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New Products Equipment

Jan 7, 1951

New Products Equipment

Jan 11, 1951

New Products Equipment

Jan 3, 1953

By Orville R. Lyons

DISCUSSION Judson S. Hubbard (The Humphreys Investment Co., Denver)—In this very interesting paper several brief references are made to the Humphreys spiral, a device used for cleaning fine coal. In Table I, Plants 76 and 77, data are given on spiral performance treating Raton and Trinidad coal. The fine coal, as fed to the spiral in these instances, is actually a table middling, hence the more easily treated material was previously removed and a large number of particles were present which were difficult to clean. Mr. W. M. Bertholf of the Colorado Fuel and Iron Co. presented a paper in February, 1946, Cleaning Table Middlings from a Coal Washery with the Humphreys Spiral Concentrator, from which I quote: "In considering the results of our tests it should be noted that the feed was our table middling, and that any real separation is a 'moral victory' as there is little material that could properly be called coal and practically no heavy rock, the consequences being that previous attempts to clean the middling have not at all been successful." Referring again to Table I, Plants 72, 73, 74, and 75, these data were obtained by Yancey and Geer and others and presented at the February 1950 Meeting, AIME, in a paper entitled Laboratory Performance Tests of the Humphreys Spiral as a Cleaner of Fine Coal. Results shown for those tests involve all particles from 8 mesh through the colloids, which admittedly is not an ideal situation for spiral feed if much refuse is contained in the —80 mesh or —100 mesh size range. As an illustration of the effect of treating too broad a size range, let us consider Plant No. 75, Kentucky No. 9 seam. Spiral feed was 8 mesh x 0. Now had this been 8x100 mesh the percentage of misplaced material would have been 8.0 pct instead of the reported 15.26 pct. Similar comparisons can be made on the other data presented with respect to the spiral. Other types of equipment show a similar trend in that whenever too fine a size is treated in a given unit process the percentage of misplaced material increases. Since the spiral is working near the finer end of the size range, it will sometimes be advantageous to treat the entire range of —8 mesh material rather than to deslime and make a fair showing on, say, the +80 or + I00 mesh. Desliming is subsequently done in any case in the dewatering or thickening operation. Results obtained by spiraling any given coal depend on factors too numerous and complex to discuss here, but there are strong indications that proper preparation of feed to the spiral can improve results obtained on some of the raw coals tested. This is clearly pointed out at the end of the aforementioned paper by Yancey and Geer. "The spiral is an extremely simple device which involves no moving parts and is constructed almost entirely of unmachined castings. Since it is such an uncomplicated mechanism, operation is simple and virtually foolproof. These characteristics, which go far toward insuring low cost operation, are attractive attributes in any coal cleaning unit." Certain equipment used in conjunction with the spiral has resulted in a decrease in the percentage of misplaced material, notably in actual practice the launder screen which is used to remove objectionable high ash fines from a spiral-washed coal product. Private correspondence with the U. S. Bureau of Mines has intimated that an additional yield of coal is possible by flotation of the spiral middling. Possible future improvements and developments may result from other methods now under consideration. Finally, some compromise must be made between the best metallurgical performance and the best practical or economical results. Mr. Lyons emphasizes in his summary this objective of overall economy in selection of equipment. G. B. Walker (American Cyanamid Co., Stamford, Conn.)—I had the pleasure of reviewing the draft of this paper and my curiosity was aroused by the data given for Tromp plants, in that all of the examples shown appeared to be 2-product separations, whereas all the Tromp plants with which I am familiar have been 3-product units. The data given for plants No. 101 and 102 appear to be taken from Tromp's brochure on his process and represent the results obtained at the Dominale plant in Holland which was operated for many years by Mr. Tromp. The plant, which was designed to treat 58 tons per hr, was sampled while treating 35 tons per hr of 3Y4x-in. coal. Example 101 appears to conform to what would result if the middling product were calculated into the refuse product, while Example 102 represents the calculation of the middling into the coal product. It is believed that Examples 103 and 104 represent the operation of the Willem-Sophie Mine in Holland recalculated on the same basis. In checking the English examples given by numbers 14, 15, 16, and 17, the same procedure seems to have been followed. These results have, apparently, been taken from an article in Colliery Engineering in August 1941, describing the initial operation of the Williamthorpe Colliery of the Hardwick Colliery Co. Two vessels are employed in this plant, one to treat soft coal and one to treat hard coal. Example No. 14 presents the results that could be obtained from the soft coal bath if the middling were calculated into the refuse, and Example 15 the results when the middling is calculated into the coal. Examples 16 and 17 represent the same expedient in the case of the hard coal bath. Of interest to this discussion is the fact that during the past year the Simon-Carves Engineering Co. in England has installed in the Williamthorpe plant their new "Sim-Car" medium cleaning system which is based on magnetic extraction and control and which is licensed under the Heavy-Media Separation Processes patents by the American Zinc, Lead and Smelting Co. This system has been described in the December 1951, issue of Colliery Engineering. It is reported that since the Williamthorpe Colliery was changed from the Tromp system of medium cleaning to the Magneto-Motive method of medium control the opera-

Jan 1, 1953

By Orville R. Lyons

DISCUSSION Judson S. Hubbard (The Humphreys Investment Co., Denver)—In this very interesting paper several brief references are made to the Humphreys spiral, a device used for cleaning fine coal. In Table I, Plants 76 and 77, data are given on spiral performance treating Raton and Trinidad coal. The fine coal, as fed to the spiral in these instances, is actually a table middling, hence the more easily treated material was previously removed and a large number of particles were present which were difficult to clean. Mr. W. M. Bertholf of the Colorado Fuel and Iron Co. presented a paper in February, 1946, Cleaning Table Middlings from a Coal Washery with the Humphreys Spiral Concentrator, from which I quote: "In considering the results of our tests it should be noted that the feed was our table middling, and that any real separation is a 'moral victory' as there is little material that could properly be called coal and practically no heavy rock, the consequences being that previous attempts to clean the middling have not at all been successful." Referring again to Table I, Plants 72, 73, 74, and 75, these data were obtained by Yancey and Geer and others and presented at the February 1950 Meeting, AIME, in a paper entitled Laboratory Performance Tests of the Humphreys Spiral as a Cleaner of Fine Coal. Results shown for those tests involve all particles from 8 mesh through the colloids, which admittedly is not an ideal situation for spiral feed if much refuse is contained in the —80 mesh or —100 mesh size range. As an illustration of the effect of treating too broad a size range, let us consider Plant No. 75, Kentucky No. 9 seam. Spiral feed was 8 mesh x 0. Now had this been 8x100 mesh the percentage of misplaced material would have been 8.0 pct instead of the reported 15.26 pct. Similar comparisons can be made on the other data presented with respect to the spiral. Other types of equipment show a similar trend in that whenever too fine a size is treated in a given unit process the percentage of misplaced material increases. Since the spiral is working near the finer end of the size range, it will sometimes be advantageous to treat the entire range of —8 mesh material rather than to deslime and make a fair showing on, say, the +80 or + I00 mesh. Desliming is subsequently done in any case in the dewatering or thickening operation. Results obtained by spiraling any given coal depend on factors too numerous and complex to discuss here, but there are strong indications that proper preparation of feed to the spiral can improve results obtained on some of the raw coals tested. This is clearly pointed out at the end of the aforementioned paper by Yancey and Geer. "The spiral is an extremely simple device which involves no moving parts and is constructed almost entirely of unmachined castings. Since it is such an uncomplicated mechanism, operation is simple and virtually foolproof. These characteristics, which go far toward insuring low cost operation, are attractive attributes in any coal cleaning unit." Certain equipment used in conjunction with the spiral has resulted in a decrease in the percentage of misplaced material, notably in actual practice the launder screen which is used to remove objectionable high ash fines from a spiral-washed coal product. Private correspondence with the U. S. Bureau of Mines has intimated that an additional yield of coal is possible by flotation of the spiral middling. Possible future improvements and developments may result from other methods now under consideration. Finally, some compromise must be made between the best metallurgical performance and the best practical or economical results. Mr. Lyons emphasizes in his summary this objective of overall economy in selection of equipment. G. B. Walker (American Cyanamid Co., Stamford, Conn.)—I had the pleasure of reviewing the draft of this paper and my curiosity was aroused by the data given for Tromp plants, in that all of the examples shown appeared to be 2-product separations, whereas all the Tromp plants with which I am familiar have been 3-product units. The data given for plants No. 101 and 102 appear to be taken from Tromp's brochure on his process and represent the results obtained at the Dominale plant in Holland which was operated for many years by Mr. Tromp. The plant, which was designed to treat 58 tons per hr, was sampled while treating 35 tons per hr of 3Y4x-in. coal. Example 101 appears to conform to what would result if the middling product were calculated into the refuse product, while Example 102 represents the calculation of the middling into the coal product. It is believed that Examples 103 and 104 represent the operation of the Willem-Sophie Mine in Holland recalculated on the same basis. In checking the English examples given by numbers 14, 15, 16, and 17, the same procedure seems to have been followed. These results have, apparently, been taken from an article in Colliery Engineering in August 1941, describing the initial operation of the Williamthorpe Colliery of the Hardwick Colliery Co. Two vessels are employed in this plant, one to treat soft coal and one to treat hard coal. Example No. 14 presents the results that could be obtained from the soft coal bath if the middling were calculated into the refuse, and Example 15 the results when the middling is calculated into the coal. Examples 16 and 17 represent the same expedient in the case of the hard coal bath. Of interest to this discussion is the fact that during the past year the Simon-Carves Engineering Co. in England has installed in the Williamthorpe plant their new "Sim-Car" medium cleaning system which is based on magnetic extraction and control and which is licensed under the Heavy-Media Separation Processes patents by the American Zinc, Lead and Smelting Co. This system has been described in the December 1951, issue of Colliery Engineering. It is reported that since the Williamthorpe Colliery was changed from the Tromp system of medium cleaning to the Magneto-Motive method of medium control the opera-

Jan 1, 1953

By E. J. Kenaedy, E. H. Robie

THOUGH the fall meeting of the Coal Division was held in the heart of the anthracite section, at Hazleton, Pa., the bituminous industry was well represented also, and the two groups found much common ground for discussion. The' technical part of the program was confined to two sessions in the morning and afternoon of the first day, Friday, Oct. 14, the evening and the following day being reserved for field trips and social functions. The attendance more than met the expectations of those in charge of the arrangements; there seemed no hint of depression here.

Jan 1, 1932

Servicing School Opening of a special factory training course in servicing earthmoving equipment is announced by the Euclid Road Machinery Co. Four [ ] beginning and four advanced one week training courses will be offered to representatives of distributors and customers. Circle No. 1 Core Drill The new Acker "Teredo" core drill, is named after the "boringest little animal in the world" to underline its function as a light, compact, portable core drill capable of depths to 600 ft. While light enough to be truck or jeep-mounted, it offers the combination of a three-speed totally enclosed transmission with either hydraulic or screw feed drill heads. Full 24-in. travel gives maximum footage per shift, 360° rotation permits freedom of hole location, a transmission mounted cathead winch is used in pulling rods and casings, and a power take-off is provided for a pump. Circle No. 2 Plastic Pipe Planned production of both flexible and semi-rigid plastic pipe is announced by Triangle Conduit & Cable Co. Rigid and high-impact pipe will be added to the line later. Three types: non-toxic, industrial, and suction, are being made and in sizes from 1/2 to 6 in. Circle No. 3

Jan 1, 1952

By Walter J. Mead

By American tradition, if not by rational decision, publicly owned natural resources have been transferred to private industry for processing. The process of transfer requires specific determination of the price which the patentee, buyer, or lessee must pay to the government in exchange for the right to develop a resource, and selection of the patentee, buyer, or lessee from among several possible contestants. Pricing of natural resources owned by the government presents a set of problems quite different from ordinary commodity pricing. Natural resources in situ are not homogeneous commodities. Within any class of natural resources, specific leasable parcels will differ in value by reason of location and accessibility, as well as quality and quantity. Thus, there is no "going price;" every lease within a specific resource class will have a different value. To complicate further the pricing and buyer selection problems, competition may not be reliable. Natural-resource markets are characterized by oligopsony conditions. In a significant number of cases, as will be shown later, there has been only one bidder for a given lease, and in most lease sales the number of bidders is equal to or less than three. As a further complication, there is great uncertainty regarding the value of specific resources, even among the best-informed buyers, as well as within the leasing agency. In some instances, particularly with regard to oil and gas resources, there may be uncertainty about the presence of resources, as well as the quantity and quality of any resources contained in the tract offered for lease. In other cases, such as oil shale and some deep ocean minerals where new technologies are involved, the presence of the resource is clearly established. There may be a relatively high degree of knowledge about the quantity and quality of the resource, but there is great uncertainty concerning the cost of production. These problems in total make it difficult for the leasing agency to appraise accurately the resource to be leased, as well as for the potential bidder to calculate a bid price that will yield him a normal profit. The pricing goal of the federal government as the seller or lessee may be to capture the economic rent; that is, the price of a resource might equal its discounted present value. A required price substantially above this amount would either generate no bids, or, in the long run, would bankrupt the buyer. A price below this amount is a disguised subsidy to the lessee. A subsidy to mineral lessees, as to any other economic interest group, as a minimum should be justified by a clear showing of net external benefits from the economic activity. In the case of timber sales by the U.S. Forest Service, the Forest Service Handbook asserts that "the aim in national forest stumpage appraisal is to determine market value,"8 and "market value" is equated to "fair market value." Regarding minerals, there is no reference in legislation or regula-

Jan 1, 1976

Considerable discussion took place at the June 18th Board of Directors Meeting concerning ways the Petroleum Branch office in Dallas could better serve its members and the essentially Petroleum Local Sections, namely the Delta, East Texas, Gulf Coast, Kansas, Mid-Continent, North Texas, Oklahoma City, Permian Basin, and Southwest Texas. The question of whether decentralization strengthens or weakens the Institute was debated, particularly as to what services could be advantageously decentralized and how both offices could keep informed on their mutual problems. Among other things, it was decided that an Auxiliary Admissions Committee could screen applications from Petroleum members before final action by the National Admissions Committee in New York. Finally it was voted, "That all administrative matters that can be properly delegated to a Branch organization may be so delegated". Final details were approved at the July 16th meeting of the Executive and Finance Committees.

Jan 1, 1952

By P. D. I. Honeyman

IN THE Southwestern copper region the event of greatest interest was the starting up of the new Hurley, N. Mex., smelter of the Chino Mines division of the Nevada Consolidated Copper Corp., which occurred in May. This plant, built as a wet-charge smelter for treating largely an all-concentrate charge, embodies in its de- sign the latest in materials-handling equipment. Noticeable around this smelter is the absence of tram cars and trackage for the handling of charge, dust and other materials. Concentrate from the mills is received in bottom- dump cars which are unloaded into a series of concentrate bins. Concentrate is then reclaimed through the bottom of the bins and discharged through a feeder on to a conveyor belt. Flux for the charge is fed on to the conveyor ahead of the concentrate charge. The belt-mixed charge is conveyed to the furnace building and discharged into the furnace charge bin ready for feeding to the reverberatory furnace. As in the McGill plant, the furnace is fed by vibrating conveyors, one down each side of the furnace.

Jan 1, 1940

By E. L. Kinsella, F. S. White

Solids fluidization utilized in two ways for the commercial production of lime is described. Crushed —6 mesh limestone is dried and dedusted in a single bed reactor, then calcined in a 5-stage reactor. Construction, operation, and results obtained with both processes are given. THE solids fluidization process brought out by the Standard Oil Development Co. in the early forties for catalytic cracking of petroleum enabled rapid transfer of large quantities of heat from gases to solids under closely controlled temperature conditions. As the technique developed, it was natural that applications for the process outside the petroleum industry would be sought. The calcination of limestone to quicklime requires the transfer of a large quantity of heat at high and closely controlled temperatures. For these reasons, this possible application was one of the first to be investigated. Laboratory work conducted by the Dorr Co. indicated that lime produced by solids fluidization would be of exceptional quality. Calculation of theoretical heat balances showed that savings in fuel could be expected. Accordingly, a pilot plant of 10 tons per day capacity was erected by the New England Lime Co. at Adams, Mass., to substantiate the process. Operation of the pilot plant, previously described,' showed that excellent lime could be produced with a saving in fuel. The work also indicated the necessity of preparing feed to remove the finer fractions if dust losses were to be held to a tolerable level. A single-stage fluidized solids drier-stripper was developed to accomplish this sizing.' Subsequently a commercial lime reactor was erected at Adams, beginning operation in June 1949, followed by air sizer facilities completed in November 1951. This paper will describe these two applications of solids fluidization. The raw material for preparation of lime by the fluidizing process is a high calcium crystalline lime- stone having the approximate chemical composition shown in Table I. The stone is first prepared by crushing and grinding in conventional equipment to pass a 6-mesh sieve. After crushing, the material is sent to the FluoDry unit for drying and dedusting. Fluidized Drying and Sizing As shown in Fig. 1, the FluoDry unit consists of a -in. cylindrical steel shell, 9-ft ID by 22-ft 6-in. overall height. Attached horizontallv at the bottom is a 6-ft diam combustion chamber, approximately 7 ft 6 in. long. A refractory constriction dome, consisting of first-quality fire brick shapes, partitions the inside into two sections. The lower section is called the windbox and the upper the bed compartment. The vertical wall of the shell is lined with 6-in. first-quality rotary kiln blocks. In the bottom of the windbox a hoppered section is formed with castable refractory to permit the windbox to be readily cleaned via a 6-in. screw conveyor. The combustion chamber is similarly lined with refractory shapes. On the 6-in. diam section, 4 in. of insulating brick, HW-26, are used. The inner combustion chamber is lined with 4-in. Korundal brick to withstand the high flame temperatures encountered. An 8-in. steel feed pipe, entering vertically through the top and fitted with an air-operated cone valve,

Jan 1, 1953

By F. S. White, E. L. Kinsella

Solids fluidization utilized in two ways for the commercial production of lime is described. Crushed —6 mesh limestone is dried and dedusted in a single bed reactor, then calcined in a 5-stage reactor. Construction, operation, and results obtained with both processes are given. THE solids fluidization process brought out by the Standard Oil Development Co. in the early forties for catalytic cracking of petroleum enabled rapid transfer of large quantities of heat from gases to solids under closely controlled temperature conditions. As the technique developed, it was natural that applications for the process outside the petroleum industry would be sought. The calcination of limestone to quicklime requires the transfer of a large quantity of heat at high and closely controlled temperatures. For these reasons, this possible application was one of the first to be investigated. Laboratory work conducted by the Dorr Co. indicated that lime produced by solids fluidization would be of exceptional quality. Calculation of theoretical heat balances showed that savings in fuel could be expected. Accordingly, a pilot plant of 10 tons per day capacity was erected by the New England Lime Co. at Adams, Mass., to substantiate the process. Operation of the pilot plant, previously described,' showed that excellent lime could be produced with a saving in fuel. The work also indicated the necessity of preparing feed to remove the finer fractions if dust losses were to be held to a tolerable level. A single-stage fluidized solids drier-stripper was developed to accomplish this sizing.' Subsequently a commercial lime reactor was erected at Adams, beginning operation in June 1949, followed by air sizer facilities completed in November 1951. This paper will describe these two applications of solids fluidization. The raw material for preparation of lime by the fluidizing process is a high calcium crystalline lime- stone having the approximate chemical composition shown in Table I. The stone is first prepared by crushing and grinding in conventional equipment to pass a 6-mesh sieve. After crushing, the material is sent to the FluoDry unit for drying and dedusting. Fluidized Drying and Sizing As shown in Fig. 1, the FluoDry unit consists of a -in. cylindrical steel shell, 9-ft ID by 22-ft 6-in. overall height. Attached horizontallv at the bottom is a 6-ft diam combustion chamber, approximately 7 ft 6 in. long. A refractory constriction dome, consisting of first-quality fire brick shapes, partitions the inside into two sections. The lower section is called the windbox and the upper the bed compartment. The vertical wall of the shell is lined with 6-in. first-quality rotary kiln blocks. In the bottom of the windbox a hoppered section is formed with castable refractory to permit the windbox to be readily cleaned via a 6-in. screw conveyor. The combustion chamber is similarly lined with refractory shapes. On the 6-in. diam section, 4 in. of insulating brick, HW-26, are used. The inner combustion chamber is lined with 4-in. Korundal brick to withstand the high flame temperatures encountered. An 8-in. steel feed pipe, entering vertically through the top and fitted with an air-operated cone valve,

Jan 1, 1953

By Herbert K. Kutter

This paper is concerned with the physical phenomena in the fracture process of presplitting and only indirectly with the establishment of the optimum presplitting parameters. Its nature is therefore qualitative, rather than quantitative.

Jan 1, 1968

TO THE. BOARD OF DIRECTORS AND MEMBERS OF THE AMERICAN INSTITUTE OF MINING AND METALLURGICAL ENGINEERS GENTLEMEN Submitted herewith are the report of the Treasurer for the year 1945 and reports for the same year of the following committees: Membership, Admissions, Papers and Publications, Mining and Metallury (Magazine), and Library. In this review of the year by the Secretary reference frequently will be made to the "Paul" Committee and to the "hotter" Committee. The first is the special committee on Divisional Relationships and the second the special Committee on Ways and Means. These two important committees, appointed by President Harvey S. Mudd under authorization of the Board of Directors on March 21, 1945, were composed as follows:

Jan 1, 1946

By H. O. Hofman

WITH the exception of lead sulphate, all common metallic sulphates are completely decomposed upon heating into metallic oxide, sulphur trioxide, sulphur dioxide and oxygen. Some give up their trioxide readily at a low temperature, others require considerable heat and much time to be completely freed from sulphur. Kerl in 1881 arranged the principal metallic sulphates as they are decomposed by a rising temperature in the following order: silver, iron, copper, zinc, nickel, cobalt, manganese and lead, lead sulphate being decomposed only slightly at a white heat. The researches of Bradford, published in 1903, show, however, that ferrous sulphate is decom¬posed at 590° C., cupric sulphate at G53° C. and argentic sulphate at 1,095° C. By the present investigation it will be seen that zinc sulphate is decomposed at 739° C. As far then as our present knowledge goes, the order in which the decomposition of the leading metallic sulphates takes place is the one given in Table I.

Jan 1, 1905

Roof Bolts An expansion shell and plug Westinghouse roof bolting assembly made for use with threaded steel rods and large flat washers or steel channel employs a plug larger in diameter than those for trolley wire service. The notched plug helps prevent shell and plug from turning. The unit is shipped complete. Circle No. 1 Fan The Jeffrey Mfg. Co. Aerodyne Midget fan is a self contained blower or exhauster for auxiliary ventilation through tubing. Operating rating with 5 hp motor is 6.5 in. maximum static pressure, and 6200 cfm free delivery volume. Weight is 340 to 475 lb and it may be furnished in open or permissible form. Circle No. 2 Heavy-Density Initial installation in the Mesabi Range country of the Wilmot-Daniels heavy-density concentrating system was a 175 ton per hour plant at the [ ] Skubic Bros. Virginia, Minn., operation. This Wilmot Engineering Co. unit has a separatory vessel providing unidirectional medium flow and as the only moving part uses a standard drag-line conveyor for lifting sink out of the bath. Circle No. 3 Portable pH Meter A low priced battery-operated portable pH meter of utmost simplicity announced by the Photovolt Corp. uses only 3 ordinary radio batteries which give over 2000 hours of service. Accuracy of 0.03 pH is claimed by the manufacturer for the model 125, and AC power line supply is available. Circle No. 4

Jan 1, 1952

By H. H. Otto

COMPARED with 1939, the year 1940 has seen no material change in the production of anthracite. Many factors seem to indicate a stabilized anthracite production of approximately 50 million tons per year. The present war has stimulated demand in the Cana¬dian and New England markets, which were formerly furnished with a portion of their needs from Great Britain and other European countries. Neither has there been any material change in the "bootleg coal" situation. This problem is more serious in the Southern anthracite field than in the Hazleton, Wilkes-Barre, and Scranton areas. One reason for this is the nearness of the Southern field to the large anthracite markets in Philadelphia, Washington, Baltimore, and Harrisburg. During the past year no new large

Jan 1, 1941

By K. Mukherjee

A quasi-thermodynamic calculation is presented for estirt~ating vacancy Parameters in fcc metals. For fcc metals the equilibrium vacancy concentration at the melting point can be approximated by a constant mole fraction. The Gibbs free energy of formation of the vacancies can then be expressed as a simple function of the absolute melting temperature alone. From this description the formation energy Ef, the vibrational entropy Sv, and the formation volume of a vacancy can be calculated in terms of known thermodynamic parameters. The calculated values are in good agree-rnent with available experimental results. IT appears that many of the physical parameters associated with lattice defects can be empirically related to thermodynamic melting parameters.'-7 Besides the implicit correlations between melting phenomenon and point defects, the melting temperature itself at atmospheric pressure can be used as a reference temperature for the purpose of comparison of vacancy concentrations in a given crystal class. The concentration at the melting point then corresponds to the maximum vacancy super saturation in the crystalline state at a fixed pressure. For pure fcc metals such as Au, Cu, Al, Ag, Pb, and Pt the mole fraction of vacancies at the melting point8 is of the order of 10*"3 to 10"1. The equation expressing the equilibrium vacancy concentration at the melting point contains three parameters: the formation energy, the vibrational entropy, and the absolute melting temperature, see Eq. [2]. Since these three parameters cover a wide range of values8 in the above-mentioned metals, it can be assumed that in other fcc metals, for which no reliable data are available, the mole fraction of vacancies at the melting point most likely lies in the range 10~3 to lO"4. This is then the basis of the calculations described in this article. Within this range the mixing entropy can be linearized and the vibrational entropy, the formation energy, and the vacancy formation volume can be calculated in terms of known thermodynamic constants. 1} LINEARIZATION OF MIXING ENTROPY The Helmholtz free energy of a crystal containing n vacancies at the melting point can be writteng as where Ef, T,, k, and S, are the formation energy of a vacancy, the absolute melting temperature, Boltz-mann's constant, and the vacancy formation entropy, respectively. After applying Stirling's approximation in Eq. [l] and minimizing with respect to n where (n/N), is the equilibrium vacancy concentration in mole fraction at the melting temperature at 1 atm pressure. If instead of setting (6~/6n) = 0 immediately after Stirling's approximation in Eq. [I], the configurational partition function is simplified, then some useful and significant results can be obtained by utilizing the experimental inforrnation After applying Stirling's approximation and rearranging is plotted as a function of (n/N) in Fig. 1. The points, not all of which are shown, are fitted by a straight line substituting from Eq. [5] into Eq. [I] and minimizing with respect to n combining Eqs. [6] and [2] It must be emphasized that Eq. [7] is only a crude approximation based on an oversimplified model of

Jan 1, 1967

By O. C. Wheeler

In order that the series of reports on oil and gas in Colombia may be complete, the report for the year 1941, which was not available for Volume 160 of the TRANSACTIONS, is given here. The report for 1945 begins on page 4o6.

Jan 1, 1946

Jan 2, 1951