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By Herbert Clark Hoover, Lou Henry Hoover

PREVIOUSLY I have dealt with the methods of separating silver from copper. There now remains the portion which treats of solidified juices ; and whereas they might be considered as alien to things metallic, nevertheless, the reasons why they should not be separated from it I have explained in the second book. Solidified juices are either prepared from waters in which nature or art has infused them, or they are produced from the liquid juices themselves, or from stony minerals. Sagacious people, at first observing the waters of some lakes to be naturally full of juices which thickened on being dried up by the heat of the sun and thus became solidified juices, drew such waters into other places, or diverted them into low-lying places adjoining hills, so that the heat of the sun should likewise cause them to condense. Subsequently, because they observed that in this wise the solidified juices could be made only in summer, and then not in all countries, but only in hot and temperate regions in which it seldom rains in summer, they boiled them in vessels over a fire until they began to thicken. In this manner, at all times of the year, in all regions, even the coldest, solidified juices could be obtained from solutions of such juices, whether made by nature or by art. Afterward, when they saw juices drip from some roasted stones, they cooked these in pots in order to obtain solidified juices in this wise also. It is worth the trouble to learn the pro- portions and the methods by which these are made. I will therefore began with salt, which is made from water either salty by nature, or by the labour of man, or else from a solution of salt, or from lye, likewise salty. Water which is salty by nature, is condensed and converted into salt in salt-pits by the heat of the sun, or else by the heat of a fire in pans or pts or trenches. That which is made salty by art, is also condensed by fire and changed into salt. There should be as many salt-pits dug as the circumstance of the place permits, but there should not be more made than can be used, although we ought to make as much salt as we can sell. The depth of salt-pits should be moderate, and the bottom should be level, so that all the water is evaporated from the salt by the heat of the sun. The salt-pits should first be encrusted with salt, so that they may not suck up the water. The method of pouring or leading sea-water into salt-pits is very old, and is still in use in many places. The method is not less old, but less common, to pour well-water into salt-pits, as was done in Babylon, for which Pliny is the authority, and in Cappadocia, where they used not only well-water, but also spring-water. In all hot countries salt-water and lake-water are conducted, poured or carried into salt-pits, and, being dried by the heat of the sun, are converted into

Jan 1, 1950

By K. Malysa

Bubble collisions with ore grains and a selective formation of the bubble-grain aggregates are necessary steps for flotation separation of useful and gangue components of an ore. For the attachment of valuable mineral grain to the colliding bubble a liquid film, separating the bubble and the grain needs to rupture during short time of their collision. High hydrophobicity of the grain surface is favorable because stability of the separating (wetting) film is much lower at such surfaces, that is, the film ruptures faster and at greater thickness. Simultaneously, it needs to be kept in mind and taken into consideration that high affinity to air is a typical feature of hydrophobic surfaces. Thus, when the hydrophobic surface is immersed into aqueous phase the air can stay attached to such surfaces and affect kinetics of the bubble attachment. The paper presents results and analysis of dynamic phenomena occurring upon the collision of the rising bubble followed by its attachment to hydrophobic (Teflon) plates of different roughness. The influence of the Teflon surface roughness, solution concentration, bubble size and impact velocity on bouncing of the colliding bubble, time of the three phase contact (TPC) formation and drainage time of the liquid film, formed between the solid and bubble surfaces, is described. High hydrophobicity, as showed earlier (Malysa et al, 2005), does not assure that each collision leads to the TPC formation and attachment of the colliding bubble. Roughness is the parameter of crucial importance for kinetics of the bubble attachment to hydrophobic surfaces (Krasowska and Malysa, 2007; Krasowska et al, 2009; Kosior et al, 2011). Enlarged roughness of the Teflon plate, from ca. 1 to 80µm, results in shortening the time of the TPC formation (bubble attachment) by over an order of magnitude - from 105 to a few milliseconds only. Higher surface roughness means that larger amount of air can be entrapped in bigger scratches and cavities of the Teflon plate during its immersion into aqueous phase. Results documenting importance of the air presence are showed and mechanism of the air facilitated TPC formation and bubble attachment to hydrophobic surfaces is described. Keywords: bubble collisions, hydrophobic surfaces, teflon plate roughness, TPC formation

Sep 1, 2012

By W. C. Holliman

Commercial production of synthetic rubber in the United States became a reality in 1931 when E. I. duPont de Nemours, Inc., announced the manufacture of Duprene, a synthetic rubber made by polymerizing r chloroprene. Duprene was later improved and reintroduced as neoprene. Since 1931 other synthetic rubbers and rubberlike materials have been announced and are now produced commercially or are in the pilot-plant stage in the United States. These include Thiokol, Buna S, Perbunan, Koroseal, Vistanex, Flamenol, Ameripol or Hycar, Chemigum, Butyl rubber, and Flexon. None of these is synthetic rubber in the strict chemical meaning of the word synthetic, as none is identical in chemical structure with natural rubber. However, all possess some of the physical properties of natural rubber, and in addition usually have some outstanding property not found in natural rubber that makes them superior for certain uses. Because of these superior qualitites, a considerable demand had arisen for synthetic rubbers before the present emer¬gency, although the price was several times that of natural rubber.

Jan 1, 1943

By Rambabu Pothina, MELO EDUARDO PIMENTA DE, Rajive Ganguli

 The mining industry is home to a mass of sensor-generated data that are critical to real-time and long-term optimization. This heavy reliance on sensor data has resulted in an undesirable development. The industry is reluctant to verify the accuracy of sensors as it would mean shutting down important processes. Sensors are typically calibrated once a year, if at all. Errors in sensors go undetected until the next calibration or until errors are so gross as to be obvious

By G. H. Damon

Since 1963, Bureau of Mines Information Circular 8179 has served the mining industry as a fundamental safety guide in the field of blasting agents. In the intervening 14 years, many changes have occurred, and this report presents revised and new recommendations which recognize these changes. For example, AN-FO is now supplied mostly premixed, whereas in 1963 much of it was mixed by the blaster; aluminum metal (A1) and other fuels are now often added to AN-FO to increase strength, and flake aluminum powder is used as a sensitizer in water gels; and water gels or slurries that are now extensively used were just coming into practical use in 1963. To provide the widest possible margin of safety, some of the Bureau's recommendations are more stringent than existing regulations,

Jan 1, 1977

By Maynard O. Serbousek

The mechanics of load transfer of fully-grouted roof bolts in coal mines has been investigated in laboratory and analytical studies. The purpose of this research is to increase the understanding and better interpret data from pull tests which are routinely performed in the field. Laboratory work includes variation of bolt length, hole diameter and grout type in pull tests. Four-foot bolts were tested in holes of 1- and 1-3/8-inch diameters. Both polyester resins and inorganic grouts were used as the anchorage medium. The bolts were strain gauged at six locations to observe the rate of load transfer from the bolt to the rock mass when a force was applied at the bolt end using standard Jack pull testing procedures and equipment. Analytical studies using closed form solutions and finite-element techniques were compared to experimental results. The models are for the elastic regime only but do include slip elements. A detailed analysis of the load transfer mechanisms from the bolts through the grout to the rock mass is presented.

Jan 1, 1984

By S M. Jowitt, G M. Mudd

"The mining industry is the source for the vast majority of the metal, mineral and energy resources we use on a daily basis. New deposits are discovered over time and are developed into mines before being rehabilitated – a sequence that when repeated can help contribute to the noble notion of ‘sustainable development’, despite the generic concept of mining being the unsustainable consumption of non-renewable resources. The scale of the modern mining industry is immense – from iron ore and coal to base and precious metals, modern mines are sometimes hundreds or thousands of times bigger than their long lost historic ancestors. We also live in a world with emerging and increasing demands for so-called technology metals (aka ‘critical’, ‘e-tech’ or ‘specialty’ metals) that are needed to feed the rapid growth in renewable energy (especially solar photovoltaic panels and wind turbines), consumer electronics, sophisticated military technologies and super alloys, amongst other uses. These elements include the rare earth elements, indium, germanium, tellurium, rhenium, selenium, gallium and many others, most of which had few or no known uses in the recent past. Although the mining industry has been successful in developing ever larger mines and increasing the scale of production, the key issues underlying the future of the industry are declining ore grades, increased tailings and waste rock generation, the presence of toxic or other impurities, balancing the economics of primary and secondary products, stricter environmental conditions, more difficult exploration, increasing community expectations, as well as the processing of more complex or refractory ores, let alone the recent volatility in world commodity markets. Here, we synthesise our recent research on many of these various issues, focusing on the need to link all areas within the mining chain from mineral resources through mining to environmental performance in order to ensure we obtain the most out of our modern mining effort. The paper presents a unique and detailed assessment of the sustainability challenges and opportunities facing modern mining – and geometallurgical thinking is at the heart of this conundrum.CITATION:Mudd, G M, Jowitt, S M, 2016. From Mineral Resources to Sustainable Mining – the Key Trends to Unlock the Holy Grail?, in Proceedings The Third AusIMM International Geometallurgy Conference (GeoMet) 2016, pp 37–54 (The Australasian Institute of Mining and Metallurgy: Melbourne)."

Jun 15, 2016

By Thomas M. Barczak

The U.S. Bureau of Mines has been conducting research to optimize the design and utilization of mine roof support systems. An objective of these efforts is to evaluate the mechanical and structural responses of various mine roof support systems under simulated load conditions in the Bureau's mine roof simulator. Underground studies are also made to evaluate the in situ behavior of support structures. The purpose of this report is to document practical applications for longwall face and gate road supports that have resulted from these studies. This report is not intended to be an all-inclusive manual on every aspect of support utilization, but it does provide a comprehensive assessment of practical considerations relating to the mechanical and structural behavior of these support systems. Forty-six recommendations are made to provide assistance to mine operators in the testing, selection, and utilization of longwall face and gate road supports. Many of these recommendations offer innovative solutions to everyday problems faced by mining personnel in the control of ground in longwall mining.

Jan 1, 1989

By E. C. Strycula

Solid-state equipment offers a number of potential advantages in the coal mining industry. These advantages can only be realized, however, through careful and judicious design of the control and protection circuitry. Problems relating to the interaction of solid-state equipment on the electrical system and the special design considerations which apply to solid-state circuitry are examined. Design guidelines are provided for solid-state applications in the areas of: (a) equipment operated from a DC trolley wire, (b) drive systems for surface mining equipment, (c) AC motor starters, and (d) electromagnetic interference.

Jan 1, 1981

By Francois P. Leroy

In the quest of studying the assigned blocks of seafloor for deep water mining, each member country of the ISA is thirsty for accurate information as to the level of resources available. Manganese nodules represent a large portion of the resources and are as precious as they are hard to locate and harvest. Resolving such challenges is what drives the technology development and yields instruments and products capable of serving this field of research. This presentation will study how manufactures of oceanographic instruments have pushed the technology envelop to in order to transform a collection of sensors and instruments into a seamless and adapted assembly working to serve the researcher and prospector in the challenging field they operate. Deep water data collection is characterized by the following challenges: ? Deployment, recovery and handling of the vehicle ? Producing high resolution at great distances ? Positioning that data with accuracy to relocate Teledyne Marine will present the work performed in its engineering laboratories to produce sub systems and systems now capable of delivering key information necessary to the proper cataloguing and exploitation of deep water mineral mining. Understanding and controlling the alternative resources available to each country will allow better management of current traditional land based minerals.

Jan 1, 2010

By William E. Eckard

Production of oil from a narrow shoestring sand presents problems unique in the oil industry. Especially important, from both an engineering end an economic standpoint, are the limitations imposed upon well patterns and spacings by the shape of the field. This report concerns a study of the Paola shoestring, Miami and Franklin Counties, Kane., where well density of 0.85 acre per well was not uncommon to insure profitable primary recovery in a reasonable time. However, such a great number of wells increased the operator's investment and reduced his profit considerably. It was the purpose of this study to investigate various well patterns and spacings applicable to water-flooding a shoestring reservoir and the effect of these factors upon recovery of oil and the most profitable operation of the pool. The designer of well patterns for a shoestring sand should evaluate carefully the edges of the shoestring, even though they may be considered too thin to drill. These comparatively thin edges contain large quantities of recoverable oil; moreover they are resaturated with oil as the pool is water-flooded.

Jan 1, 1951

By A. S. Swanson

In view of the necessity or increasing production of metallurgical fluorspar to satisfy wartime demands, 0, M. Bishop, former district engineer of the Bureau of Mines, L. W. Carrier and. J. S. Williams, senior geologist of the Federal Geological Survey, and E. H. Dawson, mining engineer of the War Production Board made a joint survey of the Illinois-Kentucky fluorite district in July 1942 to determine what steps should be taken to increase production. As part of their recommendations, a program for exploring the idle Klondike mine in Livingston County, Ky., was outlined. All the ore produced at the Klondike mine was mined above the 325-foot level, where some tonnage remains. Factors that influenced selection of the Klondike mine for exploration were favorable geological conditions, the state of mine development and the availability of pumping equipment and some usable mine and mill equipment. In December 1942, the Metals Reserve Co. leased the Klondike mine from the Salem Fluorspar Co.

Jan 1, 1949

By B. S. Butler

A. D. Mutch (Falconbridge Nickel Mines Ltd., Ona-ping, Ontario)—This contribution is prompted by the fact that the writer has recently published an article'!' which has in part the same general conclusions as B. S. Butler's, namely, the form of the standard mineral paragenesis in hypogene deposits and the parallel transition from early high temperature acid to late low temperature alkaline or neutral solutions. Since the writer also recognizes that he is not fully qualified to discuss the formation of ore deposits as a chemical problem, this discussion will be limited to summarizing other observations and will suggest how Butler's Table II might be made more effective. The form of Butler's table is not unlike that widely used by European geologists'" in which the various minerals are related to the types of ore fluids—peg-matitic, pneumatolic and hydrothermal. Thus the decrease in temperature and change in pH of the ore-bearing fluids as recognized by Butler may also be paralleled by perhaps even greater changes in composition, density, and character. W. H. Newhouse's article:" on the sequence of hypo-gene ore mineral deposition is still one of the most complete analyses of the problem. In it he makes four major observations: 1) The order of O, S, As, Sb is the same as their increasing atomic weights and the same as their melting points. 2) The order of the metallic elements is the same as the Schuermann series. 3) The general mineralogical order is paralleled by decreasing heats of formation. 4) The order is generally in decreasing hardness, higher metal content, and higher specific gravity. The order of 0, S, As, and Bi is also the same as their relative abundance. Another point worth mentioning about this series is that As, Sb, Bi, when abundant, often substitute for sulfur in the early pyrite-like minerals, whereas later in the sequence these elements appear to act more like metals. This behavior may be a further indication of the acid character of the early fluids. C. J. Sullivan"' has attempted to show that the sequence of the metallic elements is related to the order of their melting points and has discussed the interrelationship of the different types of bonding of sulfo-phile and oxiphile elements in minerals. Items 3 and 4 might best be summarized by saying that bonding of the minerals in the series appears to be from ionic to covalent to metallic, the early minerals being light in weight, hard, and near-transparent; the intermediate minerals of intermediate weight, semi-transparent, and semi-conducting; and the end minerals heavy, soft, and malleable, opaque and good conductors. A rapid fall in temperature has been assumed to be the cause of ore deposition in many deposits. Perhaps this in turn is the effect of a rapid release of energy in the form of pressure release and change of volume, the first minerals to form being those with the highest heats of formation which absorb the released energy the most rapidly. Butler's Table II could probably be streamlined and made more effective if the listed compounds were assembled as mineralogical groups as in Dana. Thus the sulfides, arsenides, antimonides, bismuthides, and sulfa salts could be arranged in AX,, AX, A2X2, etc. groups. Since these are continuous substitution series, in which the fields of stability and the heats of formation of the various individual minerals can be fairly regarded as similar, this should be accomplished with no loss of clarity. The occurrence of the individual minerals and the precise sequence of the mineral deposition in any one deposit is probably more dependent on the concentration and relative abundance of the component elements. The assembling of geological data in tabular form such as Butler's Table II will continue to be a very effective method of studying geological phenomena. The importance of this particular problem has been pointed out by C. F. Park,% who concludes that understanding of mechanisms of the standard paragenesis and interrelated problems of mineral zoning in space and time is one of the major keys to classification of ore deposits.

Jan 1, 1959

It is very apparent that the hydrogeotogicat characteristics of mineral deposits in China be dominated by meteoric factors, terrain factors and the kind of karstic aquifers as a main source threatening the mining.The hydrogeotogicat characteristics of mineral deposits in dry areas are very different from that in non-dry areas.The rote of precipitation is very important to mine dewatering.The difference of water recharge condition of a mineral deposit located upper (or under) Local erosion basis is existing. There are more than two million square kilometers of carbonate in China.Many water-bearing deposits are distributed in it.According to the karst shapes the surrounding karstic aquifers of mines can be divided into three kinds including solution fissure aquifer,karstic cave aquifer and underground stream (karst stream) aquifer. Underlier invasion is a main feature of karst water-bearing coal mine and upper tier incoming is a main feature of skarn copper and ferro mine.Swatlor pillar and collapse is a special feature of karstic water-impregnated mine.

Jan 1, 1988

By Brian P. Stapleton, Bill M. Stewart, Joel R. Warneke, Curtis C. Clark

Of the 28 accident/injury classifications listed by the Mine Safety and Health Administration, handling materials is second only to roof falls in terms of generating the highest number of reportable accidents in active underground coal mines. Two materials-handling activities that cause numerous injuries each year are the categories of “handling supplies or material, load and unload” and “moving power cables.” Mechanization and mine worker activity training are two methods that can aid in preventing these injuries. This paper describes three mechanical methods—the mobile manipulator, the in-mine hoist, and a cable-handling system—being developed and tested at the Spokane Research Laboratory of the National Institute for Occupational Safety and Health. Two of the devices are specifically designed for loading, unloading, and moving supplies and materials, and the third device is for handling trailing cables in the confined spaces of coal mines. Also described are safety solutions developed for underground coal mines geared to showing miners safe and unsafe ways of performing various materials-handling tasks.

By M. M. Rao, P. G. Winchell, R. J. Russell

A detailed analysis has been used to correlate the avalable thermodynami c da In on iron-ric11 Fe-Ni (41loys in the body-centered a, and the face-centered y phases. The inp ut injovrt~ation required by the a am lysis consists of tile heat of the a, to y transformation at 1123°K, the heat of mixing of y at 1123°K, tile specific heats of both a, and y (decomposed into Debye, electronic, and magnelic contributions), and the positional and magnetic entropies of both a, and y. PYLrrzary oirt.bul of the analysis is the free energy of each phase as a Junction of temperature and composition. FOr Fe-Ni alloys the adjustment of twenty-one parunletevs allows the accurate reproduction of enthalpy data for both phases, the heat of mixing- for y, the a/y equilibrinm compositions in the Fe-Ni phase diagram, and the usually accepted enthalpy and entropy of a and y iron. Also obtaitzed are fuirly accurate reproductions of electronic specific heat coefficients predicted from electron- to-atom ratio interpolations and To temperatuves eslimanted from transformation studies. Also considered in the calculation are the elastic constants, Curie temperatures, saturation magnlelizalion values, and indications of short- range order. The measnred activity coefficient of iron in anstetnite could not be accurately matched. The major source of uncertainty in the model is thought to be the magnetic contribution to the entropy of austenite. Calcrclations were extended to Fe-ni-C alloys using available carbon-acliuity data. The free energy of transformation from martensile to r at fixed composition was obtained as a function of nickel and carbon contetzt, and binary thetal-carbon phase diagrams Were estimaled as a function of nickel contenl. We needed thermodynamic information for Fe-Ni and Fe-Ni-C alloys at temperatures between 400" and 800°K in order to interpret the results of several phase-transformation studies. The most recent theoretical analysis of the thermodynamics of Fe-Nialloysl was based on a lumped-parameter, regular-solution model and used the Fe-Ni phase diagram available at that time.' Because significant difficulties were encountered in attempting to extend this analysis to Fe-Ni-C alloys, and because more experimental data has become available recently, we decided to attempt a new correlation. The analysis used here allows the extrapolation of measured and calculated thermodynamic values to lower temperatures and the extension of the thermodynamic analysis to Fe-Ni-C alloys. The structure of this correlation consists of expressions containing a total of twenty-one adjustable parameters. The forms of these expressions are discussed in the next section; however, a less formal summary is presented now to provide a physical overview of the model and to indicate its connections to prior work. Primary input information for this correlation is described below. The measured values of the specific heat of iron3 and its analysis475 and theoretical estimates of the specific heat of y* iron at low tempera- loys at 1123°K has been measured by solution calori-metry.7 The enthalpies of both a, and y have been measured most recently by Scheil and Saftig,B who used a dry-ice calorimeter. These data are used to formulate expressions for the heat of mixing of y and the heat of transformation of a, to y both at 1123°K. The a and y solubility limits in the Fe-Ni phase diagram have been redetermined recently9 by methods which assure a close approach to equilibrium. The a to y transformation can occur without change in nickel content or free energy at a temperature called TO; TO temperatures for various nickel contents have been estimated from transformation studies. The computed free-energy functions are adjusted by means of the parameters to fit both the phase diagram and the TO temperatures. Primary emphasis is placed on the phase diagram fit. Iron activities have been measured in Fe-Ni austenite10 between 973" and 1173°K. These activity data, which cannot be fitted accurately with our model, indicate that iron is substantially ideal in iron-rich austenite. Secondary, but helpful, information for the present correlation is provided by neutron diffraction and saturation magnetization measurements on both body-centered and face-centered Fe-Ni alloys."-'3 These results were interpreted11 in terms of composition-insensitive, localized magnetic moments on both iron

Jan 1, 1968

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 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 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 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