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By M. C. Fuerstenau, W. F. Cummins

The flotation response of quartz in the presence of calcium chloride and various fatty acids is presented. Flotation is not effected with lauric acid until calcium laurate is precipitated in solution, while flotation is obtained with the 9, 10, and 11-carbon members before precipitation of the calcium carboxylate. The active species responsible for flotation is suggested to be a basic aqueous complex, e.g. Ca(OH) (RCOO) (aq), and a possible mechanism of adsorption is given. Most of the previous work on activation in non-metallic flotation systems has involved the use of high molecular weight collectors, such as oleic acid or alkyl aryl Sulfonate.1-7 In these studies the levels of addition of collector and activator required for flotation were much above the concentrations necessary for precipitation of the metal-collector salt. In fact, Clemmer, Clemmons, Rampacek, Williams, and Stacy1 have stated, "Our experiments on a variety of materials have demonstrated that the metal salts which react with anionic collecting agents, as soaps and alkyl sulfates, to form relatively insoluble compounds may be employed as activating agents provided an optimum quantity is used at a proper pH." On the other hand, Gaudin and chang8 obtained flotation with additions of barium and lauric acid below the level required for barium lautate precipitation.

Jan 1, 1968

By Raymond Ladoo

THE milling of talc, as is the case of many non-metallic minerals, until recently, has not received adequate technical consideration, for the talc industry has become of importance only within the last decade. At first, talc was used only in the massive form, for foot warmers, griddles, and so on, and milling methods were unnecessary. As the demand for ground talc increased, producers adopted the machinery used in the milling of flour; in fact, many talc mills were rebuilt flour mills. Improvement has been slow, but today several types of grinding and separating machinery are in use; many of them, however, are still inadequate and inefficient. To determine the best methods of milling talc, it is necessary to understand the essential properties a talc must possess to fit it for a particular use. For toilet purposes, whiteness, freedom from lime and grit, fineness of grain, and good "slip" are essential. As a paper filler or coating, the talc must be white, have a good slip, be free from grit and iron, uniform, and fine grained; freedom from lime is a disputed point. Fibrous talc is supposed to be superior to massive on account of the interlocking of grains in the paper, thus increasing its strength; this point, though, is in doubt. In general, talc for the paper industry need not be of as high quality or as fine grained as that used for toilet purposes. Talc is usually bought by sample, for which reason it is difficult to state the essential properties for use in paint, rubber, roofing, and so on. The adoption of standard screen tests and standard grades by producers is necessary before an accurate basis for manufacturing or selling standards can be established. Off-color tales might be utilized, as in Germany and-Austria, by the establishment of standard grades of colored tales.

Jan 1, 1921

By Edmund C. Perhin

At the suggestion of some members of the Institute, attention is called to the record of the working of Dunbar Furnace during the twelve months ending in Jaunary, 1874. During this period, with a product of over eleven thousand gross tons, not a single ton of

By C. T. Cox

The title of this short paper necessarily implies that friction articles comprise a distinct and unique field and are different from the other metal-powder articles, such as bearings, electrical contacts, and magnets. However, this distinction is rather hard to define in that it is really one of degree and not Of kind. It would appear that the main distinction is that friction are are articles of rather large pressing area. In other words, they are articles in which the area Of the mold in which the metal powder is pressed is relatively large. Other articles made from meta1 powders are generally of rather small area, usually a few square inches, while in friction articles the area ranges up to several hundred square inches. The satisfactory production of meta1-powder friction articles involves many production problems and a large number Of these are accentuated by the large area' Since it is impossible in the short space of this Paper to describe adequately all the problems involved, I have thought it best to merely mention some Of them and to place particular emphasis upon a problem that is common to all metal-powder articles, although it is of greater importance in the making of friction articles. This problem has to do with the effect On the properties of a friction article of small variations in the composition. However, before discussing the problems, it is probably appropriate that some mention be made of the limitations on the use of friction articles. Most engineers are familiar with the general field that can be characterized as constituted by clutch facings and brake linings, and undoubtedly have heard many stories of how metal-powder friction articles have had a service life 10 times as long as nonmetallic friction materials, and of instances where metal-powder friction articles have operated satisfactorily where no other material could be used. These instances should not be regarded as criteria for the assumption that metal-powder friction articles are capable of universal use in the friction field and will always outperform other materials. On the contrary, metal-powder friction articles are unsuitable for numerous applications, either on a performance or on a cost basis. Metal-powder friction articles will not replace wooden block brakes for wagon wheels nor cast-iron brake shoes for railway car wheels, to mention just two obvious examples. Metallic friction articles cannot be used where they must act as heat insulatorsl for they have a relatively high thermal conductivity as compared with asbestos. This is a detriment in some uses, as in certain airplane brakes having hydraulic actuators provided with rubber seals. The metallic friction material readily transfers the heat developed at the braking surface back through the material to the rubber seal and destroys it. Within its limited field, metal-powder friction material has proved satisfactory, but many problems are involved in the Selection of the proper material to use in an application and in the commercial pro-

Jan 1, 1945

By Pedro L. Lizaur

INTRODUCTION The degree of success of an association between parties in establishing a new venture ultimately depends on three factors: a. the venture's underlying economic strength, which is based on the complementarity of the comparative advantages brought by each party to the negotiating table; b. the ability to reach an agreement which satisfies each party's objectives and constraints; and, c. the capacity to design and implement a funding structure which is consistent with the project economics. A thorough assessment of the venture's profitability and associated risks under alternative technical and economic scenarios is the basis for a sound "go" or "no go" decision. In-depth evaluation of the risks and rewards to each of the parties involved under alternative legal and financial structure must be the foundation for a long lasting "how to go" decision. The allocation of risks and rewards should be consistent with the objectives and constraints of all parties and the sharing mechanisms, established in the contract, should be flexible to assure the long-term stability of the agreement. Rapidly changing economic conditions during the last decade have had a dramatic impact on the envisaged allocation of risks and rewards between host countries and private investors. The effects of these changes, and the fact that the relative strengths of the parties involved may shift during the life of a project (e.g. before and after major capital investments have been made), have forced the renegotiation of a multitude of contracts. Therefore, the present and future stability of an economic agreement would depend not only on the originally designed provisions, but also on provisions which allow for the automatic adjustment of rewards to project sponsors under a variety of future economic situations. A pre-condition for the allocation and quantification of risks and rewards is the definition of standards of measurement used by each of the parties. This is critical in international negotiations when one of the parties represents the national interests of a country. The understanding and use of different standards for the measurement of rewards for risk taken between a government and private enterprise facilitate the negotiation of a satisfactory agreement. This is possible because certain trade-offs between the negotiating parties may have different relative values. STANDARDS OF MEASUREMENT OF REWARDS FOR RISK TAKEN The negotiating process takes a step forward when the parties are able to focus on their interests, explore different alternative solutions and then base results on a set of objective standards. Unfortunately, the parties frequently put more effort into "staking out" and defending positions, than into understanding their intrinsic interests. Moreover, when one party, such as a governemnt owned corporation, represents a country's national interests, the negotiation process increases in complexity. Private firms focus on commercial profitability, using discounted cash flow techniques such as NPV, IRR, or ROE. In contrast, the government is also concerned with the project's impact on the local socio-economic environment. Without entering into a discussion of alternative economic development theories and approaches, there exist several possible measures that could be pragmatically utilized by each party in evaluating the socio-economic impact of a project. The more complete measure is the National Profitability (NP). The NP is a discounted cash flow procedure similar in structure to IRR or NPV but in which the project's financial cash inflows and outflows and discount rates are adjusted to take into consideration the local conditions. The NP is calculated on an unlevered basis and all taxes and duties are removed from the project

Jan 1, 1985

By Leon W. Dupuy

SUPPLEMENT THESE tables should accompany Figs 6, 7, 8, 9 and 10, respectively. To follow Fig 6: TABLE 2[a]-Drill Rod [ ] To follow Fig 7: TABLE 3-Rod Coupling [ ]

Jan 1, 1947

By Karl J. Benecke

Though the first patent on a bucket wheel excavator (BWE) was granted in 1881 in the US, this technology was developed in Germany to the high standards of today. However, this development was only possible in parallel with development of shiftable belt conveyors and boom stackers. The combination of these three types of equipment in the open pits of the Federal Republic of Germany has made lignite the cheapest energy source for power generation, despite the low heating value of German lignite on the order of 8500 kJ/kg (3600 Btu/lb) only. Comparing the costs for fuels used in power generating on the basis of their heating value, the relation between lignite, high quality black coal, and imported crude oil is on the order of 1 to 1.5 to 2.5, hence highly in favour of lignite. These cost advantages for lignite in Germany are due mainly to the concentration of lignite mining in a few high-output mines. The largest one, Fortuna mine in the Cologne district, produced a total of 45 million tons of lignite in 1976. That equals the annual fuel need of a 5750 MW power plant running 7000 hours per year at full capacity. Altogether 95.2 million bank m3 equal to 200 million tons of overburden had to be removed to accomplish this lignite output. The largest BWE ever built is working in the Fortuna mine [(Fig. 1)]. At a digging height of 51 m above crawler level, the total vertical reach in relation to the face conveyor level is 98 m by means of its conveying bridge and loading unit. The hourly output is 10 400 bank m3. Its weight in operation is 13 000 tons and its wheel diameter 21.6 m, as high as a seven-story building. Major reasons for the development of BWE technology in Germany were: ? Lignite deposits with moderately consolidated, alluvial-type overburden (gravel, sand, loam, marl, clay, etc.) ? Great overall depth of the deposits, ranging far beyond 100 m, requiring a wide opening of the mine, hence not permitting direct overcasting of overburden. ? Multiple-seam deposits of poor-quality coal divided by reject partings, which demand a perfectly selective digging tool for clean separation. In general, these conditions are almost identical to those prevailing in the lignite deposits of Texas and neighbouring states: The type of overburden suitable for BWE digging, the overall deposit depth ranges down to around 100 m, and finally, the multi-seam occurrence with partings between seams, the latter ranging from just 1 m to a few meters in thickness. Technique As the Texas-type lignite deposits come into focus more and more as a possible fuel source in power plants to replace natural gas and crude oil, the following will deal with the BWE technology for mining a typical Texas lignite deposit under the aspect of producing enough fuel for a 500-MW power plant located at the mine mouth.

Jan 1, 1980

By G. H. Kennedy

CYCLONE thickeners are "hydraulic centrifuges" designed either to produce a maximum practical separation between the water and solids of a feed slurry or to classify the slurry solids according to particle settling rate. The possibilities of utilizing the thickener to "close" plant water circuits have been investigated.

Jan 3, 1951

By N. Lilienberg

During the past fen- years, the requirements for steel have been raised so high that soundness is more important than ever before. The old practice mas to make steel ingots of suffciently large sections to permit a considerable reduction of area in rolling and hammering to a given size, relying on the fact that by such rolling and hammering all cavities will be squeezed together and practically eliminated. The finished sizes, if found by inspection of the surface to be faultless, were therefore pronounced to be sound. But when such steel is " worked up," the manufacturer is surprised and disappointed to find that it splits, or that streaks and seams make the product unmarketable. Large sections, such as rails, beams or heavy forgings, may, within certain limits, be sufficiently strong, even if the sides of the cavities are only squeezed, and not welded, together. But it is well known that, in the interior of heavy articles, under certain conditions, forging may develop small streaks into large cavities. Small sections, steel for ordnauce and tubes, and numberless articles in the tool-trade, always show up the defects. It may be doubted whether cavities in steel ingots can ever be completely welded. The old theory is, that the silver-clear blow-holes, without the blue oxide, can be welded by suffcient working. They are, however, not empty, but are filled with carbonic oxide. It is admitted that the " blue " cavities, resulting from air mechanically drawn down into the mold during the casting, can never be welded, because the oxide does not melt, and there would be no escape for it if it did. The only way in which steel can be made satisfactory for the above-named particular purposes is by having it " dead molten." But then the trouble of piping is encountered. As is well known, a pipe is the result of the contraction of the liquid interior after the surface of the ingot has become solid by contact with the mold. When this contraction is partly

Jan 1, 1907

By Avnulf Muan, Egil Aukrust

Activity-composition curves jor cobalt oxide and manganese oxide in solid solutions with spinel-type structure have been determined by studying the equilibrium between the spinel phase and a coexisting solid-solution phase in the tewzperature range 1100" to 1400"C. Within limits of experimental error, the system displays the behavior of a regular solution. The excess integral free energy of mixing is represented by the equation . The standard free energy of formation of cobalt manganite, CoMn,O,, from the oxide components COO mzd Mn2OS at 1200°C is calculated to be -8.6 kcal. AMONG the technologically and theoretically most important oxide phases are those which crystallize with the same structure type as the mineral MgO . A120,. Although the name spinel originally was used only for this mineral, the term is generally used today to designate the whole group of oxide phases with this same structure type. It is in this wider meaning that the term is being used in the present paper. The previous literature on spinels is very extensive. There are two aspects of spinels which have attracted particular attention: the structure, including the nature and distribution of the cations present, and the physical properties (electric, magnetic). The status of knowledge in these fields has been well-summarized in recent review articles.1'2 By contrast, thermodynamic properties of spinels are virtually unknown. Delineation of the activity-composition curve over the whole composition range of a solid-solution series with spinel-type structure is the objective of the present work. The system at elevated temperatures (>1000"C) constitutes such a series. The activity-composition curves for this system can be calculated from a study of the equilibrium between the above spinel solid solution and a solid solution (Co,Mn)O with sodium chloride-type structure. Data for the latter solid solution have become available recently.3 The system, in contact with metallic CO at 1200°C, obeys Raoult's law. The determination of the activity-composition curve for the spinel phase is based on the following relations. Consider the reduction-oxidation equilibrium for cobalt ions according to the equation: Because it is impossible in practice to measure single activities of electrically charged constituents, we will treat the equilibria in terms of electrically neutral components. Eq. [I] can then formally be written as follows: where and the activities of cobalt oxide in the (Co,Mn)O and the spinel solid-solution phases, respectively, K is a constant at constant temperature, and Pa is the oxygen pressure of the gas phase. The numerical value of K can be determined from a determination of the oxygen pressure P& for the equilibrium coexistence of Cos04 and COO in the binary system Co-0. Under these circumstances be set equal to 1, and hence K = [Po Eq. [3] can therefore be written

Jan 1, 1964

By Rex W. Woods

The clue history of performance of a highly volatile type oil reservoir which is now greater than 80 per cent depleted is presented. The reservoir is at a depth of approximately 8,200 ft and includes an area greater than 7,500 acres. The reservoir has been exploited by 10 wells which to date have yielded about 10,880,000 bbl of stock tank oil by pressure depletion. Reservoir pressure has declined from an original of 5,000 psi to approximately 1,450 psi. Produced gas/oil ratio has increased from 3,200 to 23,000 cu ft/bbl with a corresponriing increase in APl gravity of the stock tank oil from 440 to 620 . Pressure and fluid data are given for different stages of depletion. INTRODUCTION In papers by Sloan,' and Cook, Spencer and Bo-browski,' properties of highly volatile type reservoir oil were discussed in detail and methods were presented for predicting performance of reservoirs containing this type of fluid. The purpose of this paper is to present performance history of a highly volatile type oil reservoir designated as Reservoir A which has been produced by pressure depletion and field separation without processing of gas GEOLOGY The reterence field which includes Reservoir A is a structural feature north of a trend of major folding along a northeast-southwest axis. In the area of development, the structure has the appearance of a dome with formation dip of three to four degrees, but structural relations between the reference field and the axis of major folding to the south have not been determined. No faulting within the field is evident. Oil and gas productive sands have been found at depths of 7,000 ft to 10,000 ft in a columnar section of Mio-Oligocene age. The sand bodies in the section are lenticular and usually continuity of sand is limited to a small area. Sand A which forms Reservoir A at a depth of 8,200 ft, however, has exceptional continuous development in the reference field. Fig. 1 shows an isopachous map of net oil sand for Reservoir A. Net thickness of oil sand at producing wells ranges from 14 to 34 ft with an average of 22 ft. Pinch-out of sand has been shown by drilling in the southwest part of the field, but extent of the reservoir on the northwest and northeast parts of the field is indicated only by thinning of the sand. The vertical oil column between the highest and lowest producing well in the reservoir is 339 ft. No water-oil contact has been found within the reservoir. As interpreted from the isopachous map, the reservoir includes about 8,900 acres with an average net sand thickness of 12 ft. Because of limited data on extent of the reservoir, the isopachous map permits only an approximation of sand volume in the reservoir. DEVELOPMENT AND PRODUCTION Reservoir A was discovered during 1938 and was developed with eight wells to the end of 1942. One well was completed during 1946 and the tenth well in the reservoir was completed during 1951. Three of the original wells and the last completion have produced from Sand A only. Six wells have produced from Sand A through the casing side of dual completions. Initial producing rates of the original wells ranged from 800 to 1,000 BOPD. Production history for the reservoir is shown in Fig. 2. Production of the reservoir was begun during 1940 and in May, 1952, peak production from seven wells was 5,300 BOPD. At the end of March, 1954. cumulative production was 10.880,000

Jan 1, 1956

P. W. SHIMER, Easton, Pa. (written discussion*).-When lump calcium cyanamid is immersed in the melt of mixed chlorides of the alkalies and alkaline earths in the manner described in the paper, the amount of sodium cyanide formed in the melt, as shown by numerous analyses, is but a small fraction of that formed by the reaction referred to by Mr. Johnson. The case-hardening effects in my process are, however, at least as good as when the common cyanide baths are used. Moreover, when compared with the cyanide baths, the gases evolved in the new process are harmless, consisting of nitrogen, carbon monoxide (which burns to carbon dioxide on the surface of the melt), and occasionally a little carbon dioxide. These gases are not irritating or poisonous, whereas the vapors arising from cyanide baths are both irritating and poisonous. The complex chemical reactions that take place in and on the surface of the melt are being investigated by the writer, who hopes, in due time, to communicate the results of his work.

Jan 7, 1919

By J. C. Holm

Although the main constituents of Portland cement are the oxides of calcium, silicon, aluminum, and iron, characteristics of the cement are seriously affected by such contaminants in the raw materials as magnesium, phosphorus, sodium, potassium, sulfur, and others of lesser importance. Sources of cement raw materials comprise a long list of minerals occurring in nature in various degrees of purity. The calcareous raw materials are generally limestone of purity varying from calcite to cement rock (a low-grade limestone of natural, almost correct chemical composition), chalk, marl, seashells, coral, and coral sand. The argillaceous raw materials supplying silicon, aluminum, and iron are mainly various forms of clay and shale, to which may be added silicious sand, iron ore, bauxite, or kaolin for minor adjustment of the chemical composition.

Jul 1, 1956

By John W. Hughes

During the course of any truck loading operation, it will become necessary to replace hauling and loading units. Timing of replacement can be selected on the basis of necessity, or guesswork, or on a schedule derived from past performance records. Replacing units too soon results in high capital costs per hour. Waiting too long results in high maintenance costs per hour. As with any phase of a mining operation, a planned schedule can reduce overall costs and keep breakdowns within reason.

Jan 10, 1976

By Glenn Alvey

THE measure of value of an oil property is approximated by the length of time it takes to "pay out;" viz., the time required for it to return the original investment. This time varies in different fields. In the Appalachian and Mid-Continent fields, a good investment pays out in about four years; in California, it requires a slightly longer time; and in the Gulf field about two years. The two principal methods for establishing these values are based on acreage, as in California, and on production, as in the Appalachian field. The method of establishing values based on production1 was worked out in the Appalachian fields and approximates the value remarkably well in some fields; but it is a rule of thumb and should be used intelligently. Briefly, the method is as follows: An arbitrary number of dollars (called the barrel-day price) multiplied by the number of barrels of settled daily production of the property gives the value.. In its crudest application, the barrel-day price is determined by the "$10 to $.01" rule, which means that the barrel-day price is one thousand times the prevailing price of oil. For instance, with oil at $3.50 per bbl. the barrel-day price would be $3500 per bbl. This rule, however, is not strictly applied, for the, barrel price is varied according to whether or not the wells "hold up." But when a barrel price for a district has been fixed it is quite general to raise or lower the price with the fluctuation in the price of oil; here the" $10 to $.01" rule is used extensively. However, the prospective purchaser takes into account tangible equipment upon the property, the extent to which the drilling program has been carried out, whether or not the wells are "shot" or natural, depth of wells, spacing of wells, paraffin trouble, etc.

Jan 1, 1921

By W. H. Corbould

The township of Cloncurry is situated in the northwestern part of Queensland, about latitude S. 20" 42' 53" and longitude E. 140" 30' 25". Townsville is the port through which all the trade passes and is about 470 miles east-northeast of Cloncurry township. The Cloncurry copper district covers an area about 200 miles long by 40 miles wide. Unfortunately the mines are very scattered over this area, there being no large groups of mines. Mount Elliott mine is situated about 70 miles south from the township of Cloncurry, and Mount Oxide mine about 150 miles north of Cloncurry. The district has been known for the last 35 years, and in the early stages a large amount of capital was expended with little to show for it; but within the last four years the railway has been extended from Townsville to Mount Elliott and about 40 miles north of Cloncurry, which has made possible the treatment of the ores of the mines on this extension. The Mount Elliott company within the last few years has smelted and converted on its mine 169,688 tons of ore for 20,554 tons of blister copper, containing 20,377 tons of copper, 35,642 oz. of gold and 28,841 oz. of silver, at a cost of about 233 per ton of blister copper, f.o.b. Townsville. This cost included all development, wages, salaries, general management, office, agency, legal expenses, freight, etc. The gold and silver contents would practically pay for freight to Europe, refining, realization charges, etc. The costs of supplies are as follows: Firewood, 15s., coke, 75s., mine timber, 54s., and coal, 60s. per long ton; explosives: dynamite and gelignite, 50s., and blasting gelatine, 65s. 6d. per case, Mount Elliott Mine The pay shoot of the orebody outcrops at the surface for about 200 ft., and lies between two slate walls about 40 ft. apart., having a general

Jan 1, 1915

WHEN the new sulphide plant started to roll at Chuquicamata last July, we broached the matter of looking in on this historic event to Burr Wheeler, then executive vice president of Chile Exploration Co. (Chilex executive offices are housed with the parent company, Anaconda, at 25 Broadway which is 23 hours and 15 minutes closer to the AIME office than the mine, counting air and automobile travel). Mr. Wheeler was at Chuqui when they turned the first shovelful of earth, has an understandable pride and affection in the mine, and kindly offered to make all arrangements. As a guest of Chilex, physical exam, injections, police clearance, passport, and airline reservations on the crack Panagra airline are procured swiftly and almost painlessly. Winter clothes were advised by Mr. Wheeler and D. M. Dunbar, who is the former's assistant and a seasoned Chuqui-ite. Both of these gentlemen obviously prefer Chuqui climate, with 364 days of sunshine, 1 ½ -in. rainfall, rare atmosphere of 10,000 ft elevation, Christmas-time earthquakes, and howling winds through June and July to the vicissitudes of New York weather. Panagra's de luxe DC-6 noses in toward land at Antofagasta, Chile, the supply and embarkation port for Chuquicamata. The Coastal Range, completely barren of green, thrusts a spur far out into the Pacific creating a crescent-shaped and protected harbor at Antofagasta. Beach gives way to pampa, to hills, and the only variation in scenery is in topographic relief. Chilex's reception committee in the person of the alert and amiable Bob Condit, assistant port agent, takes care of everything: immigration, interviews by the local press, baggage, transportation, and introduction to Chilean cuisine. The drive up to Chuqui takes about three hours, on the only two lane highway in northern Chile; hard surfaced, with a few kilometers of repair work in progress. We were fortunate to make the trip with manager Charles Brinckerhoff, who arrived the same day at Antofagasta from the seat of government at Santiago where he goes frequently to keep in touch with the company's Santiago office.

Jan 1, 1952

By J. A. Corbyn

An analysts of mining investment from the point of view of financial optimization is presented. The method uses differential equations to describe financial performance rather than the more usual method of modeling mine accounts from year to year. The analysis shows there is a optimum mine life that can be easily determined if certain simplifications are made. Tables are given to facilitate computation of the optimum life.

Jan 1, 1985

By Morris Cohen, William P. Kimball

This paper deals with the calculation of the composition of the infinitesimal trace of alloy that transfers from the liquid to the solid state at each temperature during the equilibrium solidification of a binary solid solution, and which thereby enables the compositions of the coexisting liquid and solid phases to follow along the liquidus and solidus lines respectively during the cooling. A general expressioll for the composition (6) of the liquid-to-solid transfer at each temperature has been derived: , = Zlxl{xl - P) + ZsXsiP - xs) [I] Zl(xl -P)+ Zs{P - xs) where ZL and Zs are the slopes of the liquidus and solidus lines at the given temperature, xl and xs are the compositions of the stable liquid and solid phases at the same temperature, and P is the composition of the alloy under consideration. The d equation is valid for the process of equilibrium heating as well as cooling, and may be applied to vapor-to-liquid, vapor-to-solid, liquid-to-liquid, and solid-to-solid transfers if the corresponding equilibrium diagrams are known. The d-versus-temperature curves for two alloys P1 and P2 are shown in Fig. I. In each case, the liquid-to-solid transfer has the same composition as the stable solid phase only at the temperature of the beginning of solidification, and has the same composition as the stable liquid phase only at the temperature of the completion of solidification. At each intermediate temperature, the composition of the liquid-to-solid transfer differs by a finite amount from those of the two coexisting phases. Therefore, during equilibrium cooling. the transfers must merge into the solid phase from the liquid without forming a transition phase; otherwise the condition of equilibrium would be violated. At any given temperature during solidification, the composition of the liquid-to-solid

Jan 1, 1941

By William P. Kimball, Morris Cohen

This paper deals with the calculation of the composition of the infinitesimal trace of alloy that transfers from the liquid to the solid state at each temperature during the equilibrium solidification of a binary solid solution, and which thereby enables the compositions of the coexisting liquid and solid phases to follow along the liquidus and solidus lines respectively during the cooling. A general expressioll for the composition (6) of the liquid-to-solid transfer at each temperature has been derived: , = Zlxl{xl - P) + ZsXsiP - xs) [I] Zl(xl -P)+ Zs{P - xs) where ZL and Zs are the slopes of the liquidus and solidus lines at the given temperature, xl and xs are the compositions of the stable liquid and solid phases at the same temperature, and P is the composition of the alloy under consideration. The d equation is valid for the process of equilibrium heating as well as cooling, and may be applied to vapor-to-liquid, vapor-to-solid, liquid-to-liquid, and solid-to-solid transfers if the corresponding equilibrium diagrams are known. The d-versus-temperature curves for two alloys P1 and P2 are shown in Fig. I. In each case, the liquid-to-solid transfer has the same composition as the stable solid phase only at the temperature of the beginning of solidification, and has the same composition as the stable liquid phase only at the temperature of the completion of solidification. At each intermediate temperature, the composition of the liquid-to-solid transfer differs by a finite amount from those of the two coexisting phases. Therefore, during equilibrium cooling. the transfers must merge into the solid phase from the liquid without forming a transition phase; otherwise the condition of equilibrium would be violated. At any given temperature during solidification, the composition of the liquid-to-solid

Jan 1, 1941