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By Alfred H. Bell, Charles W. Carter

In 1943, Illinois produced 82,256,000 bbl. of oil, or 5.5 per cent of the total for the United States, and ranked sixth in the nation in oil production. This represents a decline of 23 per cent from 1942, when the total Illinois production was 106,ggo,o~~ bbl. and Illinois ranked fifth. The daily average production for 1943 was approximately 225,000 bbl. Daily averages by months were as follows: Jan......... 238,000 July......... 218,000 Feb......... 240,000 Aug......... 216,000 Mar......... 237,qoo Sept........ 220,ooo Apr......... 230,000 Oct......... 220,000 May....... 221,000 Nov......... 223,000 June......; . 222,000 Dec......... z18,ooo This shows that most of the decline during the year took place between March and May, and that for the last eight months of 1943 production has been essentially steady. This means that there has been enough production from new wells drilled to balance the natural decline of the Older wells. The trends of drilling and production are shown in Fig. I and Table 3.

Jan 1, 1944

By C. W. George, Bruce Chalmers

The authors enumerate the factors which appear, from their observations and practical experience of failure of aircraft components in Great Britain, to be responsible for causing a metal or alloy to fail by stress corrosion. The essential conditions for promoting failure by stress corrosion are: (I) tensile stress at the surface of the component, (either residual or applied), and (2) an attacking medium that may be a solution or a liquid metal. Particular attacking agents are effective only on certain metals. In all instances of stress-corrosion failure experienced, cracking of an intercrystalline form has occurred and examples of such failure in aluminum alloy, steel and copper alloys are described and illustrated. The relation between microstructure and stress corrosion is mentioned and methods of investigating the susceptibility to stress-corrosion failure of metallic materials are described. The precautions to be taken in selecting materials for particular aircraft components and the importance of adequate protection against chemical attack are considered. The authors have given a factual survey of stress corrosion and have made no attempt to advance any scientific explanation of the phenomenon.

Jan 1, 1945

By R. Hoffmann

The Waelz process produces oxides of volatilizable metals from ores, metalliferous products and residues. The process was originally used for recovering zinc and lead, where tailings and residues containing those metals had accumulated at mines or smelters, but it is applicable for obtaining tin, arsenic or other volatilizable metals. It is useful when other methods of obtaining the metals from the ores or residues are too difficult or expensive or show too low a recovery. The Waelz process was developed in 1923 for the treatment of large calamine dumps in Upper Silesia, which showed zinc contents of 8 to 10 per cent. and lead contents up to 3 per cent. The rapid development of the process, from the first trials up to the plants now working or in course of erection, is shown in Fig. 1. The first industrial Waelz plant was started in 1925. Within two years the capacity of the working plants reached 700 tons material per day of 24 hr. During the year 1928 the daily capacity of the plants now at work or in course of erection will rise

Jan 1, 1928

By Ernst A. Hauser

A few years ago an Indian native of British Columbia drew the attention of white men,' to a deposit of a claylike material on King Island, at the mouth of Dean River just opposite Hunter Island in the Pacific Ocean (Fig 1 ) . The native claimed that this natural product, which is found not in solid form but either as a paste or as a thick, viscous liquid, exhibited exceptional healing properties not only for various types of skin irritation but also for internal ailments. He pointed out that the natives had been using this material very successfully for generations. Since then, systematic surveys have revealed that the deposit, covered by a humus layer of varying thickness, is far more extensive than had originally been assumed. The product as mined today is of puttylike consistency and of greenish color. If exposed to air it dries rapidly, forming a slightly gray, rather brittle product, which does not permit redispersion to its original consistency. When the natural product is rubbed on the skin, however, the presence of coarse, sandy material is revealed.

Jan 1, 1952

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 Robert J. White

Strong's equation for calculating bottom-hole pressure reduction due to gas cutting of drilling mud is corrected, resulting in a simpler equation which is easier to use. Use of the equation is illustrated by examples. It is shown that reduction of weight of a 10 lb/gal mud by 50 per cent at the surface due to gas cutting produces only n 3 per cent decrease in hydrostatic head at the bottom of a 5,000-ft well. It is also shown that at the surface 5 volumes of air per volume of mud are required to reduce the apparent mud weight from 8.5 to 6.5 lh/gal in a 3,000-ft well. Illustrative graphs are included to show the effect of various degrees of gas cutting on apparent mud weight at depths of 2,000, .5,000 and 10,000 ft and to show variation of apparent mud weight, with depth for a 100 lb/cu ft (13.37 lb/gal) mud gas cut to 90 lb/cu ft (12.03 lb/gal) at the surface. INTRODUCTION In 1938, Strong' published the following equation for calculating reduction in bottom-hole pressure due to gas cutting of drilling mud h = 1/D [p + pn/100 In p + p(1-n/100)/p(1- n-100)] where: h = depth in feet P = pressure in atmospheres at depth h due to mud column only D = hydrostatic pressure in atmospheres of a col-umn of uncut mud 1 ft high p = back pressure at well-head (in atmospheres) n/100 = fraction by volume of gas in mud at well-head at back pres-sure p This equation was recently found to contain an error due to an incor-rect expression for variation of vol-ume fraction of gas with pressure. Values calculated by the original equation are close to the correct values for small percentages of gas for which it was derived but become increasingly erroneous as the gas content increases and are completely unusable at the very high gas con-tents employed in aerated mud. DERIVATION The nomenclature used is the same as in Strong's paper. The pres-sure dP exerted by a lamina of thickness dh at a depth h ft is ex-pressed by Eq. 1 where x = volume fraction of gas at depth h dP = D (l - x)dh . . . (1) When we express x in terms of the wellhead per cent gas n, the well-head pressure p and the pressure P at depth h, the result is Eq. 2. x = (np/p+p)/(100-n) + (np/P + p) When this is substituted in Eq. 1 and rearranged to separate the var-iables the result is dh = 1/D [dp + np/100-n dp/(P + p]. Integration between appropriate lim-its results in or if the wellhead is open so that p = 1 atm and we rearrange Eq. 4, the result is loss in head = hD — P = n/100-n In (P + 1) ...(5) Eq. 5 can be solved easily by successive approximation using hD as a first approximation for P on the right-hand side and calculating a first value for loss in head. This can then be used to get a new value of P using the left-hand side of the equation. Values converge very rap-idly even for quite large values of per cent by volume gas n. EXAMPLES The effect on bottom-hole pressure of 50 per cent gas cutting of the mud in a 5,000-ft well using 10 Ib/ gal mud will be calculated, we have: h = 5,000 ft 10 X 7.48 144 X 14.7 = 0.0353 atm/ft hD = 176.5 atm n = 50 Substituting these values in Eq. 5 and using hD as a first approxima-tion of P on the right, we have, approximate loss in head = 50/50 In (176.5 + 1) = 2.30 log 177.5 = 5.17 atm. We calculate a new value of P as follows:

Jan 1, 1958

By P. E. Busby, C. Wells

FURTHER study of data used in determinations of 1—rates of diffusion of boron in austenite and 2—solubilities of boron in the a and phases of iron and steel' has provided an equation for the diffusion of boron in a iron. In brief, the previously published data were accumulated from the results of deboron-izing (and decarburizing) experiments carried out in the range of 700° to 1300°C. Diffusion coefficients (D?) for boron in austenite were calculated using the Grube solution of Fick's law. However, only solubility values were estimated from the discontinuous concentration-penetration curves, Fig. 1, which are characteristic of diffusion in two phases. Dr. Carl Wagner' has recently provided a solution for calculating D values from penetration curves of this type as follows: Cl1.1 —C8/C8- C11.1 = vp ? e ? erf (?) and D = ?/4?2 t where C11,12, C8, C11, and E have the values shown in Fig. 1. D is the diffusion coefficient, sq cm per sec; t is time of deboronizing anneal, see; and ? is a di-mensionless parameter. For a given diffusion experiment, the value of ? can be readily obtained by graphical solution from a plot of y vs the right-hand part of Eq. 1. D may then be evaluated from Eq. 2. The avplication of this solution to previously re-ported results, of which excerpts are given in Table I, permits the calculation of diffusion coefficients for boron in a iron. On the basis of these meager data, it is tentatively concluded that the diffusion of boron in a may be represented by the equation Da = 1011 e-92,900/RT where R is the gas constant, cal X 0C-1 X mol-1; and T is the absolute temperature, OK. Although the frequency factor, 106 sq cm per sec, is admittedly several orders of magnitude higher than expected, the value of Q, 62,000 cal per mol, appears reasonable and is, in fact, very similar to that for the self-diffusion of iron. It is pertinent to mention at this point that the value of Q obtained for the diffusion of boron in austenite by means of the Wagner solution is 19,000 cal per mol and is in excellent agreement with the value previously reported1 in the equation DT = 2xl0-3 e-21,000/RT [4] which was determined by the application of the Grube solution to other data. The fact that determined constants A and Q in the equation D? = A e-Q/RT were practically the same, independent of whether the Wagner or Grube solutions were used in determinations of D values, strengthened the authors' belief that the computed values of D (Table I) using the Wagner solution are reliable. The relative values in Eqs. 3 and 4 for the diffusion of boron in the a and ? phases, respectively, suggest that boron forms a substitutional solid solution in a iron and an interstitial solid solution in ? iron. The same tentative conclusion has been reached by McBride et al.3 on the basis of relative solubilities, atom diameter, and the size of the interstitial hole in a and ? iron. In connection with the data for test 14 listed in Table I, it is of interest to calculate the solubility of boron in a iron using the D value given by Eq. 3. As might be anticipated from the small movement of the interface in test 14, proper substitutions in Eqs. 2 and 1 give a low value, approximately 0.0004 pct B, at 850°C. Apparently at 835°C (test 13) it is possible to obtain 0.0018 pct B, and at 850°C only 0.0004 pct B into solution in the a phase before a second phase appears. These observations are consistent with the Fe-B constitution diagram proposed by McBride, Spretnak, and Speiser.3 References P. E. Busby, M. E. Warga, and C. Wells: Diffusion and Solubility of Boron in Iron and Steel. Trans. AIME (1953) 197, p. 1463; Journal of Metals (November 1953). 'W. Jost: Diffusion in Solids, Liquids, Gases. (1952) pp. 69-71. New York. Academic Press Inc. "C. C. McBride, J. W. Spretnak, and R. Speiser: A Study of the Fe-Fe2B System. Trans. ASM (1954) 46, p. 499.

Jan 1, 1955

By P. E. Busby, C. Wells, M. E. Warga

Fundamental data on the rate of diffusion of boron in austenite and solubility of boron in the a and y phases of iron and steel have been obtained from deboronizing experiments and provide partial explanations for some of the phenomena observed in boron steels. The rate of diffusion of boron is about the same as carbon in austenite. The solubility of boron in austenite at normal heat-treating temperatures is less than 0.001 pct. A partial tentative Fe-B phase diagram in the important low boron concentration ranges and an equation representing the diffusion of boron in austenite are presented. A LTHOUGH a search of the literature revealed ALTHOUGHthat boron diffusion had not been studied quantitatively and systematically prior to 1948, a few qualitative observations which were made by following the diffusion of boron into iron packed in ferro-boron1-3 suggest that boron obeys normal diffusion laws and that the rate of diffusion increases with increasing temperature. The claim of Cornelius and Bollenrath1 that boron does not appear to influence the rate of carbon diffusion has recently been substantiated by Wells, Batz, and Mehl.4 Calculations based on data from the paper by Campbell and Fayv indicated that the diffusion coefficient (D) for boron in iron at 900°C is approximately 3x10 sq cm per sec; a value of 2x10-7 sq cm per sec at 1038°C has been reported by Digges et al in connection with decarburizing experiments on a commercial boron steel containing 0.43 pct C. During the period 1948 to 1950 several diffusivity constant (D) values for the diffusion of boron in the y phase of iron and steel and a number of solubility values for boron in both a and y phases were reported. It was concluded tentatively as a result of Metals Research Laboratory studies that D values for boron in y and a phases are about the same as for carbon in the comparable phasesa and that carbon up to 0.4 pct did not affect the rate of diffusion of boron in y iron above 1000°C within the limits of experimental error. Whether saturation of the y or a phases with carbon would significantly affect rates of diffusion of boron through them was then and still remains in doubt. The best estimate of Q (activation energy) was reported to be about 25,000 cal, somewhat lower than that for carbon in y iron. The solubility of boron in y iron at 1000°C was thought to be higher than 0.004 pct B but not as high as a more recent analysis of available data shows it to be. The solubility of boron in a iron at 700°C was reported to be 0.0004 pct B, but it would not have surprised the authors if the true solubility value is actually lower than this. Breaks in diffusion curves which were not understood when first obtained prior to 1950 have now been recognized as indicating solubility limits, and these are included in the present paper. Experimental Procedure Two methods were employed in an effort to determine diffusion coefficients (D) for boron in austenite. Early experiments involved the use of welded couples prepared in accordance with the procedure of Wells and Mehl,' but when the results of these experiments proved to be unsatisfactory for calculating D values, studies were continued by means of deboronizing experiments. In both cases, boron analyses following the diffusion anneal were carried out spectrographically and all D values were computed using the Grube solution of Fick's law. The precision of the spectrographic method used proved to be about equal to that reported by Corliss and Scribner" —average deviation from the mean about 5 pct of the amount present when the boron content is 0.003 pct. Concentration-penetration curves obtained from spectrographic analyses of welded couples generally indicated that practically no boron was transported across the weld interface during the diffusion anneal. Furthermore the concentration-penetration

Jan 1, 1954

By G. M. Schwartz, G. A. Thiel

THE first record of the quarrying of dimension stone in Minnesota dates back to 1820 when limestone was quarried locally for part of old Fort Snelling. Limestone quarries were operated at Stillwater, Mankato, and Winona as early as 1854. Granite was quarried first at St. Cloud in 1868, and within a few years thousands of tons were shipped to widespread points. Rough dimension stone for large buildings furnished the first important market, but beginning in 1886 paving blocks were in demand. The largest shipment was in 1888, when 1925 cars were shipped from the St. Cloud area. Quartzite was quarried first at New Ulm in 1859 and somewhat later at Pipestone and elsewhere in southwestern Minnesota: The productive dolomite quarries at Kasota were opened first in 1868 and have continued as large producers of a variety of stone to the present time. At present, the industry is controlled by relatively few operators, and for that reason detailed figures on dimension stone are not released for publication. A general idea may be obtained from the data in the Minerals Yearbook for 1948. The figures for total stone produced in Minnesota are 1,804,000 tons valued at $5,090,652. Probably the largest item in the latter figure is received from dimension stone. A better idea of the situation, in relation to the country as a whole may be gained by using the data for 1930 when more companies were operating in Minnesota, and complete figures were published. In that year Minnesota produced granite valued at $2,668,119 and ranked third among the states in value. Minnesota's production of granite was almost exclusively for dimension stone. In the same year Minnesota produced 300,000 tons of limestone (dolomite) valued at $840,860, and this likewise was mainly dimension stone. In finished limestone Minnesota ranked second among the states in 1930. Sandstone and minor amounts of quartzite are the only other dimension stones that have been produced in Minnesota, but the quarries are now inactive. The commercial stones of Minnesota have been described in two reports by Bowled and by Thiel and Dutton.2 The early history of quarrying in Minnesota and extensive notes on the various rocks are given by N. H. Winchell.3 Small limestone and dolomite quarries were numerous throughout the area of Paleozoic rocks in southeastern Minnesota. Early production was largely dimension stone. With the increased use of Portland cement, most of these ceased production, and today only those at Kasota and Winona remain in operation. In recent years many quarries have reopened and new ones started, but these are devoted to the production of crushed rock and agricultural lime. As the application of modern quarrying and finishing methods increased, small companies in the granite business have dropped out, and the remaining companies have modernized their plants, purchased old quarries, and opened up new ones, thus furnishing a wide variety of granites suitable for most of the customary uses. It is the purpose of this review to present notes on' the geology and operations of each of the quarries now operating within the state. Granites and Related Igneous Rocks The term granite as used in this report includes granites, gneisses, diorites, gabbros, and other igneous rocks. The granites of greatest economic importance are found in three widely separated regions, see Fig. 1. 1-Central Minnesota in the region of the city of St. Cloud, 2-the upper Minnesota River valley region, 3-the northeastern portion of the state, commonly referred to as the Arrowhead region. The St. Cloud Region: The rocks of the St. Cloud region are mainly granites and related rock types such as monzonites and quartz diorites. The stones may be grouped into three major types, namely, pink granite, red granite and gray granite. Most of the pink granite occurs in the area to the southwest of St. Cloud. The rock is best described as stone with large pink crystals set in a finer grained black and white background. The minerals of the matrix occur in remarkably uniform sizes, and the pink crystals are sufficiently uniform in. their dis-

Jan 1, 1952

By A. T. Corey, C. H. Rathjens

INTRODUCTION Although the oil industry has been aware of the directional variability of permeability in porous rock, the directional variability of relative permeability has been largely ignored. Yet it is apparent that such an effect must be present in a system in which the distribution of oil and gas within the porous matrix is controlled by capillary forces. It is easy to visualize a rock composed of layers of fine and coarse material such that gas flow across the bedding planes would take place only after the average oil saturation had been reduced to a very low value. The fine layers, because of their greater capillarity, would remain saturated and act as barriers to the flow of gas after the coarse layers had been desaturated. Flow of gas parallel to the bedding planes would obviously take place at a much greater liquid saturation. Without more complete information concerning the geology of a reservoir than is generally available, it is not possible to predict exactly how such phenomena would affect the over-all performance of an oil field. It is possible, however, to predict qualitatively the effect of stratification on relative permeability measurements made on laboratory cores. In this investigation the effect of stratification was studied analytically by assuming that two porous materials with different capillary pressure-desaturation curves (but identical relative permeability curves) were in contact and in capillary equilibrium. As a qualitative check on the analytical results, cores having various degrees of visible stratification were used for relative permeability measurements made with fluids flowing both parallel and perpendicular to the bedding planes. A quantitative check was considered impractical because of the difficulty of devising models in which two materials of predetermined properties could be joined without the plane of contact becoming a discontinuity. THEORETICAL CONSIDERATIONS AND ASSUMPTIONS The assumption of capillary equilibrium in an oil-gas system implies that the difference in pressure between oil and gas is everywhere the same. This means that the curvature of the interfaces must be everywhere the same in order to satisfy the equation where PC is the pressure difference between phases, y the interfacial tension and r, and r2 are the major and minor radii of curvature. Depending on the pore size distribution of coarse and fine layers, the volumetric percentages of oil and gas in these layers will differ when equilibrium exists. The exact relationship can only be determined by obtaining the complete capillary pressure-desaturation curves for each of the porous materials in contact. It has been pointed out elsewhere' that the capillary pressure-desaturation curves of sedimentary porous materials can often be approximated by the relation where C is a constant and Soe is the effective saturation to oil based on a percentage of the pore volume effective to flow. In the same paper it was indicated that, as a first approximation, the values of oil relative permeability are given by and the values of gas relative permeability by For this analysis Eqs. 2, 3, and 4 were assumed to apply to each of two components of a hypothetical porous rock in capillary equilibrium. It was also assumed that each of the components had a residual wetting phase saturation of 20 per cent so that 80 per cent of the total pore volume was effective to flow. The permeability of the coarse stratum was taken as 100, and its displacement pressure was such that C in Eq. 2 had the numerical value of 1. The corresponding values for the fine stratum were 10 for the permeability and 10 for C. Units are not specified because they do not enter into the final results. The choice of the permeabilities and displacement pressure ratios was made to expedite the calculations. Any reasonable rock properties could have been chosen without changing the results qualitatively. Several arrangements of the two components were studied. Table 1 summarizes the resultant permeabilities obtained for four types of arrangement. RELATIVE PERMEABILITY CALCULATIONS The first step in the computation of relative permeability for the composite cores was the plotting of the capillary pressure-desaturation curves and the relative permeability curves for the individual components according to Eqs. 2, 3, and 4. At arbitrary

Jan 1, 1957

By P. J. Spencer, J. N. Pratt

The vapor pressure of manganese over liquid Mn-Sn alloys has been determined by a high-temperature torsion-effusion technique. Alloys containing from 8 to 100 at. pct Mn were investigated in the temperature range jrom 1280" to 1580" and the measured pressure values were used to calculate the partial and integral thermodynamic properties of the liquid alloys. The activities show small negative departures from ideality while the integral heats and excess entropies of mixing are asymmetric inform, changing from positive to negative with increasing manganese content. The possible contribution of various factors to the observed thermodynamic properties is discussed. COMPARATIVELY few thermodynamic data are available for manganese alloy systems.' Therefore, as part of a continuing program of studies of the thermodynamic properties of transition metal alloys, measurements have been made on various binary alloys involving this element. In recent publications,2~3 investigations of liquid Mn-Cu alloys and of the Mn-Au system in both solid and liquid states have been reported. For the first-mentioned system the work suggested that magnetic interactions may be responsible for the observed form of the thermodynamic properties, while in the second the influence of the electrochemical factor appears to be dominant. The present paper describes a similar study of liquid Mn-Sn alloys. Again the thermodynamic properties have been obtained from vapor pressure measurements made by use of a high-temperature torsion-effusion technique.4 A detailed description of the apparatus and of the experimental procedures used in alloy preparation and pressure measurement may be found elsewhere.2'4 EXPERIMENTAL RESULTS Sixteen alloys, ranging in composition from 8 to 100 at. pct Mn, were prepared from spectroscopically standardized manganese of 99.99 pct purity and tin of 99.999 pct purity, both supplied by Johnson-Matthey and Co., Ltd. One-gram samples of the alloys were obtained by carefully weighing appropriate amounts of the pure components into an effusion cell; this was then suspended in the apparatus and the metals melted together in situ by heating under vacuum to approximately 1550°K. After allowing sufficient time for a homogeneous liquid alloy to be formed, vapor pressure measurements were commenced. These were determined as rapidly as possible at a series of steady temperatures within the range of interest. The duration of experimental runs on individual samples was kept sufficiently short to ensure insignificant varia- tion of alloy composition during investigation. After completing pressure measurements, the alloys were rapidly cooled and their compositions checked by weighing or chemical analysis. All experiments were conducted using effusion cells machined entirely from boron nitride. Measurements were made using a variety of cells with orifice areas ranging from 0.0032 to 0.0075 sq cm and lengths of the order of 0.04 cm; the usual effusion correction factors for orifice geometry and molecular distribution were calculated using Freeman and Searcy's equation5 and had values between 0.6 and 0.75 for the orifices employed here. The vapor pressures of manganese over the alloys were measured at approximately 20°K intervals in the temperature range 1280" to 1580°K. In view of the close approximation of the measured pressures to Clausius-Clapeyron behavior in the experimental temperature range, the data for each alloy have been expressed by equations of the form: logp(atm) =-A/T + B A least-squares computer treatment was applied to the vapor pressure values in order to obtain the coefficients A and B with their associated error. The resulting equations are listed in Table I, together with the equation for pure solid manganese obtained from a previous study.4 To minimize the effect of possible apparatus calibration errors, the activities and partial free energies of manganese in the alloys were calculated by initial reference to the latter equation, obtained from identical torsion-effusion measurements. The immediately resulting thermodynamic quantities, based on a solid manganese reference state, were then converted to refer to the more appropriate supercooled pure liquid manganese standard; tabulated values of the free energies of solid and liquid manganese from Hultgren et al.' were used for this purpose. Partial entropies of solution of manganese were calculated from the temperature coefficients of the free energies and partial heats from the Gibbs-Helmholtz relationship.

Jan 1, 1969

By B. Yarar, J. Kaoma

[Introduction The critical surface tension of wetting of hydrophobic materials has been investigated extensively by Zisman et al. (1973) and relates the spreading of a liquid on a solid to the surface tension of this liquid. Thus, the Zisman ap¬proach shows that a plot of Cos 0 versus ?LV where, 0 is the contact angle and ?LV is the surface tension of that liquid in contact with its own vapor at equilibrium, produces a straight line which can be extrapolated to Cos 0 = 1. The intercept corresponds to a given ?LV, termed the critical surface tension of wetting. In instances, however, Cos 0 - ?LV plots show deviations from linearity. Alternative approaches have also included the plotting of adhesion tension (YLV COs 0) versus ?LV that can be interpreted in terms of critical surface tension data (Lucassen-Reynders, 1963). It has, on the other hand, been customary to correlate contact angle (0) with flotation data, although it is recognized that surface inhomogeneities and related contact angle hysteresis limit the interpretations pertaining to solid surface structures purely based on contact angle measurements. It is nonetheless true that 0 = 0, when the liquid is water, corresponds to a hydrophilic solid. Determination of ?c by contact angle measurements in conformity with the Zisman approach can encounter experimental difficulties, especially when solids are in a powder form. Following the reasoning that 0 = 0 corresponds to the hydrophilic state of a solid, froth flotation experiments can be expected to produce critical surface tension of wetting values for powders. The technique that consists of plotting recovery (% R) versus YLV data and extrapolating the linear part of the curve to % R = 0, has been described elsewhere (Yarar and Kaoma, 1984). This paper describes some of the results obtained by the extrapolation technique mentioned above, using various sulfide minerals. Experimental Materials Molybdenite (MoS2), sphalerite (ZnS), chalcopyrite (CuFeS2), chalcocite (Cu2S), and galena (PbS) were handsorted from massive samples and ground by mortar and pestle, and the -147 Fan fraction used in experiments; sulfur (S) was a C.P. Fisher Scientific Co. product. Method One gram powder samples were conditioned for three minutes in methanol-water solutions of predetermined surface tension values and the percents recovered by flotation using a Partridge-Smith Cell (Partridge and Smith, 1972), were plotted against each ?LV value. Results and Discussion The percent recovery versus ?LV for two naturally hydrophobic solids, i.e., natural molybdenite, MoS2 and sulfur are given in Fig. 1 where it is seen that ?c for sulfur is obtained as 31.5 mNm-1 whereas for MoS2, it is 26 mNm-1. Figure 1 also shows that the new flotation technique described, for estimating ?c is in good agreement with the Zisman method. Curves obtained by the same method for the minerals Cu2S, PbS, and ZnS are given in Fig. 2, where it is seen that for Cu2S, ZnS, and PbS, the extrapolation to % R = 0 produces ?c values of 36, 39, and 49 mNm-1, respectively. CuFeS2, on the other hand, gives a curve that does not permit such an extrapolation to obtain a ?c value with certainty. Nonetheless, treatment of the powder with 8.95 X 10-5 molar Na2S solution followed by washing with distilled water prior to flotation effects the curves as shown in the insert of Fig. 2. The type of curves given in Fig. 1 appear to be typical of hydrophobic solids as can also be observed in Fig. 3. The composition of solid and minute quantities of inclusions seem to play an important role as regards the surface properties of solids as reflected by the slope of the linear part of the % R - ?LV plot and thus the value of ?c obtained by this technique. For example, MoS2 of three different stoichiometric compositions produced the data given below. [MoS2MoS2.14Mo1.002S2 ?c mNm-126.029.031.0 dR/d?8.95.23.0]]

Jan 1, 1985

By D. D. Smith, D. P. Squier, E. L. Dougherty

A system of differential equations describing the temperature behavior of fluid injected at constant surface temperature in a well is derived and .solved analytically. A formula for the fluid temperature at any time and depth is given, as well us a special formula valid for very large times. These formulas are used to calculate temperatures for several typical cases. The results indicate that, initially, the temperature of the water entering the formation is considerably lower than the injection temperature. This condition lasts for only a short period— less than three days for most cases of practical interest. Following this highly transient period, during which the temperature of the fluid entering the formation builds up to about 50 to 75 per cent of the injection temperature. the system enters a quasi-steady state in which the temperature changes are very slow. After severl years, the bottom-hole temperature will still be 50" to 100°F lower than the injection temperature, hilt the heat losses may he tolerable. INTRODUCTION Predicting the behavior of a hot-water flood requires that the temperature of the water entering the injection interval be estimated. This report describes the development and solution of a system of equations which describes the temperature behavior of the injected water in the wellbore with certain simplifying assumptions. The only previous means known to the authors for describing such a process is that of Moss and White.' Their results appear to be close to those obtained by our method in the practical cases which were compared; this agreement is largely due to the fact that in our method temperature soon approaches a quasi-steady state, as was assumed in their method throughout. However, our model covers all times, is continuous (whereas the Moss-White model depends on breaking the depth into discrete intervals) and. we feel. more closely describes the physical problem. FORMULATION OF THE PROBLEM PHYSICAL SYSTEM AND ASSUMPTIONS The injection procedure consists of pumping water at a fixed surface temperature T., down an infinitely long cylindrical well or tubing of inner radius Any material exterior to the water column such as mud, casing, or cement is regarded as part of the formation. The general behavior of the system may be described qualitatively as follows. When the hot water is first introduced into the system, the temperature difference between the formation and the water is large, resulting in a high rate of heat transfer. As a result, the temperature adjacent to the wellbore rises very quickly. Because the segment of the formation adjacent to the wellbore largely controls the heat transfer rate, the heat transfer rate will become relatively constant when this portion has reached a temperature close to that of the water opposite it. The temperature of the water and formation then increase very slowly with time. The length of the initial highly transient period and the temperature of the water at its conclusion will be functions of depth, injection rate, injection-string radius, surface injection temperature and the physical properties associated with the water-formation system. The following additional assumptions were made. 1. There is no heat transfer by radiation in the system. 2. There is no heat transfer by conduction in the vertical direction in either the injection stream or the formation. 3. The linear volumetric and mass flow rate of the water is constant throughout the injection stream. 4. No horizontal temperature gradient exists in the injection stream. 5. The product of density and heat capacity is constant for both the water and the formation, and the formation thermal conductivity is constant. 6. Initially, both the water in the wellbore and the reservoir are at a temperature given by the (constant) ambient surface temperature plus the product of depth and geothermal gradient (assumed constant). At large distances for the wellbore (r m), the formation will remain at this temperature. 7. The water temperature and the formation temperature at r — r,, are equal for all depths D. DERIVATION OF EQUATIONS The differential equation satisfied by the fluid temperature T,(D, t), which is obtained by writing a heat balance on a cylindrical differential of volume dV of the injection string between the depths D and D i dD, is

By H. Sigurdson, T. V. Cherian, C. H. Moore

The phenomenon of recovery of cold-worked metals is interesting not only because of its practical importance but also because of its fundamental significance in solid state reactions. Although extensive investigations1,2 have already been made in an attempt to discover the mechanics of the recovery process, many of the observations have not yet been satisfactorily correlated to provide a completely consistent model for the process. The wide differences in the recovery rates of various properties can be cited as a typical example of one of the difficulties that are encountered. Frequently, for example, the electrical resistance will have almost completely recovered before any recovery in tensile strength can be detected. Of course, such differences in the recovery rates of different properties might be explained by assuming that each property is a unique function of the work-hardened state, and consequently each property exhibits its own unique recovery rate. The assumption that different properties are uniquely related to the work-hardened state cannot be denied. On the other hand, the properties that recover at different rates often exhibit more or less parallel changes upon work-hardening. This suggests that the microstructural changes attending recovery are not exactly the reverse of the changes attending work-hardening. Several types of imperfections must be postulated in order to account for this apparent anomaly. The different recovery rates for various properties, then, are due to the different recovery rales of the type of imperfection to which each property is most sensitive as well as the unique dependence of each property on the cold- worked state. This concept assumes that a simple model of the work-hardened state consisting only of one type of imperfection, such as Taylor's type of dislocation patterns, is inadequate to cope with the diversified phenomena attending work-hardening and recovery. Although current models for the work-hardened state are not useful for describing all aspects of the recovery process, the general trends of the recovery of each postulated type of imperfection as a function of time and temperature should be at least qualitatively deducible from the rather well developed laws of kinetics of reactions in the solid state. Consequently, recovery data might prove useful for elucidating some aspects of the complexities of the work-hardened state of metals. A preliminary attempt to study work-hardening by investigating recovery rates of cold-worked metals is outlined in the following pages of this report. Experimental Procedure Many properties recover when cold-worked metals are annealed below their recrystallization temperature. Therefore, electrical resistivity, thermal electromotive force, X ray diffraction line widths, X ray diffraction line intensities, elastic spring back, density and other physical and chemical properties have been used to study the recovery process. Major interest, however, has generally been directed toward the recovery of the mechanical properties such as hardness, yield strength, and tensile strength. But a search of the literature suggests that the effect of recovery on the true stress-true strain curve has been neglected, in spite of the current recognition of the fundamental importance of such an investigation. An investigation on the effect of recovery treatment on the true stress-true strain curves in tension, therefore, was undertaken in the present study. Commercially pure aluminum (99. + pet Al) in the form of 0.100 in. thick rolled sheet of 2S-O aluminum alloy was selected as the material for this investigation because rather extensive correlatable data are already available on the recovery of some of its properties. Tensile specimens having a 6 in. long gauge section and a uniform reduced section width of 0.500 in. were machined from the sheet in accordance with a design that has previously been reported.3 All specimens were selected with their axes aligned in the rolling direction. In order to eliminate the effects of previous work-hardening and the effects of machining, the specimens were annealed for 15 min. at 750°F before testing. During tensile testing the loads were measured by means of a proving ring (sensitive to 1/2 lb) in series with the specimen.4 Strains were determined from the extension of a rack and pinion strain gauge sensitive to a strain of + 0.0001. The stress was recorded as the true stress, namely

Jan 1, 1950

By Strathmore R. B. Cooke, Eugene L. Talbot

THE perfluoro acids and derivatives show unusual surface-active properties that qualify them as possible flotation reagents. They lower the surface tension of water from 15 to 20 dynes below that obtainable with the corresponding hydrocarbon compounds.1, 2 Fluorochemicals adsorb very strongly on solid surfaces to give films that exhibit larger contact angles than films of the corresponding hydrocarbons."' * The large contact angles probably result from the terminal —CF3 group. The perfluoro acids are made by electrolysis of the corresponding carboxylic acid in anhydrous hydrogen fluoride.5 From the perfluoro acids many derivatives may be obtained, such as amides, amines, alcohols, xanthates, ethers and esters and others. Since the fluorinated analogues of the conventional hydrocarbon flotation collectors possess enhanced surface properties, a few were selected for testing. Because a survey of all possible minerals and reagent combinations would be out of the question, hematite was chosen to represent a nonsulphide system and pyrite to represent a sulphide system. The fluorinated reagents used in these experiments were prepared in the research laboratories of Minnesota Mining & Mfg. Co. Some were synthesized especially for this research. They are not available cokmercially. Separation of Nonsulphide Ores: The separation of oxides from silica has always been a challenge to the flotation industry because differences in surface properties of the minerals are normally insufficient to produce clean concentrates. Oleic acid," rosin acids,' and amine salts% ave been used to considerable extent to effect separation of metal oxides and silica. The system hematite-silica was chosen to represent the nonsulphides both because of its difficulty of separation and because large tonnages of easily obtainable material are available, such as gravity concentration tailings and nonmagnetic taconites on the Mesabi Range. The wash-ore tailings used here contained approximately 35 pct iron after desliming. Samples of the material used in this work were part of the same lot used by Chang, Cooke, and Huch9 and were prepared in an identical manner. Reagents for Nonsulphide Ores: Since one of the purposes of this investigation was to compare hydrocarbons with fluorocarbons, reagents of known behavior such as oleic acid, and the alkali metal salts of certain resin acids (Dresinates), were established as standards. Hydrocarbons and fluorocarbons of comparable chain length and other experimental fluorocarbons were tried as collectors for hematite. A list of the materials used and the concentrations of their stock solutions are given in Table I. Since silica can be selectively floated from hematite by conventional reagents," a few fluorocarbon reagents were also tried for this purpose. Their composition and concentrations are given in Table 11. Most of these reagents served the dual function of collector and frother. In the case of F-11 flotation did not occur but it served as a frother when F-6 was employed as a collector. Reagent grade sulphuric acid and sodium hydroxide were used to regulate the pH. Deionized water containing less than 0.1 ppm of salts expressed as NaCl was used for all solutions and flotation tests. The pneumatic flotation cell consisted of a 350-ml fritted glass Buechner funnel with a source of filtered air which could be controlled by a needle valve." A 50-g sample of ore and 250 ml of deionized water were added to the flotation cell and stirred slowly. The reagents were added and the pulp was conditioned before air was admitted to the cell. Approximately 15 ml of the pulp were removed for pH determination before flotation was started and were then returned to the system. The pH was again measured after flotation. Air was admitted to the cell until no further flotation occurred or until the character of the float changed markedly. Both the float and the nonfloat products were filtered, dried, weighed. and assayed for iron. The cell was washed in hot water and rinsed with deionized water after each test. Occasionally the cell was cleaned with concentrated hydrochloric acid to remove iron oxide particles from the glass frit. Experimental Results: Above a pH of 8, sodium oleate was an effective collector for hematite. The emulsification of equal parts of heavy fuel oil (20"

Jan 1, 1956

By A. G. Guy

Thermodynamic activity rather than chemical composition is basic to the analysis of diffusion. This is the essential conclusion reached by Darken1-3 and by Birchenall and Mehl.4 If so, it is reasonable to expect that diffusion calculations should be carried out using activities. This paper will illustrate a method of employing activities in analyzing interstitial diffusion. For interstitial diffusion (of carbon in iron and probably generally) the diffusion of the solvent atoms, volume changes, and other such complexities not explicitly provided for in the usual diffusion equations cause a negligible error of the order of 1 pct. Therefore it is relatively easy to test the validity of an analysis based on activities in the instance of interstitial diffusion. The mathematical treatment of the more complex substitutional diffusion could be simplified once the adequacy of the activity method had been established for substitutional diffusion. Thus the present work has the purpose not only of providing a superior analysis of interstitial diffusion but also of indicating a possible approach to the more important question of an adequate treatment of substitutional diffusion. Development of the Diffusion Equation Although activities are convenient quantities to determine experimentally, they are derived from the more fundamental fugacities.9 Possible confusion in using activities can be avoided by basing equations involving their use on the relationship, dP = -D1d/ax dt [I] where, dP = the number of grams of solute crossing one cm2 in the time dt sec. D, = the diffusion constant for use with fugacities; it is assumed to be constant at a given temperature, and has units of secs. f = the fugacity of the solute in the solid solution; the units are those of pressure, dynes per cm2. x = the distance in cm. Eq 1 can be considered to be the basic form of the first Fick Law for one-dimensional diffusion. In order to convert Eq 1 into an equation involving activities, a choice of a standard or reference fugacity, f°, must be made: then. a = f [2] where a is the activity corresponding to the fugacity f. However, the value of a is also determined by the relation, a = a\c [3] where a is the activity coefficient and c is the concentration. For a given value of a (such as a = 1) it is evident that the units used for expressing concentration will affect the numerical value of a corresponding to a given amount of carbon dissolved in y-iron. Since weight per cent concentration is so widely used, this unit will be adopted as the standard in this paper. When the value off given by Eq 2 is substituted in Eq 1, the first Fick Law becomes, dP= -D,f°dl [4] Since D,f° is constant (at a given temperature), the second form of Fick's Law can be obtained in the usual manner, -dt D'f° dx [5] where c' is the concentration in g per cm3. In terms of weight per cent concentration, c, Eq 5 becomes, dc _ 100 d2a Tt = T /f w [6] where p is the density of the solid solution and will be assumed to be constant. In order to simplify Eq6, it is necessary to consider the standard state, f°. Standard states are chosen for convenience. There appears to be one especially convenient choice for the analysis of interstitial diffusion. If the activity coefficient, a, is set equal to unity at infinite dilution of the solute, 100 then — 100D1fl° is approximately equal P to the usual diffusion constant in dilute solutions. This is true since the activity, a, in Eq 6 can be replaced by the concentration, c, with little error in an infinitely dilute solution.* Here f1° is the standard fugacity necessary to achieve this standard state. It is proposed that a diffusion constant Da' be defined, Da1=100/pD1f1° [7] where A is the metal whose diffusion is * The second derivative of a is equal to the second derivative of c in dilute solution only if -da/dr- is. zero. Although theory does not require this condition, in the systems C in Fe, and Zn in Cu, dc is in fact found to be essentially zero.

Jan 1, 1950

By Tibor Stefansky, John E. Dorn

MOTT and Nabarro1-5 were first to illustrate the importance of the flexibility of dislocations in accounting for the strengthening that metals undergo due to the presence of internal-strain centers. Such strain-centers might arise from a number of causes such as radiation damage, the presence of semicoherent and coherent precipitates and clusters, as well as individually dispersed interstitial and misfit substitutional solute atoms. Each strain-center induces positive and negative shear stress fields on the slip planes of the surrounding alloy matrix. In order to effect plastic deformation, therefore, the alloy must be subjected to sufficiently high applied shear stresses to push dislocations past all such internal stress fields. If dislocations were inflexible and moved as rigid lines, they would be equally pushed and pulled by internal stress fields. At this extreme the strengthening would be vanishingly small. Dislocations, however, are not rigid; they are flexible and extensible. They wiggle between positive and negative strain-centers, thus increasing their line energy at the expense of their interaction energy with strain-centers. cottrel16 and Friedel7,8 have independently presented lucid reviews of the significance of the Mott-Nabarro dislocation-flexibility concept to the strain-center strengthening of alloys. Their analyses however were only semi-quantitative. There is evidence in the recent literature of renewed interest in a more rigorous analysis of flexibility. Thus, Gleiter9 and Gerald" have shown that the calculated strain-energy interaction between a dislocation and the stress fields of coherent precipitates can be seriously in error if the flexibility of the dislocation is not taken into account. This report will be concerned with a more detailed analysis of the problem based on the following approximations: 1) Although many types of strain-centers exist, the following analysis will be limited to the case of solute-atom strain-centers in fcc substitutional alloys. 2) To facilitate the analysis by avoiding statistical considerations, the strain-Centers are assumed to be in regular arrays on the slip plane. Although the quantitative results are somewhat dependent on the type of array that is assumed, the qualitative trends are similar for various arrays that were studied. 3) An adjustment of the results from those for square arrays to those for the more realistic case of a random distribution of strain-centers is accomplished by adopting the interesting statistical theory first introduced by Kochs,11,12 elaborated on by Dorn, Guyot, and stefansky,13 and analyzed by Foreman and Makin14 in their computerized experiments. 4) For simplicity the dislocation lines are taken to wiggle about their edge orientation and no correction is applied to their line energy for deviations from edge configurations or for the elastic interaction between segments of the now curved dislocation. It will be shown that for extremely low concentrations of atomic strain-centers the strengthening increases with the square root of their concentration. For slightly higher concentrations the strengthening rate becomes less rapid. At a critical concentration a maximum strength is obtained and a decrease in the strengthening takes place as the concentration of solute atoms is further increased. These trends are a direct consequence of dislocation flexibility. They arise from changes in the amplitude of the waviness of the dislocation line at the yield stress with solute atom concentration. Despite the simplifying assumptions that were made, the results agree qualitatively with appropriate experimental data. I) STRESS FIELDS ON SLIP PLANES Internal stresses are introduced in a lattice whenever a host atom of radius ro is replaced by another that has a different atomic radius. According to the classical theory of linear elasticity,15 the stress field about a solute atom at the origin of a spherical coordinate system is given by arr=-4G€(?_0)3 ffflfl ="W =2G€{t) f°rr^ro(l+e) UJ where G is the shear modulus of elasticity and Y, = ro(l + E) is the radius in situ, of the substituted atom. As shown by ~shelb~,'~ this approximation assumes that the bulk modulus of elasticity of the substituted atom is identical with that of the host species. ~abarro'~ suggested that the strain E can be deduced

Jan 1, 1970

By A. Kaufman

More than 3 trillion gal of water are used annually by the mineral industry. Of this, approximately 21/2 trillion gal are recirculated, the rest constituting intake water. The major users are natural gas processing plants and phosphate rock, sand and gravel, and iron ore producers. Water was used by the mineral industry for mining (6%), processing (64%), cooling and condensing (27%), and miscellaneous uses such as boiler feed and sanitary purposes (3%). Whereas total water use is dependent on the quantity of material processed and on the particular process requirements of an industry, recirculation is dependent on processing, as well as cooling and condensing requirements, quality of new water intake, and the necessity for treating new and discharged water. Consumed water, on the other hand, is dependent on the quantity of water recirculated, and temperature and humidity in the area. Based on this analysis, an increase in water use by the mineral industry of 21/2 times by 1985 is forecast. Wster intake, however, will only rise 62%, because of a substantial increase in recirculation. In one report of a special series concerning the water resources of the United States, the Senate Select Committee on National Water Resources, 87th Congress, estimated that water demand would double by 1980 and triple by 2000.' In view of the possible water deficiencies that might result from such expanded usage and the need for research guidance, the Bureau of Mines organized and carried out a statistical canvass of water use in the mineral industry for calendar year 1962. The data used in this paper, unless otherwise noted, are derived from that canvass.' The efforts in this paper are devoted toward summarization of the canvass and analysis of the data. SOME DEFINITIONS Intake: Water introduced from an external source for the first time into a given mine or plant regardless of quality. Intake water is also called new water, water withdrawn, or makeup water. Fresh Water: Water suitable for cooking and drinking. Saline Water: Water containing more than 1000 parts per million of dissolved solids. Contaminated Water: Water not suitable for domestic use, but excluding saline water. Recirculated Water: Water reused to conserve intake water. Solutions that are recycled primarily because of fixed metallurgical practices, such as copper leaching solutions containing sulfuric acid, are excluded. Gross Water Used: Recirculated water plus intake water. Also called total water used. Consumed Water: Water that is lost by evaporation, as well as water lost in product. Seepage and transferred water are not considered consumed. The use of either intake or recirculated water may result in consumption. However, because of difficulties in measuring consulmption, consumed water is defined as the residual between intake and water discharged from the mine or plant. Mineral Industry: For the purposes of this paper, mineral industry includes all metal and nonmetal surface and underground mines and their associated processing plants, as well as custom mills, coal washing plants and associated mines, petroleum and natural gas well drillers, natural gas processing plants, and secondary recovery operations. WATER USE IN THE MINERAL INDUSTRY Water used by the mineral industry constitutes a relatively minor fraction of the water withdrawn by all users. Data compiled by the U.S. Geological Survey in 1960 indicate that water withdrawals, exclusive of that used to generate hydropower, approximate 99 trillion gal annually.3 Our data indicate that water withdrawals by the mineral industry comprise only 1% of this total, or 2% of the water withdrawn by industrial users. Use by Industry: Water used by various mineral industries is shown in Table I. The table indicates that close to one-half of the gross water used by the mineral industry in 1962 was used by natural gas processing plants, followed by sand and gravel, phosphate rock, and iron ore producers. The largest aggregate users of water are also the largest users per dollar of product. For example, Fig. 1 shows that the natural gas processing and phosphate rock industries are very large users of water per dollar of product. Their recirculation per

Jan 1, 1968

By W. F. Mullen, C. W. Stickler

WITH few exceptions, unit operations in the Pennsylvania slate industry in 1950 did not differ appreciably from production methods described by Behrel and Bowles2-4 several decades ago. Many traditionally picturesque but relatively inefficient hand operations continued to contribute to high operating costs in an industry in which the margin of profit, for various reasons, was admittedly low. As part of a general program in which the Pennsylvania State College has been assisting the slate industry to solve some of its problems, time and method studies were used in an effort to determine the bottlenecks of production flow. The results are as applicable to other stone industries as they are to slate. A study of the basic elements in the production of roofing slate, structural slate, and slate blackboards among selected slate producers revealed comparatively few refinements. Any marked difference in operating method was characterized largely by the available equipment, a noticeable difference in the working properties of the rock quarried by a particular company, and by either the habit thinking or ingenuity of the individual operators. With the hope that significant economies in manufacture might result, all the unit operations were broken down into elements for study and analysis. The greater part of the study encompassed those operations from the quarry rim to the finished product; however, to obtain a reasonable synthesis of time allotments per operation, several analyses of quarrying from the finish of the wire saw cut are included for reference. The complete study of quarrying made by Bowles several years ago resulted in the introduction of the wire saw into the operation; there appears to be a need for as fundamental a change in the processing of finished slate as the wire saw was in the quarrying process. Fig. 1 illustrates the flowsheet of quarried rock from the parent bed to the quarry rim with the basic elements which contribute to the difficulty of removing slate from the ground. In Pennsylvania roofing slate is produced by one of three procedures, many operations of which are quite similar. In the traditional or classical method the quarried rock is reduced by sculping and auxiliary manual treatment to workable size and then is split and dressed (trimmed to size) in the conventional shanty. Archaic as this method might appear, there are several elements that result in substantial savings over more mechanized operations. In a modified version of this method, the block is reduced by sawing and gouging preparatory to splitting and dressing in indoor stations. This method is particularly adaptable to rock which fractures unevenly by conventional sculping methods. In the third and more modern method, reduced block received from the block maker is diamond-sawed to length and finished on a production line. Fig. 2 illustrates the flow pattern in each case. In the modified and more modern plans, dressing is done on mechanically-operated trimming machines, which appreciably reduce the fatigue factor of the operator. However, it should be noted that it is advantageous for the operator to be able to control the speed of the knife to prevent breakage of certain classes of stock. In the classical plan the splitter and dresser normally act as blockmakers also and carry their eighter slabs (equivalent in thickness to eight shingles) into the shanties themselves, all of which adds to fatigue and reduced efficiency. The extremely low investment and operating expense of the classical method has undoubtedly been of paramount importance in its continuation. Production of Mill Stock The production of mill stock is accomplished by less picturesque methods than enter into the production of roofing slate but it is, in the main, relatively more efficient because of the increased use of machinery for handling and for finishing. Mill stock can be classified into two categories as far as difference in production method is concerned: structural slate and blackboards. The significant difference in operation is caused largely by the nature of the rock used for each product with the best and easiest cleaved rock being reserved for blackboards to permit the splitting of large slabs to as little as 1/2 in. in thickness. Structural stock, on the other hand, is split into panels no thinner than 11/2 in. and

Jan 1, 1952

By R. F. Mehl, C. E. Birchenall

SINCE Maxwell1 first considered the self-diffusion process in 1872 its importance in the kinetic theory of matter has been recognized. Until the discovery of isotopes in 1913, a direct measurement of this quantity seemed impossible. The only information that could be gathered indirectly was for gaseous systems for which the kinetic theory was well developed. When methods of direct observation be-came available, investigations on self-diffusion were carried out in condensed phases. In metals these data are presumably of potential importance in the study of recovery, recrystallization, creep, sintering, and related phenomena. Following the pioneer work of Von Hevesy2 and his collaborators, who determined the rate of self-diffusion in lead with the naturally occurring thorium B isotope, several metals have been investigated. Pb, Ag³, Au.6,5, and Cu6,7,8,9 are examples of isotropic crystals existing in only one phase modification. Anisotropy of diffusion has been demonstrated in Bil6 and Znll. This paper is a study of a single metal in two allotropic forms and also of self-diffusion in a body-centered cubic lattice. Despite the fact that the measurements in each of the papers cited on self-diffusion in copper seem to be internally consistent to about 10 to 15 pet, the curves reported by different authors differ by factors of 2 to 4 at the same temperatures. This uncertainty may account, in part, for the failure to establish a successful correlation between the self-diffusion rates and other physical characteristics of the metals. No satisfactory theory of metallic self- diffusion has as yet been proposed to account for all the existing data and to permit estimation in other metals. Experimental Part: Two units of radioactive iron were used in these experiments, each a mixture of Fe53 and Fe59 (12). Fe53 decays by K electron capture and the emission of an X ray with a half life of about 4 years. Fe59 emits two beta spectra, one with a maximum energy of 0.26 Mev, the other 0.46 Mev, and gamma rays of 1.1 and 1.3 Mev, with a half life of about 44 days. They were present in nearly equal concentration initially. The composite half life started at about 50 days and increased as the Fe59 decayed, leaving Fe55 relatively more abundant. After aging a year, the half life was too long to measure significant decay in a month. The absorption properties also changed with time. Because of the importance of the absorption coefficient in the diffusion calculations, it was necessary to determine this quantity frequently over the period during which these experiments were carried out. This correction was unsuspected at the time of publication of notesl3 on this work and accounts for the discrepancy in alpha iron and for part of the discrepancy in gamma iron.* * The data in the present paper supersede those given in the notes entirely. In one note the scale of log D was inadvertently reversed. In addition to the correction for the drift in absorption coefficient, the D values for gamma iron at low temperatures were high owing to insuficient correction for diffusion occurring during heating and cooling through the high temperature part of the alpha range at a rate much slower than that employed in the runs reported here. The high temperature alpha rates are much higher than the low temperature gamma rates and correspond to large equivalent times at these temperatures. These experiments were discarded and new measurements taken. Independent experiments with the same activity units indicated a radioactive contaminant in the iron, but exhaustive attempts to isolate and identify it chemically failed. These experiments? indicate † These experiments will be discussed in a later publication from this laboratory. that the contaminant represented only a trace of little importance in the diffusion results. The active iron was plated from an iron chloride solution. Enough of the solution was dropped on a 1% in. square of filter paper to wet it thoroughly.

Jan 1, 1951