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By R. S. Busk

Niels Engel (University of Alabama, University, Ala.)— In this paper it was pointed out that the electron-gas and energy-band theory accounts for the fact that the lattice parameters exhibit a sudden change when the electron concentration (number of bonding electrons per atom) exceeds a certain number around two. This statement is said to support and prove the electron-gas theory. But this theory is not able to account for a series of experimental data. Also several expectations, deduced from this theory, are not found to exist. In Figs. 6 and 7 the energy bands of the second and third periods are given as they must be assumed in order to account for the electrical properties of the elements in these periods. In Figs. 6 and 7 the electron-gas and energy-band theory is compared with the electron-oscillator hypothesis in accounting for the properties of the elements in the second and third periods. Fig. 6 shows the second period, The energy-bands are overlapping and separated to be in agreement with the electrical conductivity of the elements. The oscillator hypothesis explains conductivity due to electron vacancies. In graphite there is a closed s-shell in every other atom and two vacancies in the others. Conductivity is therefore only maintained by migration of s-electrons in graphite. In boron there are no s-electrons. The diatomic molecules of nitrogen and oxygen and the paramagnetism of oxygen can be accounted for by a similar behavior as the s-electrons of the bonding electrons. But this explanation will deviate too much for the purpose of this discussion. Fig. 7 shows the third period. In the energy-band picture about two s-electrons are assumed in magnesium and aluminum, but only one s-electron is assumed in silicon. The diamond lattice is assumed to be controlled by a sp3 hybrid. However the electron distribution develops ideally according to the oscillator hypothesis. Only sodium, magnesium, and aluminum exhibit electron vacancies and conductivity. To account for the insulator properties in Si, P, and S in the third period it must be assumed that the four last added p-electrons must be taken up in bands containing only one electron per band.' (Compare the electron band picture in Hume-Rothery.' Hume-Rothery does not consider the insulator properties of the nonmetals.) In the second period already the first p-electron must have entered a single electron band. Based on the energy-band picture in Figs. 6 and 7, the following questions must be asked: 1—Is it consistent with the energy-band idea that electrons of the same kind (p-electrons) can be divided into separated bands? 2—Is it consistent with the energy band idea that single electron bands can exist? 3—Why are the first two p-electrons (in boron and diamond) separated into two single electron bands in the second period, but overlapping in the third period (aluminum)? 4—Why are s-electrons and d-electrons taken up in continuous overlapping bands, while p-electrons are divided into single electron bands? 5—Why do the peaks and valleys (y and w and further x and z) of the energy band below four electrons per atom not show up in the electrical conductivity of alloys? For example consider the Li-Mg system or the alloys between Mg and three electron metals where the mentioned discontinuity in the lattice parameter is found. 6—Why does the beginning of the p-electron band (x) not show up in the lattice constants similar to the filling up of the s-electron band (z) ? In magnesium alloys the electron-gas theory postulates the first Brillouin zone to be filled at about two electrons per atom. This is claimed to explain the sudden change in lattice spacing and c/a values of several magnesium alloys when the electron concentration exceeds a few percentage points over two electrans per atom. This was emphasized in the paper by Busk. If the electron-gas energy-band theory is correct a sudden change in electrical conductivity and possibly other properties .should be expected when the same electron-concentration or temperature is exceeded. A sudden change in lattice spacing or other properties should also be expected when the filling degree is such that p-electrons are introduced into the p-band, for example at x in Figs. 6 and 7. Such phenomena are at found by experiment. and If the number of electrons should vary with the energy level depending on the average number of bonding electrons per atom, the electrical conductivity should be expected to vary in accordance with the energy band layout (Figs. 6 and 7) caused by different numbers of conducting electrons at different filling up degrees. Nothing indicating such a behavior is observed. In addition to these discrepancies between the electron-gas and energy-band theory and measured data, the theory violates the principles developed along with the Bohr theory of atomic structure. According to these principles a filled shell is saturated and therefore unable to form bonds. Therefore two S-electrons per atom should form a closed or saturated shell, which has been pointed out as accounting for the inability of helium to form bonds. Beryllium, magnesium, or calcium atoms with two s-electrons should be expected to form inert atoms with properties almost like the helium atoms. Several other inconsistencies and disagreements with measured data of the energy-band theory can be mentioned. Some of these are discussed with reference to other papers. 8 Because the electron-gas and energy-band theory seems to fail on several points, I have developed another theory which can account for all the phenomena the electron-gas theory is able to account for. This new theory is further able to account for things which are impossible to explain by the electron-gas theory at the present state.

Jan 1, 1953

By W. C. Clarke

An empirical study of the nature of the embrittle-ment which occurs in martensitic and semiaustenitic precipitation hardening stainless steels upon exposure at temperatures of from about 550" to 875°F has been undertaken. This work was aimed at determining cazusation and means of controlling this phenomenon. A commercial copper bearing precipitation hardening alloy was used as a basic material for study. The effect of heat treatment variables was studied as was the effect of variations in analysis. It is concluded from the evidence that martensitic and semiaustenitic precipitation hardening stainless steels are subject to 885°F ernbrittlement similar to that observed in the straight chromium stainless steels. A characteristic of precipitation hardening stainless steels which has limited their use in certain applications is that they embrittle when held at temperatures in the range of from about 550" to 900°F. This is true to a more or less degree in all currently available alloys, either the basically martensitic type or the semiaustenitic type. The rate of embrittlement varies markedly with exposure temperature, being low at 550" to 600°F and in-creasing as the temperature increases. In spite of this embrittlement, these alloys with their unique combination of high mechanical strength, reasonable toughness, and good corrosion resistance are used in many hundreds of applications. Nevertheless, there are potential applications where the embrittle-ment described is a limiting factor. The purpose of this investigation was to study the embrittlement of these alloys and to find a way to control or eliminate it. GUIDELINES USED IN PRESENT WORK The work reported in this paper is based on a study of 17-4 PH*, a very widely used alloy. It has been used *Trademark of Armco Steel Corp., licensor. in pressurized water and boiling water atomic reactors operating at about 550°F for a number of years. As the life of such equipment is extended or operating temperatures are raised, the possibility of embrit-tlement becomes of increasing concern to materials engineers. Much investigation work was done with respect to the use of 17-4 PH at 550°F. K. C. Antony' states "Such estimation" (of an activation energy for the diffusion of chromium in iron) "would indicate W. C. CLARKE, Jr. is Senior Research Engineer, Advanced Materials Division, Armco Steel Corp., Baltimore. Md. This manuscript is based on a talk presented at the symposium on New Developments in Stainless Steel, sponsored by the IMD Corrosion Resistant Metals Committee, Detroit, Mich., October 14-15, 1968. significant secondary aging is improbable at temperatures less than 700°F within normal component service life". This statement is modified however by the recognition of the accelerating tendencies of applied stress and internal stress as well as the possible effect of irradiation. In this investigation of 17-4 PH, the H 1100 (1900°F-1 hr oil quench or air cool + 1100°F-4 hr-air cool) condition was used, partly because this condition is normally used in atomic reactors. As shown later, the precipitation hardening temperature has no real bearing on the rate of embrittlement. An exposure temperature of 800°F was selected since embrittlement at 800°F is rapid, permitting development of relative data in time periods of 400 to 500 hr. For those not familiar, a nominal present day analysis of 17-4 PH is: C Mn P S SiCrNiCuCbN 0.04 0.30 0.015 0.015 0.60 16.00 4.30 3.25 0.23 0.030 TYPICAL BEHAVIOR OF 17-4 PH Figs. 1 and 2 show the behavior of a commercial heat of 17-4 PH under the conditions defined. Characteristically, 800°F exposure causes a rapid drop in Charpy V-notch impact strength. Tensile and yield strengths gradually increase and a gradual loss of elongation and reduction of area occur, accompanied by an increase in hardness. Notched tensile strength increases to 125 hr exposure and then sharply decreases after exposure for 500 hr. The notched vs un-notched tensile ratio remains virtually constant to exposure for 125 hr (1.67 to 1.56) but drops to 1.15 after 500 hr. Tensile ductility is not alarmingly affected even after much longer exposure times than these. For example, samples aged at 1100°F for 1 hr exposed at 800°F for 4000 hr showed a drop in elonga-tion of from 13 to 11 pct and in reduction of area of from 58 to 37 pct. Notched impact is the property SmIgth KSI 3JJ[/__________^UTS-Nrteh 260 ;/- 240 —^ 200 UTS-Smooth________._, o ioo mo Sob" m Too Hours Exposure Fig. 1—Effect of exposure at 800°F for various times on notched tensile strength and smooth tensile and 0.2 pct yield strength of 17-4 PH in the H 1100 condition.

Jan 1, 1970

By Eugene A. Thiers, William V. Morris

INTRODUCTION Direct reduction processes reduce the various commercial forms of iron oxide (pellets, concentrate, fines, etc.) to metallic iron at temperatures lower than that of molten iron. Thus, this technology includes practically, all iron reduction processes other than blast furnaces and electric pig iron furnaces (whose output in terms of world production is negligible). The product of these processes which is known as direct reduced iron (DRI), or sponge iron, is primarily used as a source of metallic iron in steel-making operations. Interest in DRI, which has been significant since the early 1960s, increased significantly in recent years with the rapid growth of DRI installed capacity throughout the world. The importance of the subject for the Circum-Pacific region stems directly from the influence that DRI has on iron ore consumption and on future steel development for this region. Although there is widespread agreement that electric furnaces will continue to increase their share of global steel output, and especially so in the countries of the Pacific Steel community, some doubts exist about future scrap supplies being adequate to support growth at past rates. The authors believe that such doubts are soundly based. As this paper points out, the total supply of all metallics used in electric furnaces may not be adequate to support the extrapolated rapid growth in electric furnace steel production. This paper seeks to provide perspective on the global and Circum-Pacific prospects for DRI in light of recent energy price developments and the current recession. In this regard, the demand for DRI within the context of recent evolutionary patterns in steel-making, the outlook of DRI supply in terms of prevailing production costs, and the prospects of new technology are discussed. THE DEMAND FOR DRI Although several reports published in the last 10 years predict high rates of growth in DRI, the subject remains a controversial one. Significant growth has indeed occurred, but not to the extent anticipated in the studies summarized in Table 1. The substantial difference between previous expectations and present reality can be ascribed primarily to: (1) lower growth in steel production than formerly anticipated; (2) numerous cancellations of DRI facilities that were previously announced; and (3) a fundamental and probably irreversible change in the economics of DRI production. Note that DRI capacity at the end of 1980 was about 16 million tonnes, a significantly lower figure than any of the projections above. In addition, DRI production was only about half of capacity, reflecting the abnormally low rates of capacity utilization in this industry. [ ] Before examining the current outlook in steel, it is pertinent to note that the market for DRI is usually different in the industrialized countries of the West from that in developing countries. In the former, the available infrastructure and industry's diversification extends DRI's potential markets to numerous steelmaking, foundry, and other industrial applications, although competition from scrap and other forms of metallic iron is constant. Scrap is generally available in these countries and, therefore, DRI competes with it in electric furnace steelmaking, basic oxygen steelmaking (as a coolant), cupola foundry operations, or as an additive in the metallic charge for open hearth and blast furnaces. On the other hand, DRI in developing countries is often allocated exclusively to domestic electric furnace steelmaking or, when capacity exceeds domestic captive requirements, to export. Notwithstanding quality considerations, DRI is being and is likely to continue to be used predominantly as a source of metallics in iron and steel-making. Other uses of DRI, such as in copper cementation represent a marginal market in terms of overall tonnage and can be ignored at this point. Therefore, DRI demand is-determined by the overall availability of metallic scrap in its various forms--a function of steel production and its probable evolution. The Global Steel Outlook Given the present recession, an objective appraisal of the long-term outlook for steel is particularly difficult. On the one hand, historical trends and, especially, the inertial forces associated with such a basic industry as steel must be recognized; such trends suggest that the current stagnation with

Jan 1, 1982

By D. K. Das, P. A. Beck, S. P. Rideout

IN a previous publication1 1200°C isothermal phase diagram sections were given for the Cr-CO-Ni, Cr-Co-Fe, Cr-Co-Mo, and Cr-Ni-Mo ternary systems, in which the a phase formed narrow, elongated solid solution fields. The present investigation is concerned with the 1200°C isothermal sections of the Co-Ni-Mo, Co-Fe-Mo, and Ni-Fe-Mo ternary systems. A prominent feature of these systems is the presence of narrow, elongated µ phase fields. The crystal structure of the phase designated as µ both here and in the previous publication1 was determined by Arnfelt and Westgren.2 For the (CO, W)µ phase, named by them Co,W, (and also frequently designated as a), these authors found that the crystal system is hexagonal-rhombohedra1 and the space group is D53d — R3,. Westgren and Mag-neli3 later found that isomorphous phases exist in the Fe-W and the Fe-Mo systems (these phases are often referred to as < and E, respectively). Henglein and Kohsok4 stated that the phase described by them as Co7Mo,; (otherwise frequently designated as c) is also isomorphous with the above three. The Co-Fe-Mo system was investigated at 1300°C by Koester and Tonn,5 who found a continuous series of solid solutions between (Co, MO)µ and (Fe, MO)µ Koester6 also indicated similar uninterrupted solid solutions in the Ni-Fe-Mo system. However, since the Ni-Mo binary system does not have a phase isomorphous with F, Koester&apos;s diagram is expected to be erroneous. No data appear to be available in the literature concerning the Co-Ni-Mo system. The face-centered cubic (austenitic) solid solut,ions of iron, nickel, and cobalt, which are quite extensive in all three systems at 1200°C, are here designated as the a phase. The body-centered cubic (ferritic) solid solutions, based on iron, are designated in this report as the ? phase, in conformity with the nomenclature used previously.&apos; Experimental Procedure The alloys were prepared by vacuum induction melting in zirconia and alumina crucibles. The lot analyses for the metals used have been given.&apos; The number of alloys prepared was 46 for the Co-Ni-Mo system, 65 for the Co-Fe-Mo system, and 113 for the Ni-Fe-Mo system. The compositions of these alloys were selected with due regard to maximum usefulness in locating phase boundaries. The alloy specimens were annealed at 1200°C in an atmosphere of purified 92 pct helium and 8 pct hydrogen mixture. Alloys consisting almost entirely of the face-centered cubic austenitic a phase, or of the body-centered cubic ferritic c phase were double-forged with intermediate annealing. The double-forged specimens were then final annealed for 90 hr at 1200 °C and quenched in cold water. Alloys containing considerable amounts of any of the other phases could not be forged. Such specimens were annealed for 150 hr at 1200°C and quenched. Microscopic specimens of all alloys were prepared by mechanical polishing, in many cases followed by electrolytic polishing. Description of the polishing and etching procedures used and tabulation of the intended compositions of the alloys prepared are being published in two N.A.C.A. Technical Notes.7,8 , Many of the alloys were analyzed chemically and, in general, the results are in excellent agreement with the intended compositions. X-ray diffraction samples were prepared by filing or crushing homogenized alloy specimens and by reannealing the obtained powders in evacuated and sealed quartz tubes. After annealing for 30 min at 1200°C the tubes were quenched into cold water. X-ray diffraction patterns were made with unfiltered chromium radiation at 30 kv, using an asymmetrical focusing camera of high dispersion. X-ray diffraction and microscopic methods were used jointly to identify the phases present in each specimen. The amounts of the phases in each alloy were estimated microscopically. The phase boundaries were located by the disappearing phase method. The results were used to construct 1200°C isothermal sections for the three ternary phase diagrams. The accuracy of the location of the phase boundaries determined in this manner is estimated to approximately ±1 pct of each component. The portion of the three phase diagrams lying between the µ, P, and 6 phases on the one hand, and the molybdenum corner on the other, has not been investigated. Recently Metcalfe reported0 a high temperature allotropic form of cobalt on the basis of dilatometric results and of cooling curves. In the present work no attempt was made to search for the new phase in the cobalt corner of the Co-Fe-Mo and Co-Ni-Mo systems. No alloy was prepared with more than 80 pct Co; the alloys used were intended to locate the boundary of the a phase saturated with cL. The microstructures of the quenched a alloys near the cobalt COrner gave no suggestion of an in-suppressible transformation On quenching. The location of the boundaries of the a + ? two-phase fields in the Fe-Ni-Mo and Fe-CO-MO systems was determined entirely by the microscopic method. The face-centered cubic a alloys near the ? field transform partially or wholly into the body-centered cubic ? phase on quenching from 1200°C to room temperature. The ? formed in this manner has an

Jan 1, 1953

By C. T. Butler, W. W. Kay, R. D. Boddorff, R. L Ash

DRILLING and blasting in anthracite open-pit mines is a continuous problem to contractors and explosive engineers because of the diverse conditions caused by the nature of the geological formations, the extensive mining of the portions of coal beds near the surface, and the proximity of many strip pits to populated areas. Pennsylvania anthracite occurs in four separate long and narrow fields totaling only 480 sq miles. The coal measures are rock strata and coal beds that are considerably folded and faulted. The crests of the anticlines are eroded extensively. The beds outcrop on the mountain sides and dip under the valleys. At first only the upper portions of the syn-clines could be stripped. Now stripping to increasingly greater depths is economically possible, as is indicated by the fact that the proportion of freshly mined anthracite produced by strip mining has increased from 3.7 pct of the total tonnage in 1930 to 29.6 pct in 1950. Much of the rock overlying the deeper beds now being stripped is so extensively broken that considerable difficulty is experienced in drilling satisfactory blast holes and in using explosives in such manner as to insure a uniformly broken material easily removed by the excavating machinery. Such breaking of rock strata has occurred because the bed now being stripped has been mined extensively in former years by underground methods, and tops of gangways and chambers have subsequently failed. Draglines are used to uncover coal where the overburden can be moved with little or no re-handling. These machines range in size from those having a 2 cu yd capacity bucket on a 60-ft boom to those handling a 25 cu yd bucket on a 200-ft boom. Draglines are also used to strip to the bottom of the coal basins if the depth and the distance between the crops are not too great. For this type of operation blast holes are drilled full depth to the bed. These holes are commonly 30 to 90 ft deep; however, in exceptional cases, holes may be as shallow as 12 ft or as deep as 130 ft. Drilling is normally done for blasts of 12,000 to 60,000 cu yd of overburden, 30,000 cu yd being considered an average blast if vibration is not the controlling factor. Where the stripping of wide basins or the exposure of a moderately pitching vein makes the use of draglines impractical, dipper front shovels equipped with 4 to 6 cu yd buckets load into trucks. Overburden is removed in benches of 25 to 30 ft with blast holes drilled 4 or 5 ft deeper than the planned floor of the bench. For shovels under 5 cu yd bucket capacity the volume blasted varies from 8000 to 12,000 cu yd, whereas a volume of 30,000 to 50,000 cu yd of overburden is frequently blasted at one time for the larger shovels where vibration is not an important factor. During the past decade the churn drill, generally the Model 42-T Bucyrus-Erie blast hole drill equipped for drilling 9-in. diam holes, has become the most common blast hole drilling machine. Electricity powers half the churn drills in use and is preferred on the large strippings where electric shovels are operated and the working area is concentrated. On these operations the cost of additional electricity for the drills is less than the cost of fuel to operate diesel units because of the existing large demand load of the excavating equipment. Moreover, electric motors start more easily in cold weather and generally are less expensive to maintain. Diesel driven units are employed where a higher degree of mobility is required. The average drilling speed is 8 ft per hr, although in softer rocks a rate of 15 ft per hr is attained. Where rock is hard and strata is badly broken, drill speeds may be less than 2 ft per hr. Low drilling production results under these circumstances when loose material falling from the upper portion of the drill holes causes drill stems to be jammed. Rock formations vary so greatly in the region that a 9-in. diam churn drill bit may become dull after drilling only 2 ft or may drill satisfactorily for 56 ft; however, an average of 35 ft is usual in sandstone of medium hardness. Dull bits are hoisted to flat bed trucks by the sand line of the drill and are usually sharpened in the contractor&apos;s bit shop adjacent to the job. Care is generally taken to cover the thread end of the bit with a cap. To facilitate handling of bits around the drill, a heavy thread protector having an eye top is becoming more popular than the flat-top rubber or metal cap furnished with new bits. The 9-in. diam blast holes for a 25 to 30 ft bench are normally on 18x18 ft to 20x20 ft spacings, depending on the character of the overburden, although in broken ground 15x18 ft centers may be used to obtain better breakage and a more even bottom for the bench. The patterns of holes for shots

Jan 1, 1953

By R. D. Boddorff, R. L. Ash, C. T. Butler, W. W. Kay

DRILLING and blasting in anthracite open-pit mines is a continuous problem to contractors and explosive engineers because of the diverse conditions caused by the nature of the geological formations, the extensive mining of the portions of coal beds near the surface, and the proximity of many strip pits to populated areas. Pennsylvania anthracite occurs in four separate long and narrow fields totaling only 480 sq miles. The coal measures are rock strata and coal beds that are considerably folded and faulted. The crests of the anticlines are eroded extensively. The beds outcrop on the mountain sides and dip under the valleys. At first only the upper portions of the syn-clines could be stripped. Now stripping to increasingly greater depths is economically possible, as is indicated by the fact that the proportion of freshly mined anthracite produced by strip mining has increased from 3.7 pct of the total tonnage in 1930 to 29.6 pct in 1950. Much of the rock overlying the deeper beds now being stripped is so extensively broken that considerable difficulty is experienced in drilling satisfactory blast holes and in using explosives in such manner as to insure a uniformly broken material easily removed by the excavating machinery. Such breaking of rock strata has occurred because the bed now being stripped has been mined extensively in former years by underground methods, and tops of gangways and chambers have subsequently failed. Draglines are used to uncover coal where the overburden can be moved with little or no re-handling. These machines range in size from those having a 2 cu yd capacity bucket on a 60-ft boom to those handling a 25 cu yd bucket on a 200-ft boom. Draglines are also used to strip to the bottom of the coal basins if the depth and the distance between the crops are not too great. For this type of operation blast holes are drilled full depth to the bed. These holes are commonly 30 to 90 ft deep; however, in exceptional cases, holes may be as shallow as 12 ft or as deep as 130 ft. Drilling is normally done for blasts of 12,000 to 60,000 cu yd of overburden, 30,000 cu yd being considered an average blast if vibration is not the controlling factor. Where the stripping of wide basins or the exposure of a moderately pitching vein makes the use of draglines impractical, dipper front shovels equipped with 4 to 6 cu yd buckets load into trucks. Overburden is removed in benches of 25 to 30 ft with blast holes drilled 4 or 5 ft deeper than the planned floor of the bench. For shovels under 5 cu yd bucket capacity the volume blasted varies from 8000 to 12,000 cu yd, whereas a volume of 30,000 to 50,000 cu yd of overburden is frequently blasted at one time for the larger shovels where vibration is not an important factor. During the past decade the churn drill, generally the Model 42-T Bucyrus-Erie blast hole drill equipped for drilling 9-in. diam holes, has become the most common blast hole drilling machine. Electricity powers half the churn drills in use and is preferred on the large strippings where electric shovels are operated and the working area is concentrated. On these operations the cost of additional electricity for the drills is less than the cost of fuel to operate diesel units because of the existing large demand load of the excavating equipment. Moreover, electric motors start more easily in cold weather and generally are less expensive to maintain. Diesel driven units are employed where a higher degree of mobility is required. The average drilling speed is 8 ft per hr, although in softer rocks a rate of 15 ft per hr is attained. Where rock is hard and strata is badly broken, drill speeds may be less than 2 ft per hr. Low drilling production results under these circumstances when loose material falling from the upper portion of the drill holes causes drill stems to be jammed. Rock formations vary so greatly in the region that a 9-in. diam churn drill bit may become dull after drilling only 2 ft or may drill satisfactorily for 56 ft; however, an average of 35 ft is usual in sandstone of medium hardness. Dull bits are hoisted to flat bed trucks by the sand line of the drill and are usually sharpened in the contractor&apos;s bit shop adjacent to the job. Care is generally taken to cover the thread end of the bit with a cap. To facilitate handling of bits around the drill, a heavy thread protector having an eye top is becoming more popular than the flat-top rubber or metal cap furnished with new bits. The 9-in. diam blast holes for a 25 to 30 ft bench are normally on 18x18 ft to 20x20 ft spacings, depending on the character of the overburden, although in broken ground 15x18 ft centers may be used to obtain better breakage and a more even bottom for the bench. The patterns of holes for shots

Jan 1, 1953

By R. D. Boddorff, R. L. Ash, C. T. Butler, W. W. Kay

DRILLING and blasting in anthracite open-pit mines is a continuous problem to contractors and explosive engineers because of the diverse conditions caused by the nature of the geological formations, the extensive mining of the portions of coal beds near the surface, and the proximity of many strip pits to populated areas. Pennsylvania anthracite occurs in four separate long and narrow fields totaling only 480 sq miles. The coal measures are rock strata and coal beds that are considerably folded and faulted. The crests of the anticlines are eroded extensively. The beds outcrop on the mountain sides and dip under the valleys. At first only the upper portions of the synclines could be stripped. Now stripping to increasingly greater depths is economically possible, as is indicated by the fact that the proportion of freshly mined anthracite produced by strip mining has increased from 3.7 pct of the total tonnage in 1930 to 29.6 pct in 1950. Much of the rock overlying the deeper beds now being stripped is so extensively broken that considerable difficulty is experienced in drilling satisfactory blast holes and in using explosives in such manner as to insure a uniformly broken material easily removed by the excavating machinery. Such breaking of rock strata has occurred because the bed now being stripped has been mined extensively in former years by underground methods, and tops of gangways and chambers have subsequently failed. Draglines are used to uncover coal where the overburden can be moved with little or no rehandling. These machines range in size from those having a 2 cu yd capacity bucket on a 60-ft boom to those handling a 25 cu yd bucket on a 200-ft boom. Draglines are also used to strip to the bottom of the coal basins if the depth and the distance between the crops are not too great. For this type of operation blast holes are drilled full depth to the bed. These holes are commonly 30 to 90 ft deep; however, in exceptional cases, holes may be as shallow as 12 ft or as deep as 130 ft. Drilling is normally done for blasts of 12,000 to 60,000 cu yd of overburden, 30,000 cu yd being considered an average blast if vibration is not the controlling factor. Where the stripping of wide basins or the exposure of a moderately pitching vein makes the use of draglines impractical, dipper front shovels equipped with 4 to 6 1/2 cu yd buckets load into trucks. Overburden is removed in benches of 25 to 30 ft with blast holes drilled 4 or 5 ft deeper than the planned floor of the bench. For shovels under 5 cu yd bucket capacity the volume blasted varies from 8000 to 12,000 cu yd, whereas a volume of 30,000 to 50,000 cu yd of overburden is frequently blasted at one time for the larger shovels where vibration is not an important factor. During the past decade the churn drill, generally the Model 42-T Bucyrus-Erie blast hole drill equipped for drilling 9-in. diam holes, has become the most common blast hole drilling machine. Electricity powers half the churn drills in use and is preferred on the large strippings where electric shovels are operated and the working area is concentrated. On these operations the cost of additional electricity for the drills is less than the cost of fuel to operate diesel units because of the existing large demand load of the excavating equipment. Moreover, electric motors start more easily in cold weather and generally are less expensive to maintain. Diesel driven units are employed where a higher degree of mobility. is required. The average drilling speed is 8 ft per hr, although in softer rocks a rate of 15 ft per hr is attained. Where rock is hard and strata is badly broken, drill speeds may &apos; be less than 2 ft per hr. Low drilling production results under these circumstances when loose material falling from the upper portion of the drill holes causes drill stems to be jammed. Rock formations vary so greatly in the region that a 9-in. diam churn drill bit may become dull after drilling only 2 ft or may drill satisfactorily for 56 ft; however, an average of 35 ft is usual in sandstone of medium hardness. Dull bits are hoisted to flat bed trucks by the sand line of the drill and are usually sharpened in the contractor&apos;s bit shop adjacent to the job. Care is generally taken to cover the thread end of the bit with a cap. To facilitate handling of bits around the drill, a heavy thread protector having an eye top is becoming more popular than the flat-top rubber or metal cap furnished with new bits. The 9-in. diam blast holes for a 25 to 30 ft bench are normally on 18x18 ft to 20x20 ft spacings, depending on the character of the overburden, although in broken ground 15x18 ft centers may be used to obtain better breakage and a more even bottom for the bench. The patterns of holes for shots

Jan 1, 1952

By C. Richard Tinsley

Like most minerals, coal is inherently a demand-limited commodity. The very sedimentary nature of its occurrence implies greater availability potential than demand. But this situation is overridden by economics among fuels, between coals, and within coal blends. Such considerations make coal forecasting a very hazardous profession indeed. THERMAL COAL If one thought that the lead times involved with a mining project were very long, one has obviously not been exposed to the planning process in the electric generation business - a process seriously confounded by shifts in load growth, environmental pressures, capital intensity, security of fuel sourcing, inter-fuel economics, and so on. But as a general rule, the near-term forecasts for thermal coal can reliably be based on a bottom-up, plant-by-plant analysis. Cement plant conversions can also be reasonably estimated next in order of reliability, although they have a much wider spectrum of coal qualities and fuel sources to choose from with a notably higher tolerance for sulfur and ash. Finally, industrial demand can be assembled from the estimates for conversions by pulp/paper plants, chemical plants, etc. The industrial sector is harder to estimate, since it may involve small boilers or dual-fired units. Assessing demand in the Pacific Rim is relatively a straightforward process in the near term because the major importing countries are all located on the Asian continent with either negligible or very minor (yet stable) indigenous coal production, (itself often operated on a subsidized basis). Furthermore, all imports are seaborne. These major importers are Japan, Korea, Taiwan, and Hong Kong with Thailand, Singapore, and Malaysia up-and-coming consumers. The suppliers to this market all have substantial reserves to back up decades of exports to these countries. Australia, the US, Canada, South Africa, China, and the USSR dominate the supply side. The second oil-shock of 1979/1980 has convinced the importers that reliance on oil can be expensive and eminently interruptible. Thus, they are determined to diversify away from oil&apos; to nuclear and coal for generating electricity and for coal for other purposes where possible. This trend is seen to continue even in the face of the oil glut worldwide and oil-price reductions in early 1982. But the importers are also convinced that reliance on one coal source and, in particular, one infrastructure route for the coal chain from mine to consumer can be equally expensive and interruptible. Strikes in the US and Australia; excessive demurrage at certain ports; relegation of coal to a lower priority on multiple-use railroads in the USSR and China; and concern over escalation on high-infrastructure or high-freight coal chains are among the risks worrying the importers. As a consequence, Pacific Rim thermal coal purchases are being allocated among supplier nations, between ports, and within each country. An example of Japan&apos;s shift away from Australia and toward the US and Canada is shown in the estimates in Table 1. But the confidence of the import estimates deteriorates sharply beyond the plant conversion timetables and construction schedules in the near term. If part of the second generation of coal-fired power plants can handle lower-energy coals, the field of suppliers could widen to accept sizeable tonnages from Alaska, Wyoming, Alberta, or New Zealand resources. These supply sources generally have some infrastructure or freight advantage to compensate for their lower quality and to compete on a delivered energy-unit basis. These also offer diversification in sourcing. And the possibility of coal liquefaction in Japan further widens the sourcing network. A great number of Pacific Rim coal forecasts have been generated, especially for Japanese thermal-coal imports which are expected to grow strongly in the 1980&apos;s. Since the Japanese themselves have not yet settled their energy policy, the exact numbers are hard to call. Nevertheless, at 50 million tonnes of imports in 1990, Japan would consume 50-60% of the total Asian thermal coal imports as shown on Tables 2 and 6. The next most important consumers are the "island" nations of Korea, Taiwan, and Hong Kong (see Tables 3-5). All three are embarking on power plant developments usually with captive unloading facilities, capable of accepting more than 100,000-dwt vessels. Korea, with no-indigenous bituminous coal, is not especially enamoured with US coals, which are deemed too heavily loaded by freight and infrastructure costs -- up to 70% of the delivered price. Thermal coal contracts are presently split to Australia (70%) and to Canada (30%). Korea Electric Power Co. is already considering second-generation boilers capable of burning lower-quality coals than the present standard. Korea does burn domestic anthracite.

Jan 1, 1982

By Eckhard Nembach

The phase diagram of the system Pb-In has been investigated between -27° and + 40°C, using nzainly X-ray dijfraction. In accordance with t her mo dynamic measurements by Heumann and Predel, a segregation occurs at low temperatures, though not in the form of a nziscibility gap. THE phase diagram of the system Pb-In has been the subject of extensive investigations,1&apos;1 but recently Heumann and prede13 concluded from their thermodynamic data that a new feature should occur below room temperature. These authors observed that the maximum values for the enthalpy and entropy of mixing, which occurred at a composition of 50 at. pct Pb, were +400 and —1.7 cal per g-atom deg, respectively. From this the authors estimated that a miscibility gap should occur below 30°C, centered at 50 at. pct Pb. Resistivity measurements seemed to support this view. These authors proposed the phase diagram outlined in Fig. 1. Three phases exist at 30°C: the tetragonal indium phase with c/a > 1, the tetragonal intermediate phase a, with c/a < 1, and the fcc lead phase. During an investigation of the superconducting properties of Pb-In alloys. it has been observed4 that aging a specimen with 50 at. pct Pb for 14 days at -18°C decreased the superconducting transition temperature about 0.13"K and tripled the transition width. In this paper, the results of an investigation of the Pb-In phase diagram in the temperature range from — 2T to +40°C are reported. Superconductivity and X-ray methods have been used. 1) SPECIMEN PREPARATION The materials were provided by the American Smelting and Refining Co. According to the manufacturer their purity was 99.999 pct. The weighed amounts of the constituents were sealed in quartz tubes under an atmosphere of 10 torr helium, mixed for 24 hr in a rocking furnace at 380°C, quenched in ice water, and homogenized at 20" to 30°C below the solidus line, established by Heumann and Predel. The annealing times were 144 hr for specimens containing Less than 30 at. pct Pb and 36 hr for the remainder. 2) SUPERCONDUCTIVITY EXPERIMENTS The specimens were quenched from the homogeniza-tion treatment into ice water and their superconducting transition temperatures T, measured. The procedure used has been described in Ref. 4. The transition was detected by the change of the mutual induc- tance of two coaxial coils containing the sample. T, was defined as the temperature at which 50 pct of the total change in inductance had occurred. The repro-ducibility with which T, could be measured was i0.002"K. Then the specimens with lead contents between 38 and 75 at. pct were aged for 7 days at temperatures between -30" and 40°C. If this treatment caused T, to change by more than 0.005"K or the width of the transition to increase by more than 0.002"K, it was concluded that the specimen had undergone a phase change and no longer consisted only of the fcc lead phase: as it did immediately after homogenizing. The result is shown in Fig. 2. From this one can estimate at what temperatures and concentrations phase changes occur. The X-ray measurements were based on these preliminary results. 3) X-RAY EXPERIMENTS Because of the softness of the material, relatively coarse powders. 75 p, had to be used, which were filed in a helium atmosphere from homogenized specimens. The powders were annealed at least 30 min at temperatures between 120" and 16OJC, depending on their concentration, and quenched in ice water. Then their X-ray patterns were taken at -178°C with a Picker diffractometer, model 3488K, and a cold stage. on which the specimen was in thermal contact with a liquid-nitrogen reservoir. In this way the following relation was established for the fcc lead phase: a = 4.697 + 0.00247C for 40 5 C 5 75 11 where n is the lattice constant (A) and C is the at. pct of lead. The coarseness of the powder made it impossible to use lines with 0 > 75 deg; therefore n was averaged from lines with 45 deg 5 0 5 75 deg. The results were reproducible to within i0.05 pct. Relation [I] is very similar to the one found by Heumann and Predel at room temperature. Following this, homogenized specimens with compositions between 15 and 56 at. pct Pb were aged for at least 10 days at temperatures between -27" and

Jan 1, 1970

By R. E. Zinkham, R. J. Goodwin

A mathematical study has been made of the amount of support a cement sheath could provide to casing cemented into the earth. Several assumptions were required to make the analysis, but only two of them are limiting: (I) the pipe must be completely surrounded with cement, and (2) any mud filter cake between the cement and formation has the same physical properties as either the cement or formation. The calculations showed that little support would be provided to the pipe before an unsupported cement sheath failed in tension; however, when the cement is confined between the pipe and wellbore and is loaded in compression, the pipe could receive a considerable amount of support. In fact, the theoretical results indicate the lower grades and larger sizes of pipe could have their working pressures doubled when reasonable compressive loads were applied to a surrounding cement sheath. These data are shown in six charts. Other down-hole conditions such as setting the cement under pressure, increased temperature and cement confinement all tend to increase the potential usefulness of the sheath. Because of size limitations, a laboratory program to verify the most important results of this mathematical study would be very difficult. However, small-scale field tests would be practicable. This paper shows that, if a solid cement sheath can be obtained in the field by either primary cementing or by repair after detection of flaws by surveys such as the new cement-bond logs, the use of this approach to reducing pipe costs merits further consideration. INTRODUCTION A modification in casing design practices is proposed which may either reduce the amount and grade of steel required to contain a specified internal pressure or permit the working pressure to be increased for a specified weight and grade of pipe. One of the more important considerations in casing design is its resistance to collapse; however, Bowers&apos; and, more recently, O&apos;Brien and Goins&apos; have shown many casing programs are unnecessarily conservative in this respect, and they have indicated how savings can be made by designing for more realistic down-hole conditions. Earlier, Saye and Richardson howed that pipe costs could be reduced by considering the cement sheath as a part of the casing string when collapse resistance was being calculated. More recently, Rogers4 has raised the question as to whether a cement sheath might be considered in the design for burst resistance of the cemented casing. Calculations have been made for the increased burst resistance a cement sheath would provide for casing in a wellbore, and the results show that a sizable amount of support could be obtained in some instances. These data are presented in addition to a discussion of several other factors that are considered to affect the burst strength of pipe supported by cement. Two types of support are treated: Case I for tensile loading of the unconfined cement sheath, and Case for compressive loading of the confined cement sheath. ANALYTICAL TREATMENT AND RESULTS CASE I—TENSILE STRESSES IN AN UNCONFINED CEMENT SHEATH Conditions like this would most likely occur in a greatly enlarged portion of the hole where the cement was not in immediate contact with either the formation or a thin and hard mud cake. The mathematical analysis for this condition, as shown in the Appendix, rests on the following concepts. Pressure inside a unit length of pipe causes: (1) a tensile or tangential stress to be exerted over the longitudinal cross-sectional areas of the pipe and cement; and (2) an equal amount of strain in both the pipe and cement that is uniformly distributed over the wall thickness of each. This analysis was then used to make several calculations for a cement sheath around 51/2-in. OD pipe. The results are illustrated in Fig. 1, which shows that a tensile stress of 500 psi is imposed on a 5-in. thick sheath when the casing contains a pressure of only 1,450 psi. It also shows that a 10-in. thick sheath would be stressed to 500 psi in tension when the pipe contained a pressure of only 2,350 psi. Alternatively, if the stress analysis is made by means of the Lame thick-wall cylinder theory, the inner fibers of the 10-in. thick sheath will be stressed to 500 psi in tension when the pressure in the pipe is only 990 psi. This, of course, reveals that an unconfined sheath is of little support to the pipe in burst; however, an entirely different result is obtained when the cement is confined between the pipe and formation.

By W. B. Lilienthal, J. C. Melrose

The application of Bingham&apos;s law to the behavior of drilling fluids in a rotational viscometer permits the expression of viscometric data in terms of plastic viscosity and yield value, the flow properties of a plastic fluid. A commercially available rotational viscometer is described, and when modified to a multispeed type viscometer, is shown to provide a simple and convenient instrument for the measurement of these properties both in the laboratory and in the field. The data obtained are shown to be useful in defining and understanding mud control problems relating to chemical treatment and to the hydro-dynamic behavior of muds. INTRODUCTION The highly complex drilling fluids which are required for deep drilling often give rise to new and unusual mud control problems. Rapid and economic solutions to these problems may require, on the one hand, better understanding of the changes which contaminants and chemical treating agents produce in the colloidal and inert solids of the mud, or, on the other hand, closer control of the hydrodynamic behavior of the mud. The latter objective obviously can be achieved only if a correct rheological analysis of the flow behavior of drilling muds is available and if this is accompanied by the appropriate rheological measurements. The purpose of this paper is to describe such measurements in the field, and to show how the resulting data can be of value in solving difficult mud control problems. It is now generally recognized that Bingham&apos;s law of plastic flow can be utilized in describing the hydrodynamic behavior of drilling fluids in the non-turbulent flow range. Beck, Nuss, and Dunn&apos; have recently applied this law to the flow of mud in small pipes, and Rogers2 has reviewed the rather extensive literature on this subject. So far, however, the use of Bingham&apos;s law has been restricted to the analysis of mud flow in pipes or capillary tubes, and it has not been directly applied to the flow in rotational viscometers. In the work to be reprted, the Reiner-Riwlin3 equation for the flow of a plastic fluid in a rotational viscometer has been utilized to permit the expression of multispeed viscometric data in terms of plastic viscosity and yield value. the two absolute flow properties of a plastic fluid. With regard to the application of these measurements, the calculation of the relationship between pumping rate and pressure drop, both in the drill pipe and annular space, has long been a subject of interest. Beck, Nuss, and Dunn,&apos; following Caldwell and Babbitt: base their calculations for non-turbulent flow on Buckingham&apos;s integration of Bingham&apos;s law for pipe flow and measurements of the plastic viscosity (rigidity in their terminology) and yield value. In the case of turbulent flow, Fanning&apos;s equation is employed, and the pressure drop is relatively insensitive to the flow properties of the mud. Since flow in the drill pipe is likely to be turbulent at usual circulation rates, the plastic flow properties will chiefly influence the pressure drop in the annular space. As pointed out by Beck,&apos; the control of this component of the total pressure drop may be of special importance where lost circulation problems are encountered. Other hydrodynamic problems to which it should be possible to apply measurements of the plastic flow properties include predictions of the velocity distribution in non-turbulent flow and the critical velocity for transition to turbulence. Plastic viscosity and yield value. as abmlute flow propertie.;, will reflect the colloidal or surface-active behavior of the solids present in drilling fluids. Measurements of these properties should therefore find application in developing a better understanding of such behavior and in characterizing the type and condition of these solids. Garrison and ten Brink have utilized multispeed viscometric data in this manner. although their measurements were not expressed in terms of the absolute flow properties. In connection with the application of these measurements, it should be recognized that the presently used one-point viscosity measurements are relative in nature. The API Stormer 600-rpm measurement, for example. is a function of both plastic viscosity and yield value, as well as mud weight, and will often be misleading when its application to mud control problems is attempted. NOMENCLATURE, UNITS, AND DEFINITIONS In Fig. 1 an idealized plot is given of the flow variables involved in any viscometric measurement. It is seen that the flow behavior of plastic fluids is characterized by two constants — plastic viscosity, µp, and yield value, F. Other workers hate used the term rigidity for plastic viscosity or the term mobility for its reciprocal. The term plastic viscosity, however, emphasizes the close relation this property bears to the viscosity of a true fluid and is expressed in the familiar viscosity units of centipoises. The yield value is expressed in lbs/100 sq ft, the units adopted for gel strength measurements with the APT shearometer. Definitions of these properties based on rheological or macrc)scopic flow considerations follow from Fig. 1. The plastic viscosity of a substance obeying Bingham&apos;s equation is defined

Jan 1, 1951

By J. C. Melrose, W. B. Lilienthal

The application of Bingham&apos;s law to the behavior of drilling fluids in a rotational viscometer permits the expression of viscometric data in terms of plastic viscosity and yield value, the flow properties of a plastic fluid. A commercially available rotational viscometer is described, and when modified to a multispeed type viscometer, is shown to provide a simple and convenient instrument for the measurement of these properties both in the laboratory and in the field. The data obtained are shown to be useful in defining and understanding mud control problems relating to chemical treatment and to the hydro-dynamic behavior of muds. INTRODUCTION The highly complex drilling fluids which are required for deep drilling often give rise to new and unusual mud control problems. Rapid and economic solutions to these problems may require, on the one hand, better understanding of the changes which contaminants and chemical treating agents produce in the colloidal and inert solids of the mud, or, on the other hand, closer control of the hydrodynamic behavior of the mud. The latter objective obviously can be achieved only if a correct rheological analysis of the flow behavior of drilling muds is available and if this is accompanied by the appropriate rheological measurements. The purpose of this paper is to describe such measurements in the field, and to show how the resulting data can be of value in solving difficult mud control problems. It is now generally recognized that Bingham&apos;s law of plastic flow can be utilized in describing the hydrodynamic behavior of drilling fluids in the non-turbulent flow range. Beck, Nuss, and Dunn&apos; have recently applied this law to the flow of mud in small pipes, and Rogers2 has reviewed the rather extensive literature on this subject. So far, however, the use of Bingham&apos;s law has been restricted to the analysis of mud flow in pipes or capillary tubes, and it has not been directly applied to the flow in rotational viscometers. In the work to be reprted, the Reiner-Riwlin3 equation for the flow of a plastic fluid in a rotational viscometer has been utilized to permit the expression of multispeed viscometric data in terms of plastic viscosity and yield value. the two absolute flow properties of a plastic fluid. With regard to the application of these measurements, the calculation of the relationship between pumping rate and pressure drop, both in the drill pipe and annular space, has long been a subject of interest. Beck, Nuss, and Dunn,&apos; following Caldwell and Babbitt: base their calculations for non-turbulent flow on Buckingham&apos;s integration of Bingham&apos;s law for pipe flow and measurements of the plastic viscosity (rigidity in their terminology) and yield value. In the case of turbulent flow, Fanning&apos;s equation is employed, and the pressure drop is relatively insensitive to the flow properties of the mud. Since flow in the drill pipe is likely to be turbulent at usual circulation rates, the plastic flow properties will chiefly influence the pressure drop in the annular space. As pointed out by Beck,&apos; the control of this component of the total pressure drop may be of special importance where lost circulation problems are encountered. Other hydrodynamic problems to which it should be possible to apply measurements of the plastic flow properties include predictions of the velocity distribution in non-turbulent flow and the critical velocity for transition to turbulence. Plastic viscosity and yield value. as abmlute flow propertie.;, will reflect the colloidal or surface-active behavior of the solids present in drilling fluids. Measurements of these properties should therefore find application in developing a better understanding of such behavior and in characterizing the type and condition of these solids. Garrison and ten Brink have utilized multispeed viscometric data in this manner. although their measurements were not expressed in terms of the absolute flow properties. In connection with the application of these measurements, it should be recognized that the presently used one-point viscosity measurements are relative in nature. The API Stormer 600-rpm measurement, for example. is a function of both plastic viscosity and yield value, as well as mud weight, and will often be misleading when its application to mud control problems is attempted. NOMENCLATURE, UNITS, AND DEFINITIONS In Fig. 1 an idealized plot is given of the flow variables involved in any viscometric measurement. It is seen that the flow behavior of plastic fluids is characterized by two constants — plastic viscosity, µp, and yield value, F. Other workers hate used the term rigidity for plastic viscosity or the term mobility for its reciprocal. The term plastic viscosity, however, emphasizes the close relation this property bears to the viscosity of a true fluid and is expressed in the familiar viscosity units of centipoises. The yield value is expressed in lbs/100 sq ft, the units adopted for gel strength measurements with the APT shearometer. Definitions of these properties based on rheological or macrc)scopic flow considerations follow from Fig. 1. The plastic viscosity of a substance obeying Bingham&apos;s equation is defined

Jan 1, 1951

By W. J. Maraman, D. R. Harbur, J. W. Anderson

A device for rapidly quenching liquid metals into thin platelets has been developed at the Los Alamos Scientific Laboratory. This rapid quenching equipment is built around the technique of catching a molten drop of metal between a rapidly closing plate and a stationary plate. The design and operation of this unit are described. The closing speed of the smasher plate at impact is 12.6 ft per sec. The quenching rate for this device is controlled by the interface resistance between the plates and the platelet, and is dependent upon the heat content and density of the material being quenched. The initial quenching rate down to the freezing point of the platelet material is lo5º to 106ºC per sec. After an isothermal delay, which is poportional to the heat of fusion of the platelet material, the final cooling rate down to the temperature of the smaslier plates is l04ºto 105cº per sec. RAPID heating of metals by capacitor discharge and other methods has provided the metallurgist with a useful tool for probing into the kinetics of phase changes and the many nonequilibrium phenomena which occur during rapid temperature changes. Equally interesting studies can also be made on metals and alloys which are rapidly cooled from the liquid state.&apos; Studies in this field have been limited, however, because the rates at which metals could be cooled were many orders of magnitude slower than the rates possible for heating. In recent years many new laboratory methods have been developed to rapidly cool metals from the liquid state to ambient temperature and below.2"4 All of these methods involve spreading a liquid drop of metal into a thin foil in a very short time. The methods developed have varied from ejecting a drop of molten metal at the inside surface of a rotating cylinder or stationary curved plate to catching a falling drop of molten metal between rapidly closing plates. The equipment which has been developed at the Los Alamos Scientific Laboratory for rapidly cooling molten materials uses the latter of these two approaches. The basic design, operation, and initial results of this rapid quenching device are given in this report. APPARATUS The drop smasher, which is now being used to obtain rapidly cooled metal foils, is shown in Fig. 1. Basically the device consists of a smasher plate which is driven by a solenoid into a stationary plate. The solenoid is activated by a drop passing through the photoelectric cell and is powered by discharging an adjustable 350-v capacitor bank with a 66-amp peak current into it. This power supply is designed so that the solenoid is powered for 2 m-sec after plate closure to minimize the rebound effect. There is an adjustable time-delay mechanism between the photoelectric cell and the solenoid. Both smasher plates have changeable inserts so that a variety of materials can be used to smash the molten drop. The shaft of the moving plate is guided in an adjustable housing which has ball-bearing walls. The cabinet shown to the left of the drop smasher in Fig. 1 contains the power supply and receiver for the photoelectric cell, the time delay mechanism, and the capacitor bank. The drop smasher can be placed inside a vacuum chamber, for use with radioactive materials, with the upper plate forming the lid, as shown in Fig. 2. On top of the vacuum lid is an induction coil, powered by an Ajax induction generator, which is used to melt drops from the end of the rod extending through the vacuum seal on top the quartz tube. OPERATION The drop smasher shown in Fig. 2 is operated in the following manner. The smasher plates are separated and the unit is lowered into the vacuum chamber using a pressurized cylinder. The induction coil, quartz tube, and lid with sliding vacuum seal are then assembled on top the vacuum chamber. A rod of the material for rapid quenching studies is connected to the rod extending through the sliding vacuum seal. The vacuum chamber is then evacuated and the desired atmosphere established. The photoelectric cell is turned on, and the capacitor bank is charged and armed. Power is supplied to the induction coil, and the rod of material for rapid quenching studies is lowered into the induction field. A molten drop forms on the end of the rod, drops off, falls through the light beam of the photoelectric cell, and is then caught between the smasher plates. .

Jan 1, 1970

By A. R. Troiano, A. B. Greninger

There is need for an adequate working hypothesis that would describe at least qualitatively the crystallographic mechanism for the transformation from austenite to martensite in steel. A general theory would not only be of great assistance in the correlation of existing data and in planning future experimentation, but would also form the basis for an eventual explanation of the property changes that accompany lattice transformations. The mechanism of martensite formation described in the following pages is the outcome of two new experimental determinations: (1) the accurate evaluation of the lattice relationship between austenite and individual crystals of martensite, and (2) the measurement and analysis of the change in position that a volume of austenite undergoes when it transforms into a crystal of martensite. For this latter study, the stereographic analysis of shear was employed; this method greatly simplifies the solution of lattice-shear problems, and some space is devoted to its description. Lattiice Relationships and Habits PREVIOUS WORK The lattice relationships between austenite and martensite in carbon steels have been studied by Kurdjurnow-and Sachs,&apos; and by Wassermann;2 and in iron-nickel alloys by Nishiyama.3 Wassermann,2 and Mehl and Derge.4 The studies by Kurdjumow and Sachs and by Wassermann were made on single (austenite) crystals of quenched 1.4 pct carbon steel, and the results of these two independent studies agree closely with the postulated lattice relationships: (III)r||(0ll)a [101]r [111]a [1] Both Nishiyama and Wassermann worked with an alloy of iron plus 30 pct nickel (all austenite at room temperature), and "martensitic alpha" was formed by cooling in liquid air. They agree that the lattice relationships for these conditions are: (lll)r||(011)a [112]r[011]a [2] Mehl and Derge worked with a range of iron-nickel alloy compositions centered about 30 pct nickel. They concluded that when the transformation takes place near room temperature or above, relationship [l] holds, but if the same specimen is made to transform at -195°C, relationship [2] obtains;intermediate temperatures evidently produced a combination of these two relationships. Sachs and co-worker~,1,7 as well as Nishiyama,3 have proposed transformation mechanisms for martensite formation.* Both of the mechanisms picture the transformation as initiated by shearing movements along the octahedral [Ill] plane of austenite, followed by suitable expansion and contraction to complete the transformation. These mechanisms have been described and commented upon by Mehl, Barrett, and Smith,8 Mehl and Derge,4 Wassermann,2 and others, and generally accepted by investigators in this field. Greninger and Troiano9 have recently published the results of a detailed study of the shapes and orientation habits of martensite crystals in plain-carbon and nickel steels. They found that, contrary to previous assumptions, martensite plates form not along the octahedral planes but along austenite planes of very high indices; these results were in line with those of previous studies of martensite reactions in nonferrous alloy systems by Greninger and coworkers.6,10 Greninger and Troiano concluded that the transformation theories of Kurdjumow and Sachsl and of Nishiyama3 are untenable. Phragmén11 reached a similar conclusion. EXPERlMENTAL METHODS The object of this particular study was the evaluation of (1) lattice relationship between austenite and martensite, and (2) relationship between the martensite lattice and the martensite plate. The technique used for solving these problems was similar to that used by Greninger6 on martensitic structures in 8 copper-aluminum alloys. Briefly, the method consists of grinding and polishing a specimen on a surface parallel to an individual martensite plate and thus exposing a single martensite crystal for an area of l to 3 mm. The orientation of this exposed martensite crystal is then determined by means of a back-reflection Laue X ray pattern.12 Another pattern is obtained from the matrix crystal, and a stereo-graphic plot of data from these two patterns then provides the solution to the problem. It is necessary to repeat this process on several crystals in order to determine whether or not the solution is unique.

Jan 1, 1950

By Lewis E. Dr. Young

MINING engineers in the United States understand that mining conditions in the British coalfields are much more difficult than in most of the mines now being operated in the United States. We realize also that in the near future we must face some of these same difficult problems. Early Mechanization The progress made in mechanical loading in the United States is the result of a long struggle in many coalfields to mine with power tools safely and to increase output per man-shift. Attempts to use power to loosen coal and to transport broken coal in the U. S. may be said to date from the Stanly Header, or Entry-Driver brought from England in 1888. The principle of this boring machine was used in the McKinlay Entry-Driver, almost continuously used in the U. S. since 1920. Since 1888 experimental loaders, scrapers, and conveyors were installed with more or less success. Beginning in 1918, considerable progress was made with mobile loaders, and in 1920 the first wage agreement for the operation of mechanical loaders was made in Indiana. In 1923 the Pocahontas Fuel Co. loaded nearly 1 million tons of coal using 23 Coloders. Labor Policy The United Mine Workers of America have never officially opposed the Mechanization movement. On December 10, 1945, in a statement before the House of Representatives Labor Committee, John L. Lewis said, regarding the policy of the United Mine Workers of America: "We have welcomed progress; we have welcomed machines. We have told our people that they had to accept that condition; that it was the process of progress, and that they would have to take their chances." Recent Development In 1951 about 71 pct of the tonnage mined underground was mechanically loaded. Over 4000 shuttle cars are in service and it is estimated that much more than half of the tonnage loaded underground is produced by trackless mining. In 1947 roof-bolting was introduced extensively and it is estimated that more than 2 ½ million bolts are now being used per month in about 600 mines. The use of roof bolts has permitted the more effective and safer use of loaders and shuttle-cars. Continuous Mining The McKinlay Entry-Driver could have been used for continuous mining, but for many years it was used only .for entry driving. In 1946 the Silver machine was developed in Colorado, and in 1947 this was acquired by the Joy Mfg. Co. and called the Joy Continuous Miner. Other types of combination mining-loading machines which eliminate drilling and blasting operations are the Marietta Miner, the Colmol, the Lee-Norse Miner, the Junior Miner, the Goodman and the Konnerth machines. There are several other types in the process of development. Probably by January 1953 there will be about 250 continuous miners in operation in the U. S. Payment of Mine Labor One of the most important problems in mechanizing was the establishing of rates of pay that would be attractive to the best men. Prior to the installation of mobile loaders the hand loaders and cutters have been paid by the ton. It was felt that a system of a day&apos;s pay should be established and that piece and tonnage rates should be abolished completely. Without exception, all coal loaded in mines equipped with mobile loaders is prepared and loaded by men paid an hourly rate. Trends in Mining Research There are two diverse approaches in coal production research; to try to design a mining machine to fit current methods, or to adapt mining practice to take advantage of proven machines. A great deal of credit must go to the mine operators who have been enterprising and dynamic enough to use available equipment intensively and to discard it as soon as an improved or new machine is available. Effect of Changing Markets Formerly there was an important demand for lump and prepared coal in the larger sizes for domestic use. The use of bituminous coal for house heating has decreased so that not more than 19 pct of the annual tonnage goes to retail trade, only 12 pct is used by the railroads, and much of the retail and most of the railroad coal is in stoker size. As a result of this decline in the market for coarse coal most of the large mining operations have crushers installed in the tipples or preparation plants. Mass production at the face requires increased preparation facilities. Another important trend is in connection with complete seam mining with mechanical loading. In many mines where the immediate roof is apt to fall with the coal no effort is made to separate roof material from coal prior to

Jan 1, 1952

By F. Selig, A. S. Odeh

A second-order approximation to the exact solution of the diffusivity equation corresponding to the pressure build-up of a well producing at a variable rate is derived. This approximation is applicable when the well&apos;s shut-in time is larger than the total time elapsed since the well was first produced. The resulting equations are compact in form and easy to use. Thus, the need for Horner&apos;s&apos; theoretically precise but rather laborious solution to the above problem is eliminated. In addition, these equations apply where the use of Horner&apos;s widely known approximate method is questionable. From a practical point of view, the reported method is best suited for analysis of drill-stem tests and short production tests conducted on new wells. INTRODUCTION The utility of drill-stem and short production tests in reservoir studies has long been recognized by the reservoir engineer. If interpreted correctly they could lead to a wealth of information upon which may depend the success or failure of reservoirs&apos; analyses. Initial reservoir pressure and the average flow capacity are two quantities that are normally sought from a drill-stem and/or a short production test analysis. Pressures are the most valuable and useful data in reservoir engineering. Directly or indirectly, they enter into all phases of reservoir engineering calculations. Therefore, their accurate determination is of utmost importance. The flow capacity kh of the reservoir is indicative of its commercial capability. In addition, it can indicate the presence of a darnaged zone around the wellbore and, thus, the necessity for remedial measures. Of the several methods used to analyze drill-stem and short production tests, Horner&apos;s&apos; method is by and large the most common. It applies to an infinite reservoir and or a limited reservoir where the effect of production has not been felt by the boundary. Horner&apos;s method makes use of the so-called "point-source" solution of the diffusivity equation. The point-source solution is approximated by a logarithmic function and the superposition theorem is utilized to give the familiar pressure build-up equation where is the shut-in time, q is in reservoir barrels per day and the rest of the symbols conform with AIME nomenclature. Eq. 1 was derived for a well which produced at a constant rate q from time zero to time t and was then shut in. In actuality, such a constant rate of production does not normally obtain. Therefore, a correction must be applied to Eq. 1 to account for the varying rates of production. Horner suggested two methods. The first, which results in a theoretically accurate solution, is rather lengthy and laborious and, thus, it is not suited for routine analysis. The second which has been termed a "good working approximation" is the one used by the majority of the reservoir engineers. In the second method, Eq. 1 is modified by simply introducing a corrected time t, and writing where q is the last established production rate prior to shut-in, and t, is obtained by dividing the total cumulative production by the last established rate. Horner&apos;s original paper does not give any indication that this method of correction is based on any theoretical justification. In addition, there is a question as to what constitutes the last established rate. In case of a drill-stem test some engineers use the average rate obtained by dividing the total fluid produced by the total flow time, while others calculate the average rate by dividing the total fluid produced by the last flow-period time. Obviously, different results obtain for the different flow rates used. Because of this, a simple method to the varying-rate case was developed which is theoretically sound and which defines clearly the flow rate and its associated time to be used in the calculations. The final equation arrived at is where q* and t* are a modified rate and time, respectively, and can be easily calculated. In addition, it is shown theoretically that Horner&apos;s approximate method, if used for a variable-rate case, gives the correct pressure but would not be expected to give the correct flow capacity. MATHEMATICAL ANALYSIS The general equation governing the flow of slightly compressible fluid in porous media may be written as The elementary solution to Eq. 4, representing an instantaneous withdrawal of Q units volume of fluid at the origin at t = 0, is known as the instantaneous sink

By J. L. Huitt, B. B. McGlothlin

The introduction of new fracture propping agents that are brittle but much stronger than sand created the problem of what loading strength is required for a propping agent to be effective in a given formation. It is shown that the load at which the propping agent crushes should exceed the load at which total embedment in the fracture faces is possible. Simple laboratory tests to determine loading strength of the propping agent and embedment in the fracture faces, and use of these data in selecting a propping agent for a given formation, are discussed. INTRODUCTION One of the most important factors in the design of hydraulic fracturing treatments is the selection of a propping agent that can effectively provide the fracture flow capacity needed for stimulation of a well. Sand, once generally accepted as being synonymous with propping agent in hydraulic fracturing, is now recognized as having limited effectiveness in many formations because of its low resistance to crushing. Sand particles are brittle and have relatively low strength. Because of this property, sand particles are crushed in rocks that offer high resistance to the penetration of fracture faces by the proppant particles when the fracture attempts to close under the action of the overburden load. For rocks that offer a high resistance to penetration, deform able particles are more effective propping agents than sand. However, for this same type of rock, a propping agent that does not deform, yet does not crush, is often more effective. Thus, a rigid propping agent with sufficient strength to prevent crushing is desirable. A method for determining the strength required for a rigid propping agent to function effectively in given formations is discussed. BEHAVIOR OF RIGID PROPPANTS AND FRACTURE FACES RELATED STUDIES An early qualitative description of the reaction of propping sand in fractures was given by Hassebroek et al.&apos; In discussing fracturing in deep wells, the authors mentioned that even though propping sand entered the fractures, a high flow capacity did not result due to crushing or embedding of the propping sand. Dehlinger et al.2 in discussing the reaction of propping sand surmised that, because of the hardness of sand particles, deformation occurred in the fracture faces contacting the propping sand. In later studies,3,4 methods of determining the embedment of propping sand in fracture faces of soft rock and the critical load at which propping sand is crushed by the fracture faces in hard rock were discussed. In working with de-formable proppants, Kern et al. considered proppant particles to be deformed into cylindrical disks by action of the overburden and then pressed slightly into the fracture faces by further action of the overburden. Rixie et al.&apos;0 reported on embedment pressure and presented a method of selecting a propping agent for use in given formations. The propping agents included sand, walnut shells and aluminum pellets. All these studies have contributed materially to a better understanding of propping agent behavior; however, the strength of brittle proppants (sand, glass and ceramics) required to result in embedment rather than crushing has not been discussed. This topic will be covered in the ensuing discussion. PROPPANT PARTICLE CRUSHING—-EMBEDMENT For this discussion, a rigid propping agent is considered to be one that is brittle and fails under tensile stress when loaded to a critical value. In an earlier study4 it was shown that the Hertzian4 loading theory could be applied to a spherical brittle propping agent if the propping agent and fracture faces behaved elastically. At the failure of the proppant, the ratio of the load to the square of the diameter of the particle should be constant for a given material combination, or: Lc/dp2=C ............(1) A partial derivation of this equation from proppant and formation properties is included in the Appendix. Should a rigid particle not be crushed as a load is applied, it embeds in the fracture faces. A study3 of particle embedment in fracture surfaces has been published. The embedment can be described by an equation based on Meyer&apos;s metal penetration hardness relationships: d1/dp=B 1/2[L/dp2]m/2..........(2) In Eq. 2, B and m are constants that are characteristic of the rock; the significance of the other terms is shown in Fig. 1. A STANDARD DEFINITION FOR PROPPANT LOADING STRENGTH Eq. 1 is useful in appraising propping agent strength," but it is strictly applicable only when the area of contact between a particle and a fracture face (or loading plate)

Jan 1, 1967

By W. Weissberger, Frankiewicz, L. Pommier

Introduction In the U.S., about one-quarter of the fuel oil and natural gas consumption is associated with power production in utility and industrial boilers and process heat needs in industrial furnaces. Coal has been an attractive candidate for replacing these premium fuels because of its low cost, but there are penalties associated with the solid fuel form. In many cases pulverized coal in unacceptable as a premium fuel replacement because of the extensive cost of retrofitting an existing boiler designed to burn oil or gas. In the cases of synthetic fuels from coal, research and development still have a long way to go and costs are very high. Another option, which appears very attractive, is the use of solid coal in a liquid fuel form - coal slurry fuels. Occidental Research Corp. has been developing coal slurry fuels in conjunction with Island Creek Coal (ICC), a wholly-owned subsidiary. Both coal-oil mixtures and coalwater mixtures are under development. ICC is a large eastern coal producer, engaged in the production and marketing of bituminous coal, both utility steam and high quality metallurgical coals. There are a number of incentives for potential users of coal slurry fuels and in particular for coal-water mixtures (CWMs). First, CWM represents an assured supply of fuel at a price predictable into future years. Second, CWM is available in the near term; there are no substantial advances in technology needed to provide coal slurry fuels commercially. Third, there is minimal new equipment required to accommodate CWM in the end-user&apos;s facility. Fourth, CWM is nearly as convenient to handle, store, and combust as is fuel oil. Several variants of CWM technology could be developed for different end-users in the future. One concept is to formulate slurry at the mine mouth in association with an integrated beneficiation process. This slurry fuel may be delivered to the end-user by any number of known conveyances such as barge, tank truck, and rail. Slurry fuel would then be stored on-site and used on demand in utility boilers, industrial boilers, and potentially for process heat needs or residential and commercial heating. An alternative approach is to formulate a low viscosity pre-slurry at the mine mouth and to pipeline it for a considerable distance, finishing up slurry formulation near the end-user&apos;s plant. Finally, at the other extreme of manufacturing alternatives, washed coal would be shipped to a CWM manufacturing plant just outside the end-user&apos;s gate. Depending on fuel specifications and locations of the mine and end-user facility, any of these alternatives may make economic sense. They are all achievable in the near term using existing technology or variants thereof. The Coal-Water Mixture CWMs contain a nominal 70 wt. % coal ground somewhat finer than the standard pulverized ("utility grind") coal grind suspended in water; a complex chemical additive system gives the desired CWM properties, making the suspension pumpable and preventing sedimentation and hardening over time. Figure 1 shows the difference between a sample of pulverized coal containing 30 wt. % moisture and a CWM of identical coal/water ratio. The coal sample behaves like sticky coal, while the CWM flows readily. The combustion energy of a CWM is 96-97% of that associated with the coal present, due to the penalty for vaporizing water in the CWM. Potentially any coal can be incorporated in the CWM, depending on the combustion performance required and the allowable cost. CWMs are usually formulated using high quality steam coals containing around 6% ash, 34% volatile matter, 0.8% sulfur, 1500°C (2730°F) initial deformation temperatures, and energy content of 25 GJ/t (21.5 million Btu per st). Additional beneficiation to the 3% ash level can be accomplished in an integrated process. There are a number of minimum requirements which a satisfactory CWM must meet: pumpability, stability, combustibility, and affordability. In addition, a CWM should be: resistant to extended shear, generally applicable to a wide variety of coals, forgiving/flexible, and compatible with the least expensive processing. It was found that a complex chemical additive package and control of particle size distribution are necessary to achieve these attributes simultaneously, while maximizing coal content in the slurry fuel. Formulation of Coal-Water Mixtures A major consideration in the manufacture, transportation, and utilization of a slurry fuel is its pumpability, or effective viscosity. Most CWM formulations are nonNewtonian, i.e., viscosity depends on the rate and/or duration of shear applied. Viscosities reported in this paper were obtained using a Brookfield viscometer fitted with a T-spindel and rotated at 30 rev/min, thus they are apparent viscosities measured at a shear rate of approximately 10 sec-1. The instrument does reproducibly generate a shear field if spindle size and rotation rate are held fixed. By observing the apparent viscosities of several slurries at fixed conditions it is possible to obtain a relative measure of their viscosities for comparison purposes. A true shear stress-shear rate relationship at the shear rates at which the CWM will be subjected in industry may be obtained using the Haake type and a capillary viscometer. These viscometers are used for specific applications. However, for comparison purposes, apparent viscosities are reported.

Jan 1, 1985

By E. J. Rapperport, J. P. Pemsler

The thermodynamic activities of zinc in six solid solution Cu-Zn alloys ranging from 5 to 35 at. pct Zn were determined experimentally in the temperature range 400° to 600°C. This low temperature investigation was canducted in order to evaluate techniques developed to utilize the inherently high sensitivity of atomic absorption flocesses in the measurement of thermodynamic activities. Analytical expressions ,for the activity and actizlity coeflcient are given for the six alloys in the temperature ranges investigated. RELATIVELY few experimental methods are available for investigation of thermodynamic activities of alloys, especially in the solid state. The techniques most frequently used have been the electrochemical potential and the effusion methods, both of which have severe limitations in many instances. It is therefore desirable to expand the ability to perform such measurements in order to obtain new information as well as to provide an additional independent verification capability. In this work, we present a significant improvement in the spectrophotometric method for sensing small vapor pressures in static absorption cells. Similar techniques have been used previously;1"5 however, applications had been limited to relatively high pressures, often greater than 1 torr. Prior investigators have, for the most part, used broad spectral sources such as xenon or mercury lamps, and high intensity arcs. Hollow cathode sources were first suggested in 1956 6 and were used soon afterwards.4&apos;5 These sources offer significant improvements in sensitivity and freedom from interfering spectral lines.&apos;-&apos; EXPERIMENTAL High purity zinc was obtained from Cominco Products, Inc., and copper from American Smelting and Refining Co. Both elements were of 99.999 pct purity. Copper-zinc alloys were vacuum melted in a high fired carbon crucible with each alloy pulled from the melt as a 4 -in. diam bar. The bars were swaged to -1/4 in. rods and vacuum annealed for 160 hr at 800° + 1°C. Samples for gross chemical analysis were taken at intervals along the length of the rods to ascertain the axial zinc gradient. Electron microprobe analysis of homogenized specimens indicated that the alloys had uniform compositions over their cross sections on a macro (200 p) and micro (1 u) scale to better than *1 pct (20) of the gross composition. This tolerance was determined by counting statistics, rather than assured composition fluctuations. All SiO 2 windows were high-ultraviolet-transmission grade to minimize intensity losses. Silica absorption cells were scrupulously cleaned consecutively in organic solvents, dilute HF, and distilled water before use. The empty cells were then flamed while under a dynamic vacuum, cooled, and removed to an argon-filled glove bag. Alloy pieces were cut and filed in the glove bag to produce fresh surfaces, and then loaded into the cells. The loaded cells were temporarily sealed, removed from the glove bag, reevacuated to 10-5 torr or better, and permanently sealed. The instrument used is schematically shown in Fig. 1. The spectral emission from a commercially made hollow cathode lamp (A) of a selected element is focused through an absorption cell (B) inside a well-controlled furnace (C). The intensity of the transmitted beam is measured using the spectrometer* (D) &apos;Techtron model AA4 atomic absorption spectrometer. which contains a grating (E) that disperses the light prior to impingement on the photomultiplier (F). The monochromator grating is adjusted so that only the wavelength of interest is measured. The power supply delivered an interrupted voltage to the lamp, causing a chopped radiation output to be transmitted. The detector read only the intermittent component of radiation incident upon it, so that all continuous noise signals (furnace radiation, and so forth) were eliminated. Three recording thermocouples contained in the muffle furnace were positioned along the length of the absorption cell: one at each end and one at the center. An effort was made to keep the ends of the cell several degrees hotter than the center to avoid window condensate. Appropriate thermal corrections were then necessary to relate cell pressure to radiation attenuation. Water-cooled heat shields, as shown in Fig. 1, were found to aid signal stability by protecting the hollow cathode and the photomultiplier from furnace radiation. The furnace had a 2-in. diam muffle, Kan-thal wound, with SiO 2 windows at its ends to minimize convective effects. The hollow cathode radiation was masked and focused to form a conic beam that was a maximum of { in. diam within the furnace. Thus, the 1.5 in. diam absorption cell easily contained the entire beam. The furnace was mounted on ball-bearing slides with positive positioning detents. This arrangement allowed the removal of the entire furnace assembly from the radiation path, position [I], Fig. 1, so that frequent sampling of the unattenuated beam intensity could be obtained. In all cases the beam intensity was kept constant to 0.1 pct as judged by readings taken immediately before and immediately after data collection. Only data for absorptions of less than 80 pct were utilized, as systematic deviations from linearity were found for greater absorptions.

Jan 1, 1970

By Rex O. McLellan

The formation of a monovacancy in a metal is simulated in an elastic model by the displacement of the surface of a small spherical cavity in a large elastic continuum. The application of linear elasticity to this distortion results in a well- known formula for the energy and an expression for the concomitant entropy change due both to the shear strain in the continuum and also to the dilation of the solid resulting from the boundary conditions at the surface of the solid. Elastic data (the sliear modulus and its temperature coelficient) are used to calculate the entropy and energy of formation for many metals. Despite the simplicity of the assumptions involved, the agreement between the calculated entropies and energies and experimental values is remarkably good. In recent years there has been a large increase in measurements of the absolute concentration of mono-vacancies in metals as a function of temperature. Hence new data for both the energy and the noncon-figurational entropy of formation of monovacancies has become available. Recent measurements&apos; of the anomalous (non-Arrhenius) self-diffusion in many bcc metals has also focused interest on the prediction of the thermodynamic parameters of mono- and multi-vacancies in those metals for which no data are available. Damask and Dienes&apos; have discussed the various theoretical calculations of the energy of formation EL, of a monovacancy. These include simple models involving the breaking of atomic bonds on moving atoms from the interior of a crystal to the surface, models combining elastic calculations with surface-energy terms and detailed quantum mechanical calculations. The simler models give the correct order of magnitude of &, but tend to overestimate it by a factor of about two. The quantum mechanical calculations4"7 have been carried out for the noble and alkali metals with generally reasonably good agreement with the available Ef data. The calculation of entropy of formation Sfv14 lnvolves a fundamental calculation of the perturbation of the phonon spectrum caused by the creation of a vacancy. Huntington, Shirn. and wajda8 have given an approximate evaluation of sJV by considering an Einstein model for the localized vibrations in the immediate neighborhood of the defect and then using elastic theory to calculate the entropy associated with the shear stress field in the distorted crystal (as originally proposed by Zenerg). They also included a term due to the dilation of the crystal. They obtained a value of 1.47k for copper, in good agreement with the experimental value (1.50k). However, Nardelli and Tetta- manzi1° have recently shown that neglecting the coupling between atoms (Einstein Model) may lead to a serious error so the agreement may be somewhat fortuitous. In this work simple linear elastic theory is used to calculate the entropy and energy of formation of mono-vacancies. Despite the simplicity of some of the assumptions involved, the agreement with the available experimental data is remarkable. However. the reasonable degree of success in the application of linear elastic calculations to the excess entropy of a solute atom in a dilute solid solution1&apos; indicates that the application of elastic theory to vacancies. where the interaction of different atomic species is not involved, may not be inappropriate. THE ELASTIC MODEL The metal is assumed to be a spherical elastic continuum. A small spherical cavity of volume V = 4i;v:&apos;/3 is cut from the center. removed. and dissolved rever-sibly in the bulk of the material. TO a good approximation no net atomic bonds are broken and the material does not undergo a volume change although the externally measured volume of the body would increase by V. The radius of the sphere of metal is much larger than r Next a negative pressure is applied to the cavity causing its surface to be displaced inward by an amount simulating the relaxation of the lattice around a monovacancy. In this model the energy and entropy accompanying the distortion are taken as 4, and <. As a first approximation the equation of state for the solid is taken as: r = ro(i + *~D LiJ where K is the bulk modulus. P the hydrostatic pressure. Vo the volume of the material at 0°K and zero pressure. and d+/dT = 30. where 0 is the linear thermal expansion coefficient. The variation of entropy with hydrostatic pressure is given by the Maxwell equation: These equations give the entropy change resulting from increasing the hydrostatic pressure from 0 to P as: and since • we have: This is the entropy arising from the dilation resulting

Jan 1, 1970