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By Dale C. Matthews, Donald L. Simpson

Hecla Mining Company's Lakeshore Mine and Metallurgical complex near Casa Grande, Arizona, is the first plant in North America to utilize the roast/leach/electrowinning process for production of cathode copper from sulfide concentrates. Oxide copper ores are also mined at Lakeshore. Using sulfuric acid and sponge iron by-products of the roast/leach operation, the oxide ore is leached in vats, the copper is precipitated with iron and recovered as cement copper. This paper will describe the roast/leach facilities and discuss the operating conditions at which more than 95 percent of the copper in concentrate is made soluble in acid solutions while less than 5 percent of the iron is rendered soluble. More than 97 percent of the sulfur contained in concentrate is captured either as strong sulfuric acid or as soluble sulfates in leach liquors. The iron rich residue after leaching is pelletized and reduced to sponge iron in an SLRN reduction kiln.

Jan 1, 1981

By K. G. Davis, P. Fryzuk

WEINBERG,' in an investigation of solute distributions along unidirectionally solidified rods of dilute silver in tin alloys, concluded that, for rods of 2 mm diameter or larger, a very high degree of convective mixing takes place in the melt ahead of the advancing interface. Suggested causes for this mixing were (1) thermal convection, (2) convective currents set up by changes in fluid density associated with concentration gradients, and (3) currents set up by changes in volume during freezing. Evidence was presented that causes (2) and (3) were not primarily responsible for solute mixing. Further, convective mixing took place in horizontal rods with temperature gradients as low as 6°C per cm, putting doubt on the importance of thermal convection. In the present work, convective mixing is examined in melts with known initial solute distributions. The absence of a moving solid-liquid interface eliminates convection caused by volume changes on solidification. In the first experiment, three silica tubes 2 mm in diameter and approximately 20 cm long were filled with an alloy of 100 ppm Ag in tin (99.999 pct purity), placed adjacent to one another in a horizontal furnace, and solidified from one end at 1 cm per hr. A110, a Y emitter, was used as tracer. A few centimeters at the start of the rod were left un-melted, to determine the initial concentration Go. After solidification was complete, one sample was removed. The hot furnace was then brought back to

Jan 1, 1965

By David A. Summers, Clark R. Barker, Marian Mazurkiewicz

In May 1975 the U.S. Bureau of Mines contracted with the University of Missouri-Rolla, Rock Mechanics and Explosives Research Center to develop a Hydrominer modification to a longwall shearer unit, wherein the rotating pick-laced drums and connecting gear drives are replaced by a water jet cutting ahead. The concept of the water jet cutting head is based on using the high localized energy of the water jets to isolate a slice of coal by cutting a slot under, at the back of, and at the top of the web. The plow blade of the head then advances into the cut and wedges the coal cantilever over onto the conveyor [(Fig. 1)]. There were several potential advantages foreseen for the system; perhaps the most significant were the elimination of coal dust from the working area and the ability, with a variation in nozzle geometry, to cut webs of greater depth with a small increase in haulage horsepower. The University initially designed the head, based on experiments carried out in the laboratory, under an earlier Bureau of Mines contract. The experiments showed that it was more advantageous to work at a pressure of 68.9 mPa (10,000 psi) with an estimated flow rate of 3.15 X 10 - 8 m3/s (50 gpm) than go to the higher pressures and lower flow rates which have been advocated elsewhere.

Jan 1, 1979

By S. J. Mitchell

An analysis of bolting reinforcement of several large [approximately 18 m (60 ft) cube] pillars was performed. The many overcoring stress profiles in pillars at the mine were used to produce generalized stress distributions at various stages in pre- and post-failure. A complete stress-deformation curve was estimated from this data. The effect of pillar bolting on the load-deformation behavior was extrapolated from the observed unbolted behavior. Bolting can increase pillar strength by up to 10 percent. The effect of bolting on general mine stability was examined with a short computer analysis. The computer model was calibrated against measurements performed at the mine, and produced good agreement between measured and modeled stresses. The analysis indicated that bolting increases the bolted pillar safety factors in the event of additional pillar failure by a small amount (approximately 5 percent). Progressive pillar failure is unlikely, because arching transfers most load from yielding pillars to large unmined abutments rather than to the smaller panel pillars.

Jan 1, 1984

Manganese ore from the Black Rock, Kramer, and Black Jack mines in Tooele and Jaub Counties, Utah, are of acceptable grade, the U. S. Bureau of Mines has announced. Payment of a premium price of 252¢ per lb to the Copper Range Co., of Michigan for the output of its White Pine mine, has been agreed to by the DMPA. The contract will be limited to $28.6 million worth of copper. The agreement follows an RFC loan grant of $57 million to bring the White Pine property into production within three years. Increases of 5 to 6 cents over the Lake copper ceilings have been granted to the Calumet & Helca Consolidated Copper Co., for operation of "high cost" deposits, according to Jess Larson, DMPA administrator. Mr. Larson expects the move to add about one million lb of copper per month to the supply. The agreement can be cancelled on 60 days notice and is terminated automatically in the event copper ceilings are removed.

Jan 1, 1952

By Luther M. Krupp

A 3 ½ -mile asphalt mixed mat haulage road joins American Smelting & Refining Co.'s El Tiro copper pit northwest of Tucson and its Silver Bell mill. Two-axle trucks operate continuously over the road- way but the asphalt top shows none of the wash- board wear usually seen on dirt haulage roads during use by heavy vehicles. The following data cover construction of this road, and results of its use by Asarco and Isbell Construction Co., the road's builder.

Jan 11, 1958

BOSTON LOCAL SECTION Executive Committee HENRY L. SMYTH, Chairman ALFRED C. LANE, Vice-Chairman AUGUSTUS H. EUSTIS, Secretary-Treasurer, 131 State St., Boston, Mass. ROBERT H. RICHARDS ALBERT SAUVEUR Meets on the first Monday evening of each winter month Twenty-first Meeting The Twenty-first meeting of the Boston. Local Section of the Institute was held at the Engineers' Club, 2 Comonwealth Avenue, Boston, Monday evening, Oct. 5, 1914. Twenty members and two guests were present. The Chairman, Henry L. Smyth, presided at the dinner, at the close of which he introduced, as the speaker of the evening, John M. Longyear, who gave a most interesting talk about his work in exploring for coal on the islands of Spitzbergen, 400 miles north of the North Cape of Norway. The talk was illustrated with many photographs, which showed clearly the nature of the work and the extraordinary difficulties of the location. AUGUSTUS H. EUSTIS, Secretary.

Jan 12, 1914

By T. M. Olson, B. G. Lewis

The adsorption of selenite on bentonite, kaolinite, and an iron--coated illite was studied to determine the importance of several soil variables on selenite removal from uranium mill tailings pond seepage. Adsorption capacities of the clays of selenite varied by orders of magnitude and decreased in the following order: illite > kaolinite > bentonite. Maximum adsorption of selenite on the clays was observed between pH 2.5 and the clay's zero-point-of-charge. Substantially less selenite was adsorbed on these clays in actual mill tailings solutions than in model systems. Virtually all selenite was removed from the tailings at pH 7. The principal removal mechanism at this pH is suggested to be the adsorption of selenite on freshly precipitated metal hydroxides. It is concluded that selenite can be removed from tailings seepage in soil or in clay liners in the presence of kaolinitic clays and iron oxides. Selenite would also tend to be removed from tailings seepage in calcareous strata.

Jan 1, 1984

FIGURES covering appropriations recommended by the Budget Bureau for the Bureau of Mines at Washington for next year are now available and are as quoted below. APPROPRIATION BUDGET APPROPRIATION 1928 1929 General Expenses $ 86,000` $ 86,000 Investigating Mine Accidents 386,470 399,470 Mining Investigations in Alaska.. 10,860 10,860 Operating Mine Rescue Cars and Stations 327,630 342,630 Testing Fuel 154,000 158,500 Mineral Mining Investigations.... 99,570 125,000 Oil, Gas and Oil-Shale Investiga- tions 198,260 198,260 Oil-Shale Investigations 5,000 80,000 Expenses Mining Experiment Sta- tions 173,000 173,000 Care, etc., Buildings and Grounds, Pittsburgh, Pa 71,360 76,360 Maintenance and Operation, Fuel Yards Balance Balance Helium Investigations :.... 75,000 75,000 Helium Production and Conserva- tion 1,063,000 462.000 Potash Investigations 100,000 100,000 Economics of Mineral Industries. . 225,000 275,000 Totals $2,975,150 $2,562,080

Jan 1, 1928

By K. A. Slagle, D. K. Smith

weight obtained. Additives used in conjunction with salt in these slurries have included silica flour, calcium ligno-sulfonate and cellulose retarders, granular lost-circulation materials, bentonite and selected low-water-loss additives that are not significantly deteriorated by the presence of the chloride ion. In some other areas of South Texas, the salt-saturated slurries have been used quite extensively for improvement of the flow properties of slurries and attainment of better circulation characteristics at lower displacement rates. Concurrently with this property, the protection of shales and shaly sands is also realized, as well as useful retardation of the slurry. Resultant superior cementing jobs have been indicated by both communication tests and acoustic logs for bonding to pipe and formation.' In one section of Louisiana, a major oil company has been using salt-saturated API Class A cement with calcium lignosulfonate retarder for cementing through the Miocene at 9,000 to 10,000 ft. This is another of the situations where interbedding of sands and shales exists, creating difficulty in maintaining formation competency when a fresh-water slurry contacts the clay minerals of the formation. Further work has also been done in the shaly Miocene formation at 13,000 to 15,000 ft where fairly close water or gas contacts are encountered. Indications thus far are that better segregation of these various fluids is obtained by use of the saturated salt slurries because of their improved formation bonding characteristics. In addition to the properties of salt in this situation, attainment of turbulent flow at minimum displacement rates has also been accomplished by use of an additive to help provide exceptional dispersion and viscosity reduction of the slurry. Another oil company was encountering considerable expense in completing wells in Southwestern Louisiana due to extensive block squeeze requirements for effective separation of zones. A very effective mud program was being used to minimize washout in the shale sections and, apparently, a nearly gauge-size hole was being obtained. However, primary cementing results with fresh-water slurries were generally poor. On a few occasions when slurry was actually circulated to the surface, large pieces of shale formation were brought out of the hole with the slurry, indicating a severely water-sensitive, sloughing formation. Inhibition of shale heaving was being accomvlished in the drilling program, and immediately indone ipon circulation of the fresh-water slurry even though it contained a low-fluid-loss additive to reduce filtrate damage in the sands. The subsequent change to salt-saturated slurry yielded 11 successful primary cement jobs out of 12, compared to the previous success ratio of practically zero. Since these were deep, high-temperature wells in the range of 13,000 ft with high-pressure zones necessitating 17.5-lb/gal fluid densities, the slurry used was API Class E cement, silica flour, weight material, retarder, salt saturation (which also reduced the amount of weight material) and maintenance of low fluid loss by use of a salt-compatible additive. Other salt slurries have been used to a limited extent in this same general area for similar problems at depths ranging from 5,000 to 17,000 ft. In the shallower wells, the cement has usually been API Class A where the salt functions as a retarder, and in the deeper wells API Class E cement is used with the additional salt advantage being its increased slurry weight and inability to dissolve salt stringers. A considerable number of squeeze jobs have also been done on older wells using the salt-saturated slurries with very good results. MID-CONTINENT In North Texas, salt-water slurries have been used for cementing the Woodbine sand, Strawn sand, KMA sand and Pettit lime. Shales surrounding these formations have created the same difficulty in obtaining separation of producing zones that has been the problem in other areas. Depths in this area range from 3,400 ft for the Strawn to 7,400 ft for the Woodbine, and concentration of salt has varied accordingly. In the deeper wells, where retardation is desired, saturated salt-water cement is used; for the shallower wells, in order to provide shorter waiting-on-cement times, the amount of salt has been 18 per cent by weight of the mixing water. Results have been excellent with no reported failures on any of the salt cement jobs; where acoustic bond logs have indicated indifferent bonds previously, they are indicating very good bonding for the salt slurries. In Oklahoma various shales of Pennsylvanian age exhibit a high degree of sloughing in the presence of fresh water, causing severe washouts above and below sand formations which it is desired to isolate. This situation exists to some degree in practically all parts of Oklahoma and includes formations of other ages such as the Wood-ford shale. For the past few years, salt-saturated cements and displacement rates as high as practical have been used as a remedy for this problem, with very good results. The Layton and Bartlesville formations are two examples of shaly sands where saturated slurries have been helpful. In one area where five wells were drilled through this type of problem shale without obtaining a satisfactory primary cement job, a change was made to salt-saturated cement preceded by a suitable chemical wash for the drilling mud involved. Acoustic bond logging indicated excellent bonding, and final completion bore out this result by being trouble-free. This type of slurry has also been used extensively on squeeze jobs where shales have been heaving around the producing formations. Predominantly, the basic slurry has been either API Class A cement or a pozzolan cement—although, as deeper wells are being drilled, the use of salt in Class E cement is also increasing. Salt cement in West Texas has been used primarily to help prevent channeling through the shales around the Delaware sand, Queens dolomite and Hope lime. Many of the shaly and dirty sands of this area are sensitive to the filtrate from a fresh-water cement. Salt at 16 to 18 per cent by weight of mixing water has been added to centent, and has been effective in controlling formation damage and communication between zones in these formations. Use of these lower salt concentrations is dictated in this area by the relatively low formation temperatures where retardation of the slurry would create unduly long waiting-on-cement times. Also, quite a bit of cementing has been done in this area using salt concentrations in the accelerating range— that is, 2 to 5 per cent by weight of water. Specifically, these concentrations have been used in coiljunction with high percentages of gel to overcome the retarding effect of the calcium lignosulfonate dispersant, although there are probably several shales where these concentrations could provide some degree of formation stability. On several occasions, the salt has also been used to lower the critical velocity or rate for turbulence with the slurry, particularly in the pozzolan cements. On wells in the Hope lime, it has usually been necessary to squeeze the shale above and below the lime to get a water-free completion. Use of salt-saturated slurries has largely eliminated this

By F. E. Luborsky, K. T. Aust

RECENT interest has been shown in utilizing solid-state techniques for obtaining large oriented grains in the Alnico Alloys.1-4 Unfortunately, due to the inherent brittleness of these materials it is difficult to introduce sufficient imperfections by deformation to support the nucleation and growth of new, recrystallized grains. As a result, recrystal-lization methods for obtaining large grains, such as the strain-anneal technique, do not appear to be feasible. Steinort et a1.2 used a combination of a thermal gradient and internal strains to obtain large single crystals of Alnico 5 from a poly crystalline casting by annealing at temperatures above 1200°C. It was suggested that the strains were the result of the precipitation of the y phase which exists between -850° and 1200°C. The purpose of the present study was to determine if the grain size of the cast Alnico alloys can be markedly increased by solid state techniques involv-

Jan 1, 1963

By Ferron A. Olson

Occasionally it is good to consider the past, assess the present and project the future. Curriculum, enrollment, matriculation of graduates and changes in industry which influence mineral education are all relevant for determining what changes will be needed in educational institutions to support growth and development in the United States. It would appear likely that with environmental pressures, energy needs with present stress in fossil fuels and general societal needs for metals and minerals that mining and metallurgical engineering faces a period of growth and may be on the threshold of a new era with a vitality that has not been enjoyed for several decades. The following information is based on material obtained through questionnaires received from twelve schools accredited in mining or mineral engineering (out of 18 in the U.S.), 2 not accredited and 5 which no longer have mineral engineering disciplines. The schools presented do not include the smaller nor larges of the undergraduate programs in mining engineering.

Jan 8, 1972

By W. Hume-Rothery

RECENT interest has been shown in utilizing solid-state techniques for obtaining large oriented grains in the Alnico Alloys.1-4 Unfortunately, due to the inherent brittleness of these materials it is difficult to introduce sufficient imperfections by deformation to support the nucleation and growth of new, recrystallized grains. As a result, recrystal-lization methods for obtaining large grains, such as the strain-anneal technique, do not appear to be feasible. Steinort et a1.2 used a combination of a thermal gradient and internal strains to obtain large single crystals of Alnico 5 from a poly crystalline casting by annealing at temperatures above 1200°C. It was suggested that the strains were the result of the precipitation of the y phase which exists between -850° and 1200°C. The purpose of the present study was to determine if the grain size of the cast Alnico alloys can be markedly increased by solid state techniques involv-

Jan 1, 1963

President MRS THORNS E LLOYD 14 Green Hill Road Morristown, N J First Vice-President MRS A B PARSONS 52 Edgewood Road Scarsdale, N Y Second Vice-President MRS H A PROSSER 1001 Park Avenue New York, N Y Third Vice-President MRS HARRY J WOLF 3 Glenwood Avenue Littleneck, N Y Fourth Vice-President MRS MARK LAWRENCE REQUA 140 North Plymouth Blvd Los Angeles, Calif Fifth Vice-President MRS NEWELL G ALFORD 314 South Homewood Avenue Pittsburgh, Pa

Jan 1, 1952

By T. M. Chatard, Cabell Whitehead

The Republic mine, situated forty miles from Marcus, a station on the Spokane Falls and Northern Railroad, in the northeastern part of the State of Washington, was located in 1896, but no development-work was dolie until the spring of 1897. While much of the ore mined since then has been rich enough for shipment to smelters, a method of locally treating the lower-grade ores soon became a matter of prime importance, because only about 40 per cent. of the values could be recovered by plain amalgamation, even with ores assaying 4 to 5 ounces of gold per ton. Experiments with cyanidation, in various ways, led to the adoption of the Pelatan-Clerici process and the erection on this system of a 10-ton experimental plant, which was later increased to a capacity of 35 tons per day. The extractions by this process showed much improvement over previous work, especially when the ore was crushed to

Jan 1, 1901

By Shiou-Chuan Sun

Most previous work on sedimentation of coal1 and mineral2,3 suspensions has been conducted in graduated 1-liter glass cylinders of 6-cm diam. With this type of large container it is often difficult to see through the suspension and tedious to perform a large number of tests. Furthermore, the heavy glass walls and the graduation lines of glass cylinders cause internal and stray reflections, respectively. To obviate these difficulties, an Atlab Emulsion Viewer from Arthur H. Thomas Co. was adopted as an alternative apparatus. Equipment: The viewer,4 shown in Fig. 1, consists of: 1) a stainless steel frame rack holding 21 flat-bottom Nessler tubes or an ungraduated replica 1.64 cm ID and 1.80 cm OD, 2) a movable masked 150-w lumaline lamp behind the tubes, and 3) a scaled glass panel with 100 vertical divisions in front of the tubes. The tubes are snugly held by springs in slots formed by spacer bars, which also serve as shields to eliminate stray light. The lumaline lamp is mounted behind a slit in a movable housing so that it can be positioned behind the suspension to be examined. The lowest or 100-division line on the front glass plate is leveled with the upper side of the bottom of all tubes. The scaled portion of each tube, roughly 19 cm high and 40 ml in volume, is used to study coal and mineral suspensions.

Jan 1, 1959

By E. J. Quinn, M. F. Fogler

In a recent paper, Rawdon and Mutchlerl gave some exceptionally interesting results on the Brinell and scratch hardness of severely cold-worked metals. In their work, they found that, on continued cold rolling, the metal hardened up to a particular point and then reversed and became softer; this was true for both Brinell and scratch hardness values. The generally reported behavior2 of metals, with respect to Brinell tests on cold-worked material, is that the metals harden up to a certain point and then, on further cold rolling, no change in Brinell hardness occurs. Jeffries and Archer3 state that there is little difference between the scratch hardness of annealed and cold-worked metals; the work of Faust and Tammann4 also indicated no difference between the hardness of annealed and cold-worked copper. Rawdon and Mutchler found, when they plotted the reduction ratio (initial thickness divided by thickness after rolling) against the hardness value for the cold-rolled material, that the hardness number increased up to a reduction ratio of about 3 and then decreased and became even smaller than that for the annealed metal. This behavior was reported for both scratch and Brinell hardness; Figs. 1 and 2 show their results for Brinell hardness on the metals for which they published data. This is an exceptionally interesting phenomenon, if it occurs under all conditions of rolling, and would have an important bearing on the practice of cold

Jan 1, 1925

By George T. Bator

If confronted with the problem of pumping a mixture of slime-free sand, gravel and boulders up to six in. in diameter, at the rate of 175 tons per hr in one single-stage pump against a static head of 90 ft and a total head of 140 ft, of which 20 is on the suction side, an engineer might be forgiven for backing away from the job, especially if he were also told that the pump wearing parts must have a minimum hardness of 550 Brine11 for the sake of abrasion resistance. Yet precisely that feat has been accomplished in the gravel pit of John B. LaGarde, Inc., near Anniston, Ala. The pump used is of decidedly novel design and its successful operation since installation 1.5 years ago suggests that it may be of timely interest in numerous other applications in the mining industry, such as pump transportation of coal washer refuse or rock from open-pit's without unduly fine crushing.

Jan 9, 1950

By T. S. Spicer

The relationship of coal characteristics to the principal types of firing equipment has been known to the coal combustion engineer, but is not as familiar a subject for purchasing agents, salesmen, consumers, and executives of coal-producing and consuming companies. This general survey of characteristics determined by standard laboratory tests, of major types of combustion techniques, and of the relationships between the two is directed toward the latter audience. It will also serve as a review for those actively engaged in the combustion of coal. Although the relationship of coal characteristics to the principal types of firing equipment is well known to the experienced coal combustion engineer, apparently there is need for a summary article on this subject. The author has received numerous requests for such a paper from purchasing agents, coal salesmen, coal customers and executives of coal-producing and consuming companies. Consequently, the scope of this paper will be directed to this audience, with the hope that it may serve also as a review to others actively engaged in the combustion of coal. The magnitude of this subject is so great that only a brief general treatise is possible. The author realizes that because there are so many special cases and exceptions to the generalities which follow, he is in jeopardy of contradicting himself. It is the hope, however, that the many references cited will prove valuable to those who wish to study the details excluded by necessity, due to space and time limitations. Hence, the characteristics of coals as determined by standard laboratory tests will be discussed; the major types of combustion techniques reviewed; and then the characteristics and firing will be related. CHARACTERISTICS OF UNITED STATES COALS The coals of the United States range from lignite to anthracite and each has its own general characteristics. The extensive coal fields of the U. S. are shown in Fig. 1 and the estimated reserve according to rank for each state is illustrated in Fig. 2. Coals may be classified according to rank as shown by Table I from the ASTM Standards on Coal and Coke, D-338-38.1 The basis of this classification is ac- cording to fixed carbon and heating value (Btu per pound) calculated to a mineral-matter-free basis. The high-rank coals are classified according to fixed carbon on the dry basis; and the low-rank coals according to Btu on the moist basis. Agglomerating and slacking (weathering) indices are used to differentiate between certain adjacent groups. While rank is not itself a characteristic it does signify certain characteristics that accompany a class of fuel. Anthracite, for example, immediately implies a hard, free-burning, smokeless coal of low volatile matter, usually having an ash of high fusibility. Coals may also be classified according to grade as described by ASTM Designation D-398-37.1 This quality classification is determined by size, calorific value, ash, ash-softening temperature, and sulfur. This type of classification is not used as extensively by the industry as the rank classification. Fig. 3 shows the heat value of different ranks compared to proximate analyses. Coals may also be classified by sizes, as shown in Tables IIA and IIB, and sizes can be on both top and bottom limits. If this is done, then the coal is called double screened; otherwise, either top or bottom sizes can be specified as a limit. Bituminous coal sizing varies from field to field and depends upon the market demand. The common sizes and their main uses are outlined in Table IIA. Anthracite is usually available in many sizes at the colliery, and Table IIB summarizes standard sizes and names. Although rank, grade, and size designations help identify and describe a coal in question, there still remain other characteristics such as indicated by moisture, free swelling index, grindability tests, etc. A bituminous coal information chart Table III) suggested for use in studying the available coals in a region, lists origin and chemical and physical characteristics. Even this more comprehensive list does not completely spell out all the characteristics of a heterogenous material like coal. For example,

Jan 1, 1961

By Pradeep K. Rohatgi, Clyde M. Adams

Structures obtained on freezing of several hypo-and hypereutectic Al-Cu alloys over a range of solidification rates have been examined. Dendrite spacing, L, increases linearly with solute concentration and with the square root of the inverse freezing rate. The relationship for hypoeutectic alloys is: where rate of change of fraction solid with time, is freezing rate, C is solute concentration, (pct Cu)=1. Mass transport in inter dendritic liquid during solidification is analyzed; the experimental observations suggest maximum concentration differences and constitutional supercooling in the inter dendritic liquid increase with an increase in the solute concentration. The dendrite morphology changes with freezing rate and alloy composition. The dendrites of the a phase are parallel, uniformly spaced plates with slow freezing and rods with rapid freezing. Nonor-thogonal side branching has been observed in phases with cubic and tetragonal structures. Side branches in a dendrites are orthogonal with slow freezing and at 60 deg with rapid freezing. Formation of second-phase envelopes around the Primary phase is also discussed. DENDRITIC structure is characteristic of many types of phase transformation. The most extensively studied so far has been solidification of liquid solutions. chalmersl and coworkers have interpreted the formation of dendrites in terms of the breakdown of a planar interface. Most of the work done concerns itself with the development of an instability at the interface. Little theoretical work has been done quantitatively to relate the parameters of dendritic structure to mass transport in the liquid phase. A few empirical relations based on the experimental2'3 observations exist in the literature. Several workers2 including Brown and Adams1 have studied dendrite spacing in A1-Cu system as a function of solidification variables. In most cases, dendrite spacing has been found to increase linearly with the square root of some parameter proportional to the freezing time. The effect of solute concentration is not clear; some workers report the dendrite spacing increases with solute concentration4 whereas others report vice versa.''' ~ohatgi' has observed an increase in the spacing between ice dendrites with an increase in solute concentration in water. Tiller has also suggested that dendrite spacing should increase with solute concentration. In the present work dendrite spacing and morphology have been examined as a function of solute concentration and freezing rate. The freezing rate is defined as the fraction of liquid solidified per unit time, dfs/dß?, where f, is the fraction solid and 8 the time. The fastest freezing rate studied was 4550 times the slowest freezing rate. THEORETICAL CONSIDERATIONS It is of interest to analyze the concentration distribution in the liquid phase between growing dendrites during solidification, Fig. 1. Since this distribution is a direct consequence of the rejection of solute by the growing solid, a diffusional process, the concentration gradients increase with the freezing rate. However, when solidification rate is the only variable in a series of experiments, the interdendritic liquid regions become smaller (i.e., the dendrites become more closely spaced) with an increase in freezing rate. The main purpose of the analytical treatment of interdendritic liquid diffusion will be to reveal a tendency for dendrite spacing to decrease with increasing solidification rate in just such a way that the maximum concentration differences developed in the liquid phase are remarkably independent of freezing rate. Two rather different analyses are set forth, one pertaining to the one-dimensional diffusion which obtains in the interdendritic liquid between parallel plate-shaped dendrites, and the other to the cylindrically symmetrical diffusion around rod-shaped dendrites during early stages of solidification. The results of the two analyses are quantitatively similar, correlating dendrite spacing, maximum concentration difference, and freezing rate. First consider the simpler one-dimensional case. Two parallel plate-shaped dendrites are separated by a distance, L, between centers, Fig. 1. Solidification takes place by the thickening of these plates, with solute being rejected into the liquid. It is assumed there is no diffusion in the solid. This thickening process is slow enough and the dendrite spacing small enough that the concentration differences which develop, although interesting and important, are very small (an important assumption which is verified ex-

Jan 1, 1968