Search Documents

Remarks Of Mr. Robert W. Hunt, General Superintendent, Albany And Rensselaer Iron And Steel Company., Troy N. Y. - In discussing Dr. Dudley's two most interesting papers, I feel a natural hesitancy in disagreeing with conclusions formed after such careful and conscientious work. But I think he has made his deductions from too meagre premises. The analyses of but twenty-five samples are entirely too few to justify the establishment of so important a formula. When we consider that he indirectly proposes to regulate an interest amounting, even at the present low prices, to over $20,000,000 per annum, we may well hesitate before accepting a formula based upon the chemical and physical analyses of but twenty-five steel rails. Dr. Dudley touches the keynote in referring to the proposed labors of the Government Test Commission. They based their hopes of attaining success upon the chemical and physical analyses of a very large number of samples, and in the only branch of investigation which the short-sighted policy of Congress has allowed them to complete, i.e., chain cables, we find that a dozen, twenty-five or one hundred tests gave no satisfactory results. It was only after many hundreds that they were enabled to draw conclusions. There are so many circumstances bearing upon the life of a rail, that the task of extracting a correct result seems herculean. I presume I am right in stating that in our Northern latitudes early winter and spring months witness the breaking of the greatest number of rails, thus seeming to prove that an unstable road-bed has much to answer for. Then, again, broken and flattened wheels must be taken into account, but I am convinced that more rails have been broken by the treatment which they received before leaving the rolling-mill * The remarks of the participants in this debate have been written out by the speakers, and are here given without any attempt to retain the order of the dis¬cussion. While the report does not, therefore, preserve the vigor and spontaneity of the debate, it is believed that it gains in value by giving the matured views of the speakers. The continuation of this discussion at the Pittsburgh Meeting, May, 1879 (beginning with remarks of Mr. Cloud on page 401), is appended for convenience of reference.-T. M. D., Sec'y

Jan 1, 1879

LIST OF THE MEETINGS OF THE INSTITUTE AND THEIR LOCALITIES FROM ITS ORGANIZATION TO OCTOBER, 1904 Transactions Number Place Date Vol Page 1 Wilkes-Barre, Pa May, ?71 1 3 2 Bethlehem, Pa August, ?71 1 10 3 Troy, N Y November, ?71 1 13 4 Philadelphia, Pa February, ?72 1 17 5 New York, N Y May, ?72 1 20 6 Pittsburg, Pa October, ?72 1 25 7 Boston, Mass February, ?73 1 28 8 Philadelphia, Pa May, ?73 2 3 9 Easton, Pa October, ?73 2 7 10 New York, N Y February, ?74 211 11 St Louis, Mo May, ?74 3 3 12 Hazleton, Pa October, ?74 3 8 13 New Haven, Conn February, ?75 3 15 14 Dover, N J May, ?75 4 3 15 Cleveland, 0 October, ?75 4 9 16 Washington, D C February, ?76 4 18 17 Philadelphia, Pat June, ?76, 5 3 18 Philadelphia, Pa October, ?76 5 9 19 New York, N Y February, ?77 5 27 20 Wilkes-Barre, Pa May, ?77 6 3 21 Amenia, N Y October, ?77 6 10 22 Philadelphia, Pa. May, ?78 6 18 23 Chattanooga, Tenn May ?78 7 3 24 Lake George, N.Y. Oct. ?78 7 25 Baltimore, Md. Feb. ?79 7 26 Pittsburgh Pa, May ?79 8 28 Montreal, Canada Sept, ?79 8

Jan 1, 1923

LIST OF THE MEETINGS OF THE INSTITUTE AND THEIR LOCALITIES FROM ITS ORGANIZATION TO OCTOBER, 1904 Transactions Number Place Date Vol Page 1 Wilkes-Barre, Pa May, ?71 1 3 2 Bethlehem, Pa August, ?71 1 10 3 Troy, N Y November, ?71 1 13 4 Philadelphia, Pa February, ?72 1 17 5 New York, N Y May, ?72 1 20 6 Pittsburg, Pa October, ?72 1 25 7 Boston, Mass February, ?73 1 28 8 Philadelphia, Pa May, ?73 2 3 9 Easton, Pa October, ?73 2 7 10 New York, N Y February, ?74 211 11 St Louis, Mo May, ?74 3 3 12 Hazleton, Pa October, ?74 3 8 13 New Haven, Conn February, ?75 3 15 14 Dover, N J May, ?75 4 3 15 Cleveland, 0 October, ?75 4 9 16 Washington, D C February, ?76 4 18 17 Philadelphia, Pat June, ?76, 5 3 18 Philadelphia, Pa October, ?76 5 9 19 New York, N Y February, ?77 5 27 20 Wilkes-Barre, Pa May, ?77 6 3 21 Amenia, N Y October, ?77 6 10 22 Philadelphia, Pa. May, ?78 6 18 23 Chattanooga, Tenn May ?78 7 3 24 Lake George, N.Y. Oct. ?78 7 25 Baltimore, Md. Feb. ?79 7 26 Pittsburgh Pa, May ?79 8

Jan 1, 1923

By John R. Freeman

This paper relates entirely to the casting of brass under fluid pressure in steel dies. Die castings of metals and alloys of low melting point have been available for many years but the development of brass die castings has been relatively recent, occurring within the past five years. The successful developnlent of brass die castings has resulted from the availability of alloy steels that would give satisfactory life as dies and the development of suitablc die-casting machines. The melting point of copper is 1084" C. (1983" F.) and of a high brass about 900" C. (1652" F.), as compared to 327.5" C. (621.5" F.) for lead, 419.4' C. (786.7" F.) for zinc and 658.7" C. (1217.7" F.) for aluminum, temperatures that are indicative of the casting temperatures required for the various types of alloys, of which the melting points are somewhat lower than those of the pure metals. Type of Die-casting Machine In the well-known plunger and gooseneck types of die-casting machines used for casting the alloys of relatively lower melting point, much of the working mechanism is immersed in the molten alloy. For alloys having the relatively high melting point of brass, this obviously is impossible. Machines with a separate melting chamber are essential. Two rather distinct types are in extensive use at the present time, the Pack and Polak machines, the former designed by Charles Pack and developed at the American Brass Co., the latter developed by Joseph Polak, of Prague, Czeclioslovakia. The principles of operation of these machines have been described in articles by Pack1,2,3 and by Sieg.4

Jan 1, 1935

By John R. Freeman

This paper relates entirely to the casting of brass under fluid pressure in steel dies. Die castings of metals and alloys of low melting point have been available for many years but the development of brass die castings has been relatively recent, occurring within the past five years. The successful developnlent of brass die castings has resulted from the availability of alloy steels that would give satisfactory life as dies and the development of suitablc die-casting machines. The melting point of copper is 1084" C. (1983" F.) and of a high brass about 900" C. (1652" F.), as compared to 327.5" C. (621.5" F.) for lead, 419.4' C. (786.7" F.) for zinc and 658.7" C. (1217.7" F.) for aluminum, temperatures that are indicative of the casting temperatures required for the various types of alloys, of which the melting points are somewhat lower than those of the pure metals. Type of Die-casting Machine In the well-known plunger and gooseneck types of die-casting machines used for casting the alloys of relatively lower melting point, much of the working mechanism is immersed in the molten alloy. For alloys having the relatively high melting point of brass, this obviously is impossible. Machines with a separate melting chamber are essential. Two rather distinct types are in extensive use at the present time, the Pack and Polak machines, the former designed by Charles Pack and developed at the American Brass Co., the latter developed by Joseph Polak, of Prague, Czeclioslovakia. The principles of operation of these machines have been described in articles by Pack1,2,3 and by Sieg.4

Jan 1, 1935

By M. Felsenthal

Engineers are frequently faced with the problem of having to predict oil recovery from a solution gas drive reservoir in the early life of a field. This is often the time when actual laboratory or field-derived gas-oil permeability (kg/k0) data are not yet available. Although excellent collections of k0/k0 data for various types of rocks may be found in the literature,1,2,3 a need exists for a more detailed correlation of k0/k0 data with core properties such as porosity, permeability, clay content or pore-size distribution. It is the purpose of this article to present this type of correlation for sandstone material. The correlation is based on laboratory tests performed on over 300 core samples from 19 reservoirs in the United States and Canada. EXPERIMENTAL Cores were analyzed by routine procedures, using samples of conventional size (7/8-in. diameter, 7/8-in long) cut parallel to the bedding planes. Air permeability was measured at 1.67 atm mean pressure in a Hassler-type apparatus. Porosity was determined with the aid of a Ruska bulk volume meter and a Boyle's Law rock volume meter, An evaporation method' was used to evaluate irreducible water saturations. Core samples were saturated with 25,000 ppm NaCl brine. The brine was reduced to the irreducible saturation, and the remainder of the pore space was filled with kerosene. This was followed by multiphase flow tests using the so-called "dispersed feed" technique.5 n this technique, gas and oil (kerosene and kerosene-saturated air) were dispersed with the aid of a porous Alun-durn feed head, the face of which contained a waffle-shaped system of Lucite-lined grooves. Oil entered the back side of the feed head and emerged at the raised areas of the front face. Gas was introduced directly into the system of grooves at the front face. The gas-oil mixture then entered the test core which was kept in capillary contact with the feed head. Permeabilities were determined from rate and pressure measurements and saturations from weights. All determinations were performed at equilibrium or steady-state conditions. Pore-size distributions were determined on selected samples by a mercury injection technique.6 GENERAL CORRELATIVE TRENDS When examining data from a given reservoir, it was noted that k0/k0 vs saturation curves became generally less steep as specific air permeability increased, a development that has a favorable effect on oil displacement efficiency by solution gas drive. This trend has also been reported by others in the literature.' An effect of porosity on k0/k0 data was also noted. This effect was not generally discernible in a study of relative permeability data for a given reservoir but became apparent when data for sandstone reservoirs of similar lithology but differing average porosity were compared. For instance, in a comparison of argillaceous and/or calcareous sandstones from 11 reservoirs ranging in average porosities from 14 to 28 per cent, a definite trend was noted, indicating that for a given permeability k0/k0 curves became less favorable (i.e., steeper) as porosity increased. A similar trend was observed for a group of comparatively clean sandstones from five reservoirs ranging in average porosities from 15 to 21 per cent. For a given permeability and porosity, comparatively clean sandstones gave more favorable k0/k0 curves than argillaceous and/or calcareous sandstone or chert reservoirs. The laboratory studies also showed that least favorable k0/k0 curves were exhibited by shaly sandstone, conglomerate, and sandstone containing carbon inclusions. Table 1 lists the various source reservoirs classified by lithology types. To facilitate a correlation of k0/k0 data with core characteristcis, it was found expedient to work with

By Frank E. Woolley, Robert D. Pehlke

Jan 1, 1965

By AIME

DURING the happy and peaceful years between the Treaty of Versailles and the third New Deal, metallurgy became one of the most cosmopolitan of the sciences. Any metallurgist can name some twenty or thirty scientists whose work, in this country, in England, in Germany, or in France, Sweden, Italy, or Japan was as well known in other parts of the metal-producing and metal using world as it was locally, despite the fact that many of these men never left their native land. One of these metallurgical cosmopolites is Augustus Braun Kinzel, former Chairman of the Iron and Steel Division, A.I.M.E., and now a Director of the Institute. Gus Kinzel, however, is not only a cosmopolite by reputation; he is also a cosmopolite in fact. For many years he commuted at least twice a year between New York and the rest of the world; he is, therefore, not only an expert on the art and science of metallurgy but is equally expert in world travel and can expound with authority on the comparative quality and especially on the cuisine of the great prewar steamship lines; and being a true cosmopolite, he knows, as well as he knows the iron-chromium diagram, the best vintage years in the Gironde, Cote d'Or, and Saone-et-Loire departments in France and along the banks of the Moselle and Rhine in Germany.

Jan 1, 1946

By Don K. Smith

The Reclamation Program for the Northern Zone of the Indus Plains in West Pakistan involves the construction of 30,000 irrigation wells to serve 20 million acres with an annual pumpage of nearly 40 million acre-ft. Detailed hydrologic studies indicated that mild steel would be satisfactory for casing; however, within two years after construction, about 10% of the wells began to fail due to encrustation and corrosion of the casing. A search to find a noncor-rosive substitute for the steel casing disclosed that only fiberglass-reinforced plastic pipe satisfied all requirements. The results of initial use of fiberglass have been highly satisfactory and have resulted in a lower over-all well cost. Advances in technology pomise further reduction in prices and improvement in performance. The northern zone of the Indus Basin comprises a vast area of essentially level land in West Pakistan which is irrigated by means of a complex system of canals that distribute more water to more land than any other irrigation system in the world. In spite of the development of this extensive irrigation system, production of food and fiber has not met the requirements of the country. The major reasons that crop production has not reached anticipated levels are the lack of adequate irrigation supplies and effective subsurface drainage. As a result, yields per acre are among the lowest in the world for areas where irrigation is practiced, and many thousands of acres of valuable crop land have been removed from production or seriously affected by salinity and waterlogging. To rectify the problems of irrigation supply and drainage the Government of Pakistan has undertaken a program of Salinity Control and Reclamation which is being administered by the Water and Power Development Authority. The Authority retained Tipton and Kalmbach, Inc., of Denver, Colo., as engineers for the program in the northern zone of the Indus Basin. This program consists of the construction of about 30,000 irrigation wells to provide drainage for waterlogged lands and full irrigation supplies, including leaching requirements, for all cultivated lands. The program will ultimately ensure the productivity of 20 million acres and involve an annual pumpage from groundwater storage of nearly 40 million acre-ft of

Jan 1, 1970

By J. B. Clark

In 1933, R. paris1 published a phase diagram for the entire Mg-Ca-Zn system. He reported the existence of a ternary intermetallic phase, Mg5Zn5Ca2, which formed a quasi-binary with the magnesium solid solution. Since then, no extensive work has been reported on the system. Recently however, indications of the existence of a second ternary in-termetallic phase in equilibrium with the magnesium solid solution led to a reinvestigation of the solid phase equilibria involving the magnesium solid solution. The 335°C (635°F) isothermal section was chosen for study. Metallography and powder X-ray diffraction were selected as the best mutually corroborating methods for determining the solid phase constitution. Seventy-six alloys were prepared from singly sublimed (99.95 pct) magnesium, electrolytic (99.95 pct) zinc and USP calcium. The analyses of some of the alloys are shown in Fig. 1. The alloys were melted in a graphite crucible under a chloride flu and chill cast in a split graphite mold. Dif-fusion couples (see Fig. 2) were prepared by casting molten Mg-20 wt pct Zn alloy around a cylinder of Mg-30 wt pct Ca alloy. The alloy samples and the diffusion couples were sealed under argon in Pyrex vials and annealed in a furnace capable of controlling within 1/2°C of 335°C. At the conclusion of the anneal, the alloy samples were quenched in ice water and the diffusion couples were air cooled. Procedures standard for magnesium alloys were used for metallographic examination. Powder X-ray diffraction patterns were taken on a G. E. camera with a 14.32 cm dim using nickel-filtered copper radiation. The redetermined 335°C (635°) section of the Mg-Ca-Zn phase diagram is shown in Fig. 1. TWO ternary intermetallic phases, designated w and

Jan 1, 1962

Joseph W. RichaRds, South Bethlehem, Pa. (communication to the Secretary*): The hold experiment of Mr. James Gayley in drying the blast used in the Isabella furnace has attracted the attention of the whole metallurgical world, and has given rise to a wide discussion of the reasons for its great success. Mr. Gayley and the capitalists who backed him in his work deserve congratulations on the success of the venture, not only because it succeeded, but because they have been rewarded far beyond the maximum that could be expected from theory or probability. To state the case in its simplest terms, all that could have been predicted was: (1) that the removal of the moisture from the blaet would result in the saving of the heat required for its decomposition, representing from 3 to 5 per cent. of the heat-value of the coke used; hence about that quantity of fuel might be saved; (2) that the furnace would be somewhat more independent of variations in the weather; (3) that the campaign would be a little hotter; and (4) that the speed of the blowing-eugines would be decreased, at least in amount proportionate to the reduction in temperature of the air led to them. I do not think anyone anticipated a much larger output per day. The results actually attained were: (1) the furnace made an increase of 24.86 per cent. in the output of pig-iron per day; (2) it consumed 19.6 per cent. less coke per ton of pig-iron made; (3) the blowing-engines were run 15.8 per cent. slower; and (4) the saving in power made up for the power required to run the refrigerating-plant. In addition, the blast was hotter; the waste-gases cooler, because of their smaller volume; and there was a greater proportion of carbon dioxide to carbon

Jan 1, 1906

NEW MEMBERS The following list comprises the names of those persons who became members during the period Oct. 10, 1916 to Nov. 10, 1916. ANCHOR, HANS C., Supt., Dome Extension Mines Co., Ltd., South Porcupine, Ont., Canada. BABCOCK, EARLE J., Dean, College Of Min. Engrg., State Univ. Of N. Dak., Grand Forks, N. Dak. BIDDIS0N, P. McDONALD, Construction Engr., The Ohio Fuel Supply Co., 52 W. Gay St., Columbus, 0. BOISE, PAUL T., Asst. Mgr., Stimpson Equipment Co., Felt Bldg., Salt Lake City, Utah. BOURNE, RALPH H., Vice-Pres Whiting Foundry Equipment Co., Harvey, Ill. BROWN, EDWARD OTTO FORSTER, Min. Engr., 706-707 Salisbury House, London, E. C., England.

Jan 12, 1916

By E. H. Boswell, E. M. Cushing

The Mississippi embayment east of the Mississippi River is part of a vast geologic and hydrologic province. The abundance of water available is largely responsible for the agricultural history of the area and is perhaps the key factor in the rapidly accelerating trend toward industrialization. The multiple artesian aquifer systems that underlie the region and the alluvial aquifer along the Mississippi River are virtually undeveloped sources of fresh water in that they are yielding only a fraction of the water available. The potential yield of the 12 aquifer systems is estimated to be about 25,000 mgd (million gpd) of which only about 600 mgd is presently being withdrawn. The amount of water in storage in these systems is about 1600 trillion gal. Ground water having a dissolved-solids content of less than 500 ppm is generally available at depths of less than 1000 ft, and water having a dissolved-solids content of less than 1000 ppm is available in some places to depths of more than 3000 ft. Iron is the most common troublesome chemical constituent in the ground water. Water in varying amounts is also available from streams within the region. The amount of water which originates within the region and which leaves it as streamflow during a year averages about 50 million acre-ft (about 45,000 mgd). An additional 375 million acre-ft (about 340,000 mgd), which originated outside the region, leaves the region as streamflow during an average year. Some streams have considerable flow during periods of no precipitation and the water during these periods generally has a low dissolved-solids content. Large quantities of water from streams and waterbearing sands (aquifers) are available in the Mississippi embayment east of the Mississippi River. Most of the region is underlain by aquifer systems that will yield large quantities of water to wells, making ground water the most readily available source of fresh water. About 90% of the water used in the region is obtained from wells. Streams have been used primarily to dispose of, and dilute, wastes that have been dumped into them. The Mississippi, Ohio and Tennessee rivers, and the lower parts of the Tombigee and Yazoo rivers also serve as a means of transportation. This nominally water-rich region receives from 48 to 56 in. of precipitation in average years and is crossed by several large rivers. The largest, the Mississippi River, is the western boundary of the region discussed in this paper. The economy of the region is basically agricultural, but industry has become increasingly important since World War 11. The diversification and mechanization of agriculture have resulted in a surplus of manpower, most of which is being absorbed by the expansion of industry. Further industrial expansion probably will occur because of the available manpower, natural resources and economical transportation. Increasing demands on available water supplies will be made and the future economic growth of the region will be largely dependent upon wise utilization and management of the water resources.

Jan 1, 1969

By F. T. Davis

Many contributors have added to the fund of knowledge in the basic sciences related to mineral dressing during the past year. During 1964, the French edition of the Proceedings of the VIth International Mineral Processing Congress together with discussions was printed. Also, complete Preprints of papers delivered at the VIIth IMPC were published in September1. Over a third of the papers presented at VIIth IMPC dealt with fundamentals. COMMINUTION It has been postulated by Ponceleta that flaws need not exist before a stress is applied but rather the flaws are created at the tip of a propagating crack at a stress well below the theoretical breaking stress.

Jan 2, 1965

By S. F. Shaw

Tars paper is a review of the principal details of cyanide practice in several of the modern plants in America, mainly during the year 1908. Two of the mills, the Goldfield Consolidated and the Vets, Colorado, are not yet prepared to give data, the former having started about Jan. 1, 1909, and the latter not yet being completed. These two mills embody most of the latest methods and are therefore described as far as possible. I. CRUSHING. The principal methods of crushing ores for treatment by the cyanide process are with gyratory and jaw-crushers, stamps, Bryan and Huntington mills, and tube-mills. The first stage is usually done by gyratory or jaw-crushers, in a few cases sup-\

Jul 1, 1909

By Rodney L. Stone, David S. Cahn

As part of an over-all laboratory and plant test program to determine mixing ad other techniques for a more economic use of bentonite as an iron ore pellet binder, a settling test for measuring the bentonite content within a pellet or a batch of pellets has been developed. Through this test, it has been shown that dry fracture load is directly proportional to bentonite content in batches of pellets, but inversely propor tional to bentonite content in individual pellets of the same batch. This apparent paradox is explained by a negative correlation between a pellet's size and its bentonite content and the fact that large pellets can withstand a higher fracture load than small pellets. In past attempts to characterize green and dry iron ore pellets, the authors found large variations in the results of strength tests on closely sized pellets from the same batch.' Reasons advanced for such variations in the quality of pellets in which the binder is bentonite were the presence of internal flaws and the nonuniform distribution of the binder. Even when resulting pellet strength is good, there is still the question of whether the same strength could have been attained through a more effective use of a smaller amount of bentonite. The authors' own and other studies 2-3 have pointed out the strong dependence of pellet strength on the degree of "mixedness" of the iron ore concentrate and the bentonite binder. However, before such a relationship could serve as a guide for the development of better mixing techniques and the associated economy of

Jan 1, 1969

By Samuel M. Shallcross

The principal function of the Bell limestone mine, of the American Lime & Stone Co., at Bellefonte, Pa., is to supply raw material to the company's modern rotary kiln plant at Bellefonte. Because mining costs are naturally higher than many open quarries with more favorably lying strata, it cannot compete, except to a limited extent, in the markets for road material and fluxing stone. In the broad sense, mining does have an advantage over the average open quarry when the end products are designed for and controlled by process and final inspection for the exacting demands of the industrial and chemical markets. Approximately 80 per cent of the output of the Bell mine is sold in the industrial and chemical markets. And as higher standards are set each year for construction and agricultural work, the remainder of the mine output goes to these two classes. Mining produces more fines than open quarries, and these fines are difficult to market; on the other hand, owing to absence of contaminating clay and impure rock, a greater percentage of the output of a mine is marketable. Because of the great production of fines, rotary kilns for lime burning are necessary when the stone must be mined. In 1921 the American Lime & Stone Co. operated 19 quarries and 72 lime shaft kilns spread over an area of 40 miles between Bellefonte and Altoona, Pa. At that time the lime-production capacity of the 72 kilns amounted to approximately 700 tons per day. After 15 years the company operates three rotary kilns and six shaft kilns, with a combined output of approximately 500 tons of lime per day, concentrated in its single Bellefonte plant (Fig. 1). Its only stone-producing plants are now the limestone mine at Bellefonte and a construction-stone open quarry at Union Furnace, near Tyrone, Pennsylvania. Since the middle of 1922, the management of the American Lime R. Stone Co. has been under the direction and ownership of the Warner Company, of Philadelphia. To the Warner Company's experience, gained through successful operation of lime plants in eastern Pennsylvania for many years, and the successful solution of material-handling problems

Jan 1, 1937

Jan 1, 1959

By Pervez Patel, Martin G. Frohberg, Demetrios Papamantellos

Model experiments were carried out on the mass transfer of iodine between n-hexane and a 4 2 X 10-3 M aqueous sodium hydroxide solution. The influence of mechanical stirring by means of small gas bubbles (ca. 0.01 ml in volume) on mass transfer was examined in independent experiments. The results were described with the help of the penetration theory and in the case of bubble stirring with the help of a mathematical model based on this theory. S LAG-METAL reactions, especially those in steel-making processes, often occur under conditions where gas is evolved in the form of bubbles that break through the slag-metal interface. It is known that stirring by means of bubbles increases the mass transfer coefficient, but there has been very little quantitative work done in this field. Because of the difficulties that attach to experimental work at high temperatures this study was confined to model experiments at room temperature. EXPERIMENTAL APPARATUS The transport of iodine from an n-hexane layer into a weak sodium hydroxide solution was studied a) with stirring by means of bubbles and b) with mechanical stirring. The apparatus for the experiments with bubbles consisted of the cell, two Dreschel bottles filled with hexane in order to saturate the nitrogen flow, one flow meter, and a nitrogen gas cylinder fitted with a fine-regulating valve. Fig. 1 shows the cell consisting of a glass cylinder 33 cm in height with an overall diameter of 7.5 cm embedded in a copper flange. The flange is connected to a Plexiglas plate and to the gas inlet. The Plexiglas plate has holes of 0.2 mm diam bored into it which are spaced 1 cm from each other. For the experiments with mechanical stirring the bottom of the cell was sealed off by a Plexiglas plate. The upper layer was stirred by means of a glass stir-rer and the bottom layer with the help of a magnetic stirrer in a counter rotatory direction. Both stirrer speeds could be varied continuously. EXPERIMENTAL PROCEDURE Iodine dissolves in n-hexane producing a stable violet color thus enabling the iodine concentration in

Jan 1, 1970

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