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By O. G. Paasche, Yuan-Shou Shen

THERE is a disagreement among the various authors about the exact manner of transformation of ZrCr2. Rostokerl and others2 stated that ZrCr2 had a C-14 (MgZn2) type of structure below 1000°C and a C-15 (MgCu2) type of structure at temperatures above 1000°C. Alisova3 and others4 reached the opposite conclusion and stated that the transformation temperature is close to the melting point of ZrCr2. A literature survey shows that various investigators3'= who homogenized the specimens at a temperature higher than 1000°C have concluded that ZrCr2 had the C-15 structure at room temperature. Meanwhile, Jordan et al.4 reached similar conclusions without annealing the specimen. Other investigators1,2,6,7 who X-rayed the specimens in the as-cast condition without annealing reached different conclusions. The investigation reported herein was conducted with the aim of exploring the exact manner of transformation of ZrCr2 by various heat treatment tests. The alloys for this examination were prepared from iodide-reduced zirconium crystal bars, 99.9 pct purity, and electrolytic chromium, 99.9 pct purity. They were melted in a nonconsumable electrode arc furnace with water-cooled copper crucible in a helium atmosphere. The melting loss of each alloy was less than 1.5 pct by weight. Chemical analysis of a randomly selected specimen indicated that there was a very close agreement between calculated and analyzed compositions. Before being heat-treated each specimen was encapsulated in a vycor or quartz tube inside which an argon atmosphere was maintained at a pressure of lower than 1 atm. In determining the crystal structure of each specimen with a Debye-Scherrer camera, the standard procedure8 for X-ray quality analysis (Hanawalt method) was followed. The different series of heat treatment tests in this investigation are tabulated in Tables I and 11. The tests in Series I, specimens from 1-1 to 1-9, which were similar to Rostoker's experiment1 indicated that the transformation temperature seemed to fall between 870° and 900°C and that the crystal structure of ZrCr2 at lower temperature seemed to be of the C-14 type. However, once the compound is transformed to C-15 type, it is impossible to reverse the transformation back to the C-14 type by first heating the specimen above 900°C and then annealing it slowly below 900°C as shown in Experiments II-1 to II-3. Thus, it appears that the specimen of ZrCr2 will transform from C-14 to C-15 structure when heated above 900°C but will not transform from C-15 to C-14 when annealed slowly passing 900° C even after the extremely slow cooling process such as indicated in the experiment of Specimen II-3. As a valid transformation temperature is a temperature at which the transformation is reversible, therefore the temperature 900°C (or other temperature close to 900°C) is not the transformation temperature for ZrCr2 and the C-14 structure is not the stable structure of ZrCr2 at lower temperatures. The C-14 structure is retained at room temperature because the transformation to C-15 structure is very sluggish and the fast cooling after melting does not allow enough time for the transformation to take place. Additional energy is required to alter the metastable condition of the C-14 structure. The sluggishness of this transformation was again demonstrated through another series of experiments. Four specimens with C-14 structure were taken. Then they were annealed at 900°C but each specimen was soaked for a different period of time, Table 11. X-ray diffraction patterns of this group indicated that the C-14 structure gradually disappeared as the soaking period was lengthened. The figures listed under the column "C-14 Structure, pct" were estimated from the intensity of the d = 2.330 line of the diffraction pattern corresponding to the structure. Notice that the intensity of this line became weaker for longer soaking periods. To determine the transformation temperature of ZrCr2, specimens with C-14 structure (as-cast condition) were annealed at 1300°, 1400°, 1500°, 1550°, and 1600°C, respectively. A final specimen was first heat-treated to 1500°C in order to transform it to C-15 structure, then heat-treated at 1600°C again. From the X-ray analyses of this series of tests, Specimen Nos. III-1 to III-6, it is evident that a transition from C-15 structure at lower temperatures to the C-14 structure occurs at some temperature between 1550° and 1600°C.

Jan 1, 1969

By J. P. Zannaras

Referring to the article by R. J. Charles and P. L. de Bruyn, let us assume that W = weight of glass bar; P = weight of hammer; e = total deformation; K = unit of deformation; K = potential stress energy; E = modulus of elasticity; L = length of the bar; 7 = coefficient of inertia; h = height, ft; V = velocity, fps; and a = cross section area. The portion of kinetic energy which is effective in producing stress energy in a fixed bar struck horizontally is given by the formula" 1 + 1/3 W/P K =1+1/3w/p/(1+1/2w/p)2 P.V2/2g = Ph where 1 + 1/3 W/P ? (1 + 3W/P/(1=1/2w/p)2 [8] Putting e e = W/P =------------ From the above equation it can be seen that the maximum transfer of kinetic energy to stress energy is when e = 0 or W/P = 0 which indicates that the weight of the hammer must be very large as compared with the weight of the impacted rod. Eq. 8 diametrically opposes the conclusions reached by the authors of this article. In fact, if their suggestions were followed to the extreme when e = co when P = 0, there would be no transfer of kinetic energy to stress energy at all, as 7, becomes zero. Eq. 8 presumes that the velocity with which the stress is propagated through the bar is infinite, whereas the authors claim that the compression waves reflected are reaching the struck end of the bar prior to the complete transfer of the kinetic energy to cause such modification of the conditions there as to make them reach the reverse conclusions demonstrated by the above formula. That such interference exists is unquestionably demonstrated by the authors and others. However, if my observations are correct, such interference for this specific experiment and also for practical comminu- tion is insignificant, and the conclusions of the authors are in error and must be reversed to comply with Eq. 8. Eq. 5, w. = AE 2/2, given by the authors on page 51, is derived from the following equation (Eq. 9): K = 1/2Pe, where P = Sa, S = ?E, e = EL, and L = 1. The above formula, Eq. 9, cannot be applied in this case. This formula is applicable for static loads where the load increases from zero up to its final value, P, in such a way that the deformation at different instants is proportional to the loads acting at those instants and actually represents the area of a right triangle in the strain load diagram of base e and height P. The typical photographs shown in Figs. 3 and 4 represent the familiar strain load diagrams, and since the line of the wave marks the existence and intensity of the strain with the unquestionable conclusion that such strain has been caused by the action of a load acting continuously all along the wave until it reached the horizontal axis, the work stored at this point is represented by the area under the wave line and the horizontal axis and not by the area of the fictitious triangle given by the authors. Then if this is correct, even visual estimation of these areas at gage stations given in the typical photographs of Figs. 3 and 4 suffice to contradict the authors' calculation given in Figs. 6a and 6b and Figs. 7a and 7b. The typical photographs presented by Charles and de Bruyn show a considerable variation of the intensity of the strain at different stations but very small variation of areas which actually represent the stress energy at the corresponding stations. And, apparently, by squaring the small quantities, the authors magnified their error tenfold. J. M. Frankland's paperV iscusses the relative strain intensity and not the total energy for different types of impact loading. He states in his paper, "The reader is explicitly warned not to confuse the results in this report with those obtained when the load is applied by a blow as from a hammer. In this case the peak load rises to very large but mostly unknown values. The accompanying large deflections and stresses are the result of high values of P, not of the dynamic load factor n. According to Frankland "the dynamic load factor" is the numerical maximum of the response factor. It therefore appears that the authors followed the same procedure in obtaining the relative strain energy ab-

Jan 1, 1957

By Norman Lamont

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

Jan 1, 1958

By C. G. Dunn, M. Sharp

IN twinned crystals of the face-centered cubic metals the lattice of one twin is a mirror image of the other in a common twin boundary. When several twins appear within large grain in a sheet specimen, the twin one boundaries form a set of lines at the surface of the specimen which coincide with (111) planes of the large grain. Furthermore, for twins of the same orientation, these lines are parallel. Generally, the presence of identically oriented regions with straight parallel boundaries coinciding with a (111) plane of the surrounding crystal is strong evidence for identifying the island regions as twins of the parent crystal. However, Fig. 1, which shows the macrostructure of a large grain of copper with island regions that satisfy these conditions. is not an illustration of (111) twins. Since the reverse side of the specimen has much the same appearance, it was thought at first that these regions, which appear dark in the macrograph, actually were twins. According to X-ray data, however, these regions are second-order twins of the large crystal. With regard to their formation, these second-order twins formed by secondary recrystallization in a cube texture matrix. Growth occurred in the direction of the arrow (see Fig. 1) as the specimen moved slowly into a gradient temperature furnace as described previously.' Nucleation of the second-order twins occurred, therefore, on the ends facing opposite the arrow. If the origin of the second-order twins were due to repeated twinning, some first-order twin structure should be visible on these ends. This proved to be the case, as very small twins were readily found with the aid of a microscope, and probably could have been seen, in some instances, under ideal lighting conditions without aid of a microscope. Fig. 2 shows a cross-section view taken perpendicular to both the surface and the (111) trace of the parent crystal (visible as a straight boundary in Fig. 1) at the beginning point of growth of a second-order twin and where one first-order twin was relatively thick. In the micrograph, A is the large parent grain; B is the first-order twin of A; and C, which is a first-order twin of B; is a second-order twin of A. Between A and B and between B and C the major straight portions are traces of common (111) twin boundaries. The straight portion of boundary between A and C, however, is not a common crystallographic plane to the two lattices; it is a (111) plane of A and a (115) plane of C. Without considering the mechanism of twinning itself, the origin of the second-order twins may be accounted for in terms of repeated twinning and special growth characteristics. After each nucleation, a selective growth process can be thought of as favoring growth of the first-order twin in local spots only and favoring growth of the second-order twin to an extent comparable with that of the parent grain over relatively large areas in a way similar to that described for twinning in aluminum.' It has already been pointed out that the boundary between the large grain (A) and the second-order twin (C), which is responsible for the straight boundary portions in Fig. 1, involves a (111) plane of A and a (115) plane of C. The same combination of planes is not only possible in first-order twins, but actually appears quite frequently.3 Their prevalence in first-order twins and their presence here in second-order twins, together with the necessary occurrence of a large number of common lattice sites at the boundary, is an indication that this combination produces an "energy cusp"' boundary. (Energy cusp boundaries have been described by Shockley and Read.") The configuration of atoms near a {Ill), (115) boundary in first-order twins is of course different from the configuration near the same type of boundary in second-order twins. References 1 M. Sharp and C. G. Dunn: Secondary Recrystallization Texture in Copper. Journal of Metals (January 1952) Trans. AIME, p. 42. 2W. G. Burgers and W. May: Stimulated Crystals and Twinning in Recrystallized Aluminum. Recueil des travaux chimiques des Pays-Bas (1945) 64, p. 5. aD. Whitwham, M. Mouflard, and P. Lacombe: Discussion of W. C. Ellis and R. G. Treuting, "Atomic Relationships in the Cubic Twinned State." Trans. AIME (1951) 191, p. 1070; Journal of Metals (October 1951). 4 W. Shockley and W. T. Read: Dislocation Models of Crystal Grain Boundaries. Physical Review (1950) 78, p. 275.

Jan 1, 1953

By R. A. Oriani

The partial molal volume of hydrogen is one of the parameters that describe the elastic interaction between the solute and the stress fields about inclusions, dislocations, and cracks. As such the partial molal volume is probably of importance in the elucidation of phenomena such as hydrogen embrittlement and hydrogen yield point. A knowledge of this quantity would also be helpful in thinking about the state of dissolved hydrogen in iron. However, because of the very low lattice solubility of hydrogen in iron the usual ways of determining the lattice expansion are not practicable. It is therefore of interest to apply the thermodynamics of stressed bodies to two sets of measurements of the effect of elastic stress upon the permeability of hydrogen in order to deduce a value of the partial molal volume, VH, of hydrogen dissolved in a iron. Beck ..' and previously de Kazinczy, observed that a uniaxial tensile stress increases the permeability of hydrogen in iron and in various steels. Beck et 01. employed Armco iron and A.I.S.I. 4340 steel, whereas de Kazinczy used a steel the composition of which was 0.13 C, 0.23 Si, 0.46 Mn, 0.006 P, and 0.038 S. Upon releasing the stress the permeability increment disappeared if the stress was below the elastic limit. Both investigators employed cathodic charging to introduce the hydrogen. de Kazinczy measured the permeation through a thin-walled tube by collecting the gas, whereas Beck et al. measured the permeation through sheets of various thicknesses by a very sensitive electrochemical technique. Both investigators measured the steady-state permeation at constant rate of hydrogen ion discharge, and Beck measured in addition the hydrogen diffusivity by a time-lag technique which is independent of the boundary conditions. Beck et al. and de Kazinczy found a linear relationship between log (J,/Jo) and the stress, where Ju/Jo is the ratio of the flux of hydrogen when the metal is under uniaxial tensile stress, a, to the flux under zero stress, for the same temperature and charging current. Beck et al. found in addition that the diffusivity of hydrogen is not changed by stress. Both investigators concluded that the observed change in permeability is due to an increase in hydrogen concentration, and furthermore that the increase in concentration is due directly to the thermodynamic effect of stress upon concentration. Accepting this assessment of the situation for reasons given below, one may use the equation3j4 in order to evaluate I/H, the partial molal volume of hydrogen. This equation is valid for the domain of a/E «¦ 1 (where E is the Young's modulus) and under the assumption that hydrogen expands the lattice isotrop-ically. From the data of Beck el al, one calculates V7H - 2.0 cu cm per g-atom, and from those of de Kazinczy one obtains 1.8 cu cm per g-atom. That the increase of concentration with stress is indeed of thermodynamic origin is attested to by the facts that the experimental results conform to the thermodynamic relation, Eq. [I], and that the results are the same whether a pure iron1 or each of two different steels172 is used. Neither of these facts wou1.d necessarily be expected if the effect of stress were, rather, to increase the ratio kn/k, of the kinetic factors of the following competing reactions: H(ads) — H (dissolved) Such a change of kinetics at the surface could be an alternative explanation of the effect of stress on the permeability. Although this writer does not deem this explanation to be the correct one for the reasons given above, it must be admitted that unambiguous proof that the phenomenon has a thermodynamic origin does not yet exist. Two kinds of experiments may be suggested. One is to plate a variety of metals on the input surface of the steel and repeat the stress experiment at a variety of hydrogen charging currents. The other is to employ somewhat thicker specimens in order to be able to apply uniaxial compressive stress. Eq. [I] shows that ln(c,/c,) depends on the sign of the stress, but it is difficult to see a physical basis for which k2/kl would depend on the sign of a. The present value of V^ in a iron agrees with phragmen's5 estimate, which he based on comparisons with the lattice expansion by hydrogen of titanium, zir-

Jan 1, 1967

By Irving B. Cadoff, Alvin A. Machonis

The resistivity, Hall coefficient, Seebeck coefficient, and thermal conductivity were measured as a function of temperature for cation-rich alloy single crystals covering the composition range across the PbTe-SnTe system. Alloying of PbTe with up to 20 pct SnTe was found to have little effect on the energy gap. Above 20 pct SnTe the alloys were "p" type but below this range the sign could be varied by heat treatment. The lattice thermal resistivity of the compounds SnTe and PbTe is raised by alloying one with the other. Z values in the order the interesting values obtained. THE PbTe-SnTe system has several interesting features. For one, PbTe is a useful thermoelectric material and the possibility of improving its figure of merit by alloying with SnTe, an isomorphous compound, has been suggested since these pseudo-binary solid solutions generally have a more favorable ratio of electrical conductivity to thermal conductivity than either of the components.' Other interesting features relate to the conductivity mechanism, band structure, and stoichiometry of the compounds and their alloys. PbTe is a semiconductor with an energy gap of about 0.29 ev2 at room temperature whose conductivity sign and magnitude can be varied from "n" to "p" by controlling the proportion of lead and tellurium with respect to the stoichiometric ratio.3 Excess lead results in "n"-type conduction. SnTe is found to exist only as a "p"-type material of relatively high conductivity. This behavior is attributed to stoichiometric deviation by Brebrick4 but Sagar and Miller proposed that the behavior of SnTe must be due in part to the presence of an overlapped band. An investigation of alloys of this system, therefore, might give additional information which would permit one to evaluate which of the two proposals is the more appropriate one. Abrikosov et al.' studied the room-temperature electrical properties of these alloys and reported data for Seebeck coefficient and resistivity on poly-crystalline alloys. The present work is a more exhaustive survey of the PbTe-SnTe system. Re- sistivity, Hall coefficient, Seebeck coefficient, and thermal conductivity were measured over a wide temperature range for single crystals at 10-pct intervals of lead/tin ratio across the pseudobinary system. The relative concentration of tellurium was controlled so as to obtain metal-ion excesses in all cases. SAMPLE PREPARATION The crystals were prepared by melting elemental lead, tin, and tellurium in weighed proportions in evacuated Vycor capsules. The lead and tellurium were high-purity grades obtained from American Smelting & Refining Co. The tin was supplied by Comico. The proper calculated proportions of lead, tin, and tellurium were weighed and charged into prepared Vycor capsules prior to evacuation. The capsules were prepared from 15-mm Vycor tubing. A sharp point was worked on one end of the tube. A pyrolytic graphite coating was deposited on the Vycor walls by heating the tip to 800°C in an atmosphere of acetone-saturated argon. An additional coating of graphite was deposited on the pyrolytic coating from an Aquadag suspension. Above the coated tip the tube was reduced in diameter to form a constrictive neck. To avoid scratching the graphite coatings the charge was placed in the tube above the constriction. After a low-temperature bake, the evacuated capsule was sealed. On subsequent heating the charge melted down into the lower portion of the capsule. The crystals were grown by lowering the capsule through a Bridgman-Stockbarger furnace. The lowering rate was 1 in. per 8 hr. The upper portion of the furnace was set for 950°C and the lower portion for 800°C. In general the yield of single crystals was about 25 pct. The mixed compositions were, as expected, the most difficult to grow. The finished crystals were sectioned into 5/8-in. slices. The tip, end, and middle slices from each crystal were analyzed by X-ray fluorescence to determine the lead-to-tin ratio. The resulting values were used to plot a composition vs distance plot for each crystal. Slices were selected from each crystal, with the aid of the composition plots, to cover the complete range of compositions at 10-pct intervals. In general, the slices selected were taken from the seed end of the crystal where the longitudinal segregation (as determined from the X-ray fluorescence analysis) was a minimum. Laue single-crystal analysis and metallographic analysis was used to verify if a slice was single or polycrystal. Any grain boundaries were clearly visible in the as-cut and polished condition. In ad-

Jan 1, 1964

By D. W. Lillie

It has been demonstrated that considerable bend ductility exists in bulk specimens of polycrystalline high-purity silicon. The possibility of hot-forming at 1200°C is suggested. EXCELLENT corrosion resistance in many media and low cross section for absorption of thermal neutrons (0.13 barn) would make silicon of interest to nuclear engineers were it not for extreme brittle-ness and the difficulty of fabrication by any reasonable means. The use of silicon for structural purposes also has been considered in view of its light weight and oxidation resistance. Johnson and Han-sen' have investigated the properties of silicon-base alloys and concluded that there was no way of making pure silicon or silicon-rich alloys ductile at room temperature. In view of reports of appreciable ductility in germanium single crystals above 550°C'." and some plastic deformation in single-crystal silicon above 900oC,' the present investigation was undertaken to define more precisely the limits of high-temperature ductility in pure silicon. After this investigation was begun torsion ductility in both germanium and silicon was reported by Greiner." Through the courtesy of F. H. Horn, a small bar of cast extra high-purity silicon was obtained and small bend specimens were made from it by careful machining and grinding. All of the reported tests results were obtained from samples from this bar (bar No. 1) and one other of similar source (bar No. 2). No complete analysis was obtained but, based on analysis of similar semi-conductor grade material, metallic impurities were under 0.01 pct total. Vacuum-fusion analysis for oxygen showed a value of 0.0018 2 0.0003 pct for the first bar tested and metallographic analysis showed no evidence of a second phase. Bend tests were carried out on an Instron tensile machine using a bend fixture with a 1 -in. span loaded at the center. Supporting and loading bars were 0.250 in. round and the load was applied by downward motion of the pulling crosshead of the machine. Specimen thickness and width were approximately 0.10 in. and % in. respectively. Loading rate was controlled by holding crosshead motion constant at 0.02 ipm. In some cases a smaller specimen was used on a 5/8-in. span with a 0.129-in.-diam loading bar. The entire bend fixture was surrounded by a hinged furnace and all heating was done in air atmosphere. Temperature measurement was made with thermocouples fastened directly to the bend fixture within less than 1 in. from the specimen. Autographic stress-strain curves were recorded during each test, and breaking load, total deflection, and plastic strain could be obtained from these curves. Stress was calculated from the beam formula S = 3PL/2bh2, where P is the load in pounds, L the span in inches, b the specimen width in inches, and h the specimen thickness in inches. This formula is strictly correct only in the elastic range but has been used to calculate a nominal stress for convenience in the plastic range. The stress given is the maximum stress in the specimen. Results The results of the complete series of tests are shown in Table I. The first group of tests (specimens Nos. 1-6) showed the beginning of plastic flow at a test temperature of 900°C, so two additional tests (Nos. 8 and 9) were made at 950°C on small-size specimens from bar No. 2. Specimen No. 8 was tested in the as-machined condition, and No. 9 was heat-treated in hydrogen at 1300°C for 2 hr, cooled to 1200°C and held 1 hr, cooled to 1000°C and held 1 hr, cooled to 900°C and held 1 hr, and finally cooled to a low temperature before removal from the hydrogen. It is apparent that the heat-treatment had a significant effect on yield strength and ductility. In addition, the magnitude of the yield point was conslderably reduced in the heat-treated specimen as is shown m Fig. 1 by tracings of the stress-strain curves. After obtaining a furnace capable of reaching higher temperatures specimens Nos. 10 to 13 were tested at 1100 and 1200°C. Strain rate was increased by up to a factor of 10 to see whether the ductility observed was excessively strain sensitive. Specimen NO. 10, strained at 0.02 ipm and 1100oC, was still bending at a deflection of 0.322 in. when the load rate was increased to 0.2 ipm, resulting in immediate

Jan 1, 1959

By Wilbur I. Duvall, Wilson Blake

The microseismic method of detecting instability in underground mines was developed by the U.S. Bureau of Mines (USBM) in the early 1940's. ,3 The method relies on the fact that as rock is stressed, strain energy is stored in the rock. Accompanying the buildup of strain energy are small-scale displacement adjustments that release small amounts of seismic and acoustic energy. These small-scale disturbances, which can be detected with the aid of special geophysical equipment, are called micro-seisims or self-gene rated rock noises. It was further determined that as failure of rock is approached, the rate at which rock noises are generated increases. Thus, by monitoring a rock structure at intervals and plotting rock noise rates vs. time, a semi quantitative estimate of the behavior and stability of the structure can be made. Since sufficient use of the microseismic method is still being made by various mining and construction companies, USBM undertook a comprehensive review of the method and a study of the fundamental properties of rock noises. As all prior work on rock noises has been done with resonant-type geophones, which prevented any analysis of their vibration records, it was necessary to develop the instrumentation and field techniques in order that their properties could be investigated, such as their frequency spectrum and absorption characteristics, and to determine if both P and S-waves are generated by a rock noise. The aim of this program is the design of microseismic instrumentation which can be better utilized as an engineering tool than the presently available microseismic equipment. This new design, based on the basic properties of rock noises, should allow better utilization of these phenomena in the study and location of zones of incipient instability in both underground and open-pit mines. EXPERIMENTAL PROCEDURE To study the waveform of rock noises, it was necessary to develop a microseismic system with a broad bandwidth. To achieve high sensitivity and broad frequency response, commercial ceramic accelerometers were used. The present broad-band microseismic system consists of accelerometers as geophones, low-noise preamplifiers, high-gain amplifiers, and an FM magnetic tape recorder. This seven-channel system has a flat frequency response from 20 to 10,000 Hz, a noise level of less than 2.0 kv, and a dynamic range (including manual set attenuation) of greater than 100 db; it can detect signals with acceleration levels as low as 2 ug. The entire system is solid state and hence battery operated and portable (Fig. 1) Analysis procedures consist of playing back the 30-in-per-sec (ips) magnetic tape recordings at 1 7/8 ips to expand the time scale of a recorded rock noise event and then recording this on a high-speed direct-writing oscillograph. The oscilIographic records are then digitized and run through Fourier integral analysis computer programs to determine the frequency spectrum of a rock noise event. The oscillographic records are also examined visually to determine if both P and S-waves can be recognized in a rock noise waveform. Broad-band microseismic recordings have been made at field sites in a wide variety of rock types and in both underground and open-pit mines. Sites include the Kimbley Pit, Ruth, Nev.; the Galena Mine, Wallace, Idaho; the Colony Development Mine. Grand Valley, Colo.; the Cliff Shaft Mine, Ishpeming, Mich; and the White Pine Mine, White Pine, Mich. DATA AND DISCUSSION Analyses of the recorded data have shown that rock noise frequencies are very broad. Fig. 2 and 3 show typical rock noise events and their frequency spectrums. In addition, it is evident from these figures that the wave form of a rock noise is very complex. The wide frequency variation, 50 to 7500 Hz, is due to many variables; the effect of travel distance is the only one examined in this study. The higher frequency components of the wave are rapidly absorbed with distance or increasing travel time. Fig. 4 shows the change in waveform resulting from an additional travel distance of 195 ft. From these data, it is apparent that a resonant-type microseismic geophone cannot respond to all frequencies generated by a rock noise, and in spite of the fact that the tuned geophone is more sensitive at resonance, a geophone with less sensitivity but broader band width is much more effective in detecting rock noises. In addition, a study of broad-band microseismic records shows that both P and S-wave arrivals are easily detected, as shown in Fig. 5. All records analyzed to date show that most of the energy is in the S portion of the wave; hence, microseismic geophones should be well

Jan 1, 1970

By A. M. Johnson, M. M. Singh

The mechanism of failure under a drill bit is still improperly understood in spite of several investigations of the subject. Generally, the cratering process under static loading conditions is considered to be similar to that achieved dynamically by impact. This paper attempts to indicate that, although the sequence of fracturing in the two cases appear to be identical, at least some dissimilarities exist. For example, the width-to-depth ratios of the craters vary to some extent, and the amount of energy consumed per unit of volume of craters is unequal for the two different loading conditions. Prevalent rock penetration processes are dominated by methods utilizing mechanical attack on rock. It is, therefore, generally accepted that a better comprehension of the mechanism of rock failure under a wedge would prove beneficial towards improving present drilling techniques. Several attempts have been made in recent years to explain how craters are formed under a drill bit, but the mechanism of failure beneath a bit is still improperly understood. 1-11 Most investigators, to date, have inferred the sequence of events occurring during crater formation from analyses of force-time diagrams,1"6 from theoretical considerations,7 or from a study of the configurations of final craters.8-l0 These analyses have led to the presentation of widely divergent models for rock failure beneath a drill bit, ranging from brittle to viscoelastic. The cratering process under dynamic loading commonly is regarded as being similar to that obtained under gradually applied, or 'static', loads. But the effect of rate of loading on the action of a bit is still disputed. Some investigators11-12 maintain that there should be no such effects, whereas others have demonstrated experimentally that these exist.13-17' The purpose of the investigation reported in this paper was to examine petrographically the damage done to rock under the action of a chisel-shaped wedge, both with 'static' and dynamic loading, and to determine if rate-of-loading effects could be detected. Significant quantitative differences in crater volumes and depths were found to exist for a given consumption of energy. On the basis of this data, an attempt was made to indicate some of the rheological properties that a proposed model should possess. All the work reported herein was conducted at atmospheric pressures. EXPERIMENTAL APPARATUS AND PROCEDURE Two types of rocks were employed for most of the experiments reported in this paper, viz. Bedford (Indiana) limestone and Vermont marble. The mechanical properties of these rocks are given in Appendix A. Actually two types of Vermont marble were used, but since no marked difference could be discerned between the two varieties (as seen in Fig. 10) the data was used collectively for the analysis. Stronger rocks were not employed owing to difficulty in generation of observable craters without damage to the equipment. Six-in. diam cores were drilled from the rock samples and embedded in 8-in, diam steel pipe with 3/8-in. wall thickness, using hydrostone to fill the annulus between the core and the pipe. This procedure was adopted to confine the rock specimen so that fractures would not propagate to the edges of the cores. This goal was achieved satisfactorily for these tests because no cracks were observed to extend into the medium surrounding the rock, even when craters were formed only 1 in. from the rock core periphery. Three to four craters were formed on a core face, because the rock damage from any one crater generally did not appear to extend into the others. Whenever, interference between damaged areas around adjacent craters was suspected, the data was rejected for purposes of the analysis. The limestone and marble samples were tested with a 60-degree, wedge-shaped bit, 1 5/8-in. in length, made of tool steel. The bit shank had two SR-4 type electrical resistance strain gages, mounted axially, to record the force-time history during the loading operation. The static indentation tests were conducted using a 50-ton capacity press fitted with an adapter for drill bit attachment. See Fig. 1. The force exerted by the bit at any instant was measured with strain gages affixed to the bit shank. An aluminum cantilever, with two SR-4 strain gages mounted near its clamped end, was employed to measure bit displacement. Both sets of gages were included in Wheatstone bridge circuits,

Jan 1, 1968

By H. J. Ramey

The wellbore acts as a storage tank during drawdown and build-up testing and causes the sand-face flow rate to approach the constant surface flow rate as a function of time. This effect is compounded if non-Darcy flow (turbulent flow) exists near a gas wellbore. Non-Darcy flow can be interpreted as a flow-rate dependent skin effect. A method for determining the non-Darcy flow constant using this concept and the usual skin effect equation is described. Field tests of this method have identified several cases where non-Darcy flow was severe enough that gas wells in a fractured region appeared to be moderately damaged. The combination of wellbore storage and non-Darcy flow can result in erroneous estimates of formation flow capacity for short-time gas well tests. Fortunately, the presence of the wellbore storage eflect permits a new analysis which can provide a reasonable estimate of formation flow capacity and the non-Darcy flow constant from a single short-time test. The basis of the Gladfelter, Tracy and Wilsey correction for wellbore storage in pressure build-up was investigated. Results led to extension of the method to drawdown testing. If non-Darcy flow is not important, the method can be used to correct short-time gas well drawdown or build-up data. A method for estimation of the duration of wellbore storage effects was developed. INTRODUCTION In 1953, van Everdingen and Hurst generalized results published in their previous paper3 concerning wellbore storage effects to include a "skin effect", or a region of altered permeability adjacent to the wellbore. Later, Gladfelter. Tracy and Wilsey4 presented a method for correcting observed oilwell pressure build-up data for wellbore storage in the presence of a skin effect. The method depended upon measuring the change in the fluid storage in the wellbore by measuring the rise in liquid level. To the author's knowledge, application of the Gladfelter, Tracy and Wilsey storage correction to gas-well build-up has not been discussed in the literature. It is, however, a rather obvious application. Gas storage in the wellbore is a conlpressibility effect and can be estimated easily from the measured wellbore pressure as a function of time. Several approaches to the wellbore storage problem have been suggested. As summarized by Matthews, it is possible to minimize annulus storage volume by using a packer, and to obtain a near sand-face shut-in by use of down-hole tubing plug devices. Matthews and Perrine have suggested criteiia for determining the time when storage effects become negligible. In 1962, Swift and Kiel' presented a method for determination of the effect of non-Darcy flow (often called turbulent flow) upon gas-well behavior. This paper provided a theoretical basis for peculiar gas-well behavior described previously by Smith. Recently, Carter, Miller and Riley observed disagreement among flow capacity k,,h data determined from gas-well drawdown tests conducted at different flow rates for short periods of time (less than six hours flowing time). In the original preprint of their paper, Carter et al. proposed that the discrepancy in flow capacity was possibly a result of wellbore storage effects. Results of an analytical study of unloading of the wellbore and non-Darcy flow were recorded by carter.14 In the final text of their paper, Carter et al.!' stated that they no longer believed wellbore storage was the reason for discrepancy in their kgh estimates. In view of the preceding, this study was performed to establish the importance of non-Darcy flow and well-bore storage for gas-well testing. In the course of the study. a reinspection of the previous work by van Everdingen' and Hurst' was made, and the basis for the Gladfelter, Tracy and Wilsey' wellbore storage correction was investigated and extended to flow testing. WELLBORE STORAGE THEORY As has been shown by Aronofsky and Jenkins,11-12 Matthews," and others, flow of gas can often be approximated by an equivalent liquid flow system. The following developnlent will use liquid flow nomenclature to simplify the presentation. Application to gas-well cases will be illustrated later. First, we will use the van Everdingen-HursP treatment of wellbore storage in transient flow to establish (1) the duration of wellbore storage effects, and (2) a method to correct flow data for wellbore storage. DURATION OF WELLHORE STORAGE EFFECTS When an oil well is opened to flow. the bottom-hole pressure drops and causes a resulting drop in the liquid level in the annulus. If V. represents the annular volume in cu ft/ft of depth, and p represents the average density of the fluid in the wellbore, the volume of fluid at reservoir conditions produced from the annulus per unit bottom-hole pressure drop is approximately: res bbl-- (V, cu ft/ft) (144 sqin./sq ft) psi -(5.615 cu ft/bbl)(pIb/cuft) ........(I)

Jan 1, 1966

By G. A. Zeito

Detailed visua1 examination of outcrops was used to ob-tain data on the lateral extent of shale breaks. Thirty vertical exposures belonging to maritie, deltaic and channel depositiorral environrrrents were exatmind, surveyed and photographed. The dimensions of the outcrops ranged from 356- to 8,240-ft long and 25- to 265-ft thick. Shale breaks were found to extend laterally for significant distances. and in some sands terminates by joining other break v much more frequently than by disappearance. Consequently with regard to flaw, a gross sand consisted of both continuous and discontinuous subunits. The degree of continuity of shale breaks as well as the occurrence and spatial distribution of discontinuities were different for the three depositional environments. Statistical eva1uations were performed to determine the confidence level with which estimates derived from outcrops can be applied to reservoir sands. Results of these evaluations revealed that: (I) the lateral continuity of shale breaks in marine. sands is si~nificatit, and the estimates of lateral extent can he applied to reservoir sands with a high degree of confidence (80 to 99 per cent of the shale breaks continued more than 500 ft, with a confidence of 86 per cent); and (2) the tendency for adjacent shale breaks to converge upon each other over small distances in deltaic and channel sands is highly significant (62 to 70 per cent of the shale breaks converged in less than 250 ft, with a confidence of 50 per cent), hut the probable magnitude of the resulting sand discontinuities cannot yet he predicted with adequate confidence. INTRODUCTION Almost all of the efforts devoted to characterization of the variable nature of reservoir sands have been focussed on permeability variations. Among the widely used concepts that have emerged from these efforts are those of stratified permeabilities, random permeabilities, and communicating and noncommunicating layers of different permeabilities. This study is concerned with the presence of interbedded shales and silt laminations. These features are impermeable or only slightly permeable to flow. Therefore, knowledge of the extent to which they continue laterally and the manner in which they terminate within the bodies of gross sands is important for proper description of reservoir flow. Initial field observations made on outcrops revealed that shale breaks and the relatively thinner silt laminae have impressive lateral continuity. They appeared to divide sand sections into separate individual sand layers. Although most of the layers were continuous across the total lengths of the outcrops, some were discontinuous because the- bounding shale breaks converged. Furthermore, the discontinuous layers appeared more prevalent in channel and deltaic sands than in marine sands. Based on these initial findings, a detailed investigation was carried out to determine, quantitatively: (1) the degree of continuity of shale breaks in marine. deltaic and channel sands; and (2) the frequency and spatial distribution of discontinuities in the three environments. PROCEDURE The procedure used to obtain field data from outcrops included visual examination, surveying and photographing each outcrop. The photographs were examined carefully and important outcrop features were traced, measured and recorded. The selection of outcrops for this study was made on the basis that each outcrop should be exposed clearly to permit detailed visual examination of vertical lithology. and it should also be sufficiently long (over 200 ft) to provide useful data on the lateral continuity of lithology. Identification of the depositional environment for each outcrop was made on the basis of bedding characteristics, vertical sequence of lithology and the presence of indicative sedimentary features. Whenever possible, hand specimens of associated shales were collected to determine depositional origin. Almost one-half of the outcrops used in this study required environmental identification; the remainder had already been identified by previous investigators. Several photographs of each outcrop were usually required to cover the entire length of the outcrop. These photographs were taken from one station or several, depending on the terrain, size of the outcrop and distance to the outcrop. A Hasselblad camera, with a standard 80-mm lens and a 250-mm telephoto lens, was used. The telephoto lens permitted photographing outcrops as far as two miles away. Slow-speed films were used. either Panatomic-X or Plus-X. The final operation conducted in the field was that of surveying the outcrops. The distance of an outcrop from a point of observation was determined by a triangulation method using the plane table. The measured distance was then combined with the angle of view of the camera lens to establish a scale to be used on the photographs. Films were processed using standard processing techniques and 4.5X enlargements made. The enlargements of each outcrop were butted together to form a single panorama. Slides were also prepared on several outcrops; these were used whenever greater magnification (wall projection) was required to bring out maximum lithologic detail. The shale breaks and bedding planes in each outcrop were traced on transparent acetate film superimposed on

Jan 1, 1966

By P. G. Shewmon, H. E. Collins

A study has been made to determine the sites at which sulfur adsorption occurs on copper surfaces. measurements were made of the relative torques, Ys, at the intersection of twin boundaries with surfaces near the three low-index orientations, i.e., (100), @lo), and 011), over a range of H2S/H2 ratios. HZS concerztvations j'ro~n 3 to 1500pp)n between 830" and 1050°C were used. It is concluded that sulfur adsorption occurved preferentially though not exclusively at edge sites near the (100) and (110) surfaces in the HzS range — 700 Ppm giving rise to negative torques near these orientations. Beyond this HzS range, adsorption occurred at all sites. Near the (111) surface, 7/y little with HzS concentration up to approxiwzately 75pptn. Above this range, the results indicate adsorption is occurring OH both terrace and edge sites. SCIENTIFIC interest in surfaces and their interactions with a gaseous environment dates back to the beginning of the 19th century. The scientific luminaries of that period—Faraday, Maxwell, Rayleigh, Dewar, and Gibbs—were already concerned about such processes. However, it has only been within the past several decades that adsorption on metal surfaces has been actively studied. This increased interest in adsorption has been brought about by the advent of new and improved experimental techniques and apparatus, e.g., ultrahigh vacuum, and field-emission and ion microscopes. However, most of the work done using these techniques has been carried out at low temperatures. When adsorption studies have been made at either low or high temperatures, they usually gave no indication of the particular surface orientations or type of sites on which adsorption was occurring. In the last few years, there have been a series of studies in which the surface tension, y,, and/or its derivative with respect to orientation, 7, have been studied as a function of orientation and atmosphere.'-7 Nearly all of the work on the relative torque,* ~/y, silver annealed in hydrogen and air.6 Recently Winterbottom and Gjostein" have used a modified and more accurate Mykurian method to determine the y plot of gold in hydrogen The only work in which T/~, has been measured over a range of chemical potentials for a given solute, p2, is that of Robertson and shewmon7 on the Cu-0 system. They measured T/Y, vs Po, (10"" to 10- l3 atm) at 1000°C in various mixtures of Hz0 and HZ. From this work they estimated the value of p2 at which one half of the surface sites are occupied with oxygen, pg, as being in the range 10- l6 to 10- l5 atm of oxygen. They also found that increasing Pa increased the magnitude of ~/y, near the (111) and (100) orientations. This indicates that oxygen is not adsorbed preferentially at step edges, but uniformly over all surface sites. In addition, they did one experiment on sulfur adsorption on copper surfaces, which indicated that sulfur adsorption decreases ~/y, near the (100) orientation, while not affecting ~/y, near the (111). This could be interpreted as indicating that sulfur adsorbs preferentially at step edges near the (100). In this paper the primary objective of the work has been to carry out a study of sulfur adsorption on copper surfaces over a range of temperatures and p,. In conjunction with this work, thermal grooving at grain boundaries has been examined as a method of determining the effect of sulfur adsorption on y,. METHODS Ideally, one would like to have information on the quantity of solute adsorbed on a surface and the types of sites at which it is absorbed as a function of p2. The total quantity adsorbed or the surface excess is given by the thermodynamic equation Thus data on the variation of y, with pz indicates the value of p2 at which adsorption becomes appreciable and the quantity adsorbed. The type of adsorption site is more difficult to deduce but information on this can be obtained from the variation of rz with 8, the angular deviation of the surface orientation. This is obtained from the thermodynamic equationlg Data on t and ys as functions of p2 have been obtained by the following methods. 1) Twin Boundary Grooving—By determining the effect of adsorption on the torque, 7, where T is the variation of surface energy, y,, with orientation, it is possible to obtain some indication as to the preferred sites of adsorption. Experimentally, the torque value measured is the relative torque, 7/ys The twin boundary grooving technique suggested by Mykura'' was used in this study to determine near the three low-index orientations— (loo), (110), and (111). Mykura's equation relates 7 /yS to measurements of the di-

Jan 1, 1967

By L. W. Holm

Laboratory flooding experiments on linear flow systerns indicated that high oil displacement, approaching that obtained from completely miscible solvents, can be attained by injecting a small slug of carbon dioxide into a reservoir and driving it with plain or carbonated water. Data are presented in this paper which show the results of laboratory work designed to evaluate this oil recovery process, particularly at reservoir temperatures above 100°F and in the pressure range of 600 to 2,600 psi. Under these conditions CO2 exists as a dense single-phase fluid. It was found that a bank, rich in light hydrocarbons, was formed at the leading edge of the CO? slug during floods on long cores. Formation of this bank is probably due to a selective extraction by the C02 and, it is believed, partially accounts for the attractively high oil recoveries. In crddition to the efficient displacernerlt of oil from the pores of the rock by this process, the favorable rnobility ratio related to a C0 2-water flood also contributes to high oil recovery. A further advantage of this process is noted on limestone and dolomite rock, in that the CO1 reacts with the porous medium increasing its permeability. Flooding experiments were conducted on sandstone and vugular dolomite models. The results of this experimental work show the effect on oil recovery of type of porous medium, pore geometry, flooding length, and flooding pressure. The porosity of the cores and rilodels varied from 16 to 21 per cent and their pern~eabilities ranged from 100 to 200 md. A reconstituted West Texas reservoir oil, a West Texas stock tank oil, an East Texas stock tank oil and Soltrol were used to represent reservoir oils in this study. Oil recoveries ranging from 60 to 80 per cent of the original oil in place in these cores were obtained by CO2,-carbonated water floods at pressures between 900 and 1,800 psi, compared with conventional solution gas drive and water-flood recoveries of 30 to 45 per cent on the same cores. Oil recoveries greater than 80 per cent resulted frorn f1oods at pressures above about 1.800 psi. There high recoveries were noted from both the sandstone and the irregular Porosity carbonate cores. In all floods, additional oil was recovered by a solutiorr gas drive resulting from blowdown following the flood. Oil recoveries of 6 to 15 per cent of the original oil in place were obtained during this blowdown period. This additional recovery was found to be a function of oil remaining after the flood, decreasing with decreasing oil saturation. It was also noted that highest oil recoveries by blowdown were obtained when carborlated water rather than plain water followed the CO, slug. INTRODUCTION Miscible phase or solvent flooding processes, which are designed to increase oil recovery -from petroleum reservoirs, involve the injection of small quantities of a petroleum solvent into the reservoir, followed by an inexpensive scavenging fluid which is miscible with the solvent. Essentially complete displacement of oil from the pores of reservoir rock has been obtained by this technique. CO,, although not completely miscible with most reservoir oils at moderate pressures, is highly soluble in these oils at pressures above about 700 psi; there is appreciable swelling and reduction in the viscosity of oil when CO, is dissolved in it. Therefore, CO, could be expected to perform similarly to other oil solvents as a displacing agent. CO, is also highly soluble in water at elevated pressures, so water should be a satisfactory material to drive a slug of CO, through an oil-bearing reservoir. A favorable mobility ratio would be obtained through the reduction in viscosity of the oil and the use of water as a final displacing agent. A number of investigations of the use of CO, to improve oil recovery have been reported in the literature.2,3,4,5,6 These studies, however, have been conducted on uniform porosity sandstone at relatively low temperatures and pressures. The behavior of CO1 as a flooding agent at temperatures above its critical temperature could not be predicted adequately from these studies, particularly for the case of non-homogeneous rock. The purpose of this work was to evaluate the oil recovery efficiency of a process involving the injection of a CO2 slug followed by carbonated water, at reservoir temperatures above 100°F and in the pressure range of 600 to 2,600 psi, and to compare this process with conventional water flooding. The investigations were primarily designed to provide information on the efficiency of the process in irregular porosity carbonate rock. The effects of flooding path length, the presence of free gas, the type of oil to be recovered, and the amount of solvent required were also determined. The essential results of static phase behavior studies and experimen-

By William C. Sleppy

The nmgnetic susceptibility of heat-treatable aluminuin alloys is sensitive to chanyes such as solution or dissolution of solute and the precipitation of mew phases. By measuring the change in the magnetic susceptibility of aluminum alloys caused by various heat treatments, an empirical relation was found from which atomic arrangements in dilute binary alloys of copper, zinc, and magnesiutn in aluminum have been delineated. The relation predicts the ultimate formation of C1LA12 when copper is precipitated from solid solution in aluminum. Euidexce joy silovt- range order is found for copper in solid solution in aluminum in the sense that copper atoms avoid being nearest neighbors to an extent greater than would result from a purely random arrangertzeizt. Hume-Rothery has predicted such short-range order joy solid solution of copper in aluminum The Al-Zn system agrees with evidence obtained from X-ray scattering at small angles and predicts a tendency for zinc atoms to cluster in solid solution in aluminum. In the Al-mg system, the empirical relation indicates an approach to randor distribution of magnesium in solid solution in aluminum with a tendency for magnesium segvegation which increases with incveasing temperature. ThE magnetic properties of metals are complicated by the fact that contributions are made to them both by electrons of a "metallic" type which belong to the crystal as a whole, and by electrons in states localized on particular atoms. An expression1'2 for the bulk magnetic susceptibility of aluminum may be written as the sum of three contributions: where XA1 is the bulk susceptibility of aluminum per gram of material (in the cgs system, the units are those of reciprocal density); Xa1+3 is the diamagnetic contribution of the electrons localized in ion cores; Xa1 is. the paramagnetic spin contribution of conduction electrons often called Pauli paramag-netism: Xa1 is the diamagnetic contribution of the conduction electrons often called Landau diamag-netism. Ion core diamagnetism arises from the precession of the electron orbits which occurs when a magnetic field is applied to a system of electrons moving about a nucleus. Its contribution to the magnetic suscepti- bility is small, temperature-independent, and unaffected by alloying. The conduction electron diamagnetism is also temperature-independent and arises from the translatory motion of the electrons. For perfectly free electrons this contribution should be exactly one-third of the Pauli spin paramagnetism, but this relation is seldom even approximately true. Blythe2 determined the conduction electron diamagnetism in pure aluminum and found it to be extremely small. Any change in the conduction electron diamagnetism caused by alloying is neglected in this work. The Pauli paramagnetic contribution3 to the magnetic susceptibility of aluminum depends upon the number of electrons that occupy excited states and whose spins can be turned parallel to an applied magnetic field. The number of electrons free to turn in the field is proportional to the temperature and each spin contribution to the susceptibility is inversely proportional to the temperature. A slight temperature dependence of Pauli paramagnetism occurs when the number of electrons occupying excited states cannot increase sufficiently to balance the inverse dependence on temperature of each spin contribution. The decrease of the magnetic susceptibility of aluminum with increasing temperature is attributed to a temperature dependence of the Pauli paramagnetism. Estimates of the Pauli paramagnetism of aluminum have been made by several workers.2,4,5 All of the values are in reasonably good agreement with each other. In this work Xal at 17°C is taken as 0.761 X 10-8 cu cm per g. An expression similar to [I] can be written for the magnetic susceptibility of an aluminum base alloy containing a fractional weight percent x of solute:' Xa = (1 -x)XAl+3 +xXsoluteion * XaPauli +Xadia) [2] where X, is the magnetic susceptibility per gram of alloy, Xal'3and Xsolute ion are the ion core diamag-netic contributions, and xpauli and xdia are the Pauli and diamagnetic contributions of conduction electrons in the alloy. If the components of a mixture are not alloyed but simply mixed together in their pure states without producing a new phase, then the magnetic susceptibility of the mixture is given by the Wiedemann additivity law: Xm =x1X1 +x2x2 + ..xnxp [3] where X, is the susceptibility per gram of mixture and xnXp are the weight fractions and susceptibilities, respectively,-. for the pure components. The additivity law is not applicable to alloys because the outer electronic structures of the components are changed by alloying.' Both the Pauli paramagnetism and Landau diamagnetism are affected; hence the magnetic susceptibilitv of an alloy is usually different from that calculated using the additivity law. In this work the difference, X, -X,, is taken as a measure of the change caused by alloying.

Jan 1, 1968

By J. W. Snavely

THE high tension belt conveyor is introducing a new and tremendously expanded era of low cost bulk material handling. High tension belt conveyors are generally those installations involving very long centers, high lifts, or drops, in which the belts are stressed up to their maximum tension values, and further, where the belt construction provides tension capacity far beyond what is possible with conventional belt constructions. With these high tension installations, the magnitude of the forces involved demands careful refinement of accepted design practice in order to achieve optimum balance of all factors. No attempt will be made to evaluate the relative merits of belt conveyor haulage with other means of transportation. For present purposes, it is assumed this has already been done in favor of belt conveyor. Neither will any attempt be made to evaluate the various conveyor belt constructions now available or to balance the advantages of various types of mechanical equipment. It is also assumed that the basic haulage information on which the conveyor design is based is accurate and complete. A sustained maximum, uniform load on the belt at all times must be achieved through proper feed control and the use of adequate surge storage to level the peaks and valleys of any varying demand for the material being handled. General Belt Capacity Considerations The belt conveyor capacity tables published by various belting and conveyor equipment manufacturers vary to a considerable degree, and the ratings given are quite conservative. Of necessity, these published ratings are based on the handling of average materials under average conditions. In applying a high tension belt, all possible capacity from the belt must be obtained in order to hold its width to a minimum and thereby limit the initial cost. Two factors are involved, loading to maximum cross section area and traveling at a maximum practical speed. Belt Loading: Proper treatment of the loading of the belt will result in maximum cross section to the load, and published capacity ratings can be exceeded, sometimes by appreciable margins. On the 10-mile conveyor haul used in the construction of Shasta Dam, California, although the rated capacity of the belt line was 1100 tons per hr, at times the system handled peak loads of 1400 tons per hr, almost 25 pct better than the rated capacity. One of the large coal companies has been able to exceed rated capacity by as much as 50 pct. Loading conditions which must be controlled are: 1. Large lumps must be scalped off and rejected or the load must be primary crushed before being placed on the belt. 2. The material weight per cubic foot must be accurate, must be known for all the materials being handled, and must be known for the complete range of conditions of the individual material being handled. Long centers and high lifts magnify small differences into serious proportions. 3. Uniform feeding to the belt is most important. Various types of feeders are available, which can be used to place a constant predetermined volume of material on the belt, or, where an appreciable range of material weight exists, through electrical control actuated by current demand, to place a predetermined uniform tonnage on the belt. One long slope belt in a coal mine in Pennsylvania is being fed at three separate stations with the controls so arranged that whenever the maximum load is going onto the belt from the first station, the other two stations automatically cut out. Whenever the load from the first station drops back, the other two stations again automatically cut in. 4. Careful design of the chutes and skirts is necessary to get the load centered on the belt with a minimum of free margin along each edge. Some free margin at the edge of the belt is necessary to prevent spillage, but if the load can be kept accurately centered, this free margin area can be reduced, and more material can be carried on the belt. What can be accomplished in this respect will vary widely, depending on the nature of the material being hauled. The chute and skirt design must also protect the belt. 5. The design of chutes and skirts should also get the load traveling in the same direction and close to belt speed, so that the load comes to rest on the belt as quickly as possible. The design of the chutes and skirts is worthy of careful study, and after a system is put into operation it should be experimented with to get the best results. Belt Speed: High belt speeds should be used in high tension work. Obviously, high belt speeds enable haulage on a narrower belt, reducing initial cost. The major portion of belt wear takes place at the loading point and around the terminal pulleys. The

Jan 1, 1952

By J. D. Defilippi, E. M. Gilbert, K. G. Brickner

FCC chromium-manganese-nitrogen (Cr-Mn-N) steels differ from most other fcc materials in that these steels undergo a ductile-to-brittle transition. Transformation to martensite is considered to be responsible for this behavior in some metastable Cr-Mn-N steels. However, very stable Cr-Mn-N steels also exhibit a ductile-to-brittle transition. The results of this study indicate that deformation faulting is the probable cause of the brittle behavior of stable Cr-Mn-N steels. Deformation faulting accounts for the ductile behavior of these steels in a tension test at -320°F and brittle behavior in an impact test at -320°F. Deformation faulting also accounts for the toPological features observed on the fracture surfaces of impact specimens of these steels. FACE- centered- cubic chromium-manganese-nitrogen (Cr-Mn-N) steels differ from most other fcc materials in that these steels undergo a ductile-to-brittle transition. Many Cr-Mn-N steels transform to martensite during deformation,l-5 and several investigatorsl-3 have suggested that the brittle behavior of these steels is caused by martensite formation. However, very stable Cr-Mn-N steels also exhibit brittle behavior. Schaller and Zackeyl reported that a very stable Cr-Mn-N steel (less than 3 pct martensite formed at -320°F) exhibited a transition temperature higher than that for steels in which large volume fractions of martensite formed during testing. The explanation given by Schaller and Zackey for this observation was that in the very stable steel the martensite, because of its higher interstitial content, was more brittle than that formed in their other steels. This explanation was questioned by Tisinai and samans4 and Baldwin.6 Moreover, because the toughness of stainless martensite at cryogenic temperatures is generally very low, this explanation does not account for Thompson's7 observation that small additions of nickel (1 to 3 pct) greatly improve the toughness of high nitrogen (0.35 pct) Cr-Mn-N steels. The present paper summarizes the results of an investigation of the low-temperature brittleness in very stable Cr-Mn-N steels. The importance of the mode of deformation on the toughness of these steels is discussed. Table I. Compositions of the Steels Invertigated, Pet Steel C Mn P S Si Ni Cr N - A 0.09 14.70 0.018 0.011 0.47 0.22 18.40 0.54 B 0.12 14.90 0.001 0.008 0.48 0.14 17.80 0.38 C 0.12 14.95 0.004 0.005 0.62 3.95 18.43 0.38 MATERIALS AND EXPERIMENTAL WORK The compositions of the steels investigated are shown in Table I. Steels A and B had compositions within the limits of a proprietary Cr-Mn-N stainless steel,* whereas Steel C was similar in composition to the proprietary steel except for its 3.95 pct Ni content. All steels were hot-rolled to 1/2-in. thick plate. The plates were subsequently annealed for 1 hr at 2000°F and water-quenched. Standard longitudinal and transverse Charpy V-notch impact specimens were machined from the annealed plates. Duplicate longitudinal and transverse impact specimens were tested at 212", 80°, 32", 0°, -100°,-160°,-200°,-256", and -320°F. Longitudinal tension-test specimens were also machined from the plates and tested at a crosshead speed of 0.05 in. per min at the aforementioned temperatures. The fractured impact and tension-test specimens of all three steels were examined to determine whether martensite had formed during testing. Magnetic, X-ray, electron-diffraction, and electron-microscopy techniques were used to detect the presence of martensite in the highly deformed areas of these specimens. Metallographic examination of highly deformed areas of impact and tension-test specimens revealed the presence of dark-etching bands, such as those shown in Fig. 1. These bands were observed only in deformed samples and were thought to be associated with the low-temperature brittleness of the Cr-Mn-N steels. Accordingly, a sample 1 in. wide by 3 in. long was cut from the 1/2-in.-thick plate of Steel C. This sample was surface-ground to a in. and then cold-rolled 60 pct at -320°F. Thin foils were prepared from the cold-rolled sample and examined in a JEM electron microscope. Brightfield, dark-field, and selected-area diffraction techniques were used to determine the cause of the dark-etching bands. Fractographic experiments were also performed. Impact specimens Of Steels A, B, and C were broken at -320oF, and the fracture surfaces of these specimens were immediately shadowed with carbon. The carbon replicas were examined in a Siemens electron microscope, and attempts were made to correlate the topological features of the fracture surfaces with the deformation mechanisms that could be occurring during an impact test of these steels.

Jan 1, 1970

By C. E. Tsoutrelis

A new method for determining rock drillability in diamond drilling is discussed; the method takes into consideration both penetration rate and bit wear. The method is based on drilling a rock specimen under controlled laboratory conditions using a model bit. The technique used for determining the experimental variables is extremely simple, quick, and reliable. Drillability is then determined by the mathematics of drilling. In considering the different factors that affect diamond drilling performance, the nature of the rock to be drilled is of outmost importance since it affects significantly the drilling costs and such other variables as bit type and design, drilling thrust, and bit rotary speed. Many attempts have been made to study this effect by correlating actual drilling performances either to certain physical properties of the rock being drilled1-? or to test drilling data obtained under laboratory conditions.7-13 These attempts were aimed at providing a reliable method of predicting by simple means the expected rock behavior in actual drilling, thus giving the engineer a tool to use in estimating drilling performances and costs in different types of rock. The purpose of this paper is to describe such a method by which rock drillability (a term used in the technical literature to describe rock behavior in drilling) could be determined in diamond drilling. It is believed that the proposed simple and reliable method will cover the need of the mining industry for a workable method of measuring the drillability of rocks. It should be emphasized, however, that since drill-ability depends on the physical properties of rock and each drilling process (diamond, percussive, rotary) is affected by different or partly different rock properties,14-l6 the proposed method of determining rock drillability cannot be extended to the other drilling processes. The results presented in this paper form part of an extensive three-year research program carried out by the author in the laboratories of the Greek Institute of Geology and Subsurface Research. During this period the effects of the physical properties of rocks and of such operational variables as drilling thrust and bit rotary speed in diamond drilling were investigated in detail. DRILLABILITY CONCEPT The literature is not devoid of drillability studies. While there are a number of investigators1,3,5-7,9-0,12-13,17 who have attempted to establish by direct methods (i.e., drilling tests under laboratory conditions) or indirect (i.e., through a physical property of rock) an index from which the drilling performance in a given rock may be estimated, very few6-7,9,12, of the proposed methods seem to be of much practical value to the diamond drilling engineer and none to date has been universally accepted. Commenting on the proposed methods for assessing rock drillability, Fish14 remarks that "for a measure of drillability to be accepted it is essential that penetration rate at a given thrust and bit life are elucidated as otherwise the method is of little value." This statement should be examined in more detail by making use of the penetration rate-drilling time diagram obtained in drilling a rock under constant operational conditions. Furthermore, the merits of using this diagram to describe rock drillability will be pointed out. At the same time reference will be made to this diagram when discussing some previously proposed methods. Fig. 1 illustrates such a diagram for three rocks,A, B, and C, which have been diamond drilled under identical conditions. It is assumed here that rocks A and B have the same initial penetration rate, i.e., VOA = Vog, but since rock B is more abrasive than A, rapid bit wear occurs and as a result the fall of its penetration rate with respect to time is more vigorous than in rock A. This is shown graphically by a steeper V = f(t) (0 curve in this rock than in rock A. Rock C has a lower initial penetration rate, due to higher strength properties16 but since it is not very abrasive, only a slight fall of its penetration rate occurs during drilling (in this category are some limestone and marbles with compressive strength above 1000 kg per sq cm). It follows from the foregoing considerations that the characteristic for each rock curve (I) is a function of (i), the penetration rate of the rock Vo recorded at the instant of commencing drilling, which determines the starting point of the curve (1) on the y-axis and (ii), the abrasive rock properties which determine the rate of fall of Vo with respect to time. Thus, curve (I) provides an actual picture of the rock behavior in drilling for given operational conditions, and it can be used with complete satisfaction to assess rock drillability. It can be seen clearly from Fig. I that proposed methods for assessing rock drillability by measuring the

Jan 1, 1970

By Jerome J. English, Gordon W. Powell

An experimental investigation and mathematical analysis of the thermal-dilation behavior of the titanium alloy Ti-7Al-3Cb have shown that the linear dimensional changes associated with the polymorphic transformation need not be isotropic. The absolute magnitude of the linear dimensional change, which may be either positiue or negative, associated with the cr-p transformation is dependent upon the relutzve volumes of different orientations of the transformation product. It is hypothesized that the dilation irregulati-ties that have been observed during the polymorphic transformation of pure, coarse-grained titanium and other titanium-base alloys can be explained in the same manner. When titanium is heated above about 165O°F, the hcp a structure transforms to bcc 0. Thermal-dilatioh measurements have shown that the transformation is accompanied by a decrease in length of 0.16 pct.' Such dilation behavior would be expected because the volume of the hcp unit cell is about 0.3 to 0.4 pct greater than that of the bcc unit cell. A recent investigation2 of the thermal-dilation behavior of an experimental a-p* titanium alloy, Ti- 7A1-3Cb, containing 0.06 wt pct 0 showed that its dilation behavior during the polymorphic transformation differed substantially from that reported for unalloyed titanium. The first time the alloy was cycled through the transformation, the dilation curve closely duplicated that of unalloyed titanium. However, upon repeated cycling through the transformation temperature range, both the magnitude and the sign of the dimensional change associated with the transformation were observed to vary with each cycle. This investigation was undertaken to obtain additional data on the dimensional changes associated with the polymorphic transformation in the Ti-7A1-3Cb alloy and to determine the cause of the dimensional irregularities. After testing, the specimens were examined metallo-graphically. In addition, Laue back-reflection patterns were obtained from selected sections taken perpendicular to the specimen axes to determine the a orientations present in these sections. White radiation from a tungsten target and a 0.1-mm-diam collimator were used to produce the diffraction patterns. RESULTS Dilation Curves. Three types of thermal-dilation curves were obtained when the a-8 titanium alloy was heated and cooled through the transformation temperature range. These three types of curves are illustrated in Fig. 1. The type I curve represents what is considered normal behavior, because the dilation change is what would be expected on the basis of the volumes of the unit cells of a and p. The Type I1 curve is the inverse of Type I. Normal behavior is characterized by an expansion on cooling through the transformation, whereas a contraction takes place in the Type 11 curve. With Type ni behavior, no clearly distinguishable length change occurs during the transformation. No other anomalies that might be indicative of other phase transformations were observed in the dilation curves at lower temperatures. Apparently, the cooling rate was low enough for equilibrium to be reached during the 0 to a transformation. Table I lists the types of dilation curves observed during the polymorphic transformation as a function of the direction of measurement and cycle number. The A1 value was determined by extrapolating the low-temperature (a + 5 pct p) and high-temperature (100 pct p) segments of the dilation curves to a common temperature and measuring the difference in the or-dinates at that temperature, see Fig. 1. The transformation occurs over a temperature range in this alloy, so the magnitude of A1 is not an absolute value but depends on the choice of temperature. A mean temperature, T,, within the transformation temperature range was selected for the measurement. T, on cooling occurred about 100°C lower than T, on heating. The first time each of the three dilation specimens was heated to above the temperature, that is, Cycle 2, normal Type I behavior was observed. In Cycle 3, two deviations from normal behavior occurred. First, during cooling of the longitudinal specimen, a substantially larger expansion, +0.21 pct, was measured as 0 transformed to a compared with +0.03 pct in Cycle 2. Second, the thickness specimen was observed to undergo a contraction instead of the anticipated expansion on cooling. Continued cycling of the three specimens from room temperature to 2500°F produced additional changes in the dilation behavior. These changes did not seem to be related to the fabrication direction of the alloy because the values of a1 for the longitudinal, transverse, and thickness specimens varied unpredictably in magnitude and sign. Furthermore, both the longitudinal and transverse specimens showed all three types of dilation curves at least once during the six cycles that they received. Fig. 2 is a sketch of the transverse specimen after

Jan 1, 1967

By R. H. Richman, F. Borik

A 0.3 pct C-12 pct Cr-6 pct Ni steel was rolled to 93 pct reduclion in area as austenite at 510°C, and then partially transformed as desired to ~rlartensite by qnenching to - 196°C. Pole figures for the austenitic matrix and for the martensitic product were separately determined by an X-ray transmission method. The deforitration texture of' the warm-worked austenite is characlerized by (110)(225) components, and is thus closely similar to those produced in a brasses. The pole jigure of the martensite in partially transformed material agrees well with that which can be constructed by transfortnation of the {110)(225) orientations according to either the Kuvdjuniov- Sacks or the Nishi-yatuu relatiotship. Howeuer, an important result of this construction is that me-third of the predicted orientations are missing. A graphical analysis can then be used to show that in deformed austenite certain crystallographic variants of martensite (related to the most probable austenite slip systems) are suppressed, resulting in this preferred transformation. The evidence for preferred transformation is corroborated by the measured elastic anisotropy of warm-rolled and fully transformed H-11 steel. EXTENSIVE plastic deformation of a polycrystal-line aggregate in a manner that causes flow predominantly in one direction results in a preferred orientation of the constituent crystallites. The particular orientations that are produced depend upon the crystal structure and composition of the material, as well as upon the temperature, mode, and degree of deformation; in any case, the preferred crystallo-graphic orientations, or textures, are reflected in directionality of mechanical properties. Although such anisotropy may be exploited in certain specialized applications, it is more commonly diminished or eliminated by heat treatment lest it interfere undesirably in subsequent forming operations or in structural design. In the recently developed thermomechanical treatments that significantly enhance the strength of some steels,1,2 considerable deformation of the metastable austenite prior to the martensite transformation is essential to the strengthening process. If the austenite is textured by the deformation, and if the transformation to martensite proceeds according to one of the relationships established for transformation in annealed austenite, then it must be expected that the martensite will also possess a preferred orientation even though the multiplicity of martensite orientations possible in a given austen- ite crystal will tend to restore some degree of randomness. The existence of a residual anisotropy, both mechanical 3-6 and crystallographic,' has been substantiated. In the latter crystallographic investigation, preferred orientations were determined for the martensitic structure of an SAE 4340 steel rolled 72 pct as austenite at 833°C and then quenched. However, the choice of a composition that transformed almost completely to martensite during the quench to room temperature did not permit direct measurement of the prior austenitic texture. In fact, when the "ideal orientations'' associated with well-known fcc rolling textures were converted, alone or in combination, to martensite according to the Kur-djumov-Sachs (K-s)' or Nishiyama8 relations, the agreement obtained with the observed martensite texture was only fair at best. Recently a pertinent aspect of the austenite to martensite transformation was reported by Bokros and parker,10 who found that certain habit-plane variants of martensite were suppressed by tensile deformation of Fe-31.7 Ni single crystals prior to the necessary subzero cooling. It might be anticipated that the consequences of such preferred transformation are sustained during the formation of martensite in warm-worked austenite that has a well-developed deformation texture. The present investigation was undertaken first to establish more firmly the relation between preferred orientations in plastically deformed austenite and in the resulting martensite, and second to examine the textures for evidence of deformation-induced preferred transformation. EXPERIMENTAL PROCEDURES An alloy containing 0.3 pct C, 12 pct Cr, 6 pct Ni, and the balance iron, was selected because the mar-tensite-start temperature (M,) of about -100°C allowed convenient experimental manipulation of either austenite or martensite at room temperature. Furthermore, this composition can be readily deformed as metastable austenite at moderately elevated temperatures without intervention of appreciable isothermal or athermal decomposition products. The alloy was austenitized at 1150°C, aircooled to 510°C, rolled unidirectionally at this temperature to 93 pct reduction of cross-sectional area, and finally oil-quenched to room temperature. Partial transformation to martensite was accomplished by quenching to -196°C as needed. The rolled stock was reduced in thickness from 0.067 to 0.010 in. by etching in a solution of 5 pct HC1, 45 pct HNO3, and 50 pct water, and further thinned by careful mechanical polishing to maintain the two sides of the sheet parallel within 0.0003 in. After mechanical polishing to 0.005 in., electropolishing in 1:9 perchloric-acetic acid solution produced a final thickness of 0.002 in. The preferred orientations were determined from

Jan 1, 1968

By Eugene F. Broome, Hugh A. Walls

A diffusion measurement technique based on a shear cell comprised of only two segments is described. The diffusion boundary value problem for the finite capillary geometry is solved in general for any arbitrary initial concentration profile and is subsequently specialized for the modified shear cell problem. Effects of convection and mixing at the shear interface were found to be negligible. Mercury self-diffusion coefficients were determined from -25° to 252°C. These data are in good agreement with those found by Meyer. ALTHOUGH diffusion in liquid metals has been of interest for over two centuries, the need for measurement techniques of improved accuracy and precision has become increasingly apparent as additional data have been obtained and theory has become more refined. These conditions reflect the experimental difficulties inherent in liquid diffusion measurements, in which transport by other processes, such as convection, tends to mask the diffusive transport. Frequently the disagreement between several theoretical predictions is less than that found between different sets of data obtained for a system. Moreover, as has been shown by Nachtrieb,1 diffusion data are needed over much larger temperature ranges if the functional dependence on temperature is to be known. Thus, improved techniques must be devised if experimental data are to augment fundamental understanding of the liquid state and to meet technological needs. The available techniques have been discussed elsewhere.' Of these, only the capillary-reservoir, long capillary, and shear cell techniques will be discussed briefly in terms of experimental advantages and disadvantages. These methods served to establish design criteria for the modified shear cell described here. The capillary-reservoir technique of Anderson and saddington3 has been the most widely used method in recent years. The method offers experimental simplicity relative to other methods and has been employed for high-temperature measurements. Moreover, the mathematical relationship between the measured concentration ratio and the diffusion coefficient is such that smaller values of the ratio are achieved for a specified diffusion time relative to other methods. The amplified errors between the concentration ratio and the calculated diffusion coefficient are diminished at lower values of the ratio.' The method also permits multiple determination by the simultaneous use of several capillaries. Disadvantages of the capillary-reservoir method are primarily associated with the hydrodynamic ef- fects of convection and of placing the capillary in the reservoir. These effects are most pronounced in the region near the open end of the capillary and produce an ill-defined boundary condition between the capillary and the reservoir. Such effects are not amenable to experimental or mathematical correction2 (although this has been suggested4). The long-capillary method of Careri, Paoletti, et al.5-10 involves filling one half of a small capillary tube of 150 to 200 mm total length with material of one composition or radioactivity and the other half with the second part of the diffusion couple. This arrangement eliminates the adverse hydrodynamic effects associated with the capillary-reservoir technique; however, certain other experimental difficulties are encountered in this method. The more significant of these difficulties involve the melting, expansion, contraction, and solidification of the diffusion system. The dependence in some cases of the diffusion coefficient on the capillary diameter noted by Careri et a1.7 (termed the "wall effect") has been alternatively explained by Nachtriebl as a convection effect during solidification. In mutual diffusion measurements, the convection problems associated with melting and solidification are increased because of the differences in melting points and in expansion coefficients between the halves of the diffusion couple. However, the errors caused by convection effects within this method are usually less than those in the capillary-reservoir method. Furthermore, the concentration profile needed to determine concentration-dependent diffusion coefficients by the Boltzmann-Matano analysis can be obtained from this method. Of the previous attempts to use shear cells, only the cell used by Nachtrieb and Petit11,12 appears to have yielded good data. They reduced the mechanical complexity of the conventional shear cell by using a cell comprised of only four segments. Three of these segments were filled with ordinary mercury and the fourth with radioisotopic mercury in their determination of mercury self-diffusion coefficients. The average concentration (radioactivity) was determined in each segment following a period of isothermal diffusion. These concentration values were fitted to concentration profiles obtained from the Stefan-Kawalki tables, and the diffusion coefficients were evaluated. Thus, although the number of cell segments is reduced in their method, some information about the concentration profile can be obtained in terms of the Stefan-Kawalki analysis. Moreover, their cell is suitable for measurement of diffusion coefficients at elevated pressure, as they successfully demonstrated with mercury. Consideration of the design and experimental features of the methods discussed above suggested several criteria for the new cell: 1) a ''total" capillary system, as opposed to a capillary-reservoir system, should reduce adverse convection effects; 2) such a capillary system should avoid the problems en-

Jan 1, 1969