. The test length of the crystal is machined to a 0.6 cm diam after which the ends are masked and the test section etched heavily in HNO3, and KCN:(NH4),S2Os , solution to remove the effects of machining. The specimen is then annealed in vacuum for 8 to 12 hr at 800°C to remove any residual stresses and also to recrystallize the end sections. The recrystallized ends are necessary since experiments showed that single-crystalline end sections are too soft to transmit the desired torque. Occasionally, recrystalliza-

Jan 1, 1960

By Arnulf Muan, Carlos Landolt

Equilibria involving Cu-Pt alloys, copper oxides, and atmospheres of known ox2gen pressures have been determined at 1000&apos; and 1200 C. The data obtained have been used to calculate activity-composition relations in the alloys. A moderate negative deviation from ideality is found. At high copper concentrations, the results of the present study are in good agreement with those of previous investigators, whereas at low copper concentrations the activities obtained in this investigation are slightly higher than those reported previously. The present study is part of a research program dealing with the determination of phase relations and thermodynamic properties of copper-containing systems at high temperatures. The information available for such systems is very scanty, particularly for copper oxides and their combinations with other oxide components. Platinum is commonly used as a container in studies of oxide equilibria. To evaluate quantitatively the extent of reaction between the oxide and the container, a knowledge of activity-composition relations in Cu-Pt alloys is necessary. Such data are not available for Cu-Pt alloys in the temperature range of particular interest in the present research program, and particularly for alloys low in copper. Studies of various aspects of the systems Cu-Pt and Cu-0 have been reported in previous literature. The system Cu-Pt is known1 to form a continuous solid-solution series above 812.C, whereas ordered phases are present in certain composition ranges at lower temperatures. Thermodynamic data for the system have been reviewed by Hultgren et al.,&apos; who presented free energies of mixing at 65Oo C, mainly derived from electromotive force cell measurements by Weibke and Matthes.3 Enthalpies of mixing at 640°C have been obtained by Oriani and Murphy4 with liquid tin calorime-try. Their results differ considerably from those derived from the temperature dependence of the data of Weibke and Matthes. Thermodynamic data for the disordered alloys have been obtained by Assayag,5 and more recently by Schmahl and Minzl,6 by Myles and Darby,7 and by McCormack, Myers, and Saxer.8 The two latter sets of data7&apos;&apos; became available after the present study was completed. In the system Cu-0+ two oxides are stable at high temperatures, CuO and CuzO+ each having only minor deviations from stoichiometry. Equilibria in the liquidus temperature region of the system Cu2O-CuO have been studied by Roberts and systemsmyth,9&apos;10CuzO-CuO by Vogel and ocher,I1 by Osterwald,12 and recently the the present authors.13 The system is of the eutectic type with a eutectic temperature of 1083.C The composition of the eutectic liquid corresponds to Xcu0 = °.44, and the oxygen pressure of the coexisting gas phase is Po2 = 0.55 atm.13 Equilibrium oxygen pressures for coexistence of solid CuO and solid Cu2O have been determined by Schmahl and Muller,l4 by Gadalla, Ford, and white,l5 by Bidwell,16 and recently by the present authors.13 There is reasonably good agreement among the various sets of data. Free energies of formation of Cu2O(s) from the elements have been derived by Tretyakov,17 by Bidwell,16 by Kiukkola and wagner,18 by Pal&apos;guev and Neuimin," and by Steele and Alcock,20 There is particularly good agreement among the latter three1&apos;-20 sets of data. THEORETICAL BASIS Consider a subsolidus isothermal section of the system Cu-Pt-0, as shown in Fig. 1. Two phase as-

Jan 1, 1970

By W. S. McCain, B. A. Wilcox, A. H. Clauer

The creep and creep-fracture behavior of a Ni-200-2Th0, alloy has been studied over the temperature range 816° to 1038°C and stress range 4000 to 19,000 psi Specimens having their axes either parallel or transverse to the final sheet-rolling direction were tested in air, and the apparent activation energy for creep was found to be 92 kcal per mole, regardless of specinien orientation. The stress dependence 01- the steady-state creep rate, was satisfied by where n depended on orientation; n = 9.7 for rrzaterial transverse to the rolling direction and n = 24.3 for material parallel to the rolling direction. In the latter case, the relation was also valid. The rupture strength of material parallel to the rolling direction was -1.5 times gveater than the transverse rupture strength. Several tests in vacuum revealed that here the creep rate was higher and rupture life lower than for comparable tests in air. THERE is an increased interest today in producing improved dispersion-hardened alloys for high-temperature structural applications. This had led various materials designers to modify existing alloys, such as thoriated nickel. One system that has received considerable attention is based on chromium additions to Ni-ThO2, with the obvious motive of improving the oxidation resistance. Another effect of chromium is that of lowering the stacking-fault energy, y, of nickel. For example, the addition of 30 wt pct Cr decreases y from -225 erg per sq cm for pure nickel1 to -70 erg per sq cm.&apos; This decrease in y could have several effects on the deformation behavior. There is some evidence that cross slip of dislocations around Tho2 particles is a mechanism of tensile3 and creep4 deformation in TD Nickel (Ni + 2 vol pct ThO2) at temperatures below 0.5 the absolute melting point of nickel, T,. A decrease in ? by chromium additions should increase the difficulty of cross slip. Also it has been suggested that the high-temperature (T > 0.5Tm) rate-controlling creep process in "recrystallized" Ni-Tho2 alloys is the climb of edge dislocations over Tho2 particles.5 According to weertman6 a decrease in the stacking-fault energy should decrease the dislocation climb velocity resulting in a decreased steady-state creep rate. Thus, chromium additions to recrystallized Ni-Tho2 alloys would be expected to decrease the creep rate, all other conditions being constant. However, a difficulty arises when the stacking-fault concept is applied to high-temperature creep of dispersion-strengthened metals which are produced on a commercial or semicommercial scale. This occurs because the materials are processed so that they have a high-stored energy of cold work, and the other substructural effects could obscure any influence of stacking-fault energy per se. An example of an alloy with a high stored energy of cold work is TD Nickel bar. This material has a fibrous grain structure (1 I diam by 10 to 15 p long), and the structure is stabilized by the ThO2 particles. Annealing at high temperatures, e.g., 3 hr at 1300°C, causes no recrystallization or grain growth.4 Previous work by the authors4 showed that the high -temperature creep behavior of TD Nickel could not be related to any simple dislocation theory of creep, and this probably was associated with the complex initial structure of the material.

Jan 1, 1968

By W. A. Tiller, W. C. Johnston

The solute distribution ahead of an advancing solid-liquid interface is controlled by varying the momentum boundary layer thickness in the liquid adjacent to the interface. Single pass zone-melting experiments on Pb-Sn alloys are described in which the liquid is caused to rotate in the plane of the solid-liquid interface due to the influence of a magnetic .field rotating in this plane. The variation of the diffusion boundary layer thickness with field strength is determined. DURING the freezing of an alloy a partitioning of solute occurs at the solid-liquid interface, the magnitude depending upon the difference in the solid and liquid solubilities at the interface temperature. Because the diffusion coefficient is so small in the liquid relative to normal freezing rates, either a pileup or a depletion of solute occurs at the interface when the partition coefficient, kO, is either less than or greater than unity, respectively. This solute distribution is completely characterized by i) the solute concentration in the liquid far from the interface, C) the ratio of freezing velocityf, to diffusion coefficient, D, iii) the partition coefficient, ko, and iv) the thickness of the diffusion boundary layer, 6,, at the interface (this assumes that an electric field is not applied across the interface). For a particular system, C ko and D are fixed so that the character of the solute distribution can be changed only by a variation of either f or 6c. As is well known, the freezing velocity can be changed by varying the thermal environment of the alloy. Whereas, the thickness of the solute rich layer can be changed by varying the fluid flow conditions in the liquid. It is the purpose of this paper to describe a technique for controlling the fluid flow conditions in the liquid. During most solidification experiments the driving force for fluid flow arises from either mechanical mixing, thermal convection or electromagnetic mixing. The momentum boundary layer thickness, 6m at the solid-liquid interface, within which negligible movement of the liquid occurs, has been calculated for the special case of mechanical mixing where crystals are solidified by the Czochralski technique.l,2 The calculation of 6m for the case of thermal convection has also been made.3 In some calculations it has been assumed that the momentum boundary layer thickness, 6,, may be equated to the thickness of the diffusion boundary layer 6c, at the interface. However, as may be seen from Appendix I this is only true in very special cases and in general where a is a constant of magnitude determined by the particular liquid alloy. Neither calculations nor experimental data exist for the dependence of upon electromagnetic mixing. In this paper experiments are described in which the liquid is caused to rotate in the plane of the interface due to the torque developed on it by a magnetic field, H, rotating in this plane. The variation of is controlled by the variation of H. A magnetic field rotating in a plane perpendicular to the interface has been used for the purification of aluminum. Experimentally, we determined the variation of 5C with H by using the zone-melting technique of pfann5and a theoretical relationship of Burton et a1.2 pfann5 has shown that, after the passage of one molten zone through a long cylindrical charge of uniform concentration, CO, the solute distribution, C,, in the solid is as shown in Fig. 1. The equation describing this distribution is

Jan 1, 1962

By P. G. Shewman, T. L. Wilson

Using published surface-diffusion (D,) data and published sintering equations, it is shouln that surface difusion should dominate the neck-growth stage of intering for all materials in which D, has been measured (six metals and A1as). Also, grain boundary diffusion can be expected to contribute appreciably to shrinkage and possibly to neck growth below some critical temperature of the order of 70 pct 01- the absolute melting temperatuve. In view of the widespread conclusion in previous sintering work that volume diffusion dowzinates neck gvowth, experiments were conducted using spherical copper powders to test this conclusion. Scaling studies on neck growth at 950°and 1020°C clearly demonstrated that suyface diffusion dorninates. Kinetic studies on shrinkage gave more equivocal results that indicated an increasing role of&apos; grain boundary transport at lower temperatures. Five diarszeters from 100 to 300 u were used in the scaling sludy and a temperature range of -650&apos; 10 950 C was covered in the shrinkage studies. All experiments were conducted in dvy hydrogen. In 1949, Kuczynski published his now classic paper on the determination of the transport mechanism in sintering from the time laws of neck growth. In the interim, these laws have been applied to many systems and slightly modified by several authors. Essentially all these authors concluded that, for crystal- line materials, the dominant transport mechanism in neck growth is volume diffusion. This stems from the observation that the neck radius increases about as t"5 and that the activation energy approximates that for lattice diffusion. A related but independent series of studies stems from Mullins&apos; rigorous analysis of the growth of the groove formed where a grain boundary meets a free surface." xperimental work stemming from this analysis has shown that for each crystalline material studied (Au, Ag, Cu, Ni, Fe, Pt, Al2O3) surface diffusion was clearly the dominant transport mechanism for groove widths up to the order 10 to 20 p. The ratio of the quantity of material being carried by lattice diffusion to that carried by surface diffusion increases linearly with the groove width, so surface diffusion is dominant for all widths under 10 to 20 u. The analysis of the relative contributions of surface and volume diffusion to grain boundary grooving, and to neck growth in sintering, shows that they are quite similar. Thus, using the available surface-diffusion data and the approximate equations of Kuczynski, or the more rigorous recent equations of Nichols and Mullins, 3 it can be shown that the small necks between particles must grow almost entirely by surface diffusion. The purpose of this study was to re-examine the basis for the conclusion that the neck-growth stage of sintering proceeds by volume diffusion. Using spherical copper powders, of several different diameters, precise experimental measurements were made of both neck growth and shrinkage. Application of Herring&apos;s scaling laws to the neck-growth data clearly indicated that neck growth occurred by surface transport, even though the neck radius increased as or Using the recent analysis of Mullins and Nichols as well as published data on surface diffusion, it is shown that the observed time law, as well as actual rate of neck growth, can be satisfactorily explained by a surface-diffusion mechanism.

Jan 1, 1967

By H. I. Smith

WHEN Spain established colonies on the North American continent, some of her land grants, in what is now the United States, reserved to the Crown deposits of gold, silver, and mercury. Later mineral rights were reserved under some of the English Crown charters involving land in the eastern part of North America, with provisions for the payment of royalties thereon to the Crown. Reservation of mineral deposits to the United States Government was instituted by an ordinance of Congress on May 20, 1785, which applied to such deposits in the Northwest Territory, then north of the Ohio River and east of the Mississippi River, and provided that there should be reserved "one third of all gold, silver, lead, and copper mines, to be sold or otherwise disposed of as Congress shall hereafter direct." Little was known then of the mineral resources of the country; the Great Lakes copper region had just come into the possession of the United States by treaty and much of the western mineral land still belonged to France and Spain. The policy of leasing mineral deposits was enacted by Congress under the act of March 3, 1807, which provided that "the President of the United States shall be, and is hereby, authorized to lease any lead mine which has been or may hereafter be discovered in the Indiana Territory, for a term not exceeding five years," and in the same year the Government reserved 345,600 acres of land in northern Illinois, valuable for lead. In 1816 Congress provided that in all cases where a tract of public land containing a lead mine or salt spring was applied for by settlers on the public domain, no permission to work the mine or spring would be granted without the approbation of the President of the United States. By the act of March 1, 1847 (9 Stat. 146), the control of mineral lands was transferred, with all records, from the War Department to the Treasury Department, and by the act of March 3, 1849 (9 Stat. 395), supervisory powers over lead and other mines of the United States were transferred to the Secretary of the Interior. Following the discovery of gold in California in 1848, President Polk advocated the leasing of mineral lands acquired from Mexico under the treaty of 1848. However, owing to the lack of communication and transportation facilities and the consequent difficulty of checking on production and operations, leasing was found impracticable. Mining was permitted to be carried on in each district under rules made by the miners themselves and patterned after the Mexican mining system. To meet the situation, Congress enacted mining laws in 1866, 1870, and 1872, which provided for possession by location and for private ownership, after discovery, by patent of essentially all mineral deposits belonging to the United States, except coal. Many other acts were passed by Congress applying to specific regions and states, reserving salt, lead, or other minerals, some of which provided for the leasing of such deposits. However, very few if any leases were issued thereunder. Not until 1901 (31 Stat. 745) were the mining laws extended to include salt, and in 1910 they were revised to specify salines and associated products. At the turn of the century, it became more and more evident that the mining laws developed for metallic minerals were not practical for the development and conservation of oil and gas, coal, potash, phosphate, or oil shale. Following withdrawals by the Secretary of the Interior as authorized by the act of June 25, 1910, the Department of the Interior recommended leasing legislation; however, it was not until February 25, 1920, that the Mineral Leasing Act was passed by Congress. This act authorized leasing all public lands potentially valuable for oil, gas, coal, phosphate, sodium, or oil shale. The Organic Act, creating the Geological Survey in 1879, imposed upon its director the duty of classifying the public lands.&apos; The early years of the Survey were devoted largely to the accumulation of fundamental data and, with only minor exceptions, land classification was not seriously undertaken until 1906. Since that year, it has been actively pursued with respect particularly to leasable minerals and water power values. On March 3, 1873 (17 Stat. 607) Congress authorized the sale of coal lands of limited acreage to individuals at $10 to $20 an acre, depending on the distance from a railroad, and in 1907 a new scale of prices was adopted by the Secretary of the Interior, based, more logically, on the quality and thickness of the coal deposits, their depth below the earth&apos;s surface, and their accessibility. At that time it was much cheaper and easier to obtain incidental title to coal rights under the homestead laws at $1.25 an acre. On March 3, 1909, the first separation act (35 Stat. 844) became a law. It authorized patents, with a reservation of the coal and mining rights involved to the United States, to persons who in good faith had entered public lands under the non-mineral land laws prior to withdrawal, classification, claim, or report that such lands were valuable for coal. It solved the problem only partially, and the practice thereupon adopted by the department of making coal withdrawals "from all forms of entry" instead of "from coal entry" expedited the more complete solution effected by later acts. By the act of June 22, 1910 (36.Stat. 583) withdrawn and classified coal lands were declared subject to entry under the homestead, desert land, and Carey acts, provided a waiver of the coal rights accompanied the application, and by the act of April 30, 1912 (37 Stat. 105) the same privilege was extended to State selections and isolated tracts. The act of August 24, 1912 (37 Stat. 496) extended the separation policy to lands withdrawn for oil and gas in Utah, and finally the act of July 17, 1914 (38 Stat. 509) extended it to all nonmineral filings on public lands theretofore or thereafter

Jan 1, 1955

By L. E. Shiffman

W. J. Parton—Those operators faced with the problem of treating fine coal whether in bituminous or anthracite will find this paper most timely. I would like to take this opportunity of discussing Mr. Schiffman&apos;s paper and at the same time express certain views relating to our Tamaqua plant. I would like to ask the author what type of impeller and diffuser is used in the Denver cells? Screen analysis of products from individual cells indicate that coarser material resists flotation and only floats after greater retention time in the last few cells. Also, the need for a scavenger screen to reclaim non-floated coal particles further stresses this point. I have always felt that more efficient means of cleaning coal between 10-mesh and 28-mesh existed than flotation. Reagent and power costs are high for the flotation process. When floating +28-mesh particles, cell capacity is lowered and some of the particles are lost with the refuse. The Tamaqua plant of the Lehigh Navigation Coal Co. floats —28-mesh coal and capacity of recoverable coal is 40 tph for 1800 cu ft of Denver cells; or 0.05 tons per cu ft of cell. At Kimberly 7.75 tph for 600 cu ft of cell gives 0.013 ton per cu ft of cell. At Bessie 14 tph for 800 cu ft of cell gives 0.017 tons per cu ft of cell. It would be appreciated if the author would comment on what he feels is the upper size limit of particle to attain most efficient utilization of the flotation process. The dewatering screw is a very interesting development since it offers a simple way to prepare coal sludge for more complete clewatering by drainage or mechanical dewatering on screen or filters. In other words it could be used to accomplish the same thing as a thickener tank. I would appreciate having the author&apos;s comment on how he thinks such a screw dewaterer would work on a froth.* The process as used in floating coal at the Bessie and Kimberly plants may be referred to as more of a bulk oil float in contrast to a froth flotation process. Experiments on increasing capacity of cells is most interesting since we are going through such an experi- mental period at the present time. Recently a double overflow was installed on our No. 30 Denver cells. So far results are not conclusive. In reviewing this paper the following comments are made pertaining to investigation of methods for increasing capacity: Supercharging: Supercharged air in matte flotation or for that matter the use of the normal amount of air drawn in by the impeller would in all probability cause such an aeration in the cell as to destroy the buoyant effect given to the coal particles by the excessive amount of kerosine used. In other words, air creates an agitation zone throughout the cell, creating a boiling and thereby giving a lower recovery in the cell. It would be interesting to know whether the 7 pct increase in recovery was with no air being admitted to the stand pipe. Changing Impeller Speed: The speed of a receded disc impeller for a No. 30 cell as recommended by the Denver Equipment Co. is, I believe, approximately 250 rpm. At this speed and using supercharged air in excess of 8-oz pressure, we have observed a boiling action in the cells. In our flotation we endeavor to obtain some degree of froth flotation using pine oil as a frother. The boiling action as caused by increasing the amount of air added to the cells is detrimental to recovery in froth flotation. It is our belief that to obtain increased recovery from a cell in froth flotation, additional air must be introduced but at the same time this air must be dispersed throughout the pulp in the form of small bubbles and this can only be done by increasing the speed of the impeller. Therefore, if Mr. Schiffman decreased the speed of the No. 30 impellers and at the same time continued to use supercharged air, the boiling action may have been increased because larger bubbles developed. The lower recovery as reported could be due to this factor. Decreasing the impeller speed will definitely decrease the power consumed but may have other disadvantages. First, we believe it will permit "sanding" in the cell and this in our opinion will increase the wear on the impeller and diffuser, especially so, if there is pyrite and/or sand present in the feed. "Sanding" in the cell when air is used, as in froth flotation, will effect the dispersion of this air and cause boiling.

Jan 1, 1951

By L. E. Shiffman

W. J. Parton—Those operators faced with the problem of treating fine coal whether in bituminous or anthracite will find this paper most timely. I would like to take this opportunity of discussing Mr. Schiffman&apos;s paper and at the same time express certain views relating to our Tamaqua plant. I would like to ask the author what type of impeller and diffuser is used in the Denver cells? Screen analysis of products from individual cells indicate that coarser material resists flotation and only floats after greater retention time in the last few cells. Also, the need for a scavenger screen to reclaim non-floated coal particles further stresses this point. I have always felt that more efficient means of cleaning coal between 10-mesh and 28-mesh existed than flotation. Reagent and power costs are high for the flotation process. When floating +28-mesh particles, cell capacity is lowered and some of the particles are lost with the refuse. The Tamaqua plant of the Lehigh Navigation Coal Co. floats —28-mesh coal and capacity of recoverable coal is 40 tph for 1800 cu ft of Denver cells; or 0.05 tons per cu ft of cell. At Kimberly 7.75 tph for 600 cu ft of cell gives 0.013 ton per cu ft of cell. At Bessie 14 tph for 800 cu ft of cell gives 0.017 tons per cu ft of cell. It would be appreciated if the author would comment on what he feels is the upper size limit of particle to attain most efficient utilization of the flotation process. The dewatering screw is a very interesting development since it offers a simple way to prepare coal sludge for more complete clewatering by drainage or mechanical dewatering on screen or filters. In other words it could be used to accomplish the same thing as a thickener tank. I would appreciate having the author&apos;s comment on how he thinks such a screw dewaterer would work on a froth.* The process as used in floating coal at the Bessie and Kimberly plants may be referred to as more of a bulk oil float in contrast to a froth flotation process. Experiments on increasing capacity of cells is most interesting since we are going through such an experi- mental period at the present time. Recently a double overflow was installed on our No. 30 Denver cells. So far results are not conclusive. In reviewing this paper the following comments are made pertaining to investigation of methods for increasing capacity: Supercharging: Supercharged air in matte flotation or for that matter the use of the normal amount of air drawn in by the impeller would in all probability cause such an aeration in the cell as to destroy the buoyant effect given to the coal particles by the excessive amount of kerosine used. In other words, air creates an agitation zone throughout the cell, creating a boiling and thereby giving a lower recovery in the cell. It would be interesting to know whether the 7 pct increase in recovery was with no air being admitted to the stand pipe. Changing Impeller Speed: The speed of a receded disc impeller for a No. 30 cell as recommended by the Denver Equipment Co. is, I believe, approximately 250 rpm. At this speed and using supercharged air in excess of 8-oz pressure, we have observed a boiling action in the cells. In our flotation we endeavor to obtain some degree of froth flotation using pine oil as a frother. The boiling action as caused by increasing the amount of air added to the cells is detrimental to recovery in froth flotation. It is our belief that to obtain increased recovery from a cell in froth flotation, additional air must be introduced but at the same time this air must be dispersed throughout the pulp in the form of small bubbles and this can only be done by increasing the speed of the impeller. Therefore, if Mr. Schiffman decreased the speed of the No. 30 impellers and at the same time continued to use supercharged air, the boiling action may have been increased because larger bubbles developed. The lower recovery as reported could be due to this factor. Decreasing the impeller speed will definitely decrease the power consumed but may have other disadvantages. First, we believe it will permit "sanding" in the cell and this in our opinion will increase the wear on the impeller and diffuser, especially so, if there is pyrite and/or sand present in the feed. "Sanding" in the cell when air is used, as in froth flotation, will effect the dispersion of this air and cause boiling.

Jan 1, 1951

By R. R. Vandervoort

The creep behavior of Nb(Cb), Ta, Mo, and W was determined under conditions of constant atomic dif-fzisivity, constant stress to elastic modulus ratio, and nearly equivalent grain size, and the steady-state creep rates obtained from these tests were correlated with calculated stacking fault energies for the metals. These results, in conjunction with similar data for several fccMetals,13 suggest that stacking fault energy may influence the creep strength ofbcc metals. The interrelationship between steady-state creep rate, subgrain size, and stacking fault energy was examined. It was found that the subgrain size for a given creep stress, increased as stacking fault energy increased, but that this relationship did not cormpletely account for the effect of stacking fault energy on creep rate. The crystallography and energetics of stacking fault formation in bcc metals has been discussed by a num-ber of authors,1-5 and impurity stabilized stacking faults on (112) planes have been observed in Nb,6,7 w,8,9 Fe,] and V" by transmission electron microscopy. However, a crucial question is whether or not stack-ing faults influence the mechanical strength of bcc metals. Potentially, stacking faults could increase strength by reducing the mobility of the partial dis-locations bounding the fault, by acting as barriers to slip dislocations, and by retarding the climb of dislo-cations during high-temperature deformation. The objective of this study was to seek a correlation be-tween creep strength and stacking fault energy for several bcc metals; namely, Nb, Ta, Mo, and W. The creep behavior of most polycrystalline metals and alloys at high temperatures and moderate stresses can be described by the following relation:11,12 im=Af(s) where i, = minimum creep rate, A = constant, j(s) = a function involving metallurgical structure, a = applied stress, E = average elastic modulus at the test tempera-ture, w = constant (equal to 5 for most pure metals), D = diffusion coefficient. One factor in the structure function F(s) which sig- R. R. VANDERVOORT, Member AlME is Research Metallurgist, Process and Materials Development Division, Chemistry Department, Lawrence Radiation Laboratory, University of California, Livermore, Calif. Manuscript submitted February 28, 1969. IMD nificantly affects the creep resistance of fcc metals is stacking fault energy, and creep rate has been shown to vary directly with stacking fault energy to the 3.5 power." In the latter investigation, four fcc metals of widely different stacking fault energies (Ag, Cu, Ni, and Al) were creep tested at a constant stress to modulus ratio of 1.21 x 10-4, at a constant diffusivity of 2.7 x 10-12 sq cm per sec, and at nearly equivalent grain sizes of about 0.7 mm. The creep data were then correlated with stacking fault energies. In the present study, a similar procedure was followed. All materials used in this work were consolidated by powder metallurgy techniques. Impurity contents in the as-received materials are listed in Table I. Chemical analyses showed that no measurable contamination of the test specimens occurred during pretest annealing treatments or creep testing. Specimens with a gage section 0.75 by 0.125 by 0.050 in. were creep tested in tension in a vacuum of less than 10-9 torr. Deformation at temperature was measured by tracking fiducial marks on the gage section of the specimen with an optical comparator. Optical deformation measurements also permitted observation of the macroscopic characteristics of the deformation Table I. Typical Specimen Impurity Content, ppm Nb Ta Mo W C 45 10 155 6 O 185 30 4 10 N 30 6 3 2 H 5 I 1 <1 als 3 10 2 15 Ca <5 I3 5 Cr 5 <3 10 <5 Cu 10 50 2 15 Fc 10 10 150 35 Ni 2 150 20 <5 Si <I0 1 3 <10 Ta 100 Ti 10 8 1 Zi 15 50 1 3 Table II. Test Conditions for Constant Stress-Modulus Ratio of 6 X 10.&apos; and Constant Diffusivity of 2.7 X 10-12 sq cm per see, and Grain Size Values for the Given Pretest Annealing Treatments Literature references Pretest Annealing for E and D Treatment Stress, Temperature, ___"&apos;Values__ Grain Tempera-Metal psi "C E D Size, mm ture, .C Time hr Nb 745 1525 14 15 to 17 0.83 1650 I Ta 1220 1770 18 19.20 O.91 1800 I Mo 1975 1630 18 21 0.77 2200 I W 2140 2265 18 22 040 2400 5

Jan 1, 1970

By Robin O. Williams

Robin 0. Williams (Oak Ridge National Laboratory)— The authors have questioned the degree to which the coherency strains between the iron-rich and chromium-rich phases are isotropic as proposed in Ref. 5 on the basis of the difference between the elastic properties of the two phases. The relative magnitude of the stresses is determined by the moduli as shown by Eqs. [2], [3], and [4] of Ref. 34. However, the moduli of the two phases have no direct bearing on the uniformity of either the stress or strain within either phase. The idea that the strains are isotropic within each phase (but normally of different magnitude and always of different sign) is based entirely upon the experimental observation that X-ray line broadening has not been detected even when the particles become rather large. It has not proven possible to grow the particles sufficiently large that they lose coherency. Based upon this lack of line broadening one can estimate an upper limit for the nonuniformity of the strains within each phase as follows. It is considered possible to detect line broadening if it is as great as 10 pct of the separation of the K, doublet for the (211) line using chromium radiation. The doublet separation would correspond to a total strain of 0.0017 such that the total variation of lattice parameter relative to the average lattice is now k0.05x0.0017 or something less than ± * For the present case the strain in each phase is roughly 0.002 such that the variation of strain within a phase will not exceed 5 pct. It is stated that the expression derived for strengthening for the hydrostatic straining as observed in this system would substantially overestimate the magnitude due to dislocation flexure. This is contrary to the conclusion reached in the original paper34 for the present range of particle sizes. What is the lowest temperature at which a has been observed to form in this alloy? M. J. Marcinkowski, R. M. Fisher, and A. Szirmae (nutlzors&apos; reply)— -Williams&apos; arguments based on X-ray findings for a chromium-rich precipitate and an iron-rich matrix strained to a common lattice parameter are certainly convincing. This being the case, there are no shear components of strain associated with the precipitate-matrix aggregate to interact with the shear components of the dislocation stress fields, contrary to the opinion expressed by the present authors. On the other hand, the present authors, in spite of this error, did not expect the shear interactions to be significant. The chief objection to Williams&apos; model in the present case is that the various segments of the dislocation line are assumed to pass from one potential valley to the next independently of neighboring segments. This is only true for a highly flexible dislocation line, i.e., one whose radius of curvature is something less than the center to center distance between precipitate particles which amounts to about 90A in the present alloy. In order to maintain this curvature, an externally applied shear stress of at least 230,000 lb per sq in. would be required or about four times the observed stress. It is therefore concluded that the dislocation lines move rather rigidly through the lattice. This being the case, the forces on the dislocation resulting from the hydrostatic interaction between the stress fields of the edge-dislocation components and the precipitate particles should average out to zero; that is particles above the below the slip plane produce forces on the dislocation of opposite sign and therefore will cancel when averaged over the entire length of the dislocation. On the other hand, since the dislocation is not perfectly rigid, Williams&apos; model may lead to some strengthening, but far less than that predicted. A second and equally serious objective to using Williams&apos; strengthening model for the present alloys is that profuse wavy slip due to the motion of screw dislocations played a predominant role not only in the unaged alloys but in the fully aged ones as well. Since the screw dislocation has associated with it only shear components of stress the hydrostatic strengthening model no longer applies. In view of these arguments the present authors must reject Williams&apos; model of strengthening as being pertinent to the present alloy system. The present authors have made no detailed study of the lowest temperature at which a forms in the quenched ferritic alloys. None was ever observed n the alloys aged at 500°C so that forma-tion must occur at temperatures higher than this and was therefore not a factor in the present study.

Jan 1, 1965

By Y. Nakada, U. F. Kocks, B. Chalrners

THE orientation dependence of work hardening has previously been studied over the entire range, i.e., including special orientations of high symmetry, in aluminum1-3 and silver.* The differences between various orientations are substantial, and the trend is the same in all fcc crystals. However, there are quantitative differences in behavior between aluminum and silver at room temperature, particularly in the (100) orientation. While many experiments on gold have been reported,5&apos;9 none included the special orientations. We therefore undertook tension tests on gold crystals of the axial orientations (100),(110), (Ill), (211), and, as a representative of single slip, one whose Schmid factor was 0.5 (hereafter referred to as m = 0.5). Single crystals of dimensions 1/4 by .1/4 by 6 in. were grown from the melt1&apos; at a rate of 4 in. per hr, using gold of 99.99 pct purity obtained from Handy and Harman. A growth rate of 1/8 in. per hr, or a purity of 99.999 pct,ll produced no difference in results. The crystals were annealed at 1000°C in air for 24 hr and furnace-cooled down to room temperature, after which they were electro-polished in a solution of potassium cyanide (40 g), potassium ferrocyanide (10 g), soda (20 g), and enough distilled water to make 1 liter of solution, at a current density of 0.02 amp per sq mm. After 2 or 3 hr, a very smooth surface was obtained by this method. Nine m = 0.5, two (loo), one (110), three (Ill), and one (211; crystals were tested at room temperature in a floor-model Instron machine at a tensile strain rate of 0.5 pct per min. The accuracy of the stress measurement was k10 g per sq mm up to 500 g per sq mm, k2 pct for higher stresses. The strain measurement was accurate to t2 pct. The scatter of stress at a given strain among the crystals of the same orientation was small, *5 pct being the largest. The representative stress-strain curves for various orientations are shown in Fig. 1. Table I summarizes the work-hardening parameters as used by seeger.12 Results of other investigators are also included in this table for comparison. There are no previous data for the corner orientations. Values for m = 0.5 crystals agree fairly well with those of Berner. Tm is defined as the stress at which the stress-strain curve begins to deviate from linearity of Stage 11. However, in practice this is a very difficult value to estimate because each investigator has a different idea of linearity. Therefore, the comparison with the values of other investigators may not be valid. In the present experiment, (100) crystals had the highest 111, followed by (111) crystals. The work-hardening rate in Stage I1 was highest for the (111) crystal followed by the (100) crystals. Our value for 0x1 of m = 0.5 orientation agrees very well with those of other investigators. 1) Single-Slip orientation (m = 0.5). These crystals were oriented so that the primary-slip vector was contained in one side face. The dimension perpendicular to this side should then not change if single slip indeed takes place. Within the accuracy of measurement, this dimension did not change during the deformation. Since the accuracy is k0.2 pct, the amount of secondary slip is less than 0.7 pct of the slip on the primary-slip system at 30 pct tensile strain. This is in conformity with the results obtained by Kocks" for aluminum crystals. The tensile axis moved toward (211) during the deformation. Slip bands, Fig. 2(a), were very fine and closely spaced. Some deformation bands were observed. There were no clear-cut cross-slip traces such as the ones observed on aluminum m = 0.5 crystals. 2) (111) Crystals. The orientation of the tensile axis was stable during the deformation. From this observation, one can deduce that at least three slip systems must have operated, and probably all six because the remaining three all have cross-slip relation to one of the first three.&apos; It was very difficult to observe the slip markings. Consequently, we could not confirm by this method that six systems were operative during the deformation. At high strains (above 50 pct shear strain), this orientation had the highest stress-strain curve. At 80

Jan 1, 1964

By S. G. Gibbs

A new method for predicting the behavior of sucker-rod pumping systems is presented. The pumping system is described by a flexible mathematical model which is solved by means of partial diflerence equations with the aid of computers. Polished rod and intermediate-depth dynamometer cards can be calculated for various bottom-hole pump conditions. The technique permits simulation of a wide variety of operating conditions, both normal and abnormal. The data generated with the new technique are useful in refining the criteria for design and operation of sucker-rod systms. INTRODUCTION Sucker-rod pumping systems are used in approximately 90 per cent of artificially lifted wells. In view of this wide application, it behooves the industry to have a fundamental understanding of the sucker-rod pumping process. Oddly enough, our understanding has been rather superficial. This is evidenced by the semi-empirical formulas which have been used as the basis for design and operation of sucker-rod installations. Thoueh- we have realized the limitations of our methods for many years, it has not been computationally feasible to use more refined techniques. With the advent and widespread use of digital computers, it is now possible to handle the mathematical problems associated with sucker-rod pumping. This paper summarizes a computer-oriented method which can provide greater insight into the sucker-rod pumping process. It is hoped that this technique, and techniques which may evolve from it, will prove to be the tool needed by industry to obtain the most efficient use of rod pumping equipment. THE MATHEMATICAL MODEL Prediction of sucker-rod system behavior involves the solution of a boundary value problem. Such a problem includes a differential equation and a set of boundary conditions. For the sucker-rod problem, the wave equation is used, together with boundary conditions which describe the initial stress and velocity of the sucker rods, the motion of the polished rod and the operation of the down-hole pump. Of these items, the wave equation, the polished rod motion condition and the down-hole pump conditions are of primary importance. Discussion of the mathematical model centers about these factors. ROD STRING SIMULATION WITH THE WAVE EQUATION The one-dimensional wave equation with viscous damp- is used in the sucker-rod boundary value problem to simulate the behavior of the rod string. This equation describes the longitudinal vibrations in a long slender rod and, hence, is ideal for the sucker-rod application. Its use incorporates into the mathematical model the phenomenon of force wave reflection, which is an important characteristic of real systems. The viscous damping effect postulated in Eq. 1 yields good solutions, even though nonviscous effects such as coulcomb friction and hysteresis loss in the rod material are present. Fortunately, the nonviscous effects are relatively small, so the viscous damping approximation used in the wave equation is adequate. The coefficient v is a dimensionless damping factor which is found in field measurements to vary over fairly narrow limits. For mathematical convenience the gravity term is omitted in Eq. 1. The effect of gravity on rod load and stretch can be treated separately, as will be noted later. Since Eq. 1 is linear, the legitimacy of this procedure is easy to demonstrate. POLlSHED ROD MOTION SIMULATION The motion of the polished rod is determined by the geometry of the surface pumping unit and the torque-speed characteristics of its prime mover. By determining the motion of the polished rod, we formulate an important boundary condition. From trigonometrical considerations it can be shown that the position of the polished rod vs crank angle 0 is given by (see Fig. 1) These equations are obtained from the general solution of the "four-bar" linkage problem and can be used to describe the kinematics of any modern beam pumping unit.&apos; If prime mover speed variations are disregarded, the angular velocity of the crank is constant, and Eq. 2 can be used to predict the position of the polished rod vs time. However, the constant-speed condition leading to constant crank angular velocity is only approached in practice: hence, it is better to make provisions for prime mover speed variations in the mathematical model. The speed at which the prime mover runs is determined by its torque-speed characteristics and the torque imposed upon it. The torque that the prime mover "feels" is the net torque arising from the polished rod load and the opposing torque from the counterbalance effect. The

By Bruce Chalmers, D. C. Larson

Aluminum crystals with longitudinal-axis orientations of (111) . (110), and (100) were deforined in tension and annealed. The conditions of deformation were controlled so that the re crystallization nuclei originated in either the heavily deformed regions at saw cuts {artificial nucleation) or in the lightly deformed matrix (spontaneous nucleation). The artificial-nucleatioln experiments showed that in lightly deformed (110) and (100) crystals low-angle twist boundaries are most mobile, while in (111> crystals and heavily deformed (110) and (100) crystals high-angle tilt boundaries with near (111) rotations are favored. The spontaneous-nucleation experiments showed the existence of preferred orientations in the (111) crystals. The nonrandomness of the grain orientations is quantitatively determined through a comparison with the results which would he obtained from a randowl set of grain ovientations. PREVIOUS recrystallization studies have been performed on single crystals deformed in tension.1 7 The crystals used in these studies usually had random tensile-axis orientations and the extent of deformation was not a primary consideration. The present study concerns the recrystallization of single crystals with tensile-axis orientations of (Ill), (110), and (100). The emphasis of this work is on the influence of the tensile-axis orientation and the degree of deformation on both the nucleation and growth processes. The multiple-slip orientations were chosen because secondary slip or slip intersection promotes nucleation.1,5,8 These crystals recrystallize at lower strains than the crystals which are oriented for single slip. Also, the greatest variation in deformation behavior is exhibited by the multiple-slip orientations. The stress-strain curves for crystals with tensile-axis orientations of (111) are higher than the stress-strain curves for poly-crystals, and the stress-strain curves for crystals with tensile-axis orientations of (100) are lower (at large strains) than the stress-strain curves for the crystals which deform initially in single slip.g The recrystallization nuclei originated in either 1) the homogeneously* deformed matrix of the crys- tals or 2) the heavily and inhomogeneously deformed regions at saw cuts. The nuclei will be referred to hereafter as spontaneous and artificial nuclei, respectively. The two terms do not imply a difference in the nature of the nuclei; they imply simply a difference in the mode of introduction of the nuclei. During spontaneous nucleation very few (always less than ten) grains nucleate, while during artificial nucleation large numbers of grains nucleate. Only a fraction of the artificially nucleated grains penetrate very far into the deformed matrix during annealing. The grains that penetrate the farthest into the deformed matrix will be referred to as the dominant grains. EXPERIMENTAL PROCEDURE The thirty-five crystals used in this investigation were grown from the melt in milled graphite boats at a rate of 1.6 cm per hr. The crystals had dimensions of approximately 6 by 12 by 80 or 6 by 6 by 80 mm and the aluminum was of 99.992 pet purity. The as-grown crystals were annealed at 610°C for 24 hr and furnace-cooled. They were then heavily etched and electropolished in a solution of five parts methanol to one part perchloric acid. The crystal orientations were obtained by back-reflection Laue photographs and were accurate to ±2 deg. The tensile-axis orientations were (loo), (110), and (111). Two of the side faces of the (111) crystals were (110) lanes. The (110) crystals had both {100) and {110) side faces and the (100) crystals had (100) side faces. The crystals were deformed at a strain rate of 0.003 per min. Shear stress and shear strain were obtained by multiplying and dividing the tensile stress and strain, respectively, by the Schmid factor, m. For the (111) crystals m = 0.272 and for the (110) and the (100) crystals m = 0.408. The Schmid factor is effectively constant during deformation for all orientations. The deformed crystals were sawed into 1-in.-long specimens while the crystals were totally enclosed in a graphite boat. The sawing was performed very carefully in order to limit the plastic deformation to the sawed regions. The specimens were electropolished in the solution mentioned above to remove the sawed-end deformation as well as controlled amounts of surface material. A special stainless-steel grip was used to hold the specimens during the electropolishing treatment. The gripping faces were flat, with no teeth, to prevent the introduction of extraneous de-

Jan 1, 1964