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By Robert G. Nisle

In conducting a pressure build-up test on an oil well, it is often necessary to shut-in the well for a short time prior to initiation of the test. The effect of such a short tern shut-in on the resulting pressure build-up curve is derived. The derivation is based on the Kelvin point-source solution and is a straight forward extension of the fundarnental theory. The magnitude of the effect is evaluatecl and illustrated by an example. It is shown that if the production subsequent to the short term shut-in is at least 10 times the duration of the shrct-in, the effect will he less than 10 per cent. INTRODUCTION It often happens that before a pressure build-up test can be made an additional valve must be mounted on the wellhead, or on arrival at the well, it might be learned that the well had been shut-in several hours the previous day because of a shortage of tankage. In such cases the question is How will such an interruption of production affect the results of a pressure buildup test This work explains how to take account of such a short term shut-in in order that the test can proceed without further delay. The solution presented here makes use of the Kelvin point-source solution used by Horne1 in his treatment of the pressure build-up in wells. Use is also made of the super-position theorem. MATHEMATICAL DERIVATION The well is assumed to have been in production at a constant rate for a relatively long time (several days or more). It is then shut-in for a short time, after which it is again placed in production at the previous constant rate. It continues to produce at this rate until shut-in for a pressure build-up test. The Kelvin point-source solution is expressed by Eq. 1. The sequence of production rates is listed in Table I. TABLE 1 — SEQUENCE OF PRODUCTION RATES Time interval Production Rate At time AT the pressure will be the resultant of the sequence of production rates shown in Table 1. An expression for the super-posed effects may be derived from this table. (Effect of + q for T + ? T) + (Effect of - q for T + ?T-t,) + (Effect of + q for T + ? T - t,) + (Effect of - q for ? T) = Resultant........(2) The desired result is obtained by substituting the effect defined by Eq. 1 for the terms in Eq. 2. The result is Eq. 3. When the logarithmic approximation is made for the exponential integrals and the terms collected the result is Eq. 4. Let T — t2 = T = flowing time following short term shut-in t2 — t1 = 6 = duration of short term shut-in Then T - t1 = r + 6 Substitution of these quantities in Eq. 4 gives p(rw ?T) = P,, -When d<<t - AT then d—&apos;-, T— approaches 1. r + AT In this case the effect of the short term shut-in may be ignored. In order to get some idea of the numerical magnitudes involved take the worst possible case, when AT = 0, that is at shut-in. If the error is made less than some maximum acceptable value at this time, it will be less than the maximum for all subsequent times. d + r Let the difference between the value of y-— and 1 be less than 0.1. Then —6+r — 1 < 0.1 S < O.l T Therefore, if the flowing time following a short term shut-in is at least 10 times the duration of the short term shut-in, the error introduced by ignoring the short term shut-in will not exceed 10 per cent of T+AT A T

Jan 1, 1957

By H. M. Strong

Nickel and carbon form a metastable nickel-nickel carbide eutectic system which was ohsen)able by freezing latent-heat arvests at pressures 210 khars. The eutectic freezing temperature Is pressure had a slope of -0.9°Cper kbar. At 50 khars, the nickel-nickel carbide eutectic was at 1297° * 5°C and 0.34 mole fraction Ni3C. The composition of the eutectic increased at an initial rate of 0.004 mol fraction per kbar. The carbon content of the a phase also increased with pressure. Seveval illustrations of nickel carbide microstruc-tures are given and data on the lattice expansion of nickel in terms of carbon content are included. IRON, cobalt, and nickel form a variety of carbides with compositions varying between MeC and MC. Of the three, the carbides of iron are most easily recovered. The nickel carbides are so unstable at temperatures above 900°C that their occurrence in Ni-C alloys is unusual. Under sufficient pressure, however, the temperature range for the stability of the ferrous metal carbides is likely to be increased, or their decomposition suppressed (e.g., see Hilliard&apos; on FesC), providing an opportunity to study the unstable carbides more closely. This was found to be true for nickel carbide which, under pressure, formed a eutectic with nickel. This paper describes the conditions of formation of nickel-nickel carbide eutectic compositions and their subsequent recovery. Despite the comparative instability of the nickel carbides, something is already known about them through various chemical reactions at temperatures not exceeding a few hundred degrees, and from their recovery by the very rapid quenching of molten Ni-C alloys from temperatures of about 1450°C or above. At least four carbides of nickel have been reported: A discussion of the state of knowledge about Ni3C is given by ansen.&apos; The studies of Morrogh and williams7 who obtained Widmanstatten nickel carbide structures and of sidorenko8 who first obtained nickel carbide eutectic structures are also of interest. Sidorenko used short heating times for molten nickel in a graphite crucible followed by very rapid quenching to obtain the eutectic structures. Long heating times produced only the nickel-graphite eutectic probably due to the presence of graphite crystals in the melt which nucleated graphite crystallization. According to the early work summarized by anssen,&apos; nickel carbide may form at temperatures far above the melting point and may be recovered by very rapid quenching. More recently, Giardini and Tydings, working on diamond synthesis, found evidence for "free nickel carbide&apos;&apos; in high-pressure reactions carried to temperatures far in excess of the limit for diamond growth, followed by rapid thermal quench. They stated that nickel carbide was not found in association with diamond growth. In the present work, observations were made on the melting and solidification temperatures of Ni-C alloys as a function of composition, temperature, and pressure. The nickel-nickel carbide eutectic was found at pressures above 10 kbar and its variation with pressure followed up to 60 kbar. Nickel-nickel carbide microstructures were recovered by quenching under pressure from temperatures of about 1400°C and higher. The formation of nickel carbide structures under ordinary diamond-growing conditions was usually observed but the role of carbide formation as an intermediate step in diamond growth needs more study. EXPERIMENTAL METHODS The melting and solidification temperatures of various nickel-graphite compositions were observed by latent-heat arrests in the sample holder illustrated in Fig. 1. The samples were composed of mixtures of carbonyl nickel powder and National Carbon Co.&apos;s SP-1 graphite packed to densities of about 6.4 g per cu cm. They were contained within

Jan 1, 1965

By A. M. Skov, L. F. Elkins

First response to large-scale water flooding in the fractured very low permeability Spraberry sand has led to a new unique cyclic operation. Capacity water injection is used to restore reservoir pressure. This is followed by marly months production without water irzjection and the cycle repeated. Expansion of the oil, rock and water during pressure decline expels part of the fluids but capillary forces hold much of the injected water in the rock. At least with reservoir pressure restored and with partial water flood development, field performance has proved this cyclic operation is capable of producing oil from the nzatrix rock at least 50 per cent faster and with lower water percentage than is imbibition of water at stable reservoir pressure. INTRODUCTION The Spraberry Field of West Texas presents unusual problems for both primary production and water flooding. Extensive interconnected vertical fractures in the fractional-md sandstone permitted recovery of oil on 160-acre well spacing, but they made capillary end effects dominant. Primary recovery by solution gas drive is less than 10 per cent of oil in place. The concept of displacement of oil from the sand matrix by capillary irnbibition of water has led to field techniques which promise greatly increased oil recovery. Free exchange of laboratory research, reservoir information and results of field pilot tests among the various companies has been very important in development of this technology. Five units covering a total of 170,000 acres have been formed for water flooding, and 10 other areas covering an additional 175,500 acres are in various stages of unitization. Part of the Driver Unit reaching fillup first has demonstrated very unusual waterflood behavior and indicated numerous operating problems that will develop within and among the various units. SPRABERRY ROCK AND PRIMARY PERFORMANCE The Spraberry, discovered in February, 1949, is a 1,000-ft section of sandstones, shales and limestones with two main oil productive members: a 10-15 ft sand near the top and a 10-15 ft sand near the base. In part of the field some thinner intermediate sands are oil productive, and others are water bearing. All sands have permeabilities of 1 md or less and porosities of 8-15 per cent. Ordinary core analysis and electric and radiation logs are ineffective in differentiating between oil productive and nonprcductive sands. Sands capable of containing producible oil are best identified by mercury injection capillary pressure measurement and, in some cases, by core water saturation. About 3,500 wells have been drilled in the 500,000-acre trend. Vertical fractures were observed in practically all Spraberry cores. Continuity and interconnection of fractures were confirmed by pressure interference among wells during early development.&apos; Major fractures trend northeast-southwest as indicated by oriented cores and confirmed by five fluid injection tests, by analysis of the pressure transients observed during development,&apos;&apos;&apos; and by three interference tests in the Driver Unit Water Flood reported herein. Fracture spac- ing probably averages inches to a few feet. Spraberry wells typically produced 100-400 BOPD initially after hydrauLic fracture treatments. By 1962 oil production had declined to an average of 12 bbl/well/day, near the economic Limits of operation. Reservoir pressure had declined from 2,300 psi initially in the Upper Spraberry and 2,500 psi in the Lower Spraberry to 500-1,000 psi. Partial closing of the fractures with declining reservoir pressure is believed to be the cause of such low oil production rates at these relatively high reservoir pressures. Cumulative recovery of 208 million bbl of oil is 80 to 90 per cent of that recoverable by primary means. Performance of the entire reservoir is summarized in Fig. 1. IMBIBITION WATER FLOODING By 1952 reservoir performance indicated low primary recoveries. Most engineers, expecting serious channeling of injected fluids through the fractures, held little hope for secondary recovery. With its extensive background of research on the fundamentals of fluid flow within reservoir rocks, Atlantic&apos;s Research and Development Division on short notice in 1952 conceived that displacement of oil by capillary imbibition of water into the rock might significantly increase Spraberry recovery. Laboratory data reported by Brownscombe and Dyes scaled to probable reservoir conditions showed potential waterflood recovery equal to or greater than primary recovery with a 10-15 year flood life.= A pilot test using three 40-acre injection wells, one central producing well and 18 surrounding observation wells demonstrated technical feasibility of the process. Injection of 1.5 million bbl of water from November 1952 to August 1955 proved water entered the rock and displaced oil

By C. L. Pillar

INTRODUCTION The location, size, character of the ore de- posit and its adjacent formations will deter- mine the mining system best used for its ex- traction. The mining system chosen will have to be engineered to suit the ore deposit and the people that will extract it. What can be done in the Philippines cannot always be accomplished in the upper Northwest Territory of Canada. Mining operations developed under a free enterprise system are planned to achieve a satisfactory return on the capital required to place them into production. Hence, the choices made in planning and developing the mining system must be dictated by sound economics. The mining system planned must favor: 1. Maximum ore extraction of the deposit with minimal grade dilution. 2. The amount of capital expenditure used to develop and equip the mine must be in harmony with the financial policy of the group yet be sufficient to provide a reliable mining system. Excessive frills and extras that are not required for efficient, safe production should not be provided. 3. Mine production costs are determined by the amount of men, material, equipment and energy used in the production process. These must be kept to minimal limits in order to insure dependable, low cost production. Extras that later are needed in the production operation can be added as required by the operator. Basically block caving is a mining system that is normally used to extract deep seated, massive, low grade deposits of copper, molybdenum and iron where stripping ratios for open cast mining are economically prohibited. The caving system is limited in its selectivity. It is a mass production type of underground ore extraction that under favorable conditions is one of the most efficient, low cost mining systems in the world today. Usually block cave mining systems are large. They are capable of producing ore at a rate of 10,000 to 100,000 tons/day from large deposits at costs that are comparable with many open cast mining systems burdened by high waste to ore ratios. Block cave mining systems differ basically in the plan of the area layout, the method of undercutting and the method of draw. The balance of the mining system is the mechanical transportation of the drawn ore to the surface, the mine supply, drainage and ventilation systems. This paper deals mainly with the methods of draw. The method of draw to be used in a block caving system dictates the development plan of the mining area, is highly influential in the method of undercutting to be employed and the supply and ventilation system to be used. There are three basic methods of draw commonly used in today&apos;s operations. They are: Gravity draw Slusher draw LHD draw The type of draw planned will have a major affect on: Capital expenditure and time required to bring a deposit into production. Productivity, efficiency and cost of the production operation. Percent recovery of the ore deposit in both tonnage and grade. Degree of production reliability Fundamentally the type-of draw used must be compatible with the physical characteristics of the deposit to be extracted and the financial position of the mining operation. The type of draw chosen must work to advantage with the size, configuration, depth, strength and fracture pattern of the deposit and its adjacent formations. It must favor the financial protection of the planned mining operation. A Gravity Method of Draw requires a finely fragmented, easy flowing product from the caving action of the deposit. To obtain the desired economic advantage the ore deposit must also have sufficient area and height of column to permit minimal development cost on a per ton basis. The gravity system re- quires the maximum amount of development openings and uses the minimum amount of mechanized equipment of all the caving systems. It is unskilled, labor-intensive and is highly sensitive to size of ore fragmen-

Jan 1, 1981

By P. E. Schauer

During the initial nine-year deple-tion of the McKamie-Patton pool gas-condensate reservoir, the pressure behavior and fluid analyses indicated pressure maintenance by gas injection would be attractive relative to continued pressure depletion. As a result, a gas cycling program was inaugurated in Aug., 1949, which has since maintained reservoir pressure. In order to evaluate the benefits of this program, the recoveries for natural depletion and for cycling followed by blowdown were determined by calculating the fractional balance of the molar quantities of vapor and liquid remaining in the reservoir and produced at the surface for various stages of depletion. The results of the investigation show theoretical ultimate recovery due to the cycling program will be 42 per cent greater than would be realized under pressure depletion type operation. INTRODUCTION The benefits of gas injection pressure maintenance programs in condensate reservoirs have been recognized and qualitatively described in several papers1-8 during the past 15 years. Some of these papers also describe methods for calculating the increased recovery realized from cycling; however, as a rule, hypothetical reservoirs were used as examples".&apos;.. This paper presents an evaluation of the pressure maintenance program for the McKamie-Patton condensate reservoir and includes a description of the fractional balance method employed to determine the benefits. Reservoir Development and Characteristics The McKamie-Patton pool, Lafayette County, Ark., was opened in June, 1940, with production obtained from the oolitic Smackover lime at a depth of approximately 9,300 ft. The structure is an anticline 8 miles long by 1 to 2 miles wide, and is one of many productive Smackover structures in Southern Arkansas. Of predominant importance is the condensate-bearing gas cap portion of the reservoir, which covers approximately 4,000 acres, attains a maximum thickness of some 200 ft, and has an average thickness of 90 ft. Development of the cap was accomplished with 21 wells drilled on 160 acre spacing. An isopach map of the cap is shown in Fig. 1. In addition, an oil rim is present along most of the periphery of the pool. Production practice includes field separation of black oil, and a high pressure gathering system which carries total well stream from gas cap wells to a plant where condensate is separated and the gas is processed for recovery of natural gasoline, butane, and propane. Since the gas contains appreciable hydrogen sulfide, it is removed by amine contact, after which free sulfur is produced by the Claus process. Core analyses from 1,767 gas cap formation samples averaged 14.2 per cent porosity and 379 md dry air permeability. Connate water was restored on seven samples of gas cap rock by air-brine capillary techniques, from which the interpreted water saturation averaged 28.17 per cent. During the early life of the field, it was believed the recovery mechanism, based on several of the other regional Smackover reservoirs, might be a natural water drive. However, subsequent production and pressure history revealed that the gas cap would not be produced by water drive, but would behave as a closed reservoir. In this respect, during the nine-year period of natural depletion from initial production to Aug., 1949, the cap production of 84.3 billion

Jan 1, 1958

HIGH-GRADE manganese ore, from which manganese is obtained commercially, is not found in large quantities in any major steel-producing nation in the free world. The U. S. is a "have not" nation with respect to deposits of directly mineable high-grade manganese ore. Known resources of 48 pct Mn or better grade ore amount to less than 200,000 tons. In 1950 the U. S. steel industry consumed 1.8 million short tons of metallurgical grade manganese ore that contained about 800,000 tons of manganese. About 16 pct of the manganese content was lost in processing, so that about 650,000 tons, or 13 pounds per ton of steel actually entered into steel production. Under present practices use expands directly with steel output, and by 1975 the demand in both the U. S. and the rest of the free world is expected to be roughly 60 pet greater than in 1950. In peacetime about 80 pet of manganese consumption goes into steel production; high-manganese steel, dry cells, and chemicals account for the remainder. The manganese supply problem centers around high-grade ore for ferromanganese production. Use of ores containing less than 35 pet Mn sharply increase the costs of making ferromanganese. Use of ferro-manganese of grade below 70 pet in turn requires changes in steelmaking that increase steel cost. Under normal conditions the present small domestic production cannot be expected to increase. Major resources in the U. S. consist of 12 low-grade deposits. The cost of mining and treating these ores to extract a product as good as that yielded by imported ores is at least twice and in some cases more than four times the 1951 price of foreign ores delivered to the U. S. However, as long as trade relations and overseas shipping are not interrupted, deposits in India, Africa, and Brazil can meet steadily increasing demand at approximately present costs. Cost considerations indicate that the U. S. should continue to rely upon overseas sources for its peace-time supply, and that this situation is satisfactory. But, this does not take into account the question of how the U. S. will be able to meet its needs in war. Position of the Rest of the Free World In 1950, free world steel producers outside the United States, with a steel output of 70 million ingot tons, consumed about 1.3 million tons of metallurgical-grade ore. Their manganese ore demand, expected to increase directly with steel production, will by 1975 be about 2.3 million tons. Russia possesses over half the known manganese ore reserves of the world and is producing twice the tonnage of any other country. It supplied more than a third of the U. S. manganese requirements up to 1938 and again in 1948, but by 1950 Soviet manganese exports to the free world had virtually ceased. The free world&apos;s supply of manganese now comes mainly from India and Africa. Somewhat over 10 pet of U. S. imports came from Brazil and Cuba. Security Considerations In the event of war the U. S. might be substantially cut off from 90 pet of present sources. Reduction in manganese specifications might cut consumption by over 10 pet without seriously affecting steel quality. By elimination of losses in the production of ferromanganese savings as high as 10 pet might be possible. But, wartime manganese requirements cannot be met through conservation alone. To meet possible future emergencies the U. S. should continue its comprehensive security program for manganese, including stockpiling and research on the economic use of low-grade ore, domestic ores, the recovery of manganese from slag and the reduction of manganese requirements in steel production. If this work, including additional pilot plant operation is pursued vigorously, it should be possible in an emergency to get an adequate supply of manganese from domestic sources. The national stockpile then can be looked upon as a source of supply during the period of at least 2 years required to reach full-scale production from low-grade resources. Ferromanganese Smelting In comparison with smelting of pig iron, ferro-manganese smelting is a very wasteful process. Under present ferromanganese blast-furnace smelting practice, about 8 pet of the manganese in the furnace charge is lost to the slag, and roughly the same amount is lost to the stack gases; the total loss approaches 15 pct. Present practice is a compromise between excessive slag loss and excessive stack loss. In fact, it may be seriously questioned whether conventional blast furnace design is suitable for manganese smelting. U. S. Resources The known manganese deposits of the U. S. contain a total of 3500 million long tons of raw material and 75 million long tons of metallic manganese. More than 98 pct of this contained metal is in 12 large low-grade deposits of which the most important are those at Chamberlain, S. Dak; Cuyuna, Minn.; Aroostook County, Maine; and Artillery Peak, Ariz. Reserves of high-grade ore (48 pct Mn) amount to less than 200,000 tons. About 20 million tons of ore average over 15 pct Mn, and when grade is decreased to 10 pct Mn reserves amount to about 100 million long tons. If cut-off grade is decreased to 5 pet Mn, resources amount to 800 million long tons. Many of these low-grade ores may be beneficiated by flotation or other concentration methods. Pyrometallurgical Methods For smelting ferromanganese, it is essential to have an ore containing at least 50 pct manganese, with an Mn:Fe ratio of about 8:1. Direct smelting of 20 pct Mn concentrates is not promising. The only method that offers any promise involves two-step smelting.

Jan 1, 1952

By T. W. Guy

DuRing recent years, tremendous strides have been made in the economical use of coal. This has resulted in, and to some extent has been a result of, making the fuel specifications more and more rigid. For this reason, all producers have found it necessary to improve their preparation materially, both as to sizing and the elimination of impurities, either by more effective preparation underground or at the tipple and cleaning plant, or both. This cause and its effect in all producing fields seem likely to continue for several years at least. The splendid inherent qualities of the Pocahontas and New River coals are known all over the world, but their good reputation is only partly due to inherent qualities, and to natural conditions which generally favor loading coal comparatively free from impurities; it is due in large measure to the care and skill used, either with or without the aid of mechanical devices, to ship products consistently low in ash. The first coal from the West Virginia smokeless fields was mined and shipped near Quinnimont, on New River, in 1871, while the first shipments from the Pocahontas field were in 1883. The development of both fields progressed rapidly. At first activities followed the main lines of the Chesapeake & Ohio and Norfolk & Western railroads, and were extended later as branch lines were built from these roads. The Virginian R. R., about 1907, opened up the Winding Gulf territory, which has since become a large producer of smokeless coals from the Pocahontas and the New River measures. Early Cleaning Methods In the early days, the tipples were simple wooden structures, with bar screens for separating the fines from the lump coal. All cleaning was done by the miners at the face, or by pickers in the railroad cars. Gates were provided in the chutes by which the flow of coal could be stopped when necessary while the pickers raked the surface of the coal in the car and picked out the impurities. A large percentage of the fine coal or slack was used for making coke at the mines in beehive ovens. The

Jan 1, 1932

By Robert Stefanko

Roof bolting in coal mines has progressed very rapidly in the last decade, and today this method of support is in general use. There are many theories concerning the functions of roof bolts, but the importance of beam building is indisputable. Proper tension in the bolts minimizes shearing along bedding planes and creates a thick, competent beam from individually weak layers. Bolting must be accomplished immediately upon exposure of the roof, and bolt tension must be maintained if roof failure is to be prevented. Seams are being mined today with roof bolt support where conventional timbering was not effective1. The widespread use of continuous mining equipment was made possible by roof bolts which permit long supported spans free of obstructions.2 Since adequate anchorage is the key to successful bolting, better methods for determining the efficiency of anchorage are continually being sought. Attempts have been made to measure bolt loads, thus assessing anchorage efficiency by employing sensing devices between the bolt head and roof. 3,4,5 None of the techniques appears to be very accurate, and all have at least one serious deficiency.

Jan 5, 1962

By Harrison Everett Ashley

(Pittsburg Meeting, March, 1910.) Slimes are usually defined as all material passing a certain-sized sieve, which is invariably the finest sieve employed by each metallurgist in his tests; 100-mesh and 200-mesh have been taken as the limits by different writers in recent volumes of the Transactions ; 150-mesh is common practice. The reader of the first two volumes of Richards 1 is impressed by the inflexibility with which all grinding-arrangements are praised or condemned according as they make little or much slime. Until recently, one of the principal aims of the mill-man was to keep down the slimes. He was obliged to have separate apparatus for sand- and slime-treatment. The latter was sometimes puzzling and erratic. Often it was found most .economical to omit treatment of the slimes entirely, or to store them in immense basins or heaps, waiting for possible future improvements in methods of treatment. Recently, improved processes of agitation and filtration have made possible the successful extraction of values from many slimes. The tendency, when the metal is exceedingly finely disseminated, is to cut out all sand-treatment and to slime everything. These processes have been almost entirely mechanical in their conception, and it is the object of the present paper to show that certain chemical considerations may greatly hinder or assist their successful operation. It has long been a source of dissatisfaction to chemists that their analyses fail to be of much help to the clay-worker; that it is a matter of common occurrence for clays of closely identical ultimate chemical constitution to show the widest possible divergence in physical properties. * Published by permission of the Director of the U. S. Geological Survey. Ore Dressing (1903).

Aug 1, 1910

The Free World&apos;s largest uranium reserves are in the United States. Almost 97% of the U.S. uranium reserves occur in irregular shaped sandstone formations, widely disseminated in coarse clastic sediments that are mostly of Jurassic or Tertiary age. Without doubt, the most important deposits are located in the sandstone formations of the Ambrosia Lake district of New Mexico, near the sun-scorched town of Grantswhose proud alias, as given by the city fathers, is "The Uranium Capital of the World."

Jan 8, 1974

By R. F. Dickerson, D. A. Vaughan, A. F. Gerds

ALTHOUGH the metallurgy of uranium has been under intensive study since the early 1940&apos;s, no systematic effort has been made to identify the non-metallic inclusions in uranium. Uranium carbide (UC), which is probably the most common inclusion found in graphite-melted metal, has been tentatively identified by previous investigators, but the other nonmetallic inclusions have received little attention. Since metallography is a valuable tool in metallurgical studies, the metallographic identification of the nonmetallic inclusions in uranium is important. Such an investigation has been completed and the identification of slag-type inclusions and of uranium monocarbide, uranium hydride, uranium dioxide, uranium monoxide, and uranium mononitride is described. Metallographic Preporation It is often possible to prepare specimens for metal-lographic examination equally well by several methods. The specimens which were examined in this work were prepared by one of two acceptable methods. For the convenience of the reader, both methods will be discussed in detail and will be referred to simply as Method I or Method II in the subsequent sections. For both Methods I and 11, specimens for microscopic examination usually were mounted either in bakelite or in Paraplex room temperature mounting plastic. Method I—Specimens were ground in a spray of water on a revolving disk covered successively with 120-, 240-, and 600-grit silicon carbide papers. It was necessary to perform the final grinding operation carefully on worn 600-grit paper to keep the scratches as fine as possible. After washing and drying, the specimens were polished for 3 to 4 min on a slow speed wheel (250 rpm) covered with a medium nap cloth. Diamet Hyprez Blue diamond polishing paste, Grade 00, 0 to 2 µ, was used as abrasive with kerosene as lubricant on the wheel. Specimens were washed thoroughly in alcohol and final polished electrolytically in an electrolyte composed of 1 part stock solution (118 g CrO, dissolved in 100 cm3 H2O) with 4 parts of glacial acetic acid. A stainless steel cathode was used. At an open circuit potential of 40 v dc, a polishing time of 2 sec retained inclusions well with the bath at room temperature. If additional etching was required to sharpen the interface between the metal and the inclusions, an electrolyte composed of 1 part stock solution (100 g CrO3 and 100 cm8 H20) and 18 parts glacial acetic acid was used at room temperature. Best results were obtained by etching for from 10 to 15 sec at 20 v dc in the open circuit. Surfaces obtained by this method are suitable for microscopic examination. However, if desired, they may be etched further with other chemicals. Method 11—Rough grinding was done on a wet 180- or 240-grit continuous grinding belt. The specimen was then ground by hand successively on 240-, 400-, and 600-grit silicon carbide papers in a stream of water. Final polishing was accomplished on a 4 in. high speed wheel (3400 rpm) covered with Forstmann&apos;s cloth. Linde B levigated alumina, suspended in a 1 volume pet chromic acid solution, was the abrasive. Specimens usually were polished in 5 min or less by this technique. Often the inclusions present in the metal were identified in the mechanically polished condition. When etching was required to outline inclusions more sharply, one of the two following methods was used. In the first method, the specimen is etched lightly while electropolishing in the chromic-acetic acid solution described above (1 part of stock solution to 4 parts of acetic acid). The electrolyte was refrigerated in a dry ice-ethyl alcohol bath and specimens were etched at 60 v dc on the open circuit for 2 or 3 cycles of 3 to 4 sec each. The second technique utilizes electrolytical etching at about 10 v dc (open circuit) in a 10 pet citric acid solution at room temperature. X-Ray Diffraction Technique The major problem in the identification of inclusions in metals by X-ray diffraction techniques is the extraction of a sufficient amount of each type of inclusion to obtain an X-ray diffraction pattern. In the present study, X-ray diffraction patterns were obtained from individual inclusions of the order of 10 µ diam. The polished and etched samples shown in the micrographs were examined at a magnification of X54 or XI00 with a binocular microscope. This allowed sufficient working distance to extract the inclusions with a needle probe for powder X-ray diffraction analysis. Friable inclusions such as MgF2, CaF2, UO2, and UH3 could be freed from the metal by probing the as-polished and etched surface. The fine particles then were picked up on the end of a Vistanex-coated glass rod (0.002 in. diam) which was held in a brass adapter made to fit the powder X-ray diffraction camera. The end of the glass rod was centered in the path of the X-ray beam. In the case of the UC, UO, and UN inclusions which are smaller in size, more metallic in appearance, and less friable than the other inclusions, it was necessary to etch the inclusion in relief before extraction. UN inclusions etched sufficiently in relief in the electrolytic polishing solution described in Methods I and II by increasing the polishing time. UN inclusions were relief etched by extending the

Jan 1, 1957

By C. W. Sherman, John Chipman

IN the mathematical statement of the law of mass action, the activity of each substance consumed or produced in a reaction is used to obtain a numerical constant which is characteristic of the equilibrium of that reaction at the given temperature. The activity in many cases is equal to, or proportional to, the concentration. If this is the case, any units denoting concentrations, such as weight percentage or mol fraction, may be substituted in the equilibrium expression. It is even permissible to use mixed units provided only that each unit is that used in defining the activity of the corresponding substance. The indiscriminate use of concentration units in writing equilibrium constants sometimes leads to very erroneous results. On the other hand, what appear to be contradictory results from similar investigations often might be resolved if the activity is the quantity that is used to determine the equilibrium constant for the reaction in question. De-sulphurization serves as an important illustration. Sulphur in lron and Steel The control of the sulphur content of the finished product is one of the oldest and broadest problems in the metallurgy of iron and steel. In general, this control must be exercised through the action of a slag, and for this reason experimental studies of the distribution of sulphur between slag and metal have assumed considerable importance. Under slags of the type found in the basic open-hearth furnace the ratio (% S)/[% S] does not in general exceed about 8. Under blast-furnace conditions, however, de-sulphurization ratios of 50 to 100 are readily obtained, and under laboratory conditions using similar slags, the ratio may be as high as 400. The fact that blast-furnace metal is much more readily desulphurized than is molten steel rests upon two distinct phenomena. The first of these is connected with the slag reaction. In the open-hearth furnace, the equilibrium in the following reaction places a definite limit on the sulphur content of the slag: S + 0-- = 0 + S- - where the symbols underlined indicate elements dissolved in the liquid metal, while slag constituents are represented as ions. The high oxygen content of the open-hearth bath prevents this reaction from proceeding far enough to effect good desul-phurization. In the blast-furnace process, however, the oxygen activity is limited by the presence of carbon in the metal and in the coke bed and the controlling reaction becomes: S_+O- + C_=S- + CO(gas) [2] The second phenomenon which contributes to the easier desulphurization of blast-furnace metal is the effect of high concentrations of other elements. These elements, notably carbon, silicon, and phosphorus, increase the thermodynamic activity of sulphur several fold. As a result of this increase, the escaping tendency of sulphur from the metal phase is increased and its removal facilitated. Previous Studies It becomes, therefore, a matter of importance to determine the effects of various elements upon the activity of sulphur in the melt. The experimental approach to this problem has been made through the equilibrium between sulphur in the melt and gaseous atmospheres containing hydrogen and hydrogen sulphide. The reaction and its equilibrium constant are written as follows: S + H2(gas) =H2S(gas);K1 = -- [3] Pn2 • as where the symbol a, represents the activity of the sulphur in solution in the metal. The understanding of the chemical behavior of sulphur in steel and pig iron rests on a firm knowledge of the binary system Fe-S. A number of studies of the equilibrium have given closely agreeing results from which the activity and free energy of the dissolved sulphur may be found. The recent paper by Sherman, Elvander, and Chipman1 includes a discussion and quantitative comparison of the results of several of the significant researchesr-" on dilute solutions of sulphur in iron. The results of this study indicate that the relationship between the ratio Ph,s/p+ and the percentage of sulphur in solution is not a linear one. This

Jan 1, 1953

By John P. Ashby

Mine production blasting is a process of destruction of rock masses in order that ore may be extracted. Many open pit operations are faced with the apparently conflicting requirements of providing large quantities of fragmented rock for the processing plant and of minimizing the damage inflicted upon the surrounding pit slopes. A reasonable compromise between these two conflicting demands may often be found by means of simple engineering of production blasts. Many operations tend to rely too heavily upon traditional wall control techniques to alleviate a problem already created by the production blasts. Various production trends including use of larger blastholes and patterns have tended to aggravate the situation. These practices only serve to emphasize the need for engineered improvements. Central to blasting engineering is the process of systematic trial and evaluation. Changes to the blasting system should be made singly, starting with the simplest. This paper discusses simple changes involving drill pattern control, effective use of blastholes and explosives, adequate delaying including use of down-the-hole sequential techniques, effective utilization of free faces, and avoidance of "choked" situations. By directing explosive effort where it is needed, such changes generally result in a significant improvement of slope conditions and of production blasting cost and performance.

Jan 1, 1983

By C. Gatlin, F. Armstrong, K. E. Gray

This paper presents some preliminary results of two-dimensional cutting tests of dry limestone samples at utmospheric pressure. Cutting tips having rake angles of + 30°, + 15", 0°, - 15" and - 30" were used to make cuts on Leuders limestone samples at six depths of cut ranging from .005 to ,060 in. at cutting speeds of 15, 50, 109 and 150 ft/min. The vertical and horizontal force components on the cutting tips were recorded with an oscilloscope equipped with a polaroid camera. Motion pictures of the cutting process at camera speeds of 5,000 to 8,000 frames/sec were taken at strategic points in the variable ranges. The movies provide considerable insight into the brittle failure mechanism in rocks. It appears that chip-generating cracks usually have an initial orientation which is related to the resultant of the externally applied forces. The latter part of the crack curves upward toward the free surface being cut, this part being governed by some type of cantilever bending or prying. The linear and angular motion of the loosened chips also indicate the tensile nature of brittle failure. Analyses of the forces on the cutting tips indicate that: (I) relatively small increases in vertical loading result in large cut-depth increases for sharp tips (rake angles 2 0"); (2) tool forces increase at an increasing rate as the rake angle decreases, particularly for rake angles < 0"; and (3), for the range of this study, rate of loading had little effect on the maximum forces. Both the movies and visual inspection of the cuttings indicated that the volume of rock removed by chipping was much larger than that by any grinding mechanism, even for tips having negative rake angles. Cutting size increases with increased cut depth and rake angles, and decreases slightly at high cutting speeds, the depth of cut having by far the most influence. The amount of contact between the rock and the cutting tip was always less than the depth of cut and rarely exceeded 0.010 in. even for cuts of 0.060 in. INTRODUCTION The planing (or slicing) of various materials with a fixed blade has long been practiced by workers in many industries. For example, the farmer&apos;s plow, the carpenter&apos;s plane and the housewife&apos;s paring knife all employ this basic action. The casual observer might suspect that something so common must be quite simple; however, as in all problems involving the failure of materials, such is not the case. Industries concerned with the machining of metals have long studied these problems, and their literature on the subject is voluminous. Despite these efforts, basic knowledge is not very advanced, as may be noted from recent and comprehensive analyses of their literature.12 Metals are more subject to analysis by classical theories of elasticity and/or plasticity than are rocks, since their elastic constants and strengths are reasonably well established in many cases. In spite of this relative "simplicity", Hill9 refaces his discussion with an admission that the mathematical solution to the machining problem is not known. Photoelastic studies of both machining and milling have been performed and are discussed thoroughly by Coker and Filon.4 Rotary drilling of rocks with fixed blade or drag bits has long been practiced by the mining and petroleum industries, and considerable study has been given to defining their cutting action in terms of the pertinent variables. Essentially all the published mechanistic research on drag-bit drilling has been performed by mining engineers and has been concerned only with rocks in the brittle state. Fairhurst5-7 has worked extensively in this area and employed photographic techniques quite similar to those reported here, except at much lower speeds. His studies showed the periodic or cyclical nature of the brittle failure mechanism, in which instantaneous loads on the bit varied from some maximum value to near zero. Goodrichs has presented further data on the subject as well as a qualitative description of the process. Again the postulated mechanism is cyclical, with alternate chipping and grinding periods. The ploughing of coal is a practiced method and has been studied in some detail by English mining engineers."" Their findings have considerable general application to drag-bit drilling. Evans," in particular, has extended Merchant&apos;s metal-cutting theory" to brittle materials with some success, although certain aspects of his theory are open to question. Fish13 has recently summarized nearly all the published works concern-

By Carl J. McHargue

Mechanical twins were produced in electron-beam melted columbium by high-speed impact at room temperature and by slow or fast compression at -196°C. The composition plane of the twins was { 112} and the shear direction was <111>. Notches in the twin bands often corresponded to traces of {110) of the matrix and appeared to be untwinned regions. Markings within the twin bands were interpreted as resulting from {110} slip in the twins. THERE has been much work in recent years concerning plastic deformation by glide, and the dislocation theory relating to glide has reached a relatively high degree of development. On the other hand, there have been fewer studies of deformation by mechanical twinning, and understanding of this process is far from satisfactory. This method of deformation is of interest for at least two reasons. First, it provides a mechanism in addition to glide for the relief of stresses, and, in the bcc and hexagonal close-packed metals may result in significant amounts of plastic flow. Secondly, there is the possibility that twins may act as barriers for dislocation movement, resulting in pile-ups which could nucleate cracks. As might be expected, the bulk of the literature on mechanical twinning in the bcc metals is concerned with iron. A good summary of the work done prior to 1954 is contained in the book by all.&apos; Recently the refractory bcc metals have become increasingly important. Limited studies have shown that tantalum,2,3 molybdenum,4,5 vanadium,6,7 tungsten,&apos; and columbium9-11 deform by mechanical twinning under some conditions. Alloys of molybdenum with rhenium and tungsten with rhenium show extensive deformation by twinning at room temperature.I2-l4 Most of these studies have dealt primarily with mechanical properties at low temperatures or have shown the existence of twins, and there is only a small amount of information concerning the conditions under which they form. The subject of the present paper is the formation of twins under stress in columbium with a consideration of their morphology. EXPERIMENTAL PROCEDURE The material used for these studies was taken from an ingot of columbium which had been melted twice by the electron-be am-method. The analysis of the ingot was (in ppm): B < 1, C = 10, Fe < 100, The cast ingot contained very large grains, and it was possible to obtain single-crystal prisms which measured from ¼ to 3/4 in. on a side. A few experiments were conducted on polycrystalline plate which was prepared by rolling material from the same ingot at room temperature and annealing at 1000 in a dynamic vacuum of 10-6 mm Hg. This gave a plate in which the grains had an average diameter of 3 mm. After the specimens were cut from the ingot, the six faces were metallographically polished and elec-tropolished to remove all traces of cold work. Most of the observations were made on the surfaces of the deformed specirllens without further treatment. Occasionally, etching after deformation was desirable. In these cases, an etchant of the composition 50 parts H2O, 5 parts HNO3 25 parts HF, and 10 parts H2SO4 was found to delineate the twins very well. Unless considerable care was taken to ensure the removal of all disturbed metal left by the mechanical polishing, etching failed to reveal many of the features discussed in this; paper. The specimen&apos;s were deformed either by impact or slow compression at 77°K (liquid-nitrogen coolant), 198°K (dry ice and acetone coolant), and 298°K. The impact load was delivered by a hammer except in one case where the load was delivered by a bullet. Slow compression was carried out on a hydraulic testing machine equipped with a chamber to hold the coolant. EXPERIMENTAL RESULTS It has been generally believed that the conditions favoring the formation of deformation twins are large grains, low temperature, and impact loading. In fact, Barrett and Bakish2 found twins in tantalum only after impact deformation at 77°K, and Adams, Roberts, and Smallman10 observed twins in columbium only at 20 For these reasons, the initial experiments of this study used impact loading. Hammer blows caused many bands resembling twins in single crystals a.t 77" but not at 198°K. Only a few slip lines were observed on any of the single-crystal specimens of this study—essentially all the deformation occurred by twinning. The appearance of the twins on the as-deformed surface is shown in Fig. 1. Although both Figs. 1(a) and l(b) are photomicrographs of twins taken at the same magnification and from the same crystal, they are startlingly different in appearance. Fig. 1(a) was taken from the crystal face approximately perpendicular to the shear direction, whereas Fig. 1(b) was taken from

Jan 1, 1962

By J. Chipman, H. Towers, M. Paris

A simple radioactive tracer technique is used to measure the diffusion coefficient of calcium ion in molten slags. In a slag of 40 pct Ca0-40 pct Si0,-20 pct Al203, Dc " at 1450°C is 1.3x10-6 cm&apos; sec-&apos;. THE application of the principles of thermodynamics to steel and iron making problems has proved so fruitful that the kinetic approach has tended to be neglected. It seems probable that in some reactions the rate-determining step is the dif-fusivity of the reactants or of the products. But knowledge of the diffusion coefficients of the constituents of liquid slag and metal is singularly lacking. The present work was undertaken as a first step toward supplying such data for slags. Furthermore, any additional information on the physical properties of liquid slags might be expected to help in elucidating their structure. It is essentially a preliminary investigation, the course of which was determined more by the necessity of establishing a method than by the immediate intrinsic interest of the results. For example, the selection of calcium ion to be studied was dictated by the suitability of the isotope Ca45 in that it is a simple emitter with a long half-life. Of the other ions commonly encountered in slags, the isotopes of iron and manganese have relatively complex radiations as well as the normal disadvantage of requiring control of the oxygen potential of the atmosphere; Mg27 and Al29 have half-lives measured only in minutes; Si3&apos; has a simple decay process but its half-life of 2.8 hr is too short for preliminary studies; the only useful oxygen isotope is the stable O18; and there remain only sulphur and phosphorus both of which have suitable isotopes but were rejected as being of less fundamental interest than calcium. Similarly a lime-alumina- silica slag was used in preference to calcium silicate primarily because of its low melting point and its capacity to form a glass on fairly rapid cooling. Literature Review Very few studies of diffusion in liquid silicate systems have been reported. In order to determine the origin of diopside inclusions in felspathic rocks, Bowen1 investigated the diffusion between diopside and various mixtures of albite and anorthite. Platinum crucibles were used with diopside, the heavier of the two liquids, forming the lower half of the cell and diffusion taking place against gravity. Change in concentration along the diffusion path was found by measuring the refractive index of the quenched glass. Nearly thirty years later McCallum and Barrett2 used essentially the same method to determine the diffusion coefficient of lime in lime-alumina-silica slags. In this case the interest was to find the rate-determining step in the process of slag attack on refractory materials. In an investigation of the kinetics of the sulphur reaction, Derge, Philbrook, and Goldman8 determined the diffusion coefficient of sulphur in a typical blast furnace slag by the simple procedure of melting a slag containing 2 pct S over an identical slag sulphur-free. They make no claim to a high degree of accuracy but suggest that D, is of the order of 10-6 cm2 sec-l. Other high temperature liquid diffusion studies have been concerned with metals. Holbrook, Furnas, and Joseph4 determined the diffusion coefficients of silicon, phosphorus, sulphur, manganese, and carbon in liquid iron by immersing a small carbon crucible containing pure iron-carbon alloy in a large vessel containing iron with a high concentration of the particular element. Their results were confirmed by Paschke and Hauttmann5 using a similar method. Diffusion coefficients in silicates in the glassy state have been studied by Johnson, Bristow, and Blau6 Both Na24 and Ca45 were used as tracers but only the

Jan 1, 1954

By Clarence Woods

ONCE a millionaire&apos;s plaything, the Santo Domingo mine, in Peru, is now, because of its metallurgical problem, an engineer&apos;s nightmare. It is deep in the montaña jungles of the Amazon basin, 140 mi. northeast of Tirapata, which is a rail- way station between Puno and Cuzco, and about 250 mi. east of Mollendo on the Pacific. The discovery was 111ade by Marian(-) Quispe, an Indian, who, while searching for quinine bark, was attracted by a slab of gold quartz 1x1 the rock wall of a narrow canyon. He broke off a piece, weighing 47 Spanish ounces and, that time, worth approximately $900. This he took to Francisco Velasco and Manuel Estrada, merchants of Coaza, who persuaded Quispe to lead them to the place, five days&apos; journey on foot through a tangled wilderness. Velasco &apos; and Estrada denounced the claim

Jan 1, 1938

By T. L. Joseph

Blast furnaces are most efficient thermally when the CO2 in the top gas is highest. Oxygen introduced in the air blast is converted to CO in the combustion zones. The extent to which CO, generated in front of the tuyeres, is converted later to CO2 depends upon the ratio of ore to coke in the charge and the degree to which CO2, formed by reduction of iron oxides with CO, reverts to CO by the secondary reaction C + CO2 = 2CO. About 300 to 400 lb. of carbon&apos; per ton of pig iron is normally involved in the solution-loss reaction or direct reduction of FeO with carbon, which produces the same over-all results; that is, lower CO2 in the top gas. Rich2 has recently reported a reduction in fuel consumption at slower rates of blowing on two furnaces in spite of higher heat losses per ton of iron. Lower fuel consumption at slow operating rates was due to more complete reduction of the ore that resulted in higher CO2 in the top gas and consequently more efficient use of carbon. Kinney3 has reported substantial savings in fuel as a result of crushing and sizing the ore charge. Improvements in practice brought about by sintering magnetite concentrates, flue dust and fine ores have been due to the establishment of conditions favoring more complete reduction of the ore in the upper part of the furnace. The extent to which oxides and fluctuations in composition in pig iron affect the quality of steel and finished product needs further study. There is evidence that more thorough preheating and reduction of the ore in the upper part of the furnace tend to give a better quality of iron. Bogatzkii4 found from laboratory work that the amount of oxygen entering electrolytic iron, melted under various slags, was directly proportional to the concentration of free FeO in the slag and inversely proportional to the basicity of the slag. Herty and Gaines5 concluded that the silicate content of open-hearth steel before deoxidation is related to the concentration of silica in the pig-iron charge, indicating that most of the persistent inclusions are silica from the iron. They also found that

Jan 1, 1936

By T. L. Joseph

Blast furnaces are most efficient thermally when the CO2 in the top gas is highest. Oxygen introduced in the air blast is converted to CO in the combustion zones. The extent to which CO, generated in front of the tuyeres, is converted later to CO2 depends upon the ratio of ore to coke in the charge and the degree to which CO2, formed by reduction of iron oxides with CO, reverts to CO by the secondary reaction C + CO2 = 2CO. About 300 to 400 lb. of carbon&apos; per ton of pig iron is normally involved in the solution-loss reaction or direct reduction of FeO with carbon, which produces the same over-all results; that is, lower CO2 in the top gas. Rich2 has recently reported a reduction in fuel consumption at slower rates of blowing on two furnaces in spite of higher heat losses per ton of iron. Lower fuel consumption at slow operating rates was due to more complete reduction of the ore that resulted in higher CO2 in the top gas and consequently more efficient use of carbon. Kinney3 has reported substantial savings in fuel as a result of crushing and sizing the ore charge. Improvements in practice brought about by sintering magnetite concentrates, flue dust and fine ores have been due to the establishment of conditions favoring more complete reduction of the ore in the upper part of the furnace. The extent to which oxides and fluctuations in composition in pig iron affect the quality of steel and finished product needs further study. There is evidence that more thorough preheating and reduction of the ore in the upper part of the furnace tend to give a better quality of iron. Bogatzkii4 found from laboratory work that the amount of oxygen entering electrolytic iron, melted under various slags, was directly proportional to the concentration of free FeO in the slag and inversely proportional to the basicity of the slag. Herty and Gaines5 concluded that the silicate content of open-hearth steel before deoxidation is related to the concentration of silica in the pig-iron charge, indicating that most of the persistent inclusions are silica from the iron. They also found that

Jan 1, 1936

By H. E. Cline

A criterion for stability of a lamellar structure in two-phase alloys ulas derived froflr perturbation analysis of the steady-state solutions for eutectic growth. Both the mass and thermal diffusion were considered with boundary conditions for coupled lamellar growth. The concept of an effective liquidus slope was introduced. Excellent agreement was found with the experiments of Mollard and Flemings and the theory predicted a range of compositions on one side of the eulectic composition in which stable growth may occur with zero temperature gradient. The lamellar structure was found to be more stable than predicted by simple constitutional supercooling. The effect of impurity additions was also considered. DIRECTIONALLY solidified eutectic alloys may have a structure consisting of parallel plates or rods. It is important to know the range of composition and growth conditions that produce this ideal composite structure. Breakdown of the planar solid-liquid interface during growth may lead to a dendritic or cellular structure as in single-phase alloys. In the case of single-phase alloys, the concept of constitutional supercooling1 may explain breakdown, but in two-phase alloys the concept is no longer valid because the melting point is not given by the liquidus of one phase. Both phases must be considered in the mass and thermal diffusion problem. In the following theory a boundary condition at the solid-liquid interface was determined by using the steady-state equations of Jackson and ~unt&apos; to relate the average temperature and composition of the liquid at the interface. Then a sinusoidal perturbation in the shape of the interface was introduced to test for stability as in the analysis of Mullins and ~ekerka.~ The wavelength of the important perturbation was assumed to be much larger than the lamellar spacing, h, and the perturbation was assumed not to change the lamellar spacing, A. Both the mass and thermal diffusion equation were used with averaged quantities at the boundary to determine whether the perturbation grows or shrinks in time. A stability criterion was determined by considering the case in which the perturbation remains stationary. An example of Pb-Sn alloys was used to illustrate the validity of this theory. I) THEORY A) Temperature at the Interface. The temperature of the interface in coupled two-phase growth is close to the eutectic temperature TE even for alloys off eutectic composition. It is assumed that the interface is in local equilibrium and one expects the temperature at the intersection of the liquid phase and the solid phases a and 0 to be near the eutectic temperature. The interface is undercooled because of curvature and the deviation of the composition in the liquid from the eutectic composition. The average interface temperature Ti for steady-state growth of a lamellar eutectic with a plane interface was determined by Jackson and Hunt&apos; as given in their Eq. [17c]. Instead of using the ratio of the lamellar widths hp/h, as a parameter, the volume fraction of the 0 phase, +, will be used as it simplifies the algebra. The average interface temperature using this notation becomes: The average temperature of the interface depends on the volume fraction of the 0 phase, +, which may be related to the composition of the solid or the bulk composition of the liquid Co by: where C, and Cp are the average compositions of the solid phases. In steady-state growth, the composition of the solid is equal to the composition in the liquid far from the interface. The variation of the average interface temperature with composition is illustrated in Fig. 1 for the case of Pb-Sn alloys with a 10"4 cm lamellar spacing as calculated from Eqs. [I] and [2]. The interface temperature goes through a maximum at a composition near but not exactly at the eutectic composition. There is no reason why the composition corresponding to the maximum temperature should be equal to the eutectic

Jan 1, 1969