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By C. F. Weinaug, R. W. Farley, J. F. Wolfe

A rapid, accurate method for predicting the dew points of gas condensate systems and their subsequent normal and retrograde phase behavior with pressure decline has been developed. The method predicts dewpoint pressure, volume percent liquid, condensate content of produced gas, and the liquid and gas compositions at pressures below the dewpoint pressure. Use of a modified form of the BWR equation of state, which was established by regression calculations on experimental data from several gas condensates, provides depletion behavior predictions that are significantly improved over predictions using K-values based on convergence pressures and Standing's correlation for density. INTRODUCTION Prediction of complex hydrocarbon-mixture thermodynamics is fundamental to reservoir and gas process engineering. In particular, accurate descriptions of phase behavior are needed to plan production operations for gas-condensate reservoirs. Although analysis of reservoir behavior during producing and cycling operations can be made for simple reservoir models, extensions of these studies to more complex reservoir systems are still difficult, both with regard to numerical techniques and the phase behavior of the fluids. This report presents a mathematical method for handling the complex phase relationships encountered in retrograde condensates; it represents an advance in reservoir behavior technology in that it will aid the development of closed-form mathematical representations of total production systems. A typical phase diagram for a complex hydrocarbon mixture is shown in Fig. 1. When the reservoir temperature T, is higher than the critical temperature Tc, and lower than the critical-condensation temperature Tct' the mixture is a gas condensate. Decreasing the pressure on a condensate while maintaining nearly constant temperature will result in two phases forming at the dew point. Further decrease in pressure will cause additional liquids to be formed. This phenomenon is called retrograde condensation. As pressure continues to decrease, normal phase behavior regions are encountered (liquid vaporizes as the pressure decreases) until the low-pressure dew point is encountered. When a gas-condensate reservoir is produced, gas is withdrawn and the volume of fluids in the reservoir remains nearly constant as the pressure declines. Heavier components tend to accumulate in the liquid phase as a result of retrograde condensation, while lighter components tend to concentrate in the vapor phase. Thus, as the gas is produced the composition of the gas and the condensate

Jan 1, 1970

By Richards J. W.

J.W. RICHARDS, South Bethlehem, Pa. (communication to the Secretary?).-Mr. Howland's paper, data and conclusions have interested me intensely, and have led me to study carefully the record-of his 26 furnaces therein given. Mr. Howland is undoubtedly right in his conclusion that when expressing the amount of carbon burned at the tuyères in percentage of the total

Jan 1, 1917

By R. E. Ray, J. W. Stevenson, J. A. Berry

Conventional concrete block plastered with a cementitious coating is the most common material used in the construction of permanent stoppings to direct airflow in underground mines in the US. All mines experience various degrees of strata convergence depending on depth of overburden, geological conditions, and type of roof support employed. Strata convergence will cause cracks and joint openings in masonry stoppings, resulting insignificant air leakage losses. Where strata convergence is severe, complete structural failure of the stopping can ultimately occur. Reconstruction of damaged or destroyed stoppings adds expensive overhead to mining operations, and even greater expenses are incurred from the additional fan horsepower required to overcome leakage losses. Ideally, a stopping should maintain high resistance to airflow while yielding to strata convergence. By properly incorporating a polyisocyanurate rigid foam material within the masonry block structure, stopping service life can be increased in mines experiencing strata convergence problems such as floor heave, roof loading, and lateral rib movement.

Jan 1, 1986

By C. E. Van Orstrand

An intrusive body is a mass of igneous rock that has migrated upward, presumably from great depths. Great variations in form, composition and depth of burial occur. It is not proposed in this paper to go into all of the details of the problem. Instead, it mill be assumed here that the intrusive has the form and characteristics represented in Fig. I. According to W. 11. Emmons minerals are not deposited in appreciable quantities below the "dead line." Important amounts of ores of virtually all metals may be found around summit cupolas, but only gold, copper and zinc (in limited quantities) are usually associated with trough cupolas. Most students of ore deposits agree that temperature changes are largely instrumental in precipitating many ores in the "hood" and that the difference in temperature between the intrusive and that of the country rock may be the chief factor in determining the mineralogy of a deposit. A problem then of some interest is to correlate the principal physical features of the intrusive with the phenomena of heat conduction as evidenced by the cooling curves and the isothermal surfaces. Mathematical Theory In order to show the possible application of heat conduction to the interpretation of the processes of metalliferous deposition associated with intrusives, it will be as- sumed that the intrusive is a large par-allelopiped of dimensions, 2l, 2m, 2n. The equation that represents the flow of heat from the parallelopiped into country rock (v = o, 1 = o), which has the same thermal properties as the intrusive, is2,3 l-x v I FT 2 [2 2 — l-x m — y — m — y n — z In this equation, the origin, x = o, y = o, z = o, is at the center of the parallelopiped. v = temperature at point x, y, z, time 1. v, = initial temperature throughout the intrusive, 1 = o. k = coefficient of thermal diffusivity. a, ß, y are variables of integration. Put n = m in Eq. I, and we have v I [2/5 [2I-x 2 — l-x m — y 2 2 2 kt 2 20xt e-a2da ebrdß

Jan 1, 1946

By C. E. Van Orstrand

An intrusive body is a mass of igneous rock that has migrated upward, presumably from great depths. Great variations in form, composition and depth of burial occur. It is not proposed in this paper to go into all of the details of the problem. Instead, it mill be assumed here that the intrusive has the form and characteristics represented in Fig. I. According to W. 11. Emmons minerals are not deposited in appreciable quantities below the "dead line." Important amounts of ores of virtually all metals may be found around summit cupolas, but only gold, copper and zinc (in limited quantities) are usually associated with trough cupolas. Most students of ore deposits agree that temperature changes are largely instrumental in precipitating many ores in the "hood" and that the difference in temperature between the intrusive and that of the country rock may be the chief factor in determining the mineralogy of a deposit. A problem then of some interest is to correlate the principal physical features of the intrusive with the phenomena of heat conduction as evidenced by the cooling curves and the isothermal surfaces. Mathematical Theory In order to show the possible application of heat conduction to the interpretation of the processes of metalliferous deposition associated with intrusives, it will be as- sumed that the intrusive is a large par-allelopiped of dimensions, 2l, 2m, 2n. The equation that represents the flow of heat from the parallelopiped into country rock (v = o, 1 = o), which has the same thermal properties as the intrusive, is2,3 l-x v I FT 2 [2 2 — l-x m — y — m — y n — z In this equation, the origin, x = o, y = o, z = o, is at the center of the parallelopiped. v = temperature at point x, y, z, time 1. v, = initial temperature throughout the intrusive, 1 = o. k = coefficient of thermal diffusivity. a, ß, y are variables of integration. Put n = m in Eq. I, and we have v I [2/5 [2I-x 2 — l-x m — y 2 2 2 kt 2 20xt e-a2da ebrdß

Jan 1, 1946

By Ling Yang, John Henderson

Self-diffusion coefficients of copper in molten copper have been measured by the capillary reservoir method in the temperature range 1140o to 1260°C. The results can be represented by the equation D = [(1.46 * 0.01) x 10-3) exp [(-9710 * 710)/RT] cm2/sec. The energy of activation agrees within the limit of experimental uncertainty with that for viscous flow. The relationship between the diffusivity and coefficient of viscosity is best described by the equation D = kT/4pnr cm2/sec. MEASUREMENT was made of the self-diffusion coefficient of copper in molten copper in the temperature range 1413º to 1533ºK, using the capillary reservoir technique and CU64 as the radioactive tracer.The procedures for filling the capillaries, making the diffusion run and evaluating Dcu from the counting results were the same as described previously.1,2 All experimental operations involving the melt were carried out in a purified argon atmosphere. A graphite crucible, enclosed in a McDanel tube, was used as a container for the melt because of its satisfactory nature as a refractory material and the low solubility of carbon in copper. Graphite was also used for the capillary material. A McDanel thermocouple sheath, to which graphite radiation shields were affixed, was used to hold the capillaries. By moving this sheath through a rubber seal at the top of the McDanel tube, the capillaries could be lowered into or raised out of the melt. A Globar furnace with a constant temperature zone (± 2°C) of 2 in. was used to heat the assembly. The temperature of the furnace was the equilibrium value corresponding to a given setting of the transformer. Temperature was measured with a Pt-10 pct Rh/Pt thermocouple and varied during a run

Jan 1, 1962

By A. S. Argon, G. East

From their study of the anisotropy of grain boundary mobility in aluminum, the authors conclude that tilt boundaries have a higher mobility than twist boundaries because the atomic misfit at the pure-twist boundary is relatively small compared to the misfit at a tilt boundary for a given amount of misorientation. If this is true, then one would expect a twist boundary to have a lower grain boundary energy than the corresponding tilt boundary. Fig. 6, taken from the work of Gjostein and Rhines,10 shows that this is indeed the case for [001]-cu tilt and twist boundaries in the high-angle region, thus lending support to the authors' conclusion.

Jan 1, 1968

By John Boardman

THE latest metal-mine accident report available for the United States is that of the Bureau of Mines for the calendar year 1919. Quoting from Table 20, p. 53, of that report, we find that there were 468 men killed, 7 permanently totally disabled, 321 permanently partially disabled, 7848 injured seriously (more than 14 days disability), and 23,330 of 1 to 14 days disability. We have no records to show what the average days lost per case of accident is, but the records for the Anaconda Copper Mining Co. show that, leaving out the fatalities and total permanent disabilities, and counting those in which the lost time was one or more days, the actual days lost due to accidents, for the Butte mines and shops for five years, 1917-1921, were as follows: Accident Statistics, Butte Mines and Shops of A. C. M. Co. Rate Shifts Days Lost Year Accidents Total Shifts 10,000 Shifts Days Lost Per Acci-dent 1917 2,661 3,169,720 8.395 26,734 10.05 1918 2,765 3,545,149 7.799 39,199 14.17 1919 1,381 1,853,143 7.452 22,797 16.50 1920 1,376 1,879,410 7.321 20,164 14.65 1921 376 776,461 4.842 8,287 22.03 Total... 8,559 11,223,883 7.625 117,981 13.80 In order to place an economic value. on this loss, we will assume that all the 468 fatalities and the 7 total permanently disabled in the United States were com-pensated for at the rate which applies in the State of Montana, that is, $5000 each, and that the 8169 serious accidents in the United States were compensated for at an average of $70 per case, thus bringing the estimated compensation paid by metal-mining companies in the United States to the enormous total of $2,946,830 for the year 1919. The figure of $70 per case was obtained by dividing the total amount paid by metal-mining companies under Plan No. 1 of the Montana Compensation Law, for the first five years of its operation, by the total number of serious accidents for those years.

Jan 9, 1922

By T. G. Sieber, T. D. Tiemann

The extraction of quartz from siliceous iron ores by dissolution in sodium hydroxide solution has been described in detail in AIME Transactions. l923 data reported covered the temperature range from 230-416°F, where a continuous increase in the amount of silica extracted with increase in temperature was found. It is the purpose of this paper to describe some unexpected results of more recent work exploring principally the range of 500600°F where higher rates and greater amounts of silica extraction were antici-p ted. In brief, the experimental procedure consists in digesting the ore under pressure in solutions of sodium hydroxide, filtering the suspension and weighing and analyzing the dried residue for iron content. The amount of extraction is calculated from the weight loss or from the iron analysis of the residue and that of the original ore.

Jan 1, 1969

By S. H. Ward

Since the advent of the first airborne electromagnetic system, it has been evident that such systems were inherently limited to shallow depths of exploration of the orderof 100 to 200 feet. Hence in 1948 the author and his associates commenced a study of the feasibility of applying natural audio frequency magnetic fields to investigation of the electrical properties of the subsurface in order to provide a system capable of overcoming this limitation. This research culminated, in the summer of 1958, in the development of a new airborne prospecting device — AFMAG. This device has detected surface massive sulphide bodies while flown at heights as great as 3000 feet. Hence, by inference, it is deduced that it could find similar sulphide bodies if they were buried 2500 feet below surface and the aircraft flown at 500 feet. Thus a considerable improvement over conventional airborne electro-magnetic systems is obtainable with AFMAG. Airborne exploration in mountainous terrain involving deep valley fill now becomes possible. Examples are presented of the results of actual airborne AFMAG test surveys over known deposits of massive sulphide mineralization. Interpretation of the data is discussed with particular reference to the knowledge of size, dip, depth, depth extent, and conductivity of causative bodies as deduced from the flight records. The possibility of mapping major geologic structures, for both mining and oil exploration purposes, is discussed with the aid of examples of airborne AFMAG data. INTRODUCTION Electrical prospecting with natural audio frequency electromagnetic waves as a source has, within the last three years, become a practical reality. Both airborne and ground survey instruments under the trademark "AFMAG" (for audio frequency magnetics) have been used successfully in the search for conductive mineral deposits. It is the object of this paper to discuss the principles of airborne AFMAG and to illustrate its application by means of examples obtained over known geological situations. WHY AFMAG? In view of the large number of good airborne electromagnetic systems available for purchase or contract surveying, one may well ask, "Why another new system?". Primarily the answer lies in the fact that AFMAG does not suffer from the very limited depth of exploration available with, and inherent in, any conventional airborne electromagnetic system. AFMAG is not conventional insofar as an artificial transmitter is not required. Only a receiving and detecting device is employed. The electromagnetic fields measured are those from millions of electrical discharges in the atmosphere (e.g;..- lightning strokes). Their random distribution in time and space make these fields difficult to employ and it is only with recent advances in the electronics of geophysical instrumentation that this has become possible. A second reason for AFMAG and one of its

Jan 1, 1961

By J. E. Warren, J. H. Hartsock

An asymptotic solution to the equation that describes the flow of a slightly compressible fluid in an infinite porous medium has been used to estimate the interaction between two adjacent wells producing from a common reservoir. A direct method for approximating the interference time defined by Stevens and Thodosl has been suggested. An alternative definition for the time of interference, based on the minimum pressure change in the interference region, has been proposed; also, a direct method of determination has been prescribed. Examples have been employed to illustrate the use of both methods.

By Joseph M. Locke

The discovery of this asphaltum was made by S. H. Gilson, of Salt Lake, and since then the material has borne the local name of Gilsonite. So far as I have been able to ascertain, however, the first published notice of this discovery was made by Prof. W. P. Blake in the Engineering arid Mining Journal, of December 26, 1885, where he names the new mineral Uintahite, from the place of its discovery, the Uintah Mountains in eastern Utah. The priority of publication and the geographical fitness of the name will probably secure its acceptance by mineralogists.* The following is Prof. Blake's article. In the month of September last, a sample of peculiar asphalt was received for examination, and recently when in Provo, Utah, I had the opportunity of seeing a considerable quantity brought in from the Uintah Mountains. It is obtained in masses several inches in diameter, and apparently free from mechanically disseminated impurities. It breaks with a conchoidal fracture, is very brittle, and is readily reduced to powder in a mortar. Hardness, 2 to 25. Gravity, 1.065 to 1.070. Color, black, brilliant, and lustrous; streak and powder, a rich brown. It is a non-conductor of electricity, and is electrically excited by friction.

Jan 1, 1888

By H. J. Modi, D. W. Fuerstenau

pH effectively regulates the flotation of corundum through its control of the surface charge. Since collector ions function as counter ions in the double layer, the collector must be anionic when corundum is positively charged and cationic when it is negatively charged. Even a long-chained xanthate will float positively charged corundum. Association of the hydrocarbon chains of the adsorbed collector ions gives rise to increased adsorption and increased rate of flotation. Because of this phenomenon, neutral organic molecules aid flotation although the unionized collector cannot promote flotation independently. Na2SO4 was found to depress the flotation of corundum with animic collectors through ionic competition whereas the same salt activates corundum for flotation with cationic collectors. A close connection between ion association, electrokinetic behavior, and floatability is suggested. As part of the increasing interest in the physical chemistry of flotation, strong experimental evidence has been obtained which indicates that organic ions are adsorbed as counter ions by non-metallic oxide minerals mainly because of the electrical forces which exist at interfaces(1-3). Thus flotation of such minerals without activation should then be appreciable only when the mineral and the collector are oppositely charged. Since only limited work has been reported on the effect of surface charge upon flotation behavior(3) this general hypothesis on the flotation of insoluble oxide minerals has not been tested thoroughly. Investigating the flotation of a mineral for which extensive electrokinetic data exist yields a way to test this hypothesis more extensively. The electrokinetic behavior of corundum in solutions containing both organic and inorganic electrolytes has been studied quite thoroughly' Electro-kinetic measurements have shown that in the case of corundum, simply by controlling pH the solid surface can be charged either positively or negatively. For this reason corundum was chosen for study. The object of this paper is to present a study of the flotation of corundum and to explain the results in the light of our knowledge of adsorption mechanisms gained from streaming potential investigations. This paper is concerned mainly with the effect of surface charge on flotation with anionic and cationic collectors, but in addition such flotation phenomena as collector hydrolysis, Van der Waals attraction between hydrocarbon chains, ionic competition, and activation are discussed. While the present paper is confined to a reporting of the data obtained and some of the more immediate conclusions, it will be seen that the results, in combination with those on other systems, do promise a

Jan 1, 1961

By EDWARD B. DURHAH

(San Francisco Meeting, UCtober, 1911.) THE refinery at the San Francisco Mint takes the bullion purchased by the receiving department, and carrying more than 200 parts of precious metals in 1000, or, in mint parlance; over 200 fine, and separates and refines the various metals contained therein, using electrolytic processes exclusively. Bullion containing silver is treated in cells charged with a nitric electrolyte. These cells produce fine silver and leave a residue rich in gold. The residue from the silver-cells, together with crude gold-bullion, is treated in cells having a chloride electrolyte. These produce fine gold and leave a residue containing silver chloride. The latter is reduced to the metallic state with zinc and is then treated in the silver-cells. The various waste solutions and the wash-waters, after being freed from the bulk of their precious metals, still contain copper and other metals. These are removed by scrap-iron, and are then treated in the copper-cells, having a sulphate electrolyte. These cells produce pure copper, and collect a residue containing lead, some gold and silver, and all the metals of the platinum group that were in the bullion. This residue is relatively small, and is melted into bars and stored until sufficient accumulates to warrant treating it for platinum, etc. The refinery occupies three large and three small rooms. The large ones are, a melting-room, 30 by 34 ft.; a cell-room, 39 by 46 ft.; and a wash-room, 30 by 33 ft. The small rooms are used as foreman's office, laboratory, and generator-room, respectively. The methods here described are those in use in December, 1909, when notes for the present paper were taken.

Oct 1, 1911

By H. J. de Haan, L. Schenk

Scope for Thermal Recovery in Shell's Heavy Oil Fields in Venezuela The main heavy oil reservoirs on the East coast of Lake Maracaibo (Fig. I), known as "Bolivar Coast", initially contained some 20 billion bbl of oil in place with gravities in the range of 10 to 15° API. The current total production rate is about 400,000 B/D. Since the recovery to date is on an average only 12.5 percent of the initial oil in place, these fields offer a vast potential for secondary recovery methods. The reservoirs are characterized by moderate depth (generally 1,000 to 3,000 ft; maximum 5,000 ft), good formation properties such as net oil sand thickness (50 to 300 ft), high porosity (30 to 40 percent) permeability (1 to 3 darcies) and oil saturation (initially about 80 percent) and high oil viscosity (100 to 10,000 cp in situ), all of which are favorable for the application of thermal recovery processes. Since 1957, steam drive, steam "soak" and underground combustion have been tested or are being tested in this area.1-3 This paper deals with a major steam drive test in the Tia Juana field. The test was commenced in Sept., 1961, on the basis of encouraging results of laboratory experiments and pilot field tests, which will be discussed briefly. Early Laboratory Investigation of the Steam Drive Process In 1956 a series of model experiments was carried out in the Koninklijke/Shell Laboratorium, Amster- dam, to investigate the displacement of heavy oil by steam.' The prototype studied was a horizontal, un-consolidated heavy oil reservoir, subjected to a linear steam drive. The model, representing a slab from this reservoir along the main flow direction, consisted of a steel tube filled with oil-saturated sand, provided with layers of rock at the top and bottom to simulate conductive heat losses to cap and base rock. Lateral heat losses, perpendicular to the main flow direction, were minimized by insulating the sides of the model. Heat flow and viscosity and gravity forces were scaled by taking the steam injection rate and sand permeability inversely proportional to the geometric reduction factor of the model, and using materials (oil, steam, cap rock, etc.) identical with those of the prototype. The main feature of the process was a frontal displacement mechanism that was observed within wide ranges of injection pressure and rate, oil viscosity, initial oil saturation and sand permeability. The high stability of this front can be attributed to the high volumetric steam flow rates, combined with the reduction in oil viscosity. High recoveries were obtained due to the low residual oil saturation of about 15 percent in the zone swept by steam. The latter value pertains to the specific test conditions (heavy oil, uncon-solidated sand) and may be lower for light oil, due to the effects of steam distillation. The applicability of this experimental approach is limited, as it does not take into account the fact that

Jan 1, 1970

By AIME

NEW YORK'S largest hotel, the Pennsylvania, will be filled with mining and oil men and metallurgists the third week of February when some 3000 AIME members, their wives, and guests will gather for the Institute's 1948 Annual Meeting-its 166th general meeting. Except for the usual Sunday afternoon and evening sessions of the Mineral Industry Education Division at the Columbia University Men's Faculty Club, the big assembly will be under one top and members will not this year have to consult compass and map to find their next session. Possibly enervated by the stupendous effort of the Anniversary Celebration last spring and the plethora of highly successful fall meetings, the various committees have been a trifle slow in arranging their social and technical programs, but in mid December as we go to press there is already much to report indicative of substantial fare and high interest. The definite timetable schedule will appear in the February M&M.

Jan 1, 1948

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 LESTER W. STRAUSS

FOR fifteen months after the other dominions of the British Empire and the entire so-called sterling 11loc loosed the shackles that bound the111 to the gold standard, South Africa, giant among gold-producing nations, remained stubbornly attached to gold at the traditional ratio of 85 shillings in currency to one ounce of gold. But eventually even South Africa had to heed the dictates of trade and the obvious interests of its great gold-mining industry. In December, 1932, South Africa's currency severed its golden bonds. Today the South African pound is 011 a par wit11 the British pound.

Jan 1, 1935

By J. C. Borland, J. H. Rogerson

Jan 1, 1963

By T. S. Lundy, J. I. Federer

Chemically purified Zr95and Cb95 have been used in determining self-diffusion coefficients in the bcc phase of iodide zirconium over the temperature range of 900o to 1750°C. The temperature dependence of the diffusion coefficients could not be described by the usual Arrhenius-type equation over the entire temperature range. Values of the apparent frequency factors (D0)a and activation energies (Q)A for ZR95 varied from 4.8 x 10-6 to 2.5 x 10-2 sq cm per sec and 20,700 to 46,900 cal per mole, respectively, between 900°and 1750°C. Similarly, for Cb95, values of (Do) a and (Q)A varied from about 2.4 x 10'5 to 0.25 sq cm per sec and 26,500 to 56,800 cal per mole, respectively. The data may be described in terms of the a to ß transition temperature of 1136 °K and the absolute temperature of the diffusion anneals by the following eauations: SEVERAL studies on the diffusion of Zr95 in zirconium have been reported.1"5 The values of the constants contained in the usual Arrhenius-type equation for describing the temperature dependence of the diffusion coefficient, D = Do exp [- Q/(RT)], are summarized in Table I. The reported values of Do, the frequency factor, and Q, the activation energy, are seen to vary by factors of about 60 and 1.6, respectively. Examination of the data from any one study indicated reasonable consistency of measurements. The large discrepancies of over-all results, therefore, cannot be explained on the basis of experimental scatter. One possible explanation for the differences in results could be a varying impurity content of the zirconium. Another possibility is that the radioactive daughter, Cb95, influenced the values of some of the determined diffusion coefficients. Therefore, the first of the three purposes of this study was to reconcile the large differences in diffusion results that have been obtained. Several empirical relations have been proposed to relate the diffusion coefficients in solids with physical properties, such as the absolute melting point, the heat of fusion, and the heat of sublimation.

Jan 1, 1963