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By A. J. Griest, A. P. Young, P. D. Frost

A study was made of the effect of ß grain size on the tensile ductility of a-ß titanium alloys haet treated to strengths in the range 165,000 to 180,000 psi. It was concluded that the primary cause of $ embrittlement is the large grain size which is obtained so rapidly in many a-ß titanium alloys when heated into the ß field. It was also found that grain-boundary a and acicular intragranular a in the microstructure are not necessarily detrimental to the tensile ductility if the prior ß grain size is sufficientlv fine. BETA embrittlement occurs in a-ß alloys when the finish hot-working or stages of the subsequent heat treatment have been done at temperatures in the ß field. In order to avoid this embrittlement, for-gings must be finished at temperatures under the ß transus. For better workability, it would be desirable to forge at temperatures in the ß field. For this reason, research has been conducted to determine the cause of ß embrittlement. Although ß grain size has been considered as a possible contributing factor to ß embrittlement, only limited research has been done to evaluate its effect. The effect of addition elements on ß grain growth in unalloyed titanium has been studied by Liu.' Complete mechanical property data, however, were not obtained for correlation with grain size. Ogden and coworkers2 have investigated the effect of both a and ß grain size and grain shape in Ti-Cr-Mo alloys. Their data indicated that tensile ductility was relatively insensitive to ß grain size at annealed strength levels (140,000 psi ultimate). No study has apparently been made to determine the relationship between ß grain size and ß embrittlement in a-ß alloys heat treated to high strength (180,000 psi ultimate). The high-strength condition is that in which ß embrittlement is particularly severe. Beta grain size is not easily varied through the use of a range of annealing times and temperatures in the ß field, because of the rapidity with which ß grain growth occurs. Short-time heating techniques are needed to obtain the smallest ß grains. EXPERIMENTAL PROCEDURE In this research, the experimental procedure was as follows: 1) Tensile and microimpact specimen blanks were resistance heated to produce a range of ß grain sizes. 2) The tensile and microimpact blanks were then solution-treated in the a-ß field and aged to produce predetermined ultimate tensile strengths in the range 165,000 to 180,000 psi. Tensile and impact ductility were then correlated with a grain size for constant strength levels. Materials—The alloys Ti-6A1-4V, Ti-4A1-4Mn, and Ti-16V-2.5Al are representative of the heat-treatable a-ß types in which ß embrittlement can be severe. The compositions and ß transi of the heats studied are given in Table I. The Ti-16V-2.5Al heat was melted and fabricated to 1/4 in. round at Battelle; the other alloys were obtained as 1/4 in. round rolled from commercial heats. The micro-structures of the as-rolled alloys were fine a-ß mixtures. This structure is typical of titanium alloys hot-worked extensively in the a-ß field. Resistance-Heating Treatments to Establish ß Grain Size—For direit resistance heating, a 1/4-in.-diam s~ecimen was heated with a 3000-watt transformer rated for 1000 amp with adjustable secondary voltage. The apparatus included a spray quench fixture. Both heating and quenching periods could be automatically controlled. For temperature measurements, 28-gage Chromel-Alumel wires were tack-welded to the specimen at its midpoint. A high-speed recorder-controller was used to control the heating cycle.

Jan 1, 1960

By J. O. Brittain, E. Lautenschlager

Yield point measurements were made on polycrys-talline specimens of a iron deformed various amounts at 770, 1950, or 273°K, aged, and redeformed at 77: 195°, or 273°K. When the prestrain temperature is lower than that subsequent to aging, the yield point return is suppressed relative to specimens deformed at the same temperature both before and after aging. The degree of suppression is a function of both the magnitude of prestrain at the lower temperature and the difference between the deformation temperatures before and after aging. It is proposed that the suppression is caused by the formation of dislocation barriers during the initial low-temperature deformation. The aging kinetics of polycrystalline a-iron wires deformed at 77o or 303oK were studied at 44 " and 64 "C using internal friction measurements. No change was noted as a result of the difference in prestrain temperature. IN an earlier investigation1 it was observed that the return of the yield point was suppressed when a poly-crystalline specimen of a iron was plastically deformed at 77oK, aged at room temperature, and subsequently tested at room temperature. In order to investigate this observation, a research program was undertaken to measure the effect of prestrain temperature on the strain aging of a iron.' According to Thomas and Leak,3 return of the yield point and internal friction are similar measures of strain aging since both are dependent on solute atoms leaving the solid solution. The decrease in internal friction as a function of aging time is indicative of the removal of solute atoms from the solution, while the return of the yield point as a function of aging time gives the rate of arrival of solute atoms at the dislocations. According to Cottrell and Bilby,4 the solute atoms create an "atmosphere" which locks the dislocations and causes a return of the yield point upon restraining. In this experiment, both methods of measuring strain aging were employed in order to have two independent measurements of the strain aging phenomenon. In a previous study,5 the strain aging kinetics of a similar lot of a iron were measured for specimens which were prestrained and tested at the same temperature over the range of 77" to 273°K. Although some differences were found in the correlation of the two methods employed for measuring strain aging, the kinetics of strain aging were unaffected by the change of prestrain and test temperature. In another study,6 dislocation line tension and the density of the solute atmosphere were found to contribute to the return of the yield point when ingot iron specimens were prestrained at 303°K and tested at a lower temperature, namely 77°K. This paper is concerned with changes in strain aging kinetics produced by pre-straining at 77" to 303°K and testing at either the prestrain temperature or at higher temperatures up to 273°K. EXPERIMENTAL PROCEDURE The polycrystalline a iron specimens used in both the tensile and internal friction tests were 0.033-in. diam ingot iron wires, wet hydrogen treated and re-carburized. A more detailed procedure for processing a 3/16 in. ingot iron rod (nominal wt. pet composition: Fe - 0.013; C - 0.0125; Mn - 0.023; Si -0.005; P - 0.0023; S - 0.11; Cu - 0.004 N) to 0.033 in. diam specimens containing approximately 0.020 wt pet C and no detectable nitrogen with a grain diameter of 0.033 to 0.040 mm is given elsewhere.5 Immediately prior to testing, specimens were solution treated for 15 min at 700o ± 2°C in a static vacuum of less than 50 ?. of Hg and rapidly quenched into an ice-water bath while still enclosed in a 3 mm quartz vial. The internal friction specimens had 8-in. gage lengths and the tensile specimens had 2-in. gage lengths. The wires used as tensile specimens were first run as internal

Jan 1, 1962

By R. F. Blakely, P. E. Potter

Any stratigraphic section or bedding sequence can be synthesized if there is a transition procedure from one lithology or bedding type to another, and if thickness distributions of the different lithologies are known. Stratigraphic sections of a fluvial sandstone body were synthesized with five bedding types: cross-bedding, massive beds, parting lineation, ripple mark and mudstone. The transition procedure from one bedding type to another used dependent, Markovian random processes which have a memory that extends one step backward in the depositional process. As observed in nature, median grain size and sand wave thickness (cross-bedding and ripple mark) decline upward in the synthesized sections as proportions of the different bedding types change. Grain size and permeability were also incorporated into the sections. By changing the transition procedures, bed thickness distributions, rate of upward decline or sand wave height and length, different types of sections can be synthesized, thus making it possible to model many different sedimentation problems. INTRODUCTION This paper describes a general method for synthesizing stratigraphic sections and bedding sequences of sedimentary, metamorphic or igneous origin. Synthetic generation is of interest for several reasons. Close correspondence between real and synthetic sections suggests that the factors used in the synthesizing model may indeed be the correct ones, thus giving the investigator a check on his assumptions. Rapid, inexpensive simulation of many stratigraphic sections permits one to synthesize a rock body (sandstone or carbonate reservoir) or, on a larger scale, the fill of a sedimentary basin. Harbaughl gives an example of mathematical simulation of a carbonate basin. He simulated the basin in the hope that improved prediction would follow better understanding of the depositional processes. From the petroleum engineer's viewpoint it seems reasonable to believe that the synthetic generation of rock properties and their distribution in a reservoir should be relevant in the study of reservoirs. Any stratigraphic section or bedding sequence can be generated provided there is a transition procedure from one lithology or bedding type to another, and provided the thickness distributions of the different units are known. The transition procedure involves random processes that are either independent or dependent. If the depositional process is independent, previous deposition will have no influence on present deposition. However, if it is dependent, past deposition will influence either present or future deposition. Such a dependent depositional process can be thought of as having a memory that extends backward in time through one or more pulses of deposition. A process with a memory can be described by a Markov process. Because the concept of memory or dependence appears to be in accord with our understanding of many depositional processes, Markov processes were used to synthesize the bedding sequences of this study (see Appendix). The above methods are perfectly general and are appropriate for any stratigraphic section or bedding sequence: bedding types in a beach deposit, an evolving carbonate bank or the changing lithologic fill of a thick geosyncline sequence. We chose to synthesize a vertical profile of a fluvial sandstone body because its characteristics were well documented, much was known about fluvial processes and fluvial-deltaic sandstone bodies constitute an important class of petroleum reservoirs. CHARACTERISTICS AND ORIGIN OF FLUVIAL CYCLE The fluvial cycle has been well documented in recent years by Bersier,2 Allen3-5and Visher.6,7 Deposits from fluvial cycles range from 10 to 150 ft or more in thickness and are characterized by a "fining upwards": coarse sandstones with occasional conglomerates grade upward into medium- to fine-grained sandstone, and hence into siltstone and mudstone. The dominant sedimentary structure is inclined bedding: thick cross-beds in the lower half

WELL known member of the Institute, Henry Krumb, survived the Japanese earthquake and has written a most interesting description of his personal experience to a friend in New York, an extended excerpt from which we publish, by permission, below. Not having been written for publication it has increased value as a human document in its vivid description of personal impressions and sensations in the midst of such a catastrophe. The earthquake was the most terrible experience I have ever passed through. We arrived at Miyanoshita, Friday, Aug. 31, about 6 p.m., having left Yokohama about 2:30 that afternoon by automobile. It was a most beautiful ride, although rather warm, but not unusually so, as it has been uncomfortably hot ever since we arrived in Japan. The first part of this automobile trip was along the old highway from Kyoto to Tokyo, which is lined with fine old pine trees. There are 52 villages along this highway and we saw real Japanese country life: naked children, both boys and girls, and men wearing nothing but gee-strings. The country on either side was intensively cultivated, the green rice fields and lotus ponds making a most beautiful sight. The occasional hills were all re-forested with young pines. In places the road runs close to the ocean beaches. The last part of the trip was up a steep mountain road, cut out of the side of the mountain. On one side of the road, in the gulch below, was a roaring river. The road crosses this river several times. Miyanoshita is beautifully located on the side of a mountain about 400 ft. above this river at an altitude of 1400 ft. The grounds of the hotel are laid out in Japanese style, small lakes with fish, waterfalls and dwarf trees making a very pretty sight. On the morning of Sept. 1, after walking around the garden and the hotel, we went to our room and I started to write up a few notes. Mrs. Krumb was reading a guide book. A few minutes before noon she came over to the table where I was writing and said that it was about lunch time. Just at that moment hell broke loose. It was the first earthquake I have ever experienced and I did not immediately realize what was happening. The building was shaking as a mine office might shake when heavy blasting was going on near by. Mrs. Krumb, having experienced many earthquakes, stepped to the open door between our room and the bathroom and called to me to get out from under the chande-lier. The plaster was commencing to fall and a large wardrobe fell over. I then knew what was happening and ran to the win dow. Before I reached it a large chunk of plaster from the ceiling hit me on the head and cut my forehead and nose. Mrs. Krumb ran for the other window just as the marble mantelpiece and the dresser fell. Without any hesitation, she jumped out of the win-dow and I followed suit out of the other. Luckily neither of us sprained an ankle-we had jumped 8 ft. We started to runaway from the building but had not gone more than 25 ft. when a second shock or rather a continuation of the first became so violent and the ground under our feet was trembling so that it was almost impossible to stand up without holding on to a tree. The ground seemed to have become liquid and rocked violently, it seemed to me in a vertical direction. In some later shocks the movement was more horizontal. About this time Mrs. Krumb saw the blood on my face and commenced to break down, but only for a moment: As soon as she saw it was not serious she was all right and during the following days stood the experiences and hardships as well as the best of them:

Jan 11, 1923

By T. D. Mueller, F. C. Miller, Jr. Earlougher R. C.

In analyzing pressure buildup tests for field wells producing both oil and gas, the common practice is to use a modification of single-phase flow theory. Validity of such an approximation has been demonstrated for single-well solution-gas-drive systems. This paper indicates that such approximations are also valid for two-well solution-gas'-drive systems. From this it is inferred that the technique can be used for multiple-well systems. A computer was used to simulate the behavior of a two-well solution-gas-drive reservoir to test the validity of the above type of analysis. Simulation results indicate that pressure buildup tests in such a system can be analyzed within engineering accuracy for formation permeability and pressure. A rule of thumb is given for estimating the length of time a well must be shut in for the pressure in a nearby producing well to increase significantly. To observe such an increase, the shut-in well would have to be left shut in much longer than normal. INTRODUCTION An important technique for obtaining data concerning a producing petroleum reservoir is the pressure buildup test. Such a test, when properly conducted and analyzed, provides information on the average reservoir pressure and the permeability in the major drainage area of a well. The theory upon which the analysis of a pressure buildup test is based assumes that the behavior of the fluid in the reservoir is adequately described by the diffusivity equation.1 Use of the diffusivity equation implies that a single fluid of small and constant compressibility is flowing. To analyze a pressure buildup test in situations which involve more than one fluid phase, the single-fluid analysis is extended. This paper verifies the extension of pressure buildup analyses to two-phase, two-well systems. Miller, Dyes and Hutchinson1 have presented a technique for analyzing pressure buildup tests in circular bounded reservoirs. Their method requires that the reservoir be producing at pseudo-steady state (constant pressure gradients) prior to shut-in. An alternate reservoir model, presented by Horner,2 assumes that the reservoir is infinite. The Homer model does not assume a Pseudo-steady state prior to shut-in, but the assumption that the reservoir is infinite implies that the average pressure can be determined only if the total production prior to shut-in is small compared to the total fluid originally present. Limitations imposed by the pseudo-steady state and infinite reservoir assumptions are avoided by the technique proposed by Matthews, Brons and Hazebroek.3 Their method can be used to calculate both the Permeability and the average pressure in bounded single-well systems which are not necessarily at steady state. They also suggested determining the average pressure of a multi-well reservoir producing from pseudo-steady state by volumetrically averaging the static pressures of the individual wells. Matthews and Lefkovits4 used numerical simulation techniques to verify that this method does produce adequate results for single-phase, multiple-well systems. Perrine5 proposed modifications to the single-phase theory so that pressure buildup tests in multiple-phase systems could be analyzed. He suggested replacing the single-phase mobility (k/µ) by the sum of the mobilities of the individual phases, and replacing the fluid compressibility by an average compressibility weighted by the saturations of the separate phases. By using numerical techniques to solve the two-phase flow problem for a single-well system, he concluded that this approximation gives results within engineering accuracy. More recently, Weller6 has shown that, for a gas-oil system with a single well at the center of a circular reservoir, pressure buildup tests can be analyzed adequately by using the modification proposed by Perrine. Feller's results also indicate that, as the gas saturation increases, this analysis becomes less accurate. To date, no evidence is available to show that the Perrine approximations can be combined with the Matthews-Brons-Hazebroek technique to calculate the average pressure of a multi-well,

By C. S. Matthews, M. Prats, R. I. Jewett, J. D. Baker

By mathematical analysis it was found that injectivity history of a uniform five-spot pattern can be calculated by rather simple formulas. These calculated injectivities were found to agree rather well with injec-tivities measured in a potentiometric analog. With this as a basis, a simple method was finally developed which allows prediction not only of rate of injection but also of rate and kind of production at the production well, for a uniform five-spot. Using this method formulas for the eflective injectivity and production behavior of a waterflooded reservoir having a wide range in permeability can be calculated by considering that the reservoir consists of several layers, each having a uniform but different permeability. Rather good agreement is shown by a comparison of the observed production history of a field in the Illinois basin and that calculated by the methods just described. INTRODUCTION The importance of being able to predict the injection rates for a water flood is well known, for upon injection rate depends the life of the flood, the size of pumping and treating facilities, and the rate of oil recovery. One method of determining rates of injection is through a pilot flood. However, it appears that even if a pilot flood is resorted to, a theoretical method for calculating injection rate will be valuable in extending field results to times after inter- ference and to locations of other five-spots. It is also important to be able to predict the production history of a flood. Such prediction must generally be done by theoretical means, since in general a small pilot flood will not furnish much quantitative information in this regard because of the distortion after oil-bank interference. Methods for predicting the behavior of five-spot water floods have been proposed by Yuster and Cal-houn' and by Hurst.? However, these methods do not consider the effect of the mobility of the different fluids in the reservoir. Other investigators3,4,5,6 have determined the effect of the water-to-oil mobility ratio on the production history by means of different experimental techniques. Most of the published work applies to homogeneous sand bodies, does not provide information for determining the injection requirements of a flood, and seldom considers the rate of build-up of the oil bank as it fills up the partially depleted reservoir.* The present work was undertaken because of the lack of predictive method which takes into account mobility ratio and the rate of buildup of oil bank resulting from the void space in a partially depleted reservoir. As water is injected into the reservoir, which contains oil, water, and gas in macroscopically homogeneous saturation, it forms several banks ahead of the injection well. In each bank or region there is assumed to be only one mobile phase—water in the water bank, oil in the oil bank and gas in the gas region. The saturation in each region and a plan view of the banks are shown in Figs. 1 and 4, respectively. FACTORS AFFECTING INJECTION AND PRODUCTION RATES Results in this report are determined as functions of the three parameters, F, M, and M, , and of a fourth parameter, r,/L** which relates the size of the well to the flood spacing. The parameter F is the displacement factor defined by Hurst in Ref. 2. It determines the rate of build-up of oil bank as it fills up the partially depleted reservoir. When gravity effects are neglected, the four parameters just given are sufficient to describe the waterflood behavior for horizontal and homogeneous reservoirs having incompressible liquids. Definition of InjectIvity The dinlensionless injectivity (or injection rate) used in this report is defined by

By P. M. Kelly, E. P. Butler

The stability of a 70/30 Mn-Cu alloy aged to peak damping has been investigated using electron microscopy, X-ray diffraction, and torsional pendulum measurements. Storage at room temperature or at 100" C causes a reduction in damping capacity. This is shown to be due to the formation of subdomains which "lock" the main domain structure and so hinder their movement. After storage the damping capacity can be restored by a retransformation treatment, which generates structures identical to those found in newly aged specimens. Plastic deformation by rolling also causes a decrease in damping capacity. In this case the damping capacity can only be restored by retransformation if the amount of deformation is less than about 5 pct. THE general metallography and structure of these high damping capacity alloys has been discussed in Part I of this work.1 Part II deals with some of the variables that affect the damping capacity. In particular, the stability of the damping capacity of a 70/30 alloy aged for 2 hr at 425° C and quenched has been investigated. The temperature sensitivity of the damping capacity of a 70/30 alloy aged for 2 hr at 450° C has been reported by Birchon.2 The damping capacity begins to decrease with increasing temperature, and is very low above the M, temperature of 125°C. The cubic — tetragonal transformation is completely reversible and there is no apparent thermal hysteresis associated with the change in damping capacity. Another important effect was first reported by Dean and his coworkers.3 They noticed a decrease in the damping capacity with time for specimens of a quenched tetragonal alloy. More recently workers at the Admiralty Materials Laboratory 4 have studied the stability of an aged 70/30 alloy. They found that the damping capacity decreased to half its original value after about 1000 hr at room temperature. EXPERIMENTAL The techniques used for electron microscopy and X-ray diffraction have been described in Part I. The damping capacity was measured by means of a torsional pendulum, using rectangular specimens, 3 by 0.3 mm with a 6 cm gage length. The specific damping capacity, S.D.C., was calculated as a percent amplitude decay in free vibrations over 10 cycles, starting at an amplitude which corresponded to a 700 psi surface shear stress. Because of the stress dependence of the damping,' the values obtained were about a third those reported for a 5000 psi surface shear stress.' RESULTS a) Effect of Aging Temperature. The effect of aging temperature on the damping capacity is shown in Fig. 1. The damping capacity reaches a peak of 12 pct after aging at 400° to 425°C) then begins to decrease as the volume fraction of a Mn increases. At higher aging temperatures the structure becomes cubic again with a low damping capacity. b) Stability of the Aged Structure. The damping capacity of the aged alloy decreases with time at room temperature. This process could be accelerated by storing at 100°C, when about 100 hr were required for the damping to fall to half its original value. The results of room temperature and 100°C storage, for times up to 1000 hr, are shown in Fig. 2. The damping capacity starts to decrease after about 24 hr at 18° C and 1 to 2 hr at 100°C. It was found, however, that the damping could be almost completely restored by retransformation. The specimens were held at a temperature above the M, for a short time, 250° C for 5 min, and then quenched. The values of damping capacity for specimens that were aged, stored, and then retransformed are shown by the full points in Fig. 2. X-ray measurements of the c/a ratio and hardness readings on the specimens did

Jan 1, 1969

By M. J. Marcinkowski, K. S. Sree Harsha

A detailed numerical analysis has been made of the equilibrium configuration of partial dislocations in a blocked deformation twin under an externally applied stress. Twins made up of both pure screw and pure edge partials have been considered. The components of stress in the vicinity of the twin tip associated with each of these configurations have been plotted. It has been found that at some critical degree of oblateness the shear stress fields of the blocked screw or edge twin can both sPontaneously nucleate slip, whereas only the component of stress oxx about the edge twin can nucleate and propagate cracks. TWINNING becomes a predominant mode of plastic deformation at low temperatures and/or high strain rates. Fig. l(a) shows what must be the first step in the formation of a deformation twin, namely the formation of a loop of imperfect dislocation bounding a stacking fault. In an fcc crystal the partial dislocations have Burgers vectors of the type 1/6 a,(112) and the fault is of the intrinsic type while in the bcc crystal the partials have Burgers vectors of the type ao(lll). The stacking sequence of (111) planes in a perfect fcc crystal is given by ABC ABC, and so forth, and in one which contains a twin by ABCABACBA, and so forth. It is apparent that the stacking fault and twin give rise to no mistakes associated with adjacent close-packed planes; however, with respect to second-neighbor close-packed planes the faulted crystal has twice as many mistakes as the twin. The energy of the twin boundary may thus be taken to be one-half that of the intrinsic fault boundary. In the case of the bcc crystal the stacking sequence of (112) planes is given by ABCDEFABCD, and so forth, in a perfect crystal, by ABCDCDEFA, and so forth, in a crystal which contains a fault, and by ABCDCBAF, and so forth, in one which contains a twin. An analysis similar to that applied in the fcc crystal shows that both the fault as well as the twin involve no neighbor violations across adjacent planes. However, there are twice as many violations across second-neighbor (112) planes associated with the fault as compared to that of the twin. Thus once again the energy of the twin boundary may be taken as one-half that of the fault. It is important to note that, unlike the fcc, the faults in the bcc crystal involve first nearest-neighbor violations and are thus expected to be of much higher energy than those in fcc crystals. A more detailed analysis of the material discussed above can be found in Ref. 1. To a good approximation then, the lenticular twin shown in Fig. l(b) can be generated by adding partial dislocation loops on successive (111) planes for fcc crystals or (112) planes for bcc crystals in the manner shown, with no additional expenditure of chemical energy other than that required for the fault shown in Fig. l(a). In practice, deformation twins are much more extended than that shown in Fig. l(b) and more closely resemble one shown schematically in Fig. l(c). It is readily apparent that the free energy of the twin and matrix are identical. In those cases where the partials lead to a structural change, the free energy of the material contained within the dislocation array is lower than that of the matrix and we have the so-called martensite transformation. The present investigation is the first in a series of five major theoretical-experimental efforts which will deal with the static and dynamic behavior of twin nucleation and growth. There has been a recent surge in activity pertaining to the equilibrium shapes of twin lamellae2'3 and

Jan 1, 1969

By Robert E. Green, Kenneth Reifsnider

A microscopic X-ray diffraction technique was employed for the simultaneous study of the behavior of several families of lattice planes, whose local orientatiotz changes are manufestations of internal distortions resulting from specimen deformation. Photographs taken using aluminum were single crystals 1/64 in. In diam are presented which illustrate the appearance of various types of deformation- or growth- induced structural variations. Slip and lattice bending were detected in tensile tests for strains as small as 0.1 pct. Evidence of deformation bands, lineage structure, and void formation wns also shown. AmONG the most important methods of studying internal stresses in metals is the utilization of various X-ray techniques. The general subject of X-ray metallography has been treated in a most excellent manner by Taylor,1 and the use of X-rays for the direct observation of imperfections in crystals has recently been reviewed in an article by Newkirk2 and in the book edited by Newkirk and Wernick.3 Since the inception of metallographic X-ray analysis, there have been numerous technological developments and refinements, each with its particular advantages and disadvantages and, acrording to these, its particular applications. X-ray diffraction techniques can be divided into two general categories, that of X-ray diffraction microscopy and that of X-ray diffraction macroscopy. In the former are included such methods as those of Berg-Barrett, Lang, and Schultz2,3 which are concerned with microscopic imperfections such as dislocations. The second category includes all work concerned with the study of the condition of a crystal lattice structure as indicated by the marroscopic detail in its diffraction patterns. An example of this is the study of the diffraction manifestations of inhomogeneous plastic deformation as manifested by formation of deformation bands and inhomogeneous lattice rotations. The method used in the present investigation was an X-ray diffraction macroscopy technique. The geometry and analytical aspects of the method were similar to those of Julien and Cullity.4,5 The source was collimated with a single slit in a manner simi- lar to the "parallel beam'' method of Barth and Hosemann6 except that a continuous spectrum of radiation was employed. The apparatus produced large-beam transmission Laue patterns of thin cylindrical aluminum-wire crystals, which were deformed either in tension or torsion. Although the conventional X-ray target and interposed slit were not capable of the high resolution obtainable with a fine-focus X-ray source as employed in a microfocus apparatus, resolution was a secondary consideration in our technique, and was sacrificed to obtain sufficient intensity along a sizable length of the specimen. By using a grid indexing technique similar to that of Barth,7 we were able to study several diffraction lines from various planes simultaneously. The results of these tests give additional information with regard to the inhomogeneous deformation of single crystals, and the indexing procedure used provides a correlation between portions of the test specimen and portions of a diffracted beam. EXPERIMENTAL TECHNIQUE The experimental arrangement used is shown schematically in Fig. 1. A source of continuous X radiation from a vertically mounted Machlett X-ray tube possessing a copper target and operated at 20 kv and 10 ma was passed down a horizontal lead tube 80 cm long which terminated in an adjustable vertical brass slit. The slit opening was adjusted to correspond with the diameter of the test specimen. In front of the brass slit it was possible to place a screen wire mesh, one horizontal strand of which was a lead wire which served as a fiduciary mark, the screen itself serving as an indexing system as will be described later. Behind the screen was the test specimen which consisted of an aluminum single crystal wire 1/64 in. in diameter and 3 in. long. These 3-in.-long crystals were cut from

Jan 1, 1965

By E. I. Alessandrini, A. U. Seybolt

Selective oxidation (preferential oxidation of a single alloy component) can be an important oxidation mode in the case of alloys such as Si-Fe, Al-Fe, and so on, when heat-treating in atmospheres of low oxygen potential. It was the purpose of this work to identify the oxide films formed on iron containing 31/4 pct Si at low oxygen potentials, and to make some observations on the H2O/H2 ratios required to form them. EXPERIMENTAL METHOD HYDROGEN of varying water content offers a very convenient method of establishing a wide range of oxidizing power, or oxygen potential. The method chosen to provide a desired H2O/H2 ratio was to nearly saturate hydrogen at room temperature by bubbling the gas through water at room temperature, and then to wring out the excess water by passing the wet gas through a long glass spiral immersed in a refrigerated liquid at a desired dew point. After oxidation, the samples were examined by electron diffraction in order to identify any film which might be present. PREPARATION AND TREATMENT OF SAMPLES The samples were prepared from a Si-Fe alloy made in the laboratory using electrolytic iron and 96 pct ferro-silico11, vacuum-induction melted, hot-rolled then cold-rolled to 0.015-in. thickness. After the cold-rolling the samples were annealed at 1000°C. Transmission Laue X-ray patterns showed very little evidence of preferred orientation, but it is likely that a weak texture could have escaped notice. The chemical analysis was as follows: 3.34 Si, 0.01 Al, 0.001 0, 0.006 C, 0.002 N. Before each sample was oxidized, it was polished through 4/0 emery paper, cleaned and dried using benzene, carbon tetrachloride, acetone, absolute alcohol, and ether. The method of oxidizing the samples was as follows: Samples about 1/2 by 1 by 0.015 in. were held in the upper, cool part of a vertical vacuum furnace until the desired temperature was established in the furnace, Fig. 1. The sample was then lowered into the uniform hot zone where it was heated quickly to the desired temperature, and subjected to hydrogen of controlled moisture content (dew point) as mentioned previously. Temperatures from 400" to 1000°C were used, and dew points from room temperature to —78°C were explored. In general, the runs lasted about 6 hr, but a few runs were of different duration, as will be indicated later. After the predetermined period of time had elapsed, the specimens were withdrawn by the hollow stainless steel-quartz holder to a cool zone at the top of the furnace. EXPERIMENTAL RESULTS The results are summarized in Table I. Most of the electron-diffraction patterns were obtained by glancing-angle reflection, but in a few cases it was possible to strip the oxide films from the surface by a total immersion in a 3 pct bromine-methanol solution. Some of the thinner stripped films yielded quite satisfactory transmission patterns. However, both diffraction techniques yielded the same results; the patterns while most frequently showing a (low) tridymite, also showed a (low) cristobalite in some cases. A few patterns showed evidence of both phases. Because of the known nonequilibrium behavior of silica, it is not surprising that both forms of silica could coexist on one sample. It was noted that at fairly low dew points such as —40°C, there was a tendency for diffuse diffraction rings, suggesting a very small crystallite size. Also some subsequent experiments to be reported later show that thin silica films can be amorphous.

Jan 1, 1959

By H. D. Outmans

Present first-order theory for frontal stability and viscous fingering of immiscible liquids is improved by including the nonlinear terms in the equations describing conditions at the interface of the liquids. This leads to the revision of several conclusions which were based on first-order theory. They concern the growth rate and changing shape of a sinusoidal disturbance, particularly in relation to the wave number of this disturbance. Nonlinear aspects of effective interfacial tension are discussed and it is shown that this tension is not simply a positive proportionality constant in a linear relation between pressure difference and curvature at the interface. Scaling requirements are determined from the dimensionless groups which govern fingering. Gravity and interfacial tension invalidate a previously formulated conclusion that the shape of a finger after a given displacement is independent of the displacement velocity. Also, similarity of fingering (and, hence, of sweep efficiency in case of an unstable front) requires geometrical similarity of the initial disturbance in the model and the reservoir with a scale factor which is the same as the one for scaling down the dimensions of the reservoir. INTRODUCTION The critical velocity at which the transition zone in the vertical displacement of immiscible liquids becomes unstable was calculated by ill. More recently, the same was done for nonvertical displacements and it was also shown that the stability is affected by an effective interfacial tension between the liquids. 2-4 Although in the oil reservoir a stable front is always desirable from a recovery point of view, the necessary velocity may have to be so low that the corresponding production rate is not economical. In that case, a knowledge of the fingering unstable front is necessary for predicting recovery at break- through. Studies in this direction have not gone beyond the very moment at which fingering first occurs.5,6 Conclusions about stability and fingering in these references are all based on linear theory. In this theory the nonlinear terms in the equations describing conditions at the front are neglected. The usual justification for this lack of mathematical rigor is that the nonlinear terms can be made small relative to the linear terms and, supposedly, small causes produce only small effects. It has been recognized, however, that this is not necessarily true in the nonlinear problems of hydrodynamics.7 The hydro-dynamic stability and fingering of the front between two liquids, accelerated in a direction normal to the front, for instance, is strongly influenced by the nonlinearity of the boundary conditions.8-10 Since these boundary conditions are not unlike those arising in the problem of stability and fingering of the front during a slow immiscible displacement in porous media, it was thought that there, too, the nonlinear terms should be taken into consideration. A summary of the results obtained in linear theory and a comparison with experimental data precede the nonlinear theory developed in this paper. This summary serves to introduce some quantities which will be used in the further develop ment. It should also be pointed out that the method of higher-order approximation by which the nonlinear stability problem is solved has application in other reservoir studies.11 SUMMARY OF LINEAR THEORY 1. A plane interface remains stable if its velocity is smaller than a critical velocity. vc = (p2-p1)gn/(l/A2- l/A1 .........(1.1) This equation is derived for uniform flow in a thin layer inclined to the horizontal plane. The displacement takes place in a direction normal to the intersection of this layer and the horizontal plane. The undisturbed (line) interface is normal to the velocity. Fluid 1, the upper fluid (gas), is displacing Fluid 2 (oil). (VcQS would be the injection rate in cc/

By R. L. Schmidt, J. D. Verhoeven

The diffusion coefficients and electrotralzsport mobilities of aluminum, gallium, and arsenic have been determined in molten germanium with the capillary reservoir technique. The diffusion coefficients are slightly higher than those determined by the solidification technique of Brirton et a1.1 It was found that aluminium and gallium migrate to the cathode in molten germanium) whereas arsenic migrates to the anode under an electric field. A possible technique for producing p-n junctions by means of electric field freezing is discussed in view of the experimental data. In the past decade or so the literature has abounded with articles concerning the solid-state properties of the semiconducting elements germanium and silicon. It is surprising by comparison how little has been published concerning the liquid-state properties of these materials. In the production of doped germanium or silicon the diffusion coefficient of the dopant in liquid germanium or silicon is an important quantity. Yet, to the best of our knowledge, no one has ever made a direct measurement of the diffusion coefficient of solutes in either molten germanium or silicon. A number of authors'-4 have determined some diffusion coefficients by the indirect technique developed by Burton et al.1 This technique appears to give numbers of the correct order of magnitude but it does depend upon a number of assumptions in the analysis and also requires prior knowledge of the viscosity of the melt. In the present work a more direct measure of the diffusion coefficients of arsenic, gallium: and aluminum in molten germanium has been made. It has been shown independently by two groups of authors5, 6 that, when an electric current is passed through the interface of a solidifying metal containing an impurity, the resulting electrotransport in the liquid boundary layer at the interface offers a mechanism for control over the redistribution of the impurity accompanying the solidification. These authors show that the degree of control is proportional to the mobility, U of the impurity atoms in the liquid boundary layer, where the mobility is defined as the drift velocity relative to the solvent per unit electric field. In principle the results apply to the solidification of a doped semiconductor and offer an interesting technique for control of the doping of a semiconductor. In the present work the mobilities of aluminum, gallium, and arsenic were determined in molten germanium in order to evaluate the potential usefulness of electro-transport as a technique for solute control when applied to the solidification of doped germanium. EXPERIMENTAL PROCEDURE Both the diffusion coefficients and the mobilities were measured using high-purity alumina capillaries and a resistivity technique for analysis. A schematic diagram of the electrotransport apparatus is shown in Fig. 1 and the details of the cell design are shown in Fig. 2. For the mobility experiments electrical contact with the bottom of the capillary was made with graphite, as shown in Fig. 2. In order to prevent electrical contact with the melt the graphite was coated with a thin layer of alumina using a plasma spray torch. The cell assembly, a graphite electrode, and another assembly containing two blank capillaries were fastened to the lavite disk shown in Fig. 1. To make a run the system was evacuated and the doped germanium was outgassed at the operating temperature of 1030°C. The cell and blank capillaries were then submerged beneath the melt and a slightly positive pressure of helium was introduced to fill them. After passing current through the cell for a given time the cell and blank capillaries were raised from the melt and the furnace was shut off. The temperature of the cells dropped below the freezing point of germanium within 1 to 2 min after the furnace was shut off.

Jan 1, 1968

By E. J. Harris

Mathematical solutions to complex mine ventilation problems are possible, but often the airway network is so complex that the mathematical solution becomes tedious and impractical. A fluid network analyzer, designed and built for analyzing mine ventilation problems has been in service at the Bureau of Mines' Pittsburgh station for approximately nine years. Using this analogue as a model, the mine ventilation network is simulated electrically by a combination of series and parallel circruits laid out to conform with actual mine airways. A tungsten filament lamp, referred to as a Fluistor, is used to simulate mine airway resistance. With the analogue ventilation model established, voltages of the proper amplitude to represent ventilating pressures are impressed across the circuit at points where mine fans and airshafts are located. Comparison of mathematical solutions of complex systems against analogue results showed a maximum variance of 3% for pressures and 2% for quantities. An electrical fluid network analyzer, designed and built especially for analyzing mine ventilation distribution problems, has been in service at the Bureau of Mines, Pittsburgh, for approximately nine years. It is a nonlinear, low voltage, fluid network analyzer of the type developed by the late Malcolm S. McIlroy, Professor of Electrical Engineering, Cornell University, who cooperated with G. E. McElroy, of the Bureau of Mines, in adapting the instrument to mine ventilation systems. Several modifications have been made since the original installation, but a considerable part of this paper is drawn from G. E. McElroy's original description of the analogue.' The analysis of water or gas distribution systems2,3 led to the development of this type of network analyzer. Several similar units are now employed by utility companies for this purpose; however, the Bureau of Mines unit is the only one designed specifically for mine airflow problems. Other airflow analogues employing a similar principle have been used at the Central Research Station of the Netherlands State Mines,4 in England,5 and in South Africa.6 Information on these devices indicated they were somewhat inflexible because commercial lamps with a sufficient range of resistance are difficult to obtain. Computers for mine ventilation analysis have been developed in Germany which instead of lamps use a variable resistance to adjust for turbulent flow laws. These units are expensive, but excellent results have been reported in their application. THE ANALYZER Theory of Application: As airflow generally follows the law of turbulent fluid flow, resistance to flow is nonlinear; consequently, the problem has been to find a nonlinear resistance element of suitable range that can be used for electrically simulated airflow. Tungsten filament lamps operated on alternating or direct current approximate the square-law resistance characteristics of mine airflow over a large range below maximum or rated voltage; that is, the voltage drop varies approximately as the square of the current. Consequently, the heart of the network analyzer is a nonlinear resistor known as a Fluistor, which is simply a custom-made low voltage, tungsten filament lamp that is available in a progressive series of relative resistance values ranging from 0.05 to 500 in nominal 5% steps. However, variations in manufacturing large groups result in differences of 1 to 3%, but series arrangements required for high-loss branches can be matched within about 1%. Utilizing a combination of Fluistors and load circuits, the mine ventilation system is duplicated electrically. Intake load circuits are connected from power intake to primary points of the circuit network; segments of unregulated flow along intakes and returns are represented by Fluistors, regulated splits and leakage paths are represented by load circuits and Fluistors of proper capacity; and mine exhausts are connected to ground from the last point of the network to complete the circuit. For the special purpose of representing booster fans or natural draft conditions, boosters or separate source circuits are provided that can be inserted between any two points of a network to increase voltage to the required value. Physical Layout: The analyzer consists of three 42

Jan 1, 1963

By Milton F. Goodrich

The idea of using water-only cyclones to scalp clean coal from the feed to other devices has recently been gaining in popularity. 1,2,6 An indication of this popularity is that water-only cyclone scalping is already employed in a few commercial plants. Water-only cyclones scalp the feed to a heavy media vessel in the Warwick plant,3 to Deister tables in the Rowland plant,4 and to a heavy media cyclone circuit in the Amherst Coal Company's McGregor plant.5 Despite this trend, we found surprisingly little information in the literature on the performance of water-only cyclone scalping. Therefore, we undertook a study of its technical merits, limiting our investigation to a water-only cyclone scalper in conjunction with heavy-media cyclones. We felt this to be a reasonable combination of equipment, since both processes operate well on the same size coal. First, we developed simple mathematical relationships revealing general characteristics of the system. Next, we compared the clean coal yield and quality obtainable by the system on four different coals with that obtainable by heavymedia cyclone circuit alone and water-only cyclones middlings recirculation circuit alone. This was done by using computer program to simulate the operation of the three systems. Finally, we considered the effect that implementation of the system would have on a typical preparation plant circuit. The System The system chosen for study [(shown schematically in Fig. 1)] comprises two stages: a primary stage (PI) consisting of water-only cyclones, and a secondary stage (P2) consisting of heavy media cyclones. The water-only cyclones separate raw coal at a low specific gravity, producing a relatively small amount of high quality clean coal and a refuse containing much good coal. This refuse is then recleaned in the secondary stage, where the sharper separation of heavy media cyclones, operated at a higher specific gravity, reclaims additional clean coal. Finally, the clean coal from both stages is combined as the system's clean coal, while the refuse from the secondary stage becomes the system's refuse output. Theoretical Analysis Two assumptions lie behind the following theoretical analysis. The first assumption is that partition curves can represent not only the performance of each stage but also the performance of the system as a whole. These curves show partition number as a function of specific gravity, where partition number is either the percent or fraction of a raw coal with a given specific gravity reporting to clean coal. The second assumption is that these curves are independent of the raw coal characteristics. At any specific gravity the system's partition number is solely a function of the partition numbers of each stage. For convenience, we use the following variables in describing this relationship: g = specific gravity, PS(g) = the partition number of the system at specific gravity g, P1(g) = the partition number of the primary stage at specific gravity g, P2(g) = the partition number of the secondary stage at a specific gravity g. For this system, we can show algebraically that the relationship is: [Ps (g) = PI (g) + (1- P1(g)) P2 (9)(1)] With this equation the system's partition curve can be determined if the partition curves of each stage are known. By definition, the partition numbers P1(g) and P2(g) must each be less than, or equal to, one. Placing these constraints on Eq. (1), we arrive at the relations: [Ps(g) % P1(g) and Ps(g) % P2(g)(2)] Thus, at any specific gravity the system's partition number is always greater than that of both stages. [Figure 2] shows typical partition curves. Curve I represents the primary stage, which consists of water-only cyclones operating at a separating gravity of 1.3. (The separating gravity or the

Jan 1, 1979

By P. K. Weimer

Coinpletely integrated thin-film circuits inco?,porating more than 1000 active and passive elements have been fabricated reproducibly in the laboratory by evaporation of- all components. A 180-stage modified shift register comprising 540 CdSe TFT's, 360 resistovs, and 180 capacitors was deposited upon a glass substrate during one pump-down of the vacuum systeitl. Experimental units have been operated for more than 5000 hr at temperatures uP to 85°C without failure of any slages. The present pupper reviews the charvactevistics of evaporated thin-film transistors (TFT's) and discusses their application to integrnted circuils. INTEGRATED circuits most widely used today are based upon silicon technology, with the circuits formed on the surface of a block of single-crystal silicon1 or on a block of sapphire 2,3 upon which a thin layer of silicon has been deposited. Transistor patterns and interconnections are defined by photographic procedures using photoresist masking. Large groups of transistors are produced in batches which undergo many processing steps, some of which are carried out at elevated temperatures. Passive elements are formed by treatment of the semiconductor surface or are deposited by evaporation alongside the active elements. The size and complexity of the circuits are limited by defects in the devices and by the size of the available single-crystal chips. Capacitative coupling to the semiconducting substrate may also limit useful size and frequency response of the circuits. An alternative approach to integrated circuits is based upon the deposition by evaporation of all circuit components upon a noncrystalline, insulating substrate such as glass.4 Thin-film field-effect transistors,1'6 known as TFT's, can be deposited in large arrays on glass or plastic substrates at the same time the associated passive elements are being deposited. Although still in the research stage the all-evaporated approach is expected to offer certain advantages for many applications. In particular, the use of thin films upon a noncrystalline substrate offers the prospect of producing complex, large-area circuits not now feasible with single-crystal silicon. Important applications of this type include memory arrays for computers and imaging devices for television. The ease with which the evaporated TFT's can be deposited may permit continuous, automated production methods not possible with high-temperature batch processing. Recent advances7'8 in the fabrication of thin-film transistors have led to greatly improved reproduci-bility and life of the TFT's. Experimental circuits having over 1000 active and passive elements deposited upon a common glass substrate are currently being produced in the laboratory. The present paper reviews recent progress in the development of the TFT and in its application to integrated circuits. I) DESCRIPTION OF THE THIN-FILM FIELD-EFFECT TRANSISTOR The TFT is a field-effect transistor of the type having the control gate separated from the semiconductor by a thin insulating spacer. Although its operation resembles that of the silicon MOS transistorg its construction is based entirely on thin-film techniques. Fig. 1 shows a cross-sectional view of an evaporated TFT deposited upon a glass substrate compared with a silicon MOS transistor deposited upon single-crystal sapphire.3 The semiconductor in the TFT is a poly crystal line layer, of a material which can be readily evaporated, such as cadmium sulfide, cadmium selenide,l0 or tellurium." Silicon monoxide layers have usually served as the gate insulator, but other oxides, sulfides, and fluorides may be used. Film thicknesses range from a few hundred to a few thousand angstroms. The source, drain, and gate electrodes in the TFT are of metal. Qpical source-drain gap dimensions are 0.0003 x 0.030 in., with a gate strip whose width slightly overlaps the source and drain. The source and drain electrodes should make low impedance contacts to the semiconductor. With cadmium sulfide films, gold is a satisfactory material for underlying electrodes, while aluminum is preferable for overlying electrodes.12 Considerable variation in design of the TFT is permissible, with the electrodes being

Jan 1, 1967

By C. Chu

A theoretical investigation has been made of the forward combustion process using a one-dimensional linear mathematical model, taking into consideration the effect of the vaporization-condensation which occurs on the leading edge of the heat wave. This work involves the solution of five coupled partial differential equations. Besides the vaporization-condensation phenomenon, these equations account for conduction, convection, combustion, heat loss, diffusion and bulk fluid flow. For the one-dimensional linear model studied, the vaporization-condensation phenomenon does not induce appreciable change in the temperature at the combustion front; and its primary effect is to create a steam plateau and to increase the length of the heated zone ahead of the combustion front. This effect becomes more pronounced at lower pressures, higher porosities or reduced gas saturations. The peak temperature and the temperature profile on the leading edge of the heat wave stabilize after a certain period. The length of the steam bank remains practically constant, although the length of the water bank increases as the heat wave advances. INTRODUCTION The existence of the vaporization-condensation phenomenon in the heat-wave process and the important role played by the phenomenon have been recognized by several investigators. Kuhn and Kochl stated that steam plateaus were frequently observed on the temperature records of their experiments. The steam plateaus were attributed primarily to the vaporization and subsequent condensation of the interstitial water existing in the oil sand. Szasz2 suggested that both lighter hydrocarbons and water are vaporized on the leading edge of the heat wave, carried forward in the gas stream, and then condensed to create banks of oil and water. Martin et al suggested that the vaporization-condensation phenomenon is one of the main mechanisms of the heat-wave process, along with thermal expansion and viscosity reduction. Wilson et al. reported the existence of a steam plateau several inches in length in their small-scale tube-run experiments. However, this important phenomenon has never been taken into consideration in the numerous theoretical analyses by various authors. 5 The purpose of this work was to study the thermal aspects of a linear heat wave, taking into consideration the vaporization-condensation on the leading edge of the wave, to determine the effect of this phenomenon on the temperature profile of the reservoir, and to investigate how this effect varies when other process variables are changed. THEORY We consider a reservoir of porous medium of cross-sectional area A, extending from x = 0 to x = L. This reservoir contains, aside from the solid matrix itself, a gas phase and a "combined liquid phase" which is a combination of two immiscible liquid phases — namely, an oil phase and a water phase. The oil present in the reservoir is assumed to consist of three fractions, a noncondensable gas, a nondistillable residuum, and a vaporizable oil fraction which may be present in both the gas phase and liquid phase. Before the heat-wave process begins, preheating has taken place and has imparted an initial temperature distribution T,(x) to the reservoir. At the start of the process, a stream of oxygen-bearing gas is introduced through the face at x = 0. This gas supports the combustion of the residual fuel and supplies the heat throughout the process. In order to develop a tractable system of equations, the model properties are postulated as follows: (1) the system is isotropic and homogeneous; (2) there is a uniform fuel content throughout the reservoir; (3) combustion takes place in a moving vertical planar region of infinitesimal thickness; (4) the temperatures of the fluids and the solid matrix are identical; (5) radiation is negligible; (6) the gas and liquid saturations are uniform throughout the reservoir and remain unchanged

Jan 1, 1965

By R. T. DeHoff

A general method for determining the geometric properties of structures composed of particles which are all the same shape and size is presented. The application of the method requires a knowledge of' the qualitative shape of the particles in the structure, ad a maximum of three simple counting measurenzents, which are made on a representative plane section taken through the structure. It is also shown that the number of different kinds of measurements necessary JOY the complete description of the structure can be decreased if some independent information about individual particles is available. The geometric properties that can be determined quantitatiz~ely from counting measurements for susch structures are size, shape, number, surface area, vlolume, ad such extensive properties as volume Mction and surface area per unit volume. THE simplest kinds of measurements that may be made on a metallographic section are counting measurements. There are three such simple counting measurements, which are determined by sampling the microstructure with a point, a line, and an area. The first of these, the point count, is probably the most familiar among metallographers. The second count, the number of intersections a test line makes with particle outline, is somewhat more recent in its origin and application. The third counting measurement, the number of particle sections observed in unit area of the plane of polish, has long been used in the estimation of grain sizes. The real utility of these three counting measurements lies in the fact that they are rigorously and unambiguously related to certain extensive geometric properties of the three-dimensional structure of which the metallographic section is a sample. These relationships will be reviewed briefly below. Of somewhat secondary importance to the fundamental relationships is the observation that, if some simplifying assumptions about the geometry of the three-dimensional structure are introduced, manipulation of the counting measurements gives a more complete description of the structure. Specifically, in addition to the extensive properties which these measurements rigorously estimate, the number of particles, their size, and their shape may be determined. The purpose of the present paper is to explore the consequences of introducing the assumption of constant size and shape. A later paper will deal with the estimation of geometric properties of structures which may be characterized by a two-parameter size distribution. It should be mentioned that the introduction of this simplest of assumptions, while clearly not generally justified in metallurgical structures, is not without precedent. For example, many estimates of the number of particles per unit volume of structure, based upon a single counting measurement, are scattered throughout the literature.13 Virtually all of these developments assume a constant particle shape, e.g., spherical or polyhydral, and constant size. That such an assumption is necessary is evident from the fact that, for more general structures, more than a single parameter is required to describe the three-dimensional structure, so that the determination of a single parameter on a section would be insufficient to specify the structure. Similar developments for the estimation of particle size from a single counting measurement, e.g., routine grain-size determinations, make the same very limiting assumption,435 but have nonetheless proven of practical value. The present paper embodies a generalized approach to the development of relationships among the two-dimensional counting measurements and the three-dimensional geometry of the structure, subject to the assumption of constant particle size and shape. It is the hope of the author that by presenting the relationships and the assumptions involved in dealing with this approximation, in a single, unified treatment, the reader may be impressed with the usefulness of the counting measurements, may be guided in their application to the estimation of details of the geometry in specific structures in which he may be interested, and may be moved to apply the results, with understanding, to new structural problems. Several authors6, 7 have demonstrated independently that it is possible to obtain unbiased estimates

Jan 1, 1964

By L. N. Cosner, C. F. Austin, J. K. Pringle

Shock wave attenuation studies with three igneous rocks are reported: a spessartite elastic to low intensity stress waves, a diorite which is anelastic, and a porous scoria. The level of shock passing through a given thickness of rock has been determined by donor-receptor methods using high speed streak cameras. Test results include shock propagation velocities adjacent to the explosive, the dependence of test results upon test geometry, and the variation in shock wave attenuation in these three common igneous rock fabrics. The utilization of explosives in rock mediums involves a series of interrelated phenomena. These are the detonation process within the explosive, the transfer of energy from the explosion products to the surrounding rock medium in the form of sound or shock waves, and the transmission of the resulting waves through the rock medium to create damage in the rock mass. The subject of this paper is the investigation of the close-in phenomena that occur in the intensely shocked rock immediately adjacent to a detonating explosive charge. The specific aspects studied include propagation velocities, free surface velocities, pulse attenuations and the determination of the equations of state for the test rocks employed. In addition, a series of tests was conducted to indicate the dependence of the test results on the charge diameter utilized. The equations of state for rock materials have been investigated by a number of authors. Lombard, ',' Grine and Fowles,3,4 Zharkov, 5 Hughes and McQueen,6 Chabai,7,8 and Bass9 have published equation of state data on rock materials similar in structure or composition to those investigated in the study. Rinehart10 has prepared a voluminous tabulation of the available equation of state data from these publications and in addition has included data on many other rock and earth materials in his compilation. The reader is referred to the extensive tabulations and bibliography of Rinehart for classical studies involving the equations of state of metals and other solids and liquids. The problems of sympathetic detonation between drill holes in hard rock environments has received the attention of various authors as have the problems of explosive rock coupling close-in stress wave attenuation and explosive diameter effects. 11 to 18 In particular, the don or-receptor geometry of this report is very similar to the geometry of adjacent drill holes in rock. Most published pulse velocity and attenuation work in rock has been devoted to velocities at much lower amplitudes than those associated with close-in explosives phenomena and most attenuation studies involve transmission and attenuation across large spans of material. Excellent work in these areas has been published by the U. S. Bureau of Mines and by many individuals and groups engaged in geophysical research. SELECTION OF TEST MATERIALS A series of rock materials was desired for this test program that would be meaningful industrially, and that would also yield comparative results from a research viewpoint. Based on the availability of a series of related petro-fabrics, for which there is an abundance of physical and shock response data, three igneous rocks were selected as the test series. The applicability of shock wave studies in igneous rocks to industrial problems is readily demonstrated. Hardrock tunneling, quarrying and mining take place in igneous rocks throughout the world. From a research point of view, igneous rocks exhibit a wide variety of grain sizes and considerable diversity in composition, yet the common igneous rocks have a general similarity in their constituent mineral structures and in their grain-to-grain bonding mechanisms. The latter is based on the concept of rock formation through magma cooling and crystallization, though the degree of liquefaction in granitic plutonic masses is indeed a moot question. Three specific types of igneous rock were chosen for study. A coarse-grained granitic textured rock was desired that would serve as a representative of the widely abundant intrusive rocks of the world and

Jan 1, 1967

By T. G. Nilan

Steels containing 0.4 and 0.8 pet C have been transformed isothermally at pressures up to 34 kbuv. Decomposilion mechanisms are so intimately related to phase equilibvia that, as the equilibria shift under high pressure, the microstruclures of the decomposition producls change, maintaining at pressure the same correspondence between a given phase equilibrium and a given microstructure as a1 1 atm. A bainitic unicvo-structure occurs in these steels at high pressure that IS observed only at 1 aim abole 1.4 pct C. This strrrcl111,e 1s ruliorzalized in terms of the effect of pressure on the transformation to lower bainite. The pressuve depetlderlce of the kinetics of pearlile formation is descrihed by an absolute rule theory amalysis. The activation volume for the transformation is 7 cu cm per mlole, which is indicative of a phase-interface transformation-rate cotntrol mechanism. This fortmulation, when expressed in terms of known solule effects on the energelics of tvansformation, gives promise of explaining the effects of alloying elemenls on hnrden-abilily, particularly that of 'coball. KINETIC processes in solids are functions of the primary thermodynamic variables of state: composition, temperature, and pressure. Until the development of high-pressure techniques' that permitted the generation of sustained high pressure at high temperatures, metallurgical studies of such reactions were largely limited to isobaric conditions at atmospheric pressure. The data so obtained, and theoretical deductions based on these data, were necessarily incomplete For the particular case of austenite decomposition, a knowledge of the phenomenology of the reaction in terms of all the state variables should lead to a clarification of the process. This deeper understanding should facilitate a decision between conflicting theories that have been proposed to rationalize these phe- nomena. An analysis, derived from an understanding of the transformation mechanisms, may aid in the optimization of alloy steel development. The first studies of the effect of pressure on transformations in steel were made by Kulin et al. in 1952.' In a study of the influence of applied stress on mar-tensite formation in a 30 pct Ni steel, they found that the martensite start (M,) was depressed 8°C per kbar* by hydrostatic pressure. Jellinghaus and Friedewold3 were apparently the first to investigate the effect of pressure on isothermal transformations above the Ms. They found that the bainite transformation rate in a 1.2 pct C, 3.8 pct Mn steel was reduced by a factor of 3 by a hydrostatic pressure of 4 kbar. In both of these investigations,2,3 the M, of the steels studied was below room temperature. Austenitizing and quenching were done at atmospheric pressure, followed by the decomposition of the metastable austenite under pressure. The maximum temperature at pressure in the bainite study3 was 350°C. Until the advent of the present high-pressure devices, it was not possible to conduct isobaric high-pressure heat treatments from austenitizing through isothermal decomposition and quenching. The exploitation of high pressure as a variable in metallurgical studies was greatly advanced by the apparatus and techniques developed by Hall4 and co-workers. Utilizing these techniques, Radcliffe et a1.5 and Hilliard6 etermined the pressure dependence of phase equilibria in the Fe-C system. Hilliard and cahn7 examined the pearlite transformation rate in an AISI 1080 steel and also in a high-purity 0.92 C Fe-C alloy at 1 atm and at 34 kbar and found a 700-fold reduction in rate at pressure in the 1080 steel but only a fivefold reduction in the high-purity alloy. In agreement with the shift of phase equilibria under pressure, the microstructures were hypereutectoid at 34 kbar pressure, whereas they are eutectoid at 1 atm. Determination of the effect of pressure on carbon diffu-

Jan 1, 1968

By E. A. Gulbransen, A. Pebler

Pressure-composition isotherms have been determinedfor the systems ZrMo2 -H2 between 0" and 900°C at hydrogen pressures between 10-4 and 760 Torr. Tkese studies plus X-ray diffraction analyses of selected compositions show that these intermetallic compounds form a complete series of hydrogen solid solutions within this temperature and pressure range. The partial molar enthalpies and entropies of solution of hydrogen in the three intermetallic compounds were calculated. The solubility of hydrogen in these Laves phases can be related to their free electron concentration. ThE reaction of hydrogen with inter metallic compounds of zirconium with Laves phase-type structure has both theoretical and practical interest. The in-termetallic compounds have structures different from any of the pure metals. In addition the electron to atom ratio of the intermetallics varies appreciably. In the nuclear materials field, these materials are of interest since intermetallic compounds may exist as precipitates in commercial zirconium alloys with transition metals. From studies on the hydrogen reaction, one can establish the stability of the intermetallic compounds relative to the hydrides of the component metals. The intermetallic compounds may also be used as getters for hydrogen and as materials for hydrogen storage. This paper will present the results of equilibrium and structural investigations of the ZrCr2-H2, the ZrV2-H2, and the ZrMo2-H2 systems for the temperature range of 0" to 900°C and the pressure range of Torr to 1 atm. A complete thermochemical analysis will be made of the measurements. Some of the results have been referred to in a survey paper' covering the types of hydrogen behavior observed in zirconium alloys. LITERATURE ZrCr2 is the only intermetallic phase in the Zr-Cr system.' It exists in two allotropic modifications. Between 900" and 1000°C the hexagonal MgZa (C14) structure transforms into the cubic MgCu2 (C15) structure. Beck4 has previously shown that the intermetallic ZrCrz takes up hydrogen into solid solution up to a composition H/ZrCr2 = 1.14 at room temperature and 1 atm hydrogen. A ZrCr2 hydride was stated to have a fcc structure. The binary Zr-V system has been investigated by williams5 although Rostoker and Yamamoto 6 had given earlier a partial phase diagram. ZrV2 was the only intermediate phase found in the system. wallbaum7 reported earlier that the compound ZrV2 hp the MgZm (CJ4) type structure with a = 5.288A and c = 8.664A. This was not comfirmed by Elliot8 nor by Matthias, Compton, and corenzwit9 who reported that ZrV2 has a cubic MgCua LC15) type structure. The latter authors gave a = 7.429A. Also, several authors do not agree on the temperature of the peri-tectic horizontal. It appears that ZrV2 may exist in several modifications. A high capacity for occluding hydrogen was reported by Beck4 who found H/ZrV2 = 1.38 at room temperature and 1 atm of hydrogen. ZrMoz is the only intermetallic phase in the Zr-Mo system.10 ZrMoa is formed by a peritectic reaction of the melt with a molybdenum-rich solid solution. ZrMo2 has the C15-type structure with a = 7.59A. MATERIALS High-purity chromium, vanadium, and molybdenum were used together with grade 1 crystal bar zirconium to prepare the alloys. Table I lists the chemical analysis and the sources for the metals. Ten-gram alloy compacts were levitated and melted in an inert argon

Jan 1, 1968