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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,2'3 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 H. Herman, M. E. Fine

Kinetics of reversion and reformation of GP I were studied resistometrically in Al-1.7 at. pct Cu. The reversion process is over in roughly 1/2 minute at 205 "C irrespective of the amount of primary aging. After reversion the occurrence of an incubation time before reaging begins has been substantiated. The reaging kinetics is drastically accelerated by plastic deformation to the specimen. An incubation time is observed only if the specimen is aged before reversion. The incubation time and the effect of plastic deformation indicate that nucleation of GP I is heterogeneous. Simple clusters of copper atoms apparently do not act as nuclei for GP I. AFTER quenching aluminum-rich copper from the solid solution range, Guinier-Preston zones of the first kind, GP I, form very rapidly at room temperature. The rate, largely controlled by the concentration of vacancies, is initially most rapid1 (that is, at the time of the first measurement: 1/2 min) and decreases with time. The nucleation is thought to be athermal. If after aging for several days the GP I is dissolved by reversion at 205°C, according to measurement of Young's modulus an incubation period is observed before GP I begins to form on subsequent aging.2 Yet if the reversion is carried out immediately after quenching, both resistivity3 and modulus changes2 show no incubation effect. The zones which form after reversion have the same structure as those which form after the quench.4 Because of entropy considerations and also the short diffusion time, the solid solution after reversion, 2 min at 205°C, is probably more highly clustered than at the original solution treating temperature, 520" to 550°C. It appears most reasonable to associate with nucleation the incubation time observed on reaging after reversion. A simple cluster of copper atoms, many of which are presumed to be present after reversion, is then not a sufficient nucleus for GP I; a GP I nucleus must contain something in addition to a cluster of copper atoms. The purpose of the present note is to give some additional experimental information concerning the incubation time and rates of reaging after reversion. The existence of the incubation time has been verified by measurement of another property, the electrical resistivity. Acceleration of reaging after reversion by plastic deformation has also been investigated. In acl.dition, the kinetics of the reversion process itself was studied. EXPERIMENTAL Electrical resistance was measured by the poten-tiometric four probe method. The 1.7 at. pct Cu alloy was furnished by the Aluminum Co. of America in the form of 1/2 in. rod. The major impurities reported by Alcoa were Fe (0.002 wt pct), Si (0.003 wt pct), and Mg (0.001 wt pct). Specimens for measuremenl of resistance were prepared by rolling to 0.010 in., cutting 2 by 0.2 in. pieces, rolling the middle pclrtions of these to 0.005 in., and splitting the 0.010 in. sections up to the reduced central section to form current and potential leads. Aluminum extension wires insulated with ceramic tubes were spot welded to the leads. The specimen was supported by the lead wires. The whole specimen assembly was annealed at 500" C in an air furnace for more than 12 hr and then aged at room temperature. This was done to assure quick and complete resolution during subsequent solution treatments. These were carried out in Houghton's "430 Temper Salt" at 520'C for 1 hr. Unless otherwise specified, quenching was accomplished by quickly transferring the specimen from a salt pot to 25°C water. Aging was carried out in a 3 liter dewar of distilled water, rotated and stirred. The temperature was controlled to +0.01°C with a thermomercurial regulator in conjunction with a transistorized relay

Jan 1, 1962

By M. T. Hepworth, W. B. Sample

HYDROGEN solubility and linear contraction measurements were made at constant temperature on an alloy of titanium of constant oxygen-to-titanium molal ratio but variable hydrogen content. A cylindrical specimen of titanium (0.25 by 1.6 in.) containing 0.75 at. pct 0 and less than 0.03 at. pct N was cast from a master button of iodide process titanium which had been alloyed with titanium dioxide. Four vacuum fusion analyses, which were made along the length of the cylinder after the hydrogen solubility studies were made, revealed a variation of oxygen content of less than 0.02 at. pct. The specimen was introduced into a quartz furnace tube, annealed and outgassedat 1050"~ for about 1 hr, and then held at 800" * 0.5" for about 30 hr, during which latter time experimental data were taken. The leak rate to the furnace chamber was not sufficient to contaminate the specimen during the run as determined by leak-rate studies and vacuum fusion analyses for oxygen and nitrogen before and after the runs. The furnace chamber was attached to a modified Sieverts apparatus used to introduce measured quantities of purified hydrogen to the specimen. A quartz pushrod transmitted changes in length of the specimen to a Chevenard dilatometer. The push-rod passed through a vacuum grease seal to the dilatometer which amplified motion of the rod by a factor of 319. During hydrogen addition, the pushrod did not contact the specimen. Measured quantities of hydrogen were added to the specimen and equilibrium hydrogen pressures recorded as a function of hydrogen content. The solubility data, which appear in Fig. 1, agree well with a separate investigation made with a different apparatus. The solubility limit of the hcp a phase appears as an abrupt discontinuity in slope at 3.4 at. pct H. The solubility plot has been extended as a dashed line at this discontinuity in order to emphasize the discontinuity. The hydrogen content at which bcc P appears is not clearly defined. An arrow indicates solubility data were taken upon hydrogen addition. Upon reaching the arbitrary maximum hydrogen content of the run, the quartz pushrod was pressed against the specimen in order to record the change in length with hydrogen removal. A pressure of about 100 g per sq cm was required to overcome the friction of the vacuum seal in order to obtain reproducible linear contraction data. The contraction ratio ~2/1", change in length divided by original length, was set equal to zero for the maximum hydrogen content. The relative contraction of the specimen was observed upon removal of hydrogen in the following manner. The system was opened to the pumps for a few seconds and an unknown quantity of hydrogen was removed. The system was then isolated from the pumps by closing a stopcock and allowed to return to equilibrium. When the temperature returned to 800°C, the pressure stabilized, and contraction ceased, measurements of contraction and pressure were made. The hydrogen content of the specimen was then deduced by measuring the equilibrium PIydrogen pressure and referring to the solubility plot. Linear contraction was then plotted against interpolated values of atomic percent hydrogen. The justification for this procedure is the established reversibility of the hydrogen equilibrium.' Uniaxial compression was assumed to have no effect on hydrogen pressure. The isothermal linear contraction data are plotted on Fig. 1. An arrow indicates data were taken upon removal of hydrogen. The solubility limits of the two phase a i /3 region can be identified by discontinuities ill slope of the dilatometric plot at 9.1 and 3.4 at. pct H, agreeing well with other studies.' Dashed extensions of the plots emphasize the discontinuities. Isothermal studies of expansion made upon hydrogen addition gave curves of much smaller slope and less pronounced discontinuities. A uniaxial compressive stress tends to accentuate volume changes in going from the more open bcc phase to the hcp phase.2 Incomplete data on ex-

Jan 1, 1962

By D. E. Norquist, J. E. Moeller

The results of wear on marked balls, 4, 31/2, 3, and 2 in. diam are given. All balls were forged steel of practically the same chemical analysis and hardness. The results indicate that balls in a given mill for a given length of time will have equal diameter losses, regardless of size. IN order to determine the relative wear rates of several sizes of grinding balls, groups of 4, 31/2, 3, and 2 in. balls were marked individually and were charged, all at the same time, into each of two production mills grinding copper ore. The remainder, and vast majority, of the ball charge consisted of 2 in. diam, and smaller, white, cast iron balls. The original weight of each test ball was determined and recorded. Some of each group of test balls were recovered from the mills periodically, individually reidentified, and reweighed. The test balls were recovered during regular maintenance shutdowns, at approximately thirty-day intervals, so as to avoid disrupting operations. As soon as the weights had been recorded, each marked ball was recharged into the mill from which it had been taken. The test units were mechanically the same and theoretically received equal tonnages of feed. All of the test balls were of forged, alloy steel composition with only slight variations in chemistry that would not be expected to affect the physical properties. All were heat treated in the same manner to produce a high hardness, as equal as possible for all sizes and as uniform as possible from surface to center. Generally speaking, the hardness of the portion worn from the balls during the test ranged from 62 to 65 Rockwell C. The microstructure was, therefore, predominately martensitic. The method of marking the test balls consisted of forming a small, round hole, 3/16 or 1/4 in. diam, into the center of each test ball with a Thomas Metal Master disintegrator, which produces a hole in fully hardened steel without affecting the hardness of the surrounding metal. After the hole was formed, each test ball was individually weighed to the nearest gram and the weight was recorded. The balls were grouped as to size and each group assigned a code letter. The individual balls within the various groups were then assigned a number. A small copper disc was stenciled on one side with the group letter and on the other side with the individual ball number and dropped into the hole in the corresponding test ball. The hole was then plugged with a low-melting-point metal alloy, which could be melted out in boiling water. Half of the test balls in each group were charged into one mill and the other half into another mill, so that all test balls in each mill would be subject to, as nearly as possible, identical conditions for an equal length of time. Previous testing had indicated that the wear rates on balls of different sizes could not be accurately compared if weight loss, or percentage weight loss, were used as a basis for comparison. Fig. 1 is a graphic record of the average weight loss for each size group in mill No. 1, and it becomes readily apparent that the larger balls lose substantially more weight in a given length of time. Fig. 2 is a graphic record of the average percentage weight loss for each size group in mill No. 1, illustrating that the smaller balls definitely lose a greater percentage of their original weight in a given length of time. It was, therefore, decided to convert the actual weights of the test balls to diameter and follow the diameter losses periodically to see if the wear rates

Jan 1, 1951

By Howard E. McKinney

A high-pressure wellhead lubricator has been developed to facilitate telemetering electrical measurements from subsurface reservoirs to the surface with the well under normal flowing conditions. The field unit in use at the present time employs a 5/16-in diameter, single-conductor armored cable and is to be used in wells with surface pressures up to 5,000 psi. It has a pressure sealing element that maintains a continuous and absolute seal around the cable as it enters or leaves the tubing at speeds up to 175 ft per minute. A cable injecting device is used which obviates sinker bars or weight sections on the instrument. INTRODUCTION The development of instruments for securing physical measurements in pressure wells has been confined in the past to those instrument which would operate on a wire line and record the necessary measurements in the downhole instrument itself, or those which would operate on an electric cable in a well with the surface pressure killed by the use of weighted fluids or by the use of tubing plugs. In one case the accuracy of the measurements is questionable, and in the other the range of application is very limited. Considerable work has been done by other interests to provide effective means to accomplish the necessary telemetering. The U. S. Bureau of Mines developed a wellhead lubricator prior to 1947 which permitted a 5/16-in diameter single-conductor cable to be lowered into a well with a surface pressure of approximately 500 psi. This unit was used successfully in a number of tests in Oklahoma. A company which tests wells has recently offered on a service basis a wellhead lubricator with a 3/16-in diameter cable that reportedly operates up to 2,500 psi surface pressures. Each of the above operates on a staging principle to effect a seal. In both of these units some leakage of well fluid occurs when the cable is moved. SPECIFICATIONS FOR DESIGN In order to provide the maximum flexibility in its use, the following parameters were established for the design of our high-pressure wellhead lubricator: L An absolute well fluid seal up to 5,000 psi surface pressures. 2. Means for raising and lowering the instrument at speeds of at least 100 ft per minute. 3. Provision for the instrument to enter and leave the well without disturbing the well flow or the reservoir conditions. 4. A cable large enough to provide suitable electrical characteristics and suitable mechanical properties. 5. A method of operation that will not damage the well in any way. The present high-pressure wellhead lubricator field unit fulfills the above requirements. DESCRIPTION OF THE UNIT AND ITS OPERATION The cable selected for this use is the standard Amergraph 1H2 as manufactured by the American Steel and Wire Co. This particular cable is normally used by the Halliburton Oil Well Cementing Co. in their conventional well logging operations. Although the cable presents a noncircular cross-section (Fig. l), its diameter is very consistent; lor example, maximum diameter is 0.325 in., minimum diameter 0.314 in. This [actor permits the use of the sealing element, as later described. Early in the development of the high-pressure wellhead lubricator it was apparent that we could not effect a direct gas seal around a moving 1H2 cable. This becomes evident when an examination of the cable cross-section is made. The voids between the strands of the outer armor provide natural channels lor the flow and escape in large quantities of a low-viscosity fluid such as gas. However, it is relatively simple to

Jan 1, 1952

By Henry Leidheiser, Melvin C. Jr. Hobson

The rate of formation of the intermetallic compound, indium antimonide, at the interface between iudium and antimony at 100°C is greatly increased when a composite electrode of indium electrode -posited on antimony is made the cathode in an electrolytic cell. The amount of indium antimonide formed during electrolytic treatment at constant potential appeared to he proportional to the square root of time, but the scatter of the data, particularly at long times, makes it impossible to state this conclzlsi1:ely. The rate constant for the electrochemical synthesis was estimated to he 1.5 x 10-12 sq cm per sec. A similar- set of experiments was conducted in the absence of an applied potential but under otherwise similar conditions. The rate constant lor the thermal synthesis was less than 2 x 10-14 sq cm per, sec, at least two orders of magnitude less than obtained during electrolytic treatment. In a series of electrochemical studies it was observed that intermetallic compounds formed on the surface of polarized electrodes.1'2 The possibility of using this technique for the electrochemical preparation of intermetallic compounds was investigated and subsequently applied to the synthesis of the semiconducting III-V compounds. Gallium antimonide, indium arsenide. indium antimonide, and indium bismuthide were successfully formed by electrodepositing the Group III element from a boiling acid solution onto an electrode made of the Group V element. The following kinetic studies were undertaken on indium antimonide to obtain quantitative information on the rate of formation of this representative III-V compound under a potential gradient. EXPERIMENTAL The electrolytic cell for these experiments was a modified, three-neck, round-bottom, 500-ml distillation flask. Sealed into the side of the flask was a Luggin probe which monitored the surface of the working electrode and extended out of the flask to a small reservoir containing a saturated calomel electrode. The counter electrode was platinum. The three electrodes were connected to a Wenking po-tentiostat which maintained a preselected constant potential near the surface of the working electrode with reference to a saturated calomel electrode. All potentials noted in this paper are with reference to a saturated calomel electrode at 45° ± 5°C. The potential and the current were both monitored using Sargent Model MR recorders. The antimony electrodes were cast in graphite molds to form spheres about 15 mm in diameter with a shank 6 mm in diameter and 10 mm long. A heavy copper wire (12B & S gage) was soldered to this shank. Collodion was applied for protection to the shank and the connecting part of the copper lead. A snug-fitting O-ring was slipped over the shank and the electrode was then fitted into a teflon holder such that only the spherical portion was exposed. The electrode surfaces were cleaned and chemically polished prior to assembly and introduction into the electrolyte by etching in a modified CP-4 solution (50 parts glacial acetic acid, 10 parts concentrated nitric acid, 2 parts 48 pct hydrofluoric acid). The electrolyte was 10-2 M In+3 in 1 MH2So4 and its temperature was held constant by refluxing. The reflux condenser was open to the atmosphere and no temperature correction was made for changes in barometric pressure. The indium concentration in the electrolyte was checked from time to time by the analytical method outlined below for the determination of the amount of indium antimonide formed electrochemically. A schematic of the recorded potential is shown in Fig. 1. At point A the antimony electrode was introduced into the cell and the open-circuit potential recorded. At point B the potentiostat, preset at the desired potential, was switched on. It was switched off at point C and the potential fell to the open-circuit value of the electrodeposited indium. The

Jan 1, 1965

By J. Chipman, J. B. Gero, T. B. Winkler

D. C. Hilty—This paper is a useful and timely addition to our store of quantitative data relating to manganese distribution between slag and metal in steel-making processes. For some time, many of us have suspected that the values of Kmn derived by Körber and Oelsen might be too low, and this paper now appears to confirm that suspicion. Application of the new constant to openhearth data should prove interesting. The manganese deoxidation curves of fig. 4 agree fairly well with direct measurements of isothermal solubilities of oxygen in liquid iron containing manganese that have recently been made at the Union Carbide and Carbon Research Labs., Inc. According to the solubility data just mentioned, however, the curves for 1550" and 1600°C lie much closer to each other than the authors have indicated. In other words, the solubility measurements suggest that the logarithm of the oxygen solubility is not a linear function of the reciprocal of the absolute temperature, as the authors have assumed for their calculations. It seems possible that this discrepancy may be due in part to the authors' use of the distribution coefficient, L,,, obtained from Taylor and Chipman's curve for the solubility of oxygen in iron as shown in fig. 2. Taylor and Chipman gave the equation of this curve as —6320 Log % 0 - ---T + 2.734 Their data, however, can be fitted equally well by a curve having the equation: 13.23 x104 1.18x10" Log % O = 36.350 -13.23x10 Moreover, this curve also fits the authors' oxygen distribution data somewhat better than does the linear curve of Taylor and Chipman. Its use in the derivation of Lo for calculation of the deoxidation curves by the authors' eq 15 causes the effect of temperature on the calculated curves of fig. 4 to agree quite well with the temperature effect that has been observed. An experimental determination of the temperature coefficient of the manganese reaction appears to be desirable. J. E. Stukel—Because the authors have done such an excellent job, my comments will be confined to additional information. Very shortly Professor T. L. Joseph and I will publish the results of a study of the reaction between molten manganese and silica. It was found that electrolytic manganese, melted in silica crucibles, reacted with the silica to form a silico-manganese alloy containing 18 pct silicon (1500°C) and a silica saturated MnO-SiO, slag. Therefore, the presence of silicon and its oxides in the Fe-Mn-0 system will affect the equilibrium. Carbon is also an important factor. The higher the carbon content of the iron the less ability manganese has to reduce silica. As a matter of interest, recently a study of the manganese equilibrium in carbon saturated iron and blast furnace slags was completed at Carnegie Institute of Technology. As a comparison to the present study, 2 to 5 hr were required to reach equilibrium and temperature was a much more important factor than slag composition in determining the (Mn)/(MnO) ratio. These results will also be published in the near future. It can be seen, therefore, that the results of this paper cannot be applied directly to openhearth studies without a degree of flexibility. J. Chipman (authors' reply)—With regard to the effect of silicon on the manganese constant, this effect is, of course, known. Much more data is needed in order to establish it accurately, and I hope we can look forward to having some accurate data on that. Mr. Hilty suggests that a three-term expression for the Taylor-Chipman solubility of oxygen in liquid iron might fit a little better than the two-term equation. I think that it would be too great a compliment to the precision of the data to employ a three-term equation, and I would still recommend the simple, two-term expression.

Jan 1, 1951

By C. R. King

Most of the acid volcanic glasses such as obsidian, perlite, pitchstone, pumice, and pumicite (volcanic ash) are susceptible to some expansion if suddenly subjected to a suitably high temperature in a properly designed furnace, and subsequently suddenly cooled. Expansion results from the action of chemically combined or dissolved water expanding as a vapor within the softened heated rock particles. This expansion forms countless minute bubbles within the pasty mass of the natural glass particles. If the particles are cooled before these bubbles can escape, the resulting products are cellular, more or less spherulitized glass froths or hollow glass spheres of many types. Chemically, they are essentially aluminum silicates containing about 70 to 75 pct silica, 10 to 16 pct alumina, and 2 to 7 pct sodium plus potassium oxides. They are relatively resistant to attack by acids or alkalies, are resistant to heat up to over 1000°F, and are completely inert to insect or fungus attack. These products are of great potential value in many branches of industry as insulation materials, aggregates, fillers, abrasives, and additives. By proper selection of the perlite rock type and control of processing conditions, expanded perlite of a bulk density varying from about 2 to 20 Ib per cu ft can be • made. The physical properties of the particles comprising a product of a given bulk density also may be varied within wide limits of porosity, water absorption, and crushing strength. In general, crushing strength of expanded perlite increases in direct relation to increase in bulk density, but insulating value varies in inverse ratio to bulk density. The selection of a particular grade of expanded perlite for a given use as an aggregate is therefore always a compromise between insulating value, lightness, and friability. If porosity and water absorption are factors affecting the use of the material, factors other than bulk density are important. Some types of perlite rock tend to decrepitate excessively during expansion, resulting in a highly porous or even hygroscopic product of high friability relative to the bulk density of material produced. In general, treatment of any good perlite rock below the temperature necessary for maximum expansion, or insufficient time in the hot zone of the furnace for effective heat penetration to the core of the rock particles will result in some decrepitation and high porosity in the expanded product. On the other hand, exposure of the material to the temperature required for optimum expansion for a period of time slightly longer than that necessary for proper heat absorption will result in a slightly heavier product of extremely low porosity, i. e., a glazed surface. It is beyond the scope of this paper to describe in detail the rock types and processing methods used to produce the many types of expanded perlite in present use, or that may be produced to fill the present and future needs of industry. A few phases of the economics involved in processing and selling products made from this abundant and cheap mineral raw material, plentifully distributed in large and relatively accessible deposits in most western states and in other areas within economic shipping distance of large centers of consumption, will be treated with particular reference to the Los Angeles area. Relation of Balk Density to Use and Cost of Production Perlite differs from most other lightweight aggregates and fillers in that the raw material (perlite rock) may be quarried much as rock arid sand is mined, and then shipped into consuming areas as crude rock in open gondola cars at correspondingly low freight rates and handling costs. At processing plants in or near large consuming areas the rock is converted into relatively fragile, very bulky products which in most cases are used within a short haul of the processing plant or enter into a manufactured product made at the site of the perlite processing plant.

Jan 1, 1950

By C. Gatlin, C. E. Nemir

A common cure of lost circulation is the introduction of granular bridging agents into the mud system. Many materials, such as ground nut shells, are used for this purpose. If the trouble causing void (fracture, fissure, vug, etc.) is not too large, the granular agent forms a "bridge" across or within the opening. Successively smaller particles in the mud stream then accumulate on and/or within this bridge until normal filtration is finally established. The efficiency of many bridging agents has been studied in the laboratory using various slot testers.',' Many investigators have remarked that a granular bridging material should have the proper particle size distribution. With the exception of the broad range specified in the patent of Goins and Nash,3 here is apparently no definition as to what this distribution should be. A bridge may be initiated when several particles of lost circulation material lodge against each other in a fracture or other void. Smaller particles then may bridge the openings between the larger, previously bridged particles. This process continues until the voids become quite small and the problem becomes one of filtration. It would seem logical that an optimum particle size distribution exists, i.e., one containing the proper quantity of properly sized material to fill the successively smaller voids of the bridge. The filtration characteristics of drilling fluids may be subject to a similar analysis. It has been clearly demonstrated by many workers that the filtration behavior of various muds can be altered by particle size control.'.' Slusser, et al, divided filtration into three periods and showed that particle sizes affecting a given period did not necessarily affect other portions of the filtration curve. An analagous problem is the proper sizing of gravel, liner slots and screen sizes in various sand-exclusion problems. Here the situation is reversed in that a proper "void" size, rather than the size of the bridging agent, is sought. The classic work of Coberly 9 forms the quantitative basis for most sand-exclusion processes. It is interesting to note that, in general, Coberly's work has been overlooked by most drilling-mud researchers. Other investigators have made various studies of the effect of particle size distribution .on drilling-mud properties. As a part of their studies, Fancher and Oliphant reported 30-minute filtration loss of a variety of mixtures of particle sizes.'' Gates and Bowie noted an effect of particle size distribution on filtration, as well as on other physical properties.' MAXIMUM DENSITY THEORY A maximum density mixture has been mentioned as the possible solution for both lost circulation and mud filtration problems. Furnas 12 derived mathematically a method for obtaining maximum density of beds of packed solids, having either a given number of component sizes or a continuous gradation of sizes. This work was verified experimentally by Anderegg.13 or mixtures having a continuous grading of sizes, the interval between sizes is taken as successive screen sizes of interval 2 The ratio of the quantity of each size and the next smaller size is given by the equation Fig. I, number of size intervals of ratio 2 taken from Furnas' paper, gives the value of n + 1 for any given values of + and K, where K is the ratio of the diameter of the smallest particles to the diameter of the largest particles. Measurement by weight assumes, of course, constant density for all particle sizes. Choosing the quantity of the smallest particle size as a unit weight, the required weights of the successively larger interials are then r1 r2 r3 . ®1,2,3. Thus, the grading curve of a maximum density mixture represents a geometric pro gression of ratio r.

By C. B. Scotty, E. F. Egan

INTRODUCTION The neutron-garnma log has been used for stratigraphic correlation by the oil industry for a number of years. In the past few years, the quantitative application of the log to provide information with respect to porosity has received considerable attention. The basic concept of quantitative interpretation has been pointed out in the literature.1 It shall be the purpose of this paper to develop by empirical means a method whereby the relationship of porosity to neu. tron-gamma deflection may be predicted for various bore hole diameters. This relationship is applicable to the present commercially available neutron-gamma log run in open hole. Data available at present are insufficient to establish similar correlations for cased holes. Through the development of such a correlation, the importance of the various factors which influence the log become evident. NEUTRON-GAMMA CURVE The logging tool conisists of a source of neutrons and a means of detecting and measuring gamma rays, the detector being shielded from the direct emission from the source. The gamma rays reaching the detector have three sources of origin: (1) the natural gamma radiation emitted by the formations, (211 induced gamma radiation resulting from neutron bombardment. (3) gamma rays emitted by the source and scattered by the formation. It has been found that a neutron derived porosity correlation is best for shale-free formations. Under this condition the natural gamma ray radiation is quite low, and therefore, will be neglected in this work. The induced gamma ray radiation resulting from neutron bombardment is predominantly a function of the hydrogen atom concentration of the substance penetrated. Due to the geometry of the presently used system, the neutron-gamma curve indicates low radioactivity opposite high hydrogen concentration and high radioactivity opposite low hydrogen concentration (Figs. 1 and 2). Having a curve which measures hydrogen atom concentration, it follows that if the matrix of the formation penetrated consists only of atoms other than hydrogen, and if the fluid filling the pores is either oil or water, the curve should be an indication of porosity (both oil and water have practically the same number of hydrogen atoms per unit volume'). The above criteria for a porosity (Correlation are fulfilled in clean sandztones and limestones in which the pore volume is completely filled with liquids (oil or water), but not in formations containing either free gas or shale or both. Free gas. even under pressure, contains considerably less hydrogen per unit volume than oil and water; therefore, a variation in response on the curve would be expected. Camp- bell and Winter,' indicate that this difference in hydrogen concentration is sufficient to distinguish between sands containing water or oil and those containing dry gas. Shale is a mineral that contains hydrogen in its molecular structure in addition to the hydrogen which is present in the water of hydration. Thus, in formations containing variable amounts of shale, the hydrogen concentration indicated by the curve is not a direct indication of porosity. Bush and Mardock' have indicated that a correction may be made by use of the gamma ray curve to provide a porosity correlation. Since the induced gamma rays are predominaiitly a function of hydrogen concentration, it would be anticipated that the fluid filled bore hole would materially influence the logs. It has been pointed out that the neutron-gamma curve response decreases with increase in hydrogen concentration, therefore, the response due to the induced gamma ray component decreases with increase in fluid filled hore hole diameter. The scattered gamma ray component of the log increases with increase in bore hole diameter. Although there is an

Jan 1, 1952

By Philip D. Anderson, Ralph Hultgren

Heat contents of extremely pure iron were measured over the range 300"to 1433"K, using a diphenyl ether calorimeter. Results from three samples containing widely differing impurities agreed with one another and with Previously reported results at higher temperatures (1184 ° to 1809°K) by Olette and Ferrier. From these data a table of heat contents of iron has been Prepared which is believed to be more accurate than those previously available. CP values have been derived which are consistent with these heat contents, with the best experimental Cp data, and with the thermodynamic conditions of equilibrium between bcc and fcc iron. The opinion is expressed that low-temperature extrapolations of presently known Cp values for y-Fe are not reliable. It would seem that the thermodynamic properties of iron, which is by far our most important metal, should have been well established long ago. This is not the case, however. As discussed by Olette and Ferrier,' there is objection to every earlier heat content measurement. While the best true Cp determinations agree well at temperatures below the Curie point, there is wide divergence at higher temperatures. Several investigators have examined available data and attempted to calculate thermodynamic functions for iron that are consistent with the two equilibrium temperatures of bcc and fcc iron. The two primary efforts were those of Austin' in 1930 and Darken and smith3 in 1948. The recommended values differ considerably; integration of Austin's Cp values leads to a heat content at 1100°K which is 300 cal per g-atom higher than the value recommended by Darken and Smith. The compilation of Fisher4 in 1949 was based on the selection of Austin. In 1956, Weiss and Tauer obtained yet another set of values by resolving Cp values into components due to dilation, lattice vibration, electronic excitation, and magnetism. The magnitude of contribution by each component and its dependence on temperature was estimated by semiempirical means. Their values are not self-consistent in that they do not form smooth curves when plotted vs temperature; moreover, their calculations cannot easily be repeated since they do not give the values of some of the parameters used. Clearly, experimental values for iron were in a most unsatisfactory state. The presently described measurements of the heat content of iron were therefore undertaken, covering temperatures as high as 1433°K. While the work was in progress, the high-temperature (1193" to 1789"K) heat content measurements of Olette and Ferrier' were published; in the region of temperature overlap the present results agree with Olette and Ferrier well within experimental accuracy. It is believed that the present results, combined with those of Olette and Ferrier, provide for the first time a reliable set of heat contents of iron from room temperature to the melting point. From these data, guided by available Cp measurements, it proved possible to derive Cp, entropy, and free energy function values for @-iron from room temperature to the melting point, and for y- iron in the temperature region of its stability. Exhaustive study led to the conclusion that extrapolations of y-iron functions to room temperature were not reliable enough to be useful; hence these have been omitted from the tables. EXPERIMENTAL Materials. Three samples of extremely high purity iron from different sources, containing widely different impurities, were measured. The first of these, designated "Chipman", was kindly supplied by Dr. K. K. Kelley of the U. S. Bureau of Mines from a lot which was made many years ago by Dr. John Chipman of the Massachusetts Institute of Technology. The second, designated6'Teddington", was supplied by the National Physical Laboratory, Teddington, England, from a lot zone-refined by them. The third sample, designated "Irsid", was supplied by the Institute de Recherches de la

Jan 1, 1962

By W. R. Hibbard

It has been proposed1 on the basis of slip and flow that the ideal deformation texture of drawn wire for face-centered cubic metals is a (111) direction parallel to the wire axis. Under these considerations, an intermediate [loo] texture is permissible but should eventually change to the stable [Ill] orientation. This theory does not explain why copper and its alloys containing up to about 30 pct nickel, 5 pct zinc and 1 pct aluminum were found to have a double [Ill], [100] texture, while alloys with at least 8 pct zinc and 2 pct aluminum developed essentially a single [Ill] texture.1,2 It does suggest, however, that the [loo] component of the former alloys should disappear with additional deformation.3 Some evidence exists to support this suggestion. Howald4 reported that annealed copper wire previously drawn 93.8 pct and 98.5 pct developed a single [Ill] texture. Since, in wire, the drawn and annealed textures are similar, these wires probably had a single [Ill] deformation texture before annealing. In addition, although cold rolled polycrystalline copper and 80-20 brass were found to form different types of pole figures,5,6 single crystals of these metals when rolled from the stable (110) [112] orientation were found to produce essentially the same polo figure.7.8 It may be, therefore, that while the addition of solute elements changes the path by which the final texture is obtained, the final texture is not changed. Experimental Results The wires remaining from the previous investigation1 already drawn about 50 pct reduction in diameter were further drawn to 86 pct and then to 96.4 pct total reduction in diameter. The textures were determined after these stages by transmission X ray photograms taken with a copper K-alpha beam rotated 0 degrees toward the wire axis. It was found that the ratio of the [111].] and [100] intensities of the double texture in copper and its alloys containing 0.94 pct aluminum, 30.70 pct nickel, 2.61 pct zinc and 4.99 pct zinc increased from about 3:l for the 50 pct reduction to about 9:l for the 86 pct reduction. After 96.4 pct reduction, these wires exhibited essentially a single [lll] texture. Summary Thus, the drawn wire deformation texture of copper and its alpha solid solution alloys containing aluminum, nickel or zinc is essentially a single [Ill] texture as predicted by theoretical considerations of slip and flow.' For copper and its alloys containing up to about 1 pct aluminum, 5 pct zinc and at least 30 pct nickel, an intermediate [loo] component is found after about 50 pct reduction in diameter, but disappears after about 95 pct reduction in diameter. For alpha solid solution alloys containing at least about 2 pct aluminum and 8 pct zinc the single [Ill] texture is developed considerably more easily and is found after about 50 pct reduction in diameter. No explanation of this compositional effect is apparent. Similar work is contemplated for cold rolled and cold compressed alloys. References 1. w. R. Hibbard, Jr. and M. K. Yen: Trans. AIME 175, 126. Metals Tech., Feb. 1948, TP 2334. 2. W. R. Hibbard, Jr. and D. E. Trout, 11: Trans. AIME 185, 620. Jnl. of Melals, Sept. 1949, TN 18. 3. W. R. Hibbard. Jr.: Disc. of R. M. Brick's paper on Deformation Textures, ASM Symp. on Cold Working of Metals, Oct. 1948. 4. T. S. Howald: Disc. of Ref. 1. Trans. AIME, 175, 126. Melals Tech. Aug. 1948, TP 2449. 5. R. M. Brick, D. L. Martin and R. P. Angier: Trans. ASM (1943) 31, 675. 6. 0. Dahl and F. Pawlek: Zlsch. Melall. (1936) 28, 266. 7. C. S. Barrett and F. W. Steadman: Trans. AIME (1942) 147, 57. 8. J. E. Burke and C. S. Barrett: Trans. AIME 175, 106. Melals Tech., Feb. 1948. TP 2327.

Jan 1, 1950

By D. J. DeLazaro, W. Rostoker, R. E. Riley, M. Hansen

At very low concentrations, carbon dissolves interstitially in molybdenum resulting in a linear expansion of lattice parameter with increase of carbon in solid solution. Geometrical consideration of the relative size of carbon atom to size of interstice approximately predicts the observed volume expansion. THE element carbon, occurring in molybdenum, either as an unavoidable impurity, or purposely added, markedly affects the mechanical properties of molybdenum. Several investigators1-" have noted the occurrence of molybdenum carbide at the grain boundaries of cast molybdenum, and Fischer and Rengstorff' have shown that this intergranular constituent can induce intergranular brittleness. The appreciable change, with temperature, of the solid solubility of carbon in molybdenum, found by Few and Manning," suggests other important effects upon mechanical properties. Finally the relative atom diameters of carbon and molybdenum (the ratio of atom diameters is 0.59) are indicative, by analogy with iron (ratio of carbon atom diameter to iron atom diameter is 0.65), of a possible interstitial solid solution. If carbon dissolves intersti-tially in molybdenum, anelastic effects and age-hardening effects, similar to those observed in other body-centered cubic metals, could be expected. However, from the work of Sykes, Van Horn, and Tucker," it might be inferred that carbon forms only a substitutional solid solution with molybdenum. These considerations made it desirable to study the effect of carbon on the lattice parameter of molybdenum in greater detail than heretofore. All heat treating was done in a high temperature furnace7 built specifically for heat treatment of molybdenum. The temperatures and times of heat treatment were determined from the a solubility limit for the Mo-C system." These heat treatments were carried out in argon which was purified with respect to N, and H.!0." Purification of the argon was accomplished by passing the argon over hot (750°C) titanium and then through a magnesium perchlorate drying tower. As many as six samples were run concurrently and quenched at different times without interrupting the furnace cycle. Both the purity of the furnace atmosphere and ability to quench samples from any temperature up to 4000 °F were of prime importance in the successful heat treatment of samples for the lattice parameter investigation. Carbon Analysis The Leco Combustion apparatus was used for carbon analysis. This apparatus is capable of an accuracy of & 0.003 pct for a 1 g sample in the range below 0.10 pct. However, it is felt the degree of accuracy is somewhat better than this limit in view of the consistency evident by cross checking a number of determinations. The Battelle Analytical Laboratory consistently reported check results to within k 0.001 pct C. X-ray Measurements The molybdenum wire specimens (20 mils) were carefully filed down to about 12 mils and then etched with nitric acid to 8 mils. Carbon analyses were made on specimens before reduction in size; however, since there was no evidence of surface carburization, it is probable that the carbon was uniformly distributed throughout the sample. The resultant specimens were strain free and small enough to minimize the error in the lattice parameter determinations due to X-ray absorption. Diffraction patterns were obtained with a Debye-Scherrer powder camera 114.59 mm in diam utilizing the Straumanis type asymmetrical film mounting. Nickel-filtered copper. Ka radiation and zirconium-filtered molybdenum Ka radiation were used. Line positions on the film were measured with a traveling microscope equipped with a vernier scale permitting measurement to 0.001 cm. The average of five readings was used to determine the position of each line. The lattice parameter for each specimen was determined from the data by the extrapolation method of Bradley and Jay, Y.e., the intercept at 90" of the straight line obtained by plotting the apparent lat-

Jan 1, 1953

By P. M. Aziz, I. Markson, C. S. Barrett

The abnormal after-effect in twisted wires that occurs when untwisting is interrupted by etching con be brought under control and used to study the mechanical properties of thin surface films and how they are effected by reagents and heat treatment. Results are given of studies of oxide films on high purity aluminum. IF a wire is subjected to plastic deformation by torsion and then released, it untwists in the normal after-effect, but under certain circumstances the untwisting is abruptly lessened or reversed by the application of an etchant to the wire.1,2 This abnormal after-effect may occur, for example, if there is a coherent oxide film on the surface of the wire which is removed by the etchant. Following a suggestion of A. H. Cottrell that predicted this effect, it is attributed to dislocations that had piled up beneath the oxide layer and represents the rapid release of residual stresses caused by these dislocations. When the layer is removed, the stress relief may be by escape of piled-up dislocations from the metal, or by an activation of latent sources of dislocations located at the surface, together with rebalancing of elastic stresses to compensate for the loss of stressed material, as in a residual stress analysis determination, these mechanisms acting singly or in combination.' The slower the attack of the reagent, the more gradual is the stress relief and the smaller the change in strain rate when the reagent is applied. A study has been made of the factors that influence the magnitude of the normal and abnormal after-effects with the object of developing techniques suitable for a quantitative investigation of the influence of various surface films on dislocations in wires, and of the rate and extent of the attack on the films by different reagents. It was found that reasonable sensitivity and reproducibility could be achieved if a suitable choice of variables was made and if these variables were held constant through a series of experiments. The method was then applied to a study of oxide films produced and treated in different ways on the surface of high purity aluminum wires, and to a study of the damage to these films caused by various reagents. Experimental Procedure The material used throughout this work was prepared from 99.9968 pct Al. This high purity aluminum was melted, cast into 1/2 in. diameter ingots, and then swaged and drawn without intermediate annealing to 0.040 in. diameter wire. A sketch of the apparatus employed for twisting is shown in Fig. 1. The test wires were mounted into the apparatus by cementing one end of the wire to the beaker and the other to the tube with laboratory wax of high melting point. The length of the wire between the waxed joints was 4.2 & 0.2 cm. Extreme care was taken during mounting to avoid cold-working the wire. The wire was twisted through 335" in 2 to 4 sec by rotating the pinion on the gear box until the vertical post on the rotating table, which was initially touching the horizontal stop, was arrested by the stop. All the tests were conducted with apparatus and reagents at the same temperature (about 25°C). In all tests, except those where the duration of the initial torque was investigated, the torque was applied for a period of 2 min. At the end of this time the table was rotated back a few degrees away from contact with the stop and the wire allowed to untwist. The after-effects were measured by reflecting a beam of light from the mirror shown on the apparatus. After the wire had untwisted for 6 min, a reagent was carefully poured into the beaker and thereby applied to the surface of the wire.. In some tests the liquid in the beaker was removed after a few minutes and replaced by an-

Jan 1, 1954

By A. J. May

THE Star shaft is near the north boundary of the group of mining claims belonging to the Ground Hog Unit of the American Smelting and Refining Co., near Vanadium, N. Mex. The shaft bins and surface plant are served by a siding from the Atchison, Topeka and Santa Fe railroad, and this factor of railroad transportation influenced the choice of site. This paper describes the shaft sinking only, and does not cover the surface plant or other parts of the mine or its equipment. A. J. MAY is Engineer in Charge of Shaft Sinking, Ground Hog Unit, American Smeling and Refining Co, Vanadium, New Mexico. El Paso Meeting, October 1948. TP 2737 A. Discussion of this paper (2 copies) may be sent to Transactions AIME before Feb. 28, 1950. Manuscript received Nov. 29, 1948; revision received June 22, 1949. Experience with this shaft seems of interest because of the mechanical mucking, good rate of progress, and the costs obtained at the present level of labor and material costs. The shaft has four compartments, as shown in fig. 1. Equipment: Riddell Mucker: The mucking was done by a clamshell bucket and a Riddell mucker, which, as in other shafts sunk with this machine, consisted of a carriage mounted on axles with double flanged wheels that traveled back and forth on a swinging track, parallel to the long axis of the shaft (fig. 2 to 6). Three air motors were mounted on the carriage; one hoisted the clam, one operated the bucket opening and closing device, and the third moved the carriage along the track. The carriage was designed with guide shoes and could be hoisted to the surface in either skip compartment without trouble (fig. 4). During blasting operations the clam was tied on the rails and the carriage was hoisted up a few sets to protect it from flying rock. No attempt was made to hoist the carriage and clam together lest the clam catch in the timbers. The track on which the carriage operated was built of extra heavy 6 in. pipe with 1x2 in. strap welded on top for rails. A Yzx4 in. angle was welded on the bottom of the 6 in. pipe with a 1 in. round rod welded in the angle for a filler and additional strength. The end or cross pieces of the track which kept the track to gauge, were also made of reinforced, heavy 6 in. pipe and were bolted to the long members on which the carriage traveled (fig. 2 and 3). This section of track was used, instead of heavy railroad rails, for two reasons: (1) this section would bend before it snapped and was much safer for the men in the bottom; and (2) it was a better blasting shield, and protected the timbers better, in fact, only five wall plates were broken by blasting in 1926 ft of shaft, although 150 to 225 lb of 40 pct powder was loaded per round, depending on the ground conditions. The swinging track was supported by four % in. hoisting cables anchored to the end plates. There were also four safety cables fastened two to three sets above the carriage, which would catch the carriage if one of the supporting cables should fail for any reason (fig. 7). Clamshell Buckets: Two clams were used, each of % yard capacity, both manufactured by Blaw-Knox, Nos. 662 and 663. The No. 663 clam was 4 in. wider and 5 in. shorter than the No. 662, but seemed to dig and load more satisfactorily. It was easier to hoist and lower when it came up for repair. It did not turn over as easily, had less spill

Jan 1, 1951

By Fredrick C. Pearson, Albert Brown, Emil R. Ermert

EARLY in 1946 the Shen-Penn Production CO., a subsidiary of the Philadelphia and Reading Coal and Iron Co., was organized to operate the Shenan-doah Stripping, one of the largest open-pit anthracite mines in the world. This mine is located in the Western Middle Field near Shenandoah, Schuylkill County, Pa., and involves the removal of approximately 60,400,000 cu yd of overburden to permit the recovery of 9,200,000 gross tons of rough cleaned coal from an area 8000 ft long and 2700 ft wide, with a maximum depth of 400 ft. Operations began in August 1946, and within the next few years 31,811,-000 cu yd of overburden and 2,994,000 gross tons of rough cleaned coal had been removed. During the early days of open-pit mining operations, steam was the primary motive power. However, as the size of the equipment increased, so did the problems of fuel, water, labor, and maintenance. Because of its efficiency and convenience, electric power rapidly replaced steam. Later the modern diesel engine was developed, and today practically all stripping equipment is either electric, diesel-electric, or diesel-powered. In locations where electric power is not readily available or where operations are scattered over a large area, diesel power is favored. At Shenandoah operations are highly concentrated in a relatively small area, and this fact, coupled with the availability of ample electric energy, indicated the selection of electric-powered equipment. Since this was a new company, it was necessary to purchase every item, from the smallest tools to stripping shovels. Although the organization period was hampered by the postwar scarcity of materials, an excellent opportunity was afforded to set up a thoroughly modern plant. This paper will describe the power facilities, with particular emphasis on the more unusual features. The substation is a major item in a power distribution system, and a simple arrangement utilizing high quality equipment is an excellent investment. With this in mind, a 3000-kva unit type substation was selected and installed. This unit is made up of three sections, which are assembled simply by bolting together the various sections and connecting the power leads, see Fig. 1. The transformer proper, rated at 3000 kva, is oil-filled and nitrogen-sealed, having a 66,000-v Delta primary and 4160-v Wye secondary with a grounded neutral and 46-ohm ground resistor. The function of this resistor will be described later. Electrical energy is purchased from a public utility and is delivered to the main substation at 66,000 v over one or the other of two incoming lines. These lines terminate on a high voltage switching section on which high voltage fuses and Thyrite lightning arresters are installed. The outgoing feeder switching unit is made up of the following: 1—An auxiliary compartment consisting of potential and current transformers with necessary terminal blocks for connecting to power company metering equipment. 2—Another auxiliary compartment containing a control transformer, battery, and battery charger for the furnishing of power for tripping and reclosing of power circuit breakers. The assemblies in these auxiliary compartments are mounted on carriages that can be rolled in and out with ease. Potential transformers are readily accessible for inspection and fuse replacement. When withdrawn from the operating position they are completely de-energized and grounded. 3—Two feeder breaker compartments, each with a 1200-amp, 5000-v, solenoid-operated magneblast air circuit breaker, voltmeter, ammeter, overcurrent relays, and a ground relay. These power circuit breakers can be quickly and safely withdrawn or repaired. A built-in isolating mechanism is used for lowering the breaker to a transfer truck for repair or inspection or as a means of disconnecting the breaker from the source of power as an added precaution when working on power lines. Thus inspec-

Jan 1, 1953

By H. Matlock

Beam-columns with continuous or discontinuous transverse and angular loads and elastic restraints are represented mathematically in a manner corresponding to finite-element mechanical models. Solutions for linearly elastic cases are accomplished by direct recursion-equation elimination of unknowns, and for cases involving nonlinear loads and supports, by repeated trial-and-adjustment of complete elastic-type solutions. Five practical applications are presented by which various capabilities of the general method are illustrated. The examples include simulation of a pipeline launching and the bending and collapse of a conductor pipe in deep-water drilling operations. INTRODUCTION The diversified and complex operations being conducted in support of the production of offshore oil have produced a wide variety of new problems in structural mechanics. Many of these problems cannot be solved by conventional analytical or experimental approaches and have therefore stimulated inquiry into new methods of solution. It is the purpose of this paper to give a brief description of an analytical method for solving nonlinear beam-column problems and to illustrate the generality of the method by applying it to several problems related to offshore operations. Although the data for all of the examples are artificial, the cases discussed will be recognized as being based on actual situations. DESCRIPTION OF METHOD The analytical approach which is to be described stems from research on offshore foundations, in particular, the study of lateral-load behavior of foundation piles. The method represents a generalization of a technique which was suggested by Gleser' and extended by Focht and McClelland2 and Reese and Matlock." To maintain generality and therefore versatility in the method, a considerable variety of input data is considered. Fig. 1 illustrates the various types of loads and restraints which might be applied to a short segment of a beam. Each of the terms illustrated in the figure is shown acting in a positive sense. Capital letters are used to designate concentrated quantities whereas the corresponding lower-case symbols indicate effects which are distributed in some way along the length of the beam. The transverse loads and the elastic restraints may be divided into two classes: (1) loads Q and q and springs S and s, which act normal to the axis of the beam, and (2) couples T and t and rotational springs R and r, which act in an angular sense. In addition, there is an axial force P which may be constant or may vary along the length of the beam. The bending stiffness of the beam (the product EI of the modulus of elasticity and the moment of inertia) is designated by the symbol F. The assumptions of conventional elementary beam theory provide the basis for the present method. Among these are the neglect of shearing and axial deformations and the limiting of consideration to straight beams of symmetrical cross-section. Lateral deflections are considered to be small compared to original dimensions. A deformed element of such a beam is shown in Fig. 2a. The curvature of the beam is approximated by the second derivative of the deflection y with respect to distance x along the beam. It is assumed that the material of the beam is linearly elastic and therefore the relation of Eq. 1 between curvature and bending moment M is the ordinary expression from elementary beam theory. A generalized beam element is shown in Fig. 2b. The element has been deflected in a positive direction by an amount y and tilted through a small positive angle dy/dx. The various loads and elastic restraint reactions are detailed in the figure. Temporarily, only distributed effects are considered; provision for concentrated loads and restraints will be made subsequently. Eq. 2 in Fig. 2b is obtained by summing the forces and moments acting on

By S. R. Mitchell, M. C. Fuerstenau, A. M. Gaudin

The two principal attributes of a thickener pulp are its settling rate and the ultimate pulp density of the thickened mud. Testing for evaluation of thickening attributes of a pulp has usually been done batch-wise by placing the pulp in a one-liter glass graduated cylinder and noting the position of the boundary between clear liquor and mud as a function of time. Refinements in testing have included repulping a thickened mud to various dilutions and evaluating the settling rate on these various repulped muds. This is considered to make possible an estimate of the settling rate as a function of pulp density and therefore to pinpoint the slowest settling pulp which ought to be critical from the standpoint of thickener plant design. Finally, tests are sometimes made with model-size continuous thickeners of arbitrary size. In batch tests it is generally accepted that the behavior of a pulp is described by a curve such as the one shown in Fig. 1, in which the position of the boundary between clear liquor and mud (the mudline) is plotted against time. It has also been assumed that the initial settling rate (the slope of the line segment AB) is descriptive of the pulp and independent of the size and shape of the container. Where the settling rate is slower and clearly a function of time (portion CD of the settling curve), it has been assumed that the data are not of much use because of the intrusion of compacting phenomena. The next important datum is the height. PE, which is a measure of the so-called ultimate pulp density. This quantity is assumed to be characteristic of the pulp and independent of the container. When actual data are recorded, results are rarely exactly according to this theory and numerous deviations may be noted. For example, some pulps seem to require an appreciable delay before beginning to settle, as in line AF. This is spoken of as representing the need for an induction time for flocculation. It has seemed desirable to explore thickener data with a more sensitive charting tool than is afforded by the coordinates of Fig. 1. Instead of relating the position of the mudline to time, it has seemed desirable to relate the rate of descent of the mudline to time. This, in effect, amounts to charting the slope of the line in Fig. 1, or the derivative of its ordinates, against the same abscissas. Fig. 2 shows the new chart for the curve ABCDE of Fig. 1. When this new tool was applied to data obtained, for example, with sized clay pulps, astonishing differences appeared. Apparently the traditional tool conceals differences instead of revealing them, whereas the new method emphasizes them. It seems, also, that both charting methods have their uses. In this article attention is focused on the effects of pulp density and container height as they affect the settling behavior of flocculated suspensions of a sized kaolin. The thesis by M. C. Fuerstenau' gives more details than this summary, as well as some information about the effect of other variables. Sized fractions of kaolin were used, supplied through the courtesy of S. C. Lyons of the Georgia Kaolin Co. Large batches were made by agitation in a flotation machine and in a glass jar equipped with a mixer. The settling vessels were 2, 4, and 6-in. diam glass cylinders of various heights. Pulp Dilution: The effects of pulp dilution on sedimentation behavior are shown in Figs. 3, 4, and 5. Fig. 3 shows data on pulps ranging from 2.44 to 16.7 pct solids initial pulp density, flocculated with Separan and charted in the traditional manner. At least two of the lines appear nearly straight in their early sections, but neither of the others does. Each of the curves in this figure includes a region labeled

Jan 1, 1960

By S. T. Wlodek, John Wulff

Dense, adherent, and ductile coatings of chromium can be applied to Molybdenum by selectively freezing out the chromium solute from a supersaturated copper-or tin-rich liquid alloy. The successful exploitation of this technique depends on the control of variables common to any freezing process. Under the most favorable combimtion of supersaturation, nucleation, and mass-transfey, coatings as thick as 0.004 in. can be obtained. In exploratory experiments it was found that a coating of chromium may be applied to molybdenum by immersing the molybdenum body in a supercooled copper-chromium or tin-chromium melt and selectively freezing out the contained chromium onto the molybdenum body. Supercooling of the liquid metal plating bath can be achieved by cooling, or the maintenance of thermal or concentration gradients in the melt. The technique is similar to conventional dip-plating procedures where the sample is immersed in a molten bath of the pure plating medium, except that in these studies, the plating medium consisted of a dilute solution of chromium in liquid tin or copper. The success of this method requires that the base material to be plated be isomorphous with the coating and insoluble in the plating bath. In addition, the plating bath, while having an appreciable solubility for the coating component, must have negligible solid solubility in the solid plate. Such relationships exist in the molybdenum-chromium, chromium-tin, and chromium-copper systems. Liquid tin and copper are satisfactory as the plating solvent, because although chromium is appreciably soluble in both of these liquid metals, solid inter-solubility is almost negligible, and no compound formation occurs. The same relationships exist between molybdenum and copper or tin except that the solubility of molybdenum in liquid tin or copper is insignificant. It is this combination of solubility relationships, as well as the completely isomorphous nature of the molybdenum-chromium system, which allows the formation of a chromium coating on molybdenum by the selective freezing mechanism. Since the main deterrent to the widespread use of molybdenum for high-temperature structural applications is its poor oxidation resistance, the formation of a dense and ductile chromium coating on molybdenum may well be of commercial significance. In addition, the basic principle of coating formation by selective freezing should be applicable to other metallic or even nonmetallic systems. The precipitation of the solute from a liquid metallic solution, for the formation of a protective coating, has not been previously considered in the literature. Frequently, however, a similar phenomenon has been described in the corrosion of metallic heat exchangers by liquid metals1 wherein temperature gradients in the liquid metal heat-transfer medium result in the formation of layers or deposits of metallic residue2 in the cooler portions of the system. Impregnating techniques using liquid baths have been tried as a plating process. Semchyshen and Barr, for instance, have successfully diffused chromium into molybdenum by immersing the molybdenum specimen in a liquid tin-chromium or copper-chromium alloy. This simple holding technique fails to produce a layer of pure chromium and requires prolonged immersion to allow for the diffusion-activated enrichment of the molybdenum. During the course of this investigation, most of the phase relations published for the copper-chromium4 and molybdenum-chromium4 systems, were found reliable. It was necessary, however, to investigate the solubilities of chromium and molybdenum in liquid tin as well as the solubility of molybdenum in liquid copper. These determinations were made by a simpie weight loss technique on materials of the same purity as used in the plating studies. The results of these solubility studies are given in Tables I and I1 and indicate that although the solubility of molybdenum in liquid

Jan 1, 1961

By E. I. Salkovitz, F. W. von Batchelder

DURING the last few years several papers1-' have been published in which internal friction measurements have been used to determine the quantity of carbon or nitrogen dissolved in a iron. This method is based on the fact that, in pure Fe-N and Fe-C alloys, nitrogen and carbon cause peaks in the internal friction vs. temperature curve; at a frequency of 1 cycle per sec (cps) these peaks appear at $-200 and +360C, respectively, and if internal friction is expressed as Q-1, which is equal to times the logarithmic decrement, this figure will, by coincidence, give the weight percentage of nitrogen or carbon in solid solution.' In most of the studies published, very pure iron (Puron) was used. In one case the influence of manganese on the behavior of nitrogen in a iron was mentioned.4 It would be of great value, especially for the study of aging and related phenomena, if this method could be applied to commercial mild steel with norrnal percentages of manganese, phosphorus, sulphur, etc. As a rule, in such steels carbon and nitrogen are present together, and the amounts of these elements in solid solution should preferably be determined separately. The fact that their internal friction peaks appear at different temperatures (+36° and + 20°C in pure iron) seems promising for such a selective determination. It is necessary, however, that the peaks are narrow enough not to interfere with one another, and further, that there is no effect from carbon on the behavior of nitrogen in stress induced diffusion, and vice versa. According to Fast,' however, in the presence of manganese the nitrogen peak gets wider and appears at a higher temperature nearer the carbon peak, and thus the prospects for selective determination are reduced. (The carbon peak was not affected by the presence of manganese.) But even if fully quantitative de- terminations of the two elements are not attained, some relative figures on the sum of them and an indication of which one is the predominant one, would be of value. Some results from experiments along these lines will be reported here. An internal friction measuring device was assembled mainly following a description by KG." The measurements were also carried out as reported in that paper. Table I gives the chemical compositions of the four different materials used in this investigation. All materials were drawn to wires with diameter about 0.8 mm, and the analyses refer to these final shapes. Determination of Nitrogen Peak Wires from steels A, B, and C were decarburized in wet hydrogen (about 30 pct H2O) at 700°C until no carbon or nitrogen could be found by chemical analysis. No peak was then found in the internal friction. The wires were further annealed at 580°C for 16 hr in hydrogen bubbled through a solution of 6.8 pct NH3 in distilled water. Chemical analyses gave 0.04 pct N in A and C, and 0.06 pct in B. After annealing at 580°C for 15 min in a lead bath and water quenching, the internal friction was immediately measured. The resulting curves are shown in Fig. 1. At these high values of the internal friction the accuracy is comparatively poor; at Q-1 - 0.030 it is estimated to be 0.002. In order to make possible a calculation of the activation energy for diffusion of nitrogen, measurements were made at two different frequencies. Steel A shows rather broad peaks, and their temperatures can hardly be expected to be very accurate. Steels B and especially C are better in this respect. The finding of Fast' that manganese broadens the nitrogen peak is con-

Jan 1, 1953