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By J. R. CAIN

SAMUEL L. HOYT, ? Nela Park, Cleveland, Ohio (written discussion?). The work that Dr. Cain is doing on gases in steel should have a highly important bearing on investigational work in connection with steel-making practice. We found, for example, in our work in connection with the use of manganese in open-hearth practice that we needed expressions for the manganese efficiency and the "condition" of the steel. To get these figures we assumed that we would need to know the amount of FeO at different stages of the heat and the amounts of the gases present. This required simultaneous analyses of our samples for FeO and the gases and Dr. Cain seems to be the only investigator who has considered the analytical work from this point of view. That he has done so is very encouraging and it is to be hoped that his work will solve the mys-teries now surrounding this neglected phase of steel metallurgy. Those interested in the Ledebur method for use in connection with the efficiency of manganese as a "deoxidizing " agent will he disappointed to learn that more recent work at the Bureau indicates that Ledebur determinations are not reliable. The principal source of error seems to be due to the partial reduction of the ferrous oxide by the carbon present in the steel. However, it seems like an unnecessary criticism of the Ledebur method to state (p. 1319) that it proved of little value because it showed little differences in oxygen for a series of steels treated with ,various reagents and showing variations in physical properties and free-

Jan 12, 1919

Members Dues Resignations, Suspensions and Expulsions Institute Meetings Board of Director?s Meetings Directors and Officers Duties of Officers Committees Nomination and Election of Officers Publications Divisions, Local Sections, Affiliated Societies Amendments [As REVISED FEBRUARY 21, 19281 ARTICLE I MEMBERS-QUALIFICATIONS AND ELECTION , SEC. 1. The membership of the Institute shall comprise six classes, namely: 1. Members; 2. Honorary Members; 3. Senior Members; 4. Associates; 5. Junior Associates; 6. Rocky Mountain Members. All shall be equally entitled to the privileges of membership, excepting that Junior Associates, and all Members and Associates whose residence shall be outside of the United States of America, Mexico and Canada shall not be entitled to vote. SEC. 2. Members: A person to be eligible for election or transfer into the class of Member must be at least 27 years of age and must have had at least six years' employment in the practice of engineering, mining, geology, metallurgy, or chemistry, during at least three years of which he must have held positions of responsibility in one or more of these fields. This shall not apply to Rocky Mountain members.

Jan 1, 1928

By Wilson Blake

As a part of a USBM-ASARCO cooperative rock-burst research program, a burstprone stope pillar at the Galena mine was successfully destressed. Destressing was accomplished by blasting a single line of long holes in the footwall of the vein. As a result of destressing, the pillar was fractured and softened; hence it yielded, releasing a large amount of stored elastic strain energy nonviolently. In addition, the high stress in the pillar was shifted out around the stope walls and in the sandfill. Both broad-band microseismic monitoring and seismic velocity surveys were used to evaluate the destressing test. The mechanics of destressing were determined by finite element computer model studies of destressing. Results of the field destressing test agreed remarkably well with the predicted results from the computer model.

Jan 1, 1973

By Theodore Nagel

Fuel-oil, natural gas and coke oven gas, producing the higher temperatures of open-hearth current practice, have been gradually displacing producer gas the lowest cost fuel for open hearth operations. The lower temperatures of combusts on products from producer gas is caused by nitrogen dilution. Practical Application of Combustion Thermochemistry One pound of carbon burned to CO produces 3,960 B.T.U. and one pound of carbon burned to C02 produces 14,140 B.T.U. The second unit of oxygen uniting with gasified carbon (CO) produces (14,140 - 3,960) 10,180 B.T.U. which is (10,180 - 3,960) 6,220 B.T.U. more heat than produced by the first unit of oxygen forming CO by uniting with solid carbon. A review of the relative combustion heating values of commercial gaseous fuels reveals CO requires a minimum of air for combustion and because of minimum nitrogen dilution and the high thermal release from CO higher temperature combustion products are produced from CO than from natural gas or from coke-oven gas under similar combustion conditions. Inert nitrogen diluent lowers the calorific value of fuel gas and its diluting effect is cumulative in lowering the temperature of the products of total combustion. It is not only logical but practical in partial combustion, converting bituminous coal to gas, to generate the gas with reduced nitrogen dilution.

Jan 1, 1936

By CHARLES F. RAND

PRESIDENT CHARLES F. RAND,1 NEW YORK, N. Y. PAST PRESIDENTS CHARLES KIRCHHOFF,1 NEW YORK, N. Y. JAMES F. KEMP,2 NEW YORK, N.. Y. FIRST VICE-PRESIDENT BENJAMIN B. THAYER,1 NEW YORK, N. Y. TREASURER GEORGE C. STONE,1 NEW YORK, N. Y. SECRETARY EMERITUS ROSSITER. W. RAYMOND, NEW. YORK; N. Y. SECRETARY BRADLEY- STOUGHTON NEW YORK, N. Y.

Jan 2, 1914

By A. U. Seybolt

A. U. Seybolt (General Electric Research Laboratory)— As pointed out in an earlier paper,41 it appears to be very difficult to nucleate Si3N4 in Si-Fe of silicon content up to around 5 pet. Therefore, one observes, as did Pearce, that equilibrations with nitrogen gas yield only nitrogen in solid solution at temperatures above about 700°C, or, as Pearce found, 770°C. Evidently, the free energy of formation of Si3N4 only becomes high enough at -770°C to overcome the reluctance of Si3N4 to nucleate. However, as mentioned in Ref. 41, if some Si3N4 is first formed by a mixture of ammonia and hydrogen, one can then replace this gas mixture by nitrogen gas, and either increase or decrease the amount of Si3N4 present at any temperature by suitable adjustment of nitrogen pressure: that is, to equilibrate with Si3N4. In the equilibration experiments cited in Ref. 41, equilibrium was approached from both sides, and it was found that samples up to 944oC, at least, were in equilibrium with Si3N4. Higher temperatures were not employed, as this would have necessitated a redesign of the apparatus for using nitrogen pressures in excess of 1 atm. To summarize, the results of Pearce's experiments and those of Ref. 41 cannot be directly compared because two quite different equilibria were studied. Therefore, the statement by Pearce on p. 1398 indicating apparent error in Ref. 41 is unjustified. M. L. Pearce (author's reply)— There was limited evidence obtained in the current investigation which would indicate that excessive "supercooling" did not occur. A small piece of the same resulting from heat treatment No. 5 in Table III was subsequently held at 800°C for 16 hr in 95 pet N-5 pet H. Isotope-

Jan 1, 1964

By R. Neilson Clark

The discovery of a thin pay streak, yielding carbonates of copper; native silver, and perhaps chloride of silver, was made on the 9th of April, 1874, within the trachytic belt which forms part of the Sierra Mojada. The discoverer named it the Humboldt Mine. On the 2d of May, 1874, another discovery was made, in a northwest direction from the Humboldt, at about five hundred feet distant, this was named the Pocahontas Mine. After some exploration these two discoveries were proven to be on the same vein. To the southeast of the Humboldt a claim had already been taken up, called the Virginia; and to the northwest of the Pocahontas, one called the Southeast Leviathan. On these' last two this same vein has been found and worked. This paper will therefore treat of the Humboldt-Pocahontas vein, as worked on these four claims, to wit: beginning at the northwest, the Southeast Leviathan, the Pocahontas, the Humboldt, and the Virginia claims. Since the spring of 1874, there has been sunk on this vein a total of twenty-seven hundred and fourteen feet of

Jan 1, 1879

By Arthur C. Simmons

The Pennsylvania-grade oil industry suffered a serious decline in 1938, which can be largely accounted for by the decrease in the use of lubricating oil. Production was considerably lower than in previous years and prices were very much lower. Operating profits undoubtedly were lower than the year 1933, for the average price of Bradford crude in 1938 was $1.898 as compared with $1.86 in 1933, and the difference in average price of $0.04 per barrel was more than offset by increased operating costs and taxes. Bradford Field Production in the Bradford field in the state of Pennsylvania averaged 36,759 bbl. per day in 1938 as compared with 41,300 bbl. in 1937. The decline in average daily production of 4541 bbl. can be attributed to low market price and pipe-line proration rather than to the actual physical capacity of the field. Pipe-line proration was in effect for the last eight months of the year and the daily average production per month fluctuated between a maximum of 41,852 bbl. per day in March 1938 and a minimum of 33,649 bbl. per day in November. Production figures for Bradford field have been corrected to include only the parts of the Bradford field that arc within the state of Pennsylvania, but the well-completion data for the Bradford field cannot be segregated and include those of the entire Bradford field, part of which is in Sew York state. Production from the Bradford field was obtained almost wholly by water-flooding and no radically new methods or practices occurred. Intensive research work was carried on both by individuals and companies and as a cpooperative enterprise, and minor improvements are gradually occurring in spacing, shooting, application of pressure and water conditions. Drilling Central and Southen Pennsylvania.—Pennsylvania production in central and southern Pennsylvania was obtained largely by air and gas repressuring together with the usual amount of natural production, and the repressuring operations in other than the Bradford field have not

Jan 1, 1939

By Roy E. Dickerson, W. M. O Connor

The production of crude petroleum of the Bacuranao field, Cuba, fell off rapidly because no new wells Mere drilled. In December 1938, the total was 15 bbl. per day. The estimated average from this serpentine field for the year is 20 bbl. per day. The Motembo area produced an estimated average of 160 bbl. per day. Production in July was 215,946 gal of gasoline, or 165 bbl. per day. In August production was higher because a new well in the concession, the Luisa Marcela, produced 189 drums the first day and required pit storage. The Atlantic Refining Company of Cuba started a deep test upon a long, narrow, surface-defined anticline 3 km. south of Remedios, a town on the north coastal plain of Santa Clara province, in December 1938. The Atlantic Refining Co. is doing extensive seismograph arid gravity-meter work in Matanzas arid Santa Clara provinces. The Shell company was rigging for a deep test in western Havana province at a location about 2 km. west of the town San Antonio dc los Banos New Petroleum Law More serious attention was given by some of the major oil companies to the development of petroleum in Cuba as a, result of the passage of a Petroleum Law ill that country on May 9, 1938. Under the old mining lam of Cuba, which gave no special treatment to petroleum, the usual provisions giving reasonably satisfartory guarantees to encourage investmerit of foreign capital were either entirely lacking or were 30 ambiguously expressed as to require legislative action. Under the new law, Government royalty is fixed at 10 per cent with the provision that it will be reduced to 9 per cent on crude petroleum that is refined in Cuba. Royalty to the surface owner is 1 per cent. A surface tax on a sliding scale from 10¢ to 406 per hectare per year is applicable to all exploitation concessions granted under the law or adapted to its provisions. So export tax is payable upon petroleum. Stability of taxation

Jan 1, 1939

By Harry Seltz, J. C. DeHaven

InteRmetallic compounds are formed in many binary metal systems. Some compounds are stable to their melting points, and others decompose at lower transition temperatures. Even those of the first class are dissociated in the liquid state, as indicated by the continuous form of their solubility curves at their melting points1. While the lattice structures of some of these compounds have been determined, their thermodynamic properties have not been investigated. In this paper is described the determination of the free energy and heat of formation of the compound CdSb, which is of the first class mentioned above, melting congruently at 455' C. This compound shows a rhombic structure, and the lengths of the edges of the elementary cell containing four molecules are: a = 6.52, b = 8.60, c = 4.16 A.' There are three possible methods of determining the free energy of formation of a compound of this type. The first method, applying the third law of thermodynamics, requires the measurement of its heat capacity preferably to liquid hydrogen temperatures, and a calorimetric determination of its heat of formation. The second method involves the study of the equilibrium of the compound in some gas reaction, such as: CdSb + CO² = CdO + CO + Sb From the known free energies of formation of CdO, CO² and CO the free energy of formation of CdSb could be calculated. The third method measures the electromotive force of a galvanic cell in which the cell reaction is the reversible formation of the compound from the elements. The first method is generally applicable, but requires elaborate experimental equipment. The second method can not be used for compounds melting at low temperatures, owing to the difficulty in establishing equilibrium. The electromotive force method, therefore, seemed to offer

Jan 1, 1935

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 expression for the composition (6) of the liquid-to-solid transfer at each temperature has been derived: d= Zlxl(xl - P) + Zsxs(P - xs)/Zl(xl - P) + Zs(P - xs) [1] where ZL and Zs are the slopes of the liquidus and solidus lines at the given temperature, Xl and 28 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 6 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 Walter Miller

Developments in oil refining were so varied during 1938 that a refiner had to be alert or be left behind. The long-talked-of conversion of oil refining into a true chemical industry using petroleum as a raw material was hastened, particularly in the realm of motor-fuel manufacture, by the increased understanding and use of catalytic processes. The petroleum refiner's vocabulary has been extended to include alkylation, cyclization, aromatization, and isomerization. There are other devel: opments of a similar nature, but these are now considered commercially feasible under proper conditions. New Equipment Less expensive equipment and processes encouraged new construction and replacement. Estimates of money spent in the United States on building new plants and remodeling existing installations during 1938 place the sum at not less than $200,000,000, a noteworthy amount in a year marked by a business recession. The commercial application of small-scale catalytic polymerization of refinery gases made one of the latest advances available to the smaller operators, who usually are faced with unit installation and production costs higher than the large refinery enjoys. Competition was thereby fostered. Outstanding in this respect was the construction of two or more polymerization plants in small refineries at extremely low installation costs, with amortization measured in months instead of years. Houdry Processes Bursting like a bombshell late in the year was the disclosure of the extent of the development of the Houdry processes of catalytic cracking, viscosity breaking, gasoline treatment, desulphurization, and polymerization, said to be applicable to almost any raw petroleum stock and yielding gasoline of exceptionally high octane number. This process is claimed to be particularly adapted to once-through cracking of aliphatic hydrocarbons, and when combined with any of the conventional thermal

Jan 1, 1939

By R. V. Whetsel, V. R. Gargias, J. W. Ristori

WoRld consumption of petroleum and its substitutes in 1941, the amount of which obviously is largely conjectural, is estimated at 2,066,653,000 bbl. This is 48,689,000 bbl. more than the previous year and is an all-time high. Except for the United States, this figure does not include consumption for military purposes. Consumption in the United States also reached an all-time high during 1941, totaling 1,492,000,000 bbl., or 158,230,000 bbl. more than the previous peak year of 1940. On the other hand, it is estimated that civil consumption in countries outside of the United States decreased 109,541,ooo bbl. as compared with the previous year. Demand for military purposes and/or additions to stocks in countries outside of the United States is estimated at 304,507,000 bbl. during 1941, compared with 209,635,000 bbl. in 1940. This increase was due largely to blitzkrieg warfare on several fronts. especially Russia; entailing large expenditures of petroleum by both sides because of the immense area covered by the fighting forces, the long supply lines necessary and the intensity of the fighting. It is interesting to note in this connection that Axis-controlled countries, excluding Japan, had an estimated production of approximately 89,000,000 bbl. of petroleum and its substitutes in 1941. The peacetime consumption of these countries in 1938, for example, was about 183,000,000 bbl. It is believed that the minimum to which civil consumption could possibly be re-duced in wartime is 20 per cent of that of peacetime, which would call for a minimum consumption of 37,000,000 bbl. in these countries in 1941 for civil purposes. This

Jan 1, 1942

By Gilbert H. Cady

HE application of geology to problems arising A in coal mining engineering and coal preparation has, in general, been somewhat remote, or the geological problems have involved such simple forms of geological knowledge that the attention of specialists in this field has not been commonly thought necessary. Furthermore, the geology of coal beds and coal mining has received but scant attention in our educational system, even in mining education; so that coal mining engineers have become somewhat conditioned against geological thinking. Geologists, on the other hand, have commonly failed to realize that there are geological aspects to coal mining and coal preparation problems. A further reason why geology receives so little consideration in coal mining undertakings in this country lies in the fact that our coal supplies are, or have been thought to be, almost unlimited, have been easily accessible, and very cheaply mined. Conditions have been changing within recent years. Failures can be less easily endured. Great inroads have been made on our bonanza deposits of easily mined coal and the increasing cost of coal and the increasing difficulty of finding it in easily accessible and large quantities places greater and greater importance on accurate information and good technique in exploration. It seems probable, therefore, that the opinions and aid of geologists will be more commonly sought than in the past in the exploration for coal and in the development and operation of coal mines, and analyses of mining conditions, preparation, and utilization.

Jan 1, 1951

By Henry A. Stiff

The classification and correlation of water analysis data presents many problems which can be solved by graphic methocis. The pattern system, a new type of graphic procedure described in this communication, is believed to have several advantages over older methods. Examples of the application, of the pattern system to the solution of problems encountered in petroleum production are given. INTRODUCTION Several graphic methods for presenting analytical water data have been developed and are now in use.1,2,3,4 It is believed, however, that a recently developed type of graph called the "pattern" offers several advantages over other methods. This system presents a better picture of the total salt concentration than is usual in such graphs. The effect of dilution or concentration has been reduced to a minimum, and at the same time distinction between various types of water has been improved. The system is extremely versatile, yet so simple it can be plotted on ordinary graph paper and adapted to almost any type of filing system. DISCUSSION The essential feature of the pattern system is the graph shown in Fig. 1. Horizontal lines extending right and left from a vertical line at zero form the graph. Positive ions are plotted to the left while negative ions are plotted to the right. The figure immediately beneath each ion gives the scale. Most oil field waters can be plotted on a scale where 100 milli-equivalents of sodium and chloride and 10 milliequivalents of each of the other ions are represented by one scale unit. For highly concentrated brines, 1,000 milliequivalents of sodium and chloride and 100 milliequivalents of each of the

Jan 1, 1951

By Arthur C. Simmons

Oil production and activity in northern and central Pennsylvania was slightly less in 1939 than in the previous year, but owing to higher average prices 1939 was undoubtedly a better business year. The last quarter showed markedly increased activities throughout all of the Pennsylvania fields. Production, Stocks and Price Storage of Pennsylvania crude oil at pipe lines and refineries totaled 5,413,000 bbl. on Dec. 31, 1938, and declined during the year 1,124,000 bbl. to a total of 4,319,000 bbl. at the end of 1939. The stocks of crude at the end of the year represent the lowest point reached in Pennsylvania-grade crude storage in recent years. Stocks increased slightly during April, May and June, but decreased during all other months of 1939. The Bradford field production within the state of Pennsylvania averaged 35,340 bbl. per day throughout 1939, which represents a decrease of 1419 bbl. a day from the 1938 average. The production in central and southern Pennsylvania increased 1176 bbl. per day, averaging 12,159 bbl. throughout 1939. Table 1 includes annual production for the part of Bradford field situated within the state of Pennsylvania, for central and southern Pennsylvania, and for the entire state of Pennsylvania. A definite segregation of production between the Bradford field and central and southern Pennsylvania is slightly ambiguous because a portion of the oil from the newly discovered Music Mountain pool is included statistically in each area. In all probability the entire increase and some small addition to the production from southern Pennsylvania can be attributed to oil produced from the Music Mountain pool. Within the Bradford field, six price changes occurred throughout the year. At the beginning of 1939 the price of Bradford crude oil was $1.80 per barrel, whereas by the end of the year it had risen to $2.50. The weighted average price for Bradford crude during 1939 was $2.059 per barrel.

Jan 1, 1940

By Iley B. Browning, R. E. Strouder, Coleman D. Hunter, Ralph N. Thomas, George M. Straughan

Activity in the oil fields of the state was at a low ebb during the year because of the longest period of low prices that has yet prevailed, which has been detrimental to both the eastern and western sections of the state. Production for the state as a whole shows a drop of 209,192 bbl. during 1939, the total being 5,356,963 bbl. The loss is in the production of the western division, where a loss of approximately 300,000 bbl. more than offset a gain of approximately 100,000 bbl. in the eastern division. The loss in the western division can be attributed to decline in drilling activity due to the low prices prevailing, which were caused by flooding of the normal markcts with cheap Illinois crude. The gain in the eastern division is the result of repressuring operations begun in previous years and now showing results, and not to any renewed drilling activity. Gas development in western Kentucky during 1939 was of minor importance. In eastern Kentucky approximately 50 producing gas wells were drilled, which were sufficient for present market with excess reserves already developed. With the severe winter and additional industry load every gas well connected has been on line for the past three months. Although all demands are being met, development will be greatly increased during 1940 to meet depletion. From the geological point of view, the drilling activity in the western division developed additional information of benefit. Several wells on blocks of acreage assembled in previous years were drilled in the deeper parts of the Western Coal Basin—southern part of the Illinois Basin— giving for the first time accurate information about the Pennsylvanian and lower formations down to and through the Devonian.

Jan 1, 1940

By Willard H. Tracy

The method of seismic reflection prospecting has many times been compared to sound ranging, a process that became familiar to many during the World War. According to this very simple theory, the dynamite goes off and sends out a compression wave, which meets a reflecting horizon and returns to the surface, where it is recorded and the elapsed time of its travel in the earth accurately determined. Computations are then made on the general theory that the longer the elapsed time, the greater the depth of the reflecting bed. While this serves to give an idea of the fundamental basis of the process, it suggests a simplicity that does not exist in the life history of the various waves set up by a dynamite explosion in the earth. To begin with, a seismic wave in the earth does not obey the same simple laws of propagation that apply to a sound wave in the air. The property of strength in shear possessed by solids introduces a factor that sets such waves apart from the ordinary air waves. Also, the transmission charactcristics of the earth vary widely from place to place, and a fairly accurate knowledge of the space relationships of these variations is necessary if the final results are to be understood. Besides the waves recorded and used in the reflection computations, there are many

Jan 1, 1940

By F. C. Farnham

In this paper it is shown that the vertical component of the earth's magnetic field for the area of the United States can be very closely approximated by assuming it to be the sum of the vertical components of two magnetic fields. The first of these is the field of the centered dipole described by J. Bartels,l the axis of this dipole intersecting the earth's surface at two antipodal points, the one in the Northern Hemisphere being at latitude 78.5°N. and longitude 69°W., and the dipole having such strength that the vertical component of its field at its axis pole is 0.63 oersted. The second field is that due to a second dipole situated halfway between the center of the earth and a point on the earth's surface at latitude 38.5°N., longitude 91.5°W., the axis of this dipole being along this radius, the south pole being toward the surface, and the dipole being of such strength that its field at the point on the surface mentioned above is 0.069 oersted. Using the field computed on this basis, tables of latitude and longitude correction factors were computed and are included in the paper. It is also shown that the secular variation in the earth's magnetic field may be roughly accounted for by assuming it to be due to motion of the second dipole described above. Although there is an error in the equation used for computing the strength of the field due to the second dipole, the distribution of the field computed is very nearly that of the assumed arrangement of dipoles. Subsequent work by the author reveals that minor changes can be made in the location of the second dipole, which will make the computed field fit the observed field even more closely. It has also been found2 that the vertical component of the field may be represented equally well by a purely empiric relationship.

Jan 1, 1940

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 expression for the composition (6) of the liquid-to-solid transfer at each temperature has been derived: d= Zlxl(xl - P) + Zsxs(P - xs)/Zl(xl - P) + Zs(P - xs) [1] where ZL and Zs are the slopes of the liquidus and solidus lines at the given temperature, Xl and 28 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 6 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