Search Documents

By H. M. Chance

The great outspread of the coal measures over portions of thirtyone of the sixty-seven counties of Pennsylvania, and the large number of workable seamy comprising the coal series,—together with some workable seams lately shown to belong to the (so-called) barren measures,—-create the impression that these fields contain a practically inexhaustible supply of fucl, and those who have estimated or attempted to estimate their available tonnage have generally promulgated this view. But the actual total contents of this coal-field is of no importance to us at present; calculations including all seams, whether thick enough to mine or not, whether pure enough to furnish a marketable fuel or not, whether accessible at reasonable depth or not, are of no practical value. As coal producers, we are interested not in the total contents, but in the total amount of easily accessible coal of good quality contained in beds thick enough for remunerative mining. The estimates contained in this payer refer exclusively to workable and accessible coal of commercial value,—we may call it available" coal. I am not aware that any one has as yet attempted to estimate in

Jan 1, 1882

By W. Lawrence Austin

Jan 1, 1884

The Western World's gold reserves now exceed 23,000 mt (750 million oz), 65% of which exist in South Africa. Although several major mines are reducing production or closing because of depletion of reserves, new mines or expansions of existing mines are coming on-stream which will maintain an annual production of 684 mt (22 million oz) of gold well into the 1990s. These new operations by the South African mining industry represent the largest expansion since the opening of the Witwatersrand gold fields in 1886. Included in three new mines being opened is that of Anglo American Corporation's Elandsrand plant, their fir& new gold venture in South Africa in seventeen years. Current average grade of South African mines is 8.2 g Au per mt (0.24 oz per st); and while the cost of the Elandsrand 135,000 mt (149,000 st) operation, including mine development, was about $314 million, it is estimated that the cost of a comparable operation started today and completed in the mid-1980s would be of the order of $480 million. New mines to exploit low-grade ore bodies are, therefore, likely to be few in number, and further expansion will undoubtedly be in the form of extensions to existkg operations where cash flow can be used to finance development. The authors' first monograph, "Gold and Silver Cyanidation Plant Practice," devoted a section to South African cyanide plant operation; and it is believed that this new volume would not be complete without a description of Elandsrand, South Africa's newest gold plant. The Elandsrand mine is adjacent to Anglo American's Western Deep Levels on the Far West Rand. The decision to go ahead with the development was taken in mid-1974 from the results of exploration drilling carried out over a period of .lo years. Results of 17 bore holes and 68 intersections of the Ventersdorp Contact Reef had indicated a gold-.bearing reef less than one meter thick at a depth of 1,800 to 3,000 meters (5,900 to 9,840 ft). Preliminary studies indicated a mine of 900 km (560 miles) of underground workings would yield 725,000 kg (23. 3 million oz) of gold from 60 million mt (66 million st) of ore to be milled over a period of 34 years. Eventually, when the mine is in full production, the total hoisting capacity will be 300,000 mt per month (331,000 st) for a milling capacity of 225,000 mt per month (248,000 st). The Elandsrand surface facilities have been built on a low range of 0 hills to take maximum advantage of the 10 slope in transporting ore

Jan 1, 1981

Flexibility is the keynote in designing modern exploration drills that and mobility. Add to the flexibility of individual drills the wide range of models, and the man looking for a drill has ample choice today. Weight? Choose from models as light as 50 lb or as heavy as 10,000 lb. Hole capacity? From less than 1 in. for smallest core drills to 20 in. or more for auger types. Transportation? The lightest go by packsack (in fact, that is one trade name) ; others are designed to go by Jeep, truck, on skids or are built on light trailers. Power? Select air power, gasoline or diesel engine, electric motor, or use a power take-off from the vehicle on which the drill is mounted. Drill bits offer almost as much variety as the drilling machines themselves. Many drills are suitable for a variety of uses, and often adapt to several types of bits with ease. Some of the types available are: diamond core, diamond reaming, rotary, auger, shot, and special soil sampling tools.

Oct 1, 1955

By Albert E. Wiggin

PagE I. Early History of Boston & Montana Mill at Great Falls (1891 to 1905). 210 a. Original Mill Built in 1891.........210 b. Coarser Concentration Tried...211 c. Screen Sizing of Fine Jig Feed Introduced..211 d. Installation of Finer Grinding.......211 e. Steam Stamp Tried in Place of Blake Crushers..... 211 j. Mill Increased from Three to Six Sections........ 213 g. Tonnage Increased from 300 to 450 Tons per Section... 212 h. Round Tables Replaced by Wilfley Tables....212 I1. Hancock Jig Replaces Evans Jig...212 a. Description of Hancock Jig...213 - b. Tests Made on- Hancock Jig..213 1. Treating Natural Feed..215 2. Treating Sized Feed..215 3. Treating Classified Feed .215 c. Tests Made on Evans Jig...216 III. Richards Pulsator Classifier System...218 a. Experimental Work.....218 b. Installation of System in Section No. 4,....... 220 IV. Woodbury Classifier and Jig System.............222 V. The Great Falls System................ 222 a. As Installed at Anaconda............ 224 1. Coarse Crushing and Jigging Division...... 225 2. Hancock Jig Division........... 226 3. Fine Middling Division.......... 229 4. Table Division............. 230 5. Slime Division.........230 b. Special Features of Great ails Flow sheet....... 231 1. Development of Hancock Jig Flow Sheet..... 231 2. Development of Finishing Table Flow Sheet.... 232 3. Treatment of Coarse Middling Table Products .. 232 4. Results of Test Made on 500-Ton Section at Great Falls Mill...........234 VI. Comparison of Great Falls and Evans System at Anaconda.... 236

Jan 1, 1914

By J. E. Strongman

This paper describes a system dynamics model of the international copper system. The development of the model is described regarding the questions it was designed to address, model boundary, major sectors and actors, the availability of data, the copper life cycle, and major supply and demand dynamics. A base forecast is presented describing future supply, demand, capacity, prices, trade flows, scrap flows and capital expenditures from 1976-1990 for the major producing and consuming market economy blocs.

Jan 1, 1977

By Howard I. Smith

The mineral trona was discovered on Government land in 1938, about 18 miles west of the town of Green River, Wyo., in the core of the John Hay, Jr., well, a test well drilled for oil by the Mountain Fuel Supply Co. in sec. 2, T. 18 N., R. IIO W., sixth principal meridian. Although no oil or gas was reported, the drilling led to a discovery of great potential economic importance and exceptional scientific interest. Trona is a relatively rare mineral found at various places in playa deposits but not previously found at any great depth. It is composed of hydrous sodium carbonate and sodium bicarbonate (Na2CO3 NaHCo3.2H2O). Pure trona con-tains the equivalent of 70.35 per cent of sodium carbonate. Total sodium computed to carbonate times 1.42 equals the percentage of trona in the absence of other sodium carbonate minerals in the sample. Analyses Two short pieces of core sent to the author a few days after the completion of the Hay well were analyzed by R. C. Wells† and found to be exceptionally Pure trona. A brief article on this discovery has already been published.1 Arrangements were then made through W. T. Nighten-gale‡ for the author to inspect and sample the core. The company log of the well included notations of sodium salt crystals from a depth of 1190 to 1820 ft. Not being able to identify all the minerals present, the author selected several specimens of the core for petrographic examinations and sampled the sections of trona for analysis. J. J. Fahey, of the Geological Survey, examined the specimens and reported most of the crystals to be a new anhydrous sodium carbonate and calcium carbonate mineral (Na2CO 3.2 CaCO3), which he named shortite,² after Maxwell N. Short." He analyzed the samples of trona, with the results shown in Table I. In addition to the 10 ft. 1 in. of trona in the first section, it is reasonable to assume that the 9 ft. 8 in. for which no core was available for sampling is either i mostly trona or some other soluble salt, but it should not be included in calculating | reserves. In the part of the core between i 1590 ft. 3 in. and 1600 ft. 4 in. the material insoluble in cold water, amounting to about 5 per cent, was estimated petrographically I to contain 70 per cent clay, 25 per cent shortite, and 5 per cent pyrite. Accompanying Minerals Fahey later secured about 600 ft, of the core for a detailed examination and study

Jan 1, 1942

New York Meets first Wednesday after first Tuesday of each month. DAVID H. BROWNE, Chairman. PERCY E. BARBOUR, Vice-Chairman. A. D. BEERS, Secretary, 55 Wall St., New York, N. Y. C. A. BOHN, Treasurer. Boston Meets first Monday of each winter month. W. E. C. EUSTIS, Chairman. R. L. AGASSIZ, Vice-Chairman. E. E. BUGBEE, Secretary-Treasurer, Mass. Inst. of Technology, Boston, Mass. ALBERT SAUVEUR, H. L. SMYTH. Columbia Holds four sessions during year. Annual meeting in September or October. STANLY A. EASTON, Chairman. FREDERIC KEFFER. Vice-Chairman. LYNDON K. ARMSTRONG, Secretary-Treasurer, P. O. Drawer 2154, Spokane, Wash. D. C. LIVINGSTON. FRANK A. ROSS.

Jan 10, 1916

By Richard H. Willey

Efficient handling of large tonnages in open-pit mining demands, primarily, an abundance of well fragmented rock. To accomplish this, a drilling and blasting department composed of a well-knit, versatile group of workers and supervisors must be established. Some costs will remain relatively on the same level over a period of years, while others can be greatly lowered as will be shown. 'The Utah Copper Division, Kennecott Copper Corp., Bingham Canyon, Utah, has been ever alert for improvements in operating methods and equipment to gain increased efficiency and lower costs. Bingham Canyon MIne The greatest dimension of the mine is 8000 ft northeast-southwest with a width of 5000 ft southeast-northwest. From the lowest level, at an elevation of 6040 ft above sea-level, the mountain rises in 27 benches on the west side to W level (elevation 7800 ft) and 21 benches on the east side to Q level (elevation 7460 ft). At the inception of open-pit mining in 1906, the overcapping of leached porphyry had to be removed to reach a commercial grade of sulphide ore. The overcapping or waste now remaining is quartzite with intercalated limestone beds. The limestones are usually soft in nature except in the south-middle portion of the mine where they have been meta-morphized along the contact zone. This area usually gives drilling and blasting operations a great deal of trouble. Here occurs the greatest amount of secondary blasting, as the well-established fracture planes cause the altered beds to break into large boulders. Several massive quartzite "ribs" occur in the overburden, and as a result, the uniform breakage is difficult to obtain. The major quartzite areas have been subjected to complex folding, fracturing and faulting because of the intrusion of the underlying stock. The monzonite porphyry, which carries the commercial values, presents no serious drilling problem because of its softness and extensive minute fracturing throughout the mass. A series of major slips or faults pass through the ore body which, although of considerable advantage to the drilling and blasting department, sometimes works to the disadvantage of the track department. Drilling an11 blasting of the porphyry apparently becomes easier as depth is attained. but highly siliceous streaks throughout the pit still present difficulties. At no place is the rock of such character as to allow excavation without preparations. On certain higher elevations or levels, old fill material can be dug by the shovels, but only at some risk to equipment because of bank slippage. Past Methods At the outset of shovel operations in 1906, drilling was done with the Ingersoll-Rand F-24 piston drill mounted on an un-

Jan 1, 1949

By John E. Willson, Ben L. Seegmiller

A portable electronic instrument was designed and constructed to detect unknown stress magnitudes in rocks. The principle used to detect stress is based on the propagation velocity method. This method allows the stress in a rock subjected to a load of unknown magnitude to be determined, provided that the wave velocity-stress relationship for similar rock is known. This is accomplished by measuring the travel time of longitudinal mechanical waves passing between two points a set distance apart in a rock. The velocity of the wave is calculated and the stress determined from the wave velocity-stress relationship. If the sending and receiving transducer spacing is constant, a time vs. stress relationship rather than the velocity-stress relationship may be used. The method is nondestructive and tests can be made without drilling or otherwise disturbing the rocks. The first studies undertaken in the United States to determine stress in rocks using propagation velocity techniques were reported by Obert1,2 in 1939 and 1940. The Soviet Union first reported using propagation methods to study rock pressures in 1951.8 Success of the method led to the development of a pulse-type ultrasonic seismoscope4 in 1953. Using this instrument, Ivanov and Betaneli5,6 in 1963 succeeded in devising and testing under field conditions a method of investigating coal pillar stresses. In 1967 Osipova7 reported results of similar studies in the Nakhichevan salt mines. In France, Tincelin8 has used the propagation velocity method to study the stress distribution in iron ore pillars. Uhlmann9 has investigated stresses in salt and potash pillars in Germany, using velocity techniques. Determination of uniaxial stress by propagation velocity methods is limited to rocks which have readily detectable wave velocity-stress variations. The present stress detection instrument is restricted in application to rocks which have a velocity change under stress of at least 300 fps. Examples of rocks which meet this requirement are sandstones, coal, and possibly some limestones. Testing of this instrument was limited to a laboratory study and the results may or may not be indicative of what would be found in a field test. A program of field experiments to study the feasibility of using this instrument to determine mine pillar and tunnel stresses is in progress. Instrument Design The instrument has two main components: A probe and a control-display unit. The probe is a hand-held device to which two identical rodlike transducers are rigidly mounted. Coaxial cable connects the probe to the control-display unit which is mounted in an enclosed carrying case measuring 7 % x 9 x 13 in. The instrument is designed so it may be carried and operated by one man. Weight of the probe and enclosed control-display unit is approximately 20.1b. The probe consists of two transducers identical in construction. One transducer is used to convert electronic pulses to mechanical waves and transmit these waves into a rock. The other detects the transmitted waves in the rock and converts them back into electronic signals. The basic element in both transducers is a piezoelectric crystal. The crystal is a disk made of lead titanate zirconate and has a natural resonant frequency of 400 kHz ±1% in the thickness mode. A schematic of one of the two identical transducing elements is shown in [Fig. 1.] A spacing of 6 in. between sending and receiving transducers has been found to be most satisfactory. The control-display unit consists of a pulse generator and a 1-in. oscilloscope. Various electronic devices are used for the power supply, amplification, and calibration. The amplitude of the square wave from the pulse generator can be continuously varied between 0 and +20 vdc. Pulse width can be set at 1, 2, 3, or 4 µsec. The repetition rate of the pulse can have the following values: 50, 75, 100, 150, 200, 250, 300, 400, 500, 750, and 1000 Hz. The oscilloscope delay system allows the travel time of the longitudinal wave passing through a rock to be measured to an accuracy ±0.1 µsec in the range from 0 to 995 µsec. Fig. 2 is a schematic of the various electronic sections in the control-display unit. Laboratory Testing The first step in using the instrument is to develop a velocity-stress or a time-stress curve for the par-

Jan 1, 1972

By Michael J. Bailey, Peter M. Douglass

INTRODUCTION Spoil pile slope failures can have costly consequences. In- stability in the form of a single major event or as a recurring problem can 'mean lost production, lost resources and damaged mining equipment. In extreme but not uncomnon cases, a major spoils slide can force the closure and abandonment of a pit. Slope stability is affected by mine operating practices as we1 l as geologic conditions and material parameters. Mine operators can enhance spoil pile stability through constructive changes in their operations. Attention to the causes of in- stability can lead to development of operating practices tailored to site specific problems. Action aimed at limiting future instability is frequently more cost effective than continually "coping" with unstable spoils. The effect of mine operations on material properties is often overlooked because the "data" are not easily quantified nor input directly into stability analysis equations. We have found, however, that miners' experience with their own operation, as well as data pooled from similar operations, yields relation- ships which can be utilized to solve stability problems. The repetitive nature of area type surface coal mines with successive spoil pile rows further enables the development of useful site specific relationships. Stability problems can be mitigated by applying these relationships.

Jan 1, 1983

NEW MEMBERS The following list comprises the names of those persons who became members during the period of June 10, 1918, to July 10, 1918. ALLPORT, JAMES H., Cons. Engr Barnesboro, Pa. ANDERSON, G. E., Engr., Exploration Dept., American Smelt. & Refin. Co.,Tucson, Ariz. BAKER, HARRY A., Capt., Co. M, 53d Pioneer Infantry, Camp Wadsworth, Spartanburg, S. C. BEALL, ROBERT STEPHENS, Supt., Empire Zinc Co. (of Colorado), Canon City, Colo. BLAYLOCK, SELWYN GWILLYM, Mina & Met. Engr., Asst. Gen'l Mgr., Cons. Min. & Smelt. Co. of Canada, Ltd., Trail, B. C., Canada. BOTTERILL, THOMAS CLARK, Min. Engr., Belmont Surf Inlet Mines, Ltd., Surf Inlet, B. C., Canada. BOWMAN, MAURICE Asst. Supt., New Idria Quicksilver Min. Co., Idria, San Benito Co., Cal. BROOKS, EARL W Chief En r. Inland Collieries Co. Harmarville Pa. BROWN, DEWITT W Chief Chem., Prime Western Spelter Co., Iola, Kansas BUISSON, ARTHUR Min. Engr., Dept. of Mines, Sussex St., Ottawa, Canada. BUNYAN, F. W Chem., Southern Pacific Railway Co., Sacramento, Cal. BURNETT, ARCHIBALD Supt., Swansea Lease Inc., Swansea, Ariz. BURTON, GEORGE E., Resident Geol., Empire Gas & Fuel Co., Varsity Shop Bldg., Norman, Okla.

Jan 8, 1918

By Robert E. Delavault, Harry V. Warren

IN the worldwide search of buried orebodies and for entirely new areas of mineralization, geo-chemistry is taking on an increasingly important role. Indeed, geochemistry itself is splitting into various specialties-hydrogeochemistry, pedogeo-chemistry, and biogeochemistry. This article primarily relates to developments in these fields in British Columbia, but many of the remarks are applicable to the whole continent.

Jan 10, 1953

Since the comprehensive review of the Persian fields presented by Sir John Cadman last year, operations have proceeded normally. No developments of especial importance fall to be recorded and it remains only to bring up to date the full information given at the beginning of 1933. Controlled production from the Masjid-i-Sulaiman and Haft Kel fields has been maintained at slightly higher rates than during 1932. The figures for the past five years are as follows: These represent crude oil and products piped to the coast but exclude products reinjected into the reservoir, a process that has been in continuous operation at Masjid-i-Sulaiman during the period under review. The systematic delimitation of the Haft Kel field has been continued during the past year and results have been sufficiently encouraging to justify the inception of a wider scheme for distribution of production. Drilling has been resumed recently in the Persian sector of the Naft Khaneh field, and preliminary survey work is in progress for the selection of a site for a refinery at Kermanshah arid the construction of a connecting pipe line. Investigations in connection with the scientific control of reservoir were dealt with in considerable detail in last year's review. This work has been steadily pursued during 1933 and certain of the investigations have been the subject of papers presented to the World Petroleum Congress held in London in July of last year.

Jan 1, 1934

By Ralph Sweetser

THE present state of iron blast-furnace practice is metallurgical rather than mechanical; the tend-ency is toward intensity rather than toward ex-tension. The engineers have built blast furnaces big enough and strong enough, and have furnished accessory equipment ample and accurate enough for the present state of the art, but the metallurgical side has been too much neglected; the metallurgist, rather than the engi-neer, is now the man on whom the present and future progress in iron blast-furnace practice depends. The mining engineer has produced great tonnages of iron ores, and has kept ahead of the demands for quantity; now the metallurgist is improving the chemical and physical qualities of this product by ore-dressing and other forms of beneficiation. For a generation or more, the principles of mechanics have had most influence in the advancement of iron blast-furnace practice; atten-tion now is given more to the principles of metallurgy, chemistry, and ore-dressing. This metallurgical progress is taking place inside and outside the blast furnace. The two great determining factors of the inside operation are the slag, and the rate of combustibility of the coke. Outside the fur-nace, the progress is, and will be, along the lines of more careful mixing of ores and iron-bearing materials, in the sizing and washing of limestone, and in the char-acter and structure of byproduct coke.

Jan 3, 1922

By Louis G. Bailey

This paper .reviews some of the key developments which have been made in the synthesis of the III-V compound semiconductors and the associated progress in obtaining high-quality material for device development. The history of the investigation of the semi-conducting properties of these materials has indicated the need for synthesis techniques capable of producing rnaterial of high chemical purity and physical perfection. The progress in the area is described, and the present status of quality of several compounds is discussed. In addition, recent studies of localized epitaxial deposition of GaAs into semi-insulating GaAs substvates for the development of arrays of devices ave reviewed. In conclusion, some important areas for future research and developrnent are discussed. INTEREST in III-V compounds as semiconductors dates back to the period 1950 to 1952, when Goryunova, Ioffe, and, in particular, Welker determined that 111-V compounds were structural analogs of the group IV elements carbon, silicon, germanium, and tin and that they were also semiconductors.'-3 Since that time interest in the properties of these materials has ex- panded rapidly. During 1953 and 1954, the first reports of rectification, photoconductivity, and optical absorption in these materials came from several investigators. In 1955, recombination radiation from samples of GaAs, InP, and GaSb was reported by ~raunstein .' This radiation was produced by injected minority carriers from point and large-area contacts. From 1955 to 1960, efforts increased on preparing large, pure specimens of these materials for the study of basic physical phenomena and device exploration. By 1960, materials preparation and the understanding of the physics of some of the materials had advanced to where some very interesting and potentially useful phenomena came under study. The first observation of electric-field-induced changes in the optical absorption edge (Franz -Keldysh effect) of 111-V compounds was reported for GaAs by Moss in 1961.' In 1962 the study of recombination radiation advanced rapidly. Keyes and Quist6 and Pankove and Berkey-heiser7 reported high radiative efficientices obtained from recombination, and then the first injection electroluminescent lasers in GaAs were announced by Hall ef al.,' by Nathan et al.,O and by Quist ef al.,'O and in Ga(As, P) alloys by Holonyak and Bevacqua." Hil-sum has reviewed the early work leading to the first observations of laser action in GaAS." Recombination processes in GaAs, Gap, and the other 111-V com-

Jan 1, 1968

By E. O. Jones

DURING the heating of cold-worked nickel silver, the tendency of the material to crack is well known. The present research deals with this question, and may conveniently be divided into the following sections: Changes in these alloys during heating and cooling, determination of the temperature at which cracking occurs, effect of grain size, quenching cracks, methods of overcoming annealing cracking. The work is far from complete, in particular the influence of impurities on this tendency has not been investigated, but the results so far obtained lead to certain definite conclusions, which are of theoretical and practical importance. CHANGES IN ALLOYS DURING HEATING AND COOLING During the annealing of many metals at a temperature just below that at which recrystallization sets in, there is evidence of some change, the effect of which is to harden and embrittle the material. This effect has been most clearly demonstrated in the cases of aluminum, copper, brass, and nickel silver, and appears to be a common property of cold-worked metals and alloys, or, at any rate, the non-ferrous ones. The effect would obviously offer an explanation for certain types of annealing cracking, but the trouble is so much more common in the nickel silvers than in the other alloys that some special cause should be looked for. There is, however, fairly good reason for believing that similar cracking may occur in some of the brasses; D. Bunting suggests that the a brasses toward the saturation limit are subject to a transformation closely allied in nature to that known to occur in the nickel silvers at around 320° C. Although the existence of this critical temperature range was known, it did not necessarily follow that this transformation was responsible for the trouble under investigation, so the first portion of this paper deals with the attempts made to determine whether other critical changes might not occur in these alloys. There were already reasons for the belief that such would prove to be the case, as the mechanical properties of the nickel

Jan 7, 1925

By James E. Gingrich

The new Track Etch technique for uranium exploration has been utilized in several survey programs conducted during the last few years. The results from these programs have been very encouraging, and new uranium ore bodies have been discovered by using this new technique. The method is being used in several exploration programs in various locations around the world. This exploration technique utilizes small pieces of special radiation-sensitive plastic film to detect the presence of radon gas which is released by uranium ore bodies. Because of the selectivity and sensitivity of the technique, ore bodies not normally detected with other surface or airborne monitoring methods are found. Since no large equipment or special training of personnel is needed, the technique is easily used in field operations. The basis for the Track Etch method, its application in field exploration programs, and the results obtained to date in locating uranium ore bodies are discussed.

Jan 1, 1976

By H. I. Aaronson, W. L. Winterbottom, G. M. Pound

On the basis of a statistical thermodynamic treatment of the data of smithz2 on the activity of carbon in austenite, a Darken and smith23 deduced that the interaction energy, wy, between carbon atoms occupying nearest-neighboring interstitial sites is repulsive. Aaronson, Domian, and pound 24 (ADP) have applied two different statistical thermodynamic analyses to the same data. One analysis, a composite of the treatments of Darken and Smith,23 Speiser and Spret-nak," and Kaufman, Radcliffe, and Cohen,26 primarily takes account of the positional entropic effects of wy in dilute solutions. The other, due to Lacher 27 and Fowler and Guggenheim," is also applicable to more concentrated solid solutions. The equations which both analyses produce for a,, can be rearranged so that, when In a,, is plotted against the appropriate function of the carbon content of the austenite, the plot will have a slope of unity when the correct value of wy is employed. Since no other constant need be simultaneously evaluated in order to make this determination, ascertaining the most probable value of wy from Smith's data on the bases of these analyses was an elementary problem in least-squares statistics. ADP demonstrated that the wy's obtained from both analyses vary with temperature in a statistically significant manner. McLellan, Gerrard, Horowitz, and sprague 29 (MGHS), on the other hand, have recently made a new statistical thermodynamic study of a,, and have concluded from this study that wy is independent of temperature. The equation which they derived for a,, is: where 0 = ratio of the mole fraction of carbon atoms to that of iron atoms, z = number of sites from which occupancy is excluded by the presence of a carbon atom and the repulsive character of its interaction with nearest-neighboring carbon atoms (z = zb in Ref. 24), and x = a geometric parameter taking account of overlapping of the exclusion shells of nearby carbon atoms. z is 1 when wy = 0 and 13 when wy = Q. For a given value of z there is a definite value of X . In the absence of an equation connecting z and X, MGHS computed geometrically the value of x at several integral values of z; x increases from 0.47 to 8.67 as z is increased from 2 to 5. MGHS fitted Eq. [I] to the a,, data of Ellis, Davidson, and Bodsworth30 at 925° and 1050°C and to the data of smithz2 at 1000°C. Confining z to integral values in the range 4 to 6, and also somewhat restricting AG, the values of z, X, and AG were sought which would minimize the average root mean square percent deviation, D, of the calculated a,, values from those obtained experimentally. Finding that D was almost always smallest when z = 5, they concluded that z is independent of temperature. Since:23, 26 where R = gas constant and T = absolute temperature, and w,, was considered to be similarly invariant, this statement cannot be strictly true. The temperature range employed, however, was small and the interval between the values of z tested was sufficiently large so that the results could still be consistent with a constant The statistical treatment of the a,, data applied by MGHS is clearly quite approximate. Since more than three values of a,, are available at each temperature, z, and X, and AG have actually been over deter mined, rather than underdetermined as their treatment implies. In order to make more complete and exact use of the a,, data, we shall employ the Legendre Method of Least Squares, as described by Whittaker and Robinson. This technique permits conversion of the overdetermined system of equations produced by the substitution into Eq. [I] of the available pairs of a,, and 0 data at a given temperature into an even determined system. Solution of the latter system yields the most probable value of each of the three constants. This procedure will allow a statistically rigorous test to be made of the conclusion drawn by MGHS in respect of the temperature dependence of In order to obtain linear iiequations of conditions" from Eq. [I], the exact values of the three unknown constants are replaced by G/RT = =/RT + y, where z, i, and aG are estimated values of the constants. This allows the conditional equations to be written in the form:'l where fi -f6, i, =/RT) = the right-hand side of Eq. [I] for a given pair of ayi and values. When applied to Eq. [I], these relationships become: The i equations of condition are reduced to three "normal equations" in the manner discussed by Whittaker and Robinson. The normal equations are then solved for a, ß, and y. Both of these operations are most conveniently performed by means of the computer technique of Winterbottom and Gjostein.32 This technique was used iteratively until the value of 0 (the most sensitive of the three correction factors) became 10.01. (Until they became small, a, 8, and y

Jan 1, 1969

By L. D. Jaffe

IT is now well established that quenched and tempered titanium alloys have much better ductility when the quenching is from a two phase a-B structure, rather than from an all B structure. The corresponding microstructural differences, however, have not been shown in previous publications. Accordingly, specimens were cut from a % in. rod of commercial RC-130A, containing 7.9 pct Mn and 0.12 pct C, which had been previously hot rolled, heated 1 hr at 1100°F, and air cooled. (The same heat has been studied by others." 7 Samples about 1/4 in. cube were heated in helium 1/2 hr at 1450' or 1700°F, quenched in brine, tempered in helium 1 hr at various temperatures up to 1250°F, and quenched in brine. They were then sectioned and metallo-graphically examined, using an etchant of HF-HNO, in glycerine. As quenched from 1700°F, the microstructure observed was clear /3. (Probably also present was U, as the hardness was 400 Vhn, but w is not yet reliably revealed by any metallographic technique.) When the /3 quenched alloy was tempered at a high temperature, a precipitated as a grain boundary film

Jan 1, 1957