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By M. N. Shetty

LARGE copper whiskers were grown from cuprous iodide by reduction with hydrogen at about 500°C. Carefully selected single-crystal whiskers of [loo], [110], and [Ill] orientations were used and the whisker shapes and cross sections are shown in Fig. 1. Spec-trographic analysis of a typical batch of whiskers showed that the composition was better than 99.9 pct with iron and silicon as the major impurities. The test specimens varied from about 70 to 400 u in diam and they did not show a conspicuous yield drop as observed in very fine whiskers (diam <25 u), tested by Brenner.1 The characteristics of the stress-strain curves were similar to those of bulk single crystals, even though the maximum flow stresses reached in some orientations were comparable to the yield stresses observed in fine whiskers. Mechanical properties of whiskers of different materials and copper whiskers up to about 100 u in diam have been reviewed,&apos; and a mechanism of slip band propagation in fine whiskers has been recently suggested.3 Whiskers in this work were tested in a floor-model Instron testing machine using low strain rates. (Details of the testing procedure, diameter dependence of the yield stress, and the characteristics of the load elongation and stress-strain curves have appeared esewhere.4) Due to the extensive deformation, >50

Jan 1, 1970

By M. L. Samuels

DURING the period from 1910 to 1920, there was a lively interest in. the subject of grain growth and many papers were published, followed by interesting discussions. Questions dealing with the fundamentals of grain growth-why and how it occurs-were treated in papers by Howe,1 Jeffries,2 Sauveur,3 Chappell,4 Beilby,5 Mathewson -and Phillips,6 McAdam,7 Carpenter and Elam,8 Stead and Carpenter,9 Ruder,10 as well as others. Since that decade, much indeed has been done regarding the practical control of grain size, and it is now possible to order material having a size specified in the American Society for Testing Materials classification. Also, one hears the term "spliced boundaries" used in connection with certain tungsten lamp filaments" wherein it is important to prevent "sagging" between consecutive turns of the helix.12 This practical use of a certain knowledge as to the things that influ-ence or even control grain growth should not be taken as an indication that the subject has been thoroughly explored and that nothing more can be learned from fundamental studies. It is with this thought in mind that a report of some observations and experiments on abnormal grain growth is believed justified. Abnormal grain growth is met with in heat-treating high-carbon steels in the austenitic range,13 in the harden-ing treatments of high-speed steels,14,15 and in the low-temperature annealing of strained low-carbon steels as in sheet and wire material. Entirely aside from these instances of exaggerated grain growth, which some might consider as freakish, it is thought that abnormal growth is simply a case where the growth forces and the forces tending to prevent growth are almost, but not quite, evenly balanced. Information relative to grain-growth characteristics in general may be obtained from a study of abnormal growth conditions, which may be looked upon as vantage points. Reflection will show at once that if growth forces are great in comparison to inertia or resistance to growth, many crystals start to grow and, for that reason, none becomes very large, whereas if inertia is predominant no growth at all takes place. Under conditions in which

Jan 1, 1938

By K. Matsuda, H. Tanaka, M. Mamiya, H. Majima

Copper cementation was studied from both thermodynamic and kinetic aspects. The temperature effect of copper cementation, which has been recognized as an anomalous result, and the rate enhancement phenomenon observed after the initial linear step are, in particular, focused in this work. The main results obtained are as follows; 1) Free energy changes of copper cementation reactions, calculated by the use of the "Correspondence Principle" of Criss and Cobble are rather insensitive to temperature. 2) A Flow-cell assembly consisting of a special cupric ion electrode, a calomel electrode and a potentiometer is particularly useful for the continuous measurements of copper cementation rate. 3) Two first-order reaction rate constants for the CU2+- Fe system were successfully determined by the use of the flow-cell assembly. 4) Activation energies determined for the initial rate and the 9 maximum rate of CU2+ - Fe system are both 4.6 kcal/mole. This fact suggests that the mechanisms of the initial reaction and the final reaction are essentially the same and both reactions are rate controlled by the diffusion in a boundary layer. The difference in the rate constants of them may fie explained by the effect of the nature of surface deposits. 5) Qualitative explanation of the rate enhancement phenomenon from the initial rate was successfully made by applying Bockris "Penetration Model."

Jan 1, 1976

By E. Gaujot

IN connection with the question of coal waste and economy in mining, we would call the attention of those interested to an apparatus invented by M. Dernencourt, Superintendent of the Anzin Division of the Anzin Coal Company, North of France. This apparatus is known in France and Belgium under the name of prop screw-jack (vis botte), and has been used with good results in the above-named countries for some years past. M. Ponson gives, in his " Trait6 de I&apos;exploitation des Mines," a description of it (page 533), but as the description given is old, the work not widely known in this country, and as some valuable improvements have been made since, I thought it might be useful to give a description of it, having seen it in &apos;operation in 1867, while in Europe to attend the great Exposition, and on a scientific tour to the mining districts of France, Germany, Belgium, and Italy. The prop screw-jack is composed of the following pieces : I. The body or column B, Fig. 4 [Plate (I)], of oak or yellow pine, sawed square, the bark taken off, and any length, proportionate to the vein. The smallest are 10 inches diameter at the base, and 9 inches at the top, the height being from 12 to 15 inches less than the size of the vein. In the axis of this column, and at the top end, is a cylindrical opening or hole, C, 22 inches diameter, 10 inches deep, for the screw, S. II. Two wrought-iron rings, R R, to strengthen the two extremities of the column ; the rings must be put on hot. III. A cast,-iron washer, E, with hole in centre a little larger than the screw, to be put on the top of the column, and on which the nut is to rest; the top side of this washer must be faced on the lathe, also the bottom of the nut, to prevent friction. IV. The screw, S, having a total length of 12 inches and a diameter of 24 inches (for very high veins this diameter may be increased to 3 inches), and has on its top a wrought-iron plate, T,

By J. S. Kirkaldy, R. J. Brigham

AS part of a program to investigate the diffusive properties of dilute ternary austenites we have made a determination of the effect of chromium on the activity of carbon in ? iron. Samples of pure iron and Fe-Cr alloys were simultaneously equilibrated at 1000°C with atmospheres of controlled CO/CO2 ratio following the procedures of Darken and Gurry 1 and smith.&apos; The 0.020 in. thick samples were analysed for carbon by microcombustion analyses3 to yield a set of isoacti-vity curves. The latter were converted to activity coefficient (standard state at infinite dilution) plots by combination with Smith&apos;s data2 for the activity of carbon in pure iron. Table I shows the compositions of the base alloys used while Fig. 1 shows the experimental results superimposed on a set of curves generated by the relation In?C=6.9NC- 10.7 Ne In the notation of wagner4 the interaction parameter is the second coefficient on the right, Sgr = - 10.7 This can be compared with a rather inaccurate value deduced from the transient equilibrium diffusion data of Kirkaldy et al.&apos; as The authors are indebted to the American Iron and Steel Institute for financial support. This material is condensed from a B.Sc. Thesis submitted to Mc-Master University by R.J.B.

Jan 1, 1963

Francis Drake, Bulawayo, Rhodesia, So. Africa (communication to the Secretary *):—I should like to place on record some data in addition to those given by Mr. Canby in his paper. I regret that my notes have been destroyed so that I can give no accurate measurements of the water jacket that I am about to describe. This furnace mas erected in Cerro Gordo, Inyo county, Cal., early in 1875, and I think it quite possible that it was the first applied in lead smelting. It was made of plate iron and elliptic in shape, the inner dimensions being about 54 by 42 in. by 48 in. high. The distance between the inner and outer plates was about 6 in. Tuyere holes, one at the back and two on each side, about 12 in. in diameter, were made in this, and in these were placed cast-iron water tuyeres about 16 in. long, the diameter of the blast orifice at the point being about 3 in. The height from tuyeres to feed door was about 9 ft., but the top of the charge was kept about 5 ft. above the tuyeres. There was a space of about 12 in. between the jacket and the top brick-work. This brick-work was supported by a cast-iron plate resting on four cast-iron columns. At the beginning, the jacket was lined with air-dried radial bricks, made of crushed quartz and fire-clay, as it was thought that the jacket would not stand the heat on its bare plates. After a short time the practice was altered and no lining mas put in. The jacket was closed at the top and had a steam drum connected by two pipes at the back. This steam drum was connected to the boiler in which the steam was made for driving the Baker blower, the rock breaker and the pumps. The bottom of the jacket mas also connected to the boiler. The jacket was run under boiler pressure (80 Ib.) for some time, but eventually cracks developed in the inner plate between the tuyere holes,

Jan 1, 1913

Uranium, discovered in 1949 at Rum Jungle, 40 miles south of Darwin, N. T., was mined and processed to U3O8 from 1954 to 1963 by the Territory Enterprises Pty. Ltd. TEP is a Government company managed by Conzinc RioTinto of Australia Ltd. During this period, the uranium oxide was sold under contract to the Combined Development Agency, a joint Anglo-American uranium procurement agency. When the contract terminated in 1963, more than 31/4 million pounds of uranium oxide had been delivered which had been mined from three open pits. Copper ores, found with the uranium, necessitated the addition of a copper circuit to the concentrator. Copper concentrates containing 12,981 pounds of copper were also produced. Rum Jungle was the largest single industrial enterprise in the Northern Territories and, as such, was an important economic and social factor in this sparsely settled tropical region. To stretch out the life of this enterprise for the above reasons, and with the added possibility that the uranium market might improve, the Commonwealth mined out and stockpiled 650,000 tons of ore containing 9.6 lb of U,O, per ton, which is sufficient to sustain the treatment plant at 200 tpd until about 1971. In the plant, uranium is recovered from solution by solvent ex- traction. Current output is being stockpiled pending suitable market conditions.

Jan 10, 1964

By David P. Shoemaker, Clara B. Shoemaker

It has been shown for an important class of complex transition intermetallic compounds (a, P, R, 6, and p phases) characterized by "normal" coordination [CN12 (icosahedral), CN14, CN15, CN16/ that interatomic distances nay be calculated to a good approximation as the sum of characteristic atomic radii. Two radii, one for major ligands and one for minor ligmds, are specified for each atom, except in the case of CN12 where only a miaaor-ligand radius is specified. The same appears to be true of transition-metal phases of simpler struc-ture: Laves phases (CN12, CN16), and p-tungsten phases (CN12, CN14). In the case of known examples of the more complex phases, a simple rule is given which specifies these radii. However, only a fraction of the known examples of the simpler phases obey this rule closely. To include the latter phases the rule may be modified by considering the radii as linear functions of the weighted average of the Pauling CN12 radii of the two kinds of atonzs, with the radii weighted according to the over-all chemical composition of the alloy. With very few exceptions interatomic distances for both tlze complex and the simpler transition phases can b$ predicted with this modified rule to within 0.06A. ManY intermetallic compounds are known of composition A,By, in which A is a transition element to the left of the manganese column in the periodic table and B is a transition element in or to the right of it. Frequently the coordination numbers (CN) found in these compounds are CN12 (icosahedral), CN14, CN15, and CN16 (called "normal" coordinations by Frank and Kasperl). Well-known examples are the cubic and hexagonal Laves phases which have CN12 and CN16, and the 0-tungsten (CrsO) phases which have CN12 and CN14. In the more complicated (often ternary) phases, such as the a phase,2 the Beck phases p3 and R~, the 6 phase,5 and the p p atoms occur with CN12, CN14, CN15, and (except for a) CN16; in many cases several crystallographically independent atoms of one particular CN occur in the asymmetric unit. A large number of independent interatomic distances are found in these complicated phases, varying from 20 in the a phase to 94 in the 6 phase. These distances show a large spread; they vary, for example, from 2.358 to 3.278A in the 6 phase. In our analysis of these distances we found that in each of these compounds every atomic position can be characterized by either one or two radii. The CN12 positions are characterized by a single radius, The higher coordinated positions are characterized by two radii, namely: the CN14 positions by 4 in the direction of the twelve "5-coordinated" ligands3 (called &apos;minor" by Frank and Kasperl) and by r:, in the direction of the two "6-coordi-nated" ligands (called "major" by Frank and Kasper); the CN15 positions by r15 for the twelve minor and r:, for the three major ligands; the CN16 positions by rlE for the twelve minor and r:, for the four major ligands. We have expressed the experimentally determined interatomic distances in observational equations as the sums of the appropriate pairs of these characteristic radii and the value of these radii have been determined by the method of least Squares. Despite their wide range, the interatomic distances could then be predicted by the sums of these atomic radii with an average deviation in any one compound of 0.06A or less. The results are summarized in Table I. Inspection of the radii thus obtained shows that in the structures in Table I the radii (in A) are given to a first approximation by the simple relationship: Where CN is the coordination number (12, 14, 15, or 16), and A = 1 for major ligands and = 0 for minor ligands. The interaLomic distances can be predicted within about 0.1A by sums of these atomic radii. Another phase belonging in this group with CN12, 14, 15, and 16 is the y phase & B7, in which A is molybdenum or tungsten and B is iron or cobalt. Recently the M%C phase has been refinedE and the observed distances also agree well with those calculated with Eq. [I]. (In the original determination of the structure of W6FeV7 the F$(II)-W(II1) distance was erroneously given as 2.84A, but we have recalculated it fro? the published parameters and found it to b? 2.57i4, in good agreement with the value of 2.6A predicted with Eq. [I.].) Many binary transition alloys are known to crystallize with the simpler structures having "nor-

Jan 1, 1964

By Walter R. Hibbard

BACKOFEN&apos; reported recently that "the deformation texture of cold-drawn OFHC copper wire, after a reduction in area of 97.3 pct, may still be described as a composite of [lll.] and [loo] directions aligned parallel to the wire axis." In the introduction, he indicated that this was in contrast to the work of Hibbard,&apos; who reported a single [111] texture after a reduction of 96.4 pct. Unfortunately Backofen stated that this was a reduction in area when actually it was a reduction in diameter, as is clearly stated in the reference. Moreover, the results of Backofen are in complete agreement with the results of Hibbard. Backofen&apos;s 97.3 pct reduction in area is an 83.3 pct reduction in diameter, after which he foundadouble [ll11 and[l001texture with the former predominating. Similarly, Hibbard; after an 86 pct reduction in diameter found a double [Ill] and [I001 texture with the former predom- inating. Hibbard, however, when he drew the wire further to 96.4 pct reduction in diameter, found primarily a single [Ill1 texture as illustrated by Fig. 2 of ref. 3. Here also, Hibbard- reported evidences of the [loo] recrystallization texture found by Backofen. It might also be pointed out that Backofen not only drew his wire 97.3 pct reduction in area but also etched them over 99 pct reduction in area from 0.125 to 0.01 in. diam. Hibbard&apos;s wires were drawn directly to size. In summary, the deformation texture of cold-drawn copper wire still may be described as primarily a single Clll] texture after a sufficient amount of drawing, such as 96.4 pct reduction in diameter." a

Jan 1, 1952

By Basil B. Zavoico

PRODUCTION of crude it in the United States during 1939 totaled about 1.255,776,000 barrels, an average of 3,440,482 barrels per day, 3.41 per cent above the 1938 output of 1,214,355,000 barrels but 1.83 per cent below the record pro¬duction of 1,279,160,000 barrels, in 1937. However only the two-week shutdown of oil fields in the Southwestern States in August and September prevented the domestic crude production from establishing an all-time record in 1939. Demand for all petroleum products for the first ten months of 1939 showed an increase of 7.04 per cent over the similar period of 1938. Domestic demand for all petroleum products was particularly benefited by the increasing industrial activity, advancing 8.37 per cent above the like period of the preceding year equivalent to a volume increment of 256,810 barrels per day; with motor-fuel demand gaining 5.83 per cent and demand for all fuel oils gaining 12.15 per cent over the corresponding period of 1938. The export demand for the first ten months of 1939 was slightly below the export movements during the same period of 1938, declining 0.56 per cent. The European war was a major factor in 1939 for the petroleum industry in the United States, even if, at the end of the year, the war had not yet resulted in the expected large shipments to England and France.

Jan 1, 1940

By B. D. Harden

FOR over fifty years the Spanish mine, 21 miles northeast of Nevada City, in Nevada County, California, has been one of the Bradley properties. Between 1883 and 1889 it was operated by the late Frederick W. Bradley and P. R. Bradley. The ore averaged only about $1 a ton at that time but the mine was credited with a production of about $900,000 in that period. The property was then closed down until 1922, when the Bradley interests reopened it and continued development for the next nine years, when a 50-ton mill was built. This began operation in April, 1931. This was a selective flotation plant, with the tailing treated on Wilfley tables, and operated on ore from the No. 4 and No. 16 tunnel stopes. This ran from $3 to $6 in gold, 2 to 3 oz. of silver, copper 0.6 per cent, lead 1.5,

Jan 1, 1935

By Charles Austin

IN an earlier series of studies on 18-8 stainless steel at 600°, 700°, and 800°C.1 one pretreatment was used throughout; viz., 15 min. in hydrogen at 950°C., followed by an air quench. Several manufacturers of this alloy since have expressed doubt as to the suitability of the temperature employed, recommending instead the more customary Strauss treatment as promising superior results. In this subsequent investigation on the effects of the temperature of pretreatment several interesting points have arisen, which are described in this paper. Previous work on our equipment had shown a marked difference between alloys of "similar chemical composition" that had been manu-factured by different companies. Accordingly, one mill-bar length was selected from which to prepare all specimens. It could then be assumed that any marked differences in creep characteristics would be due to effects resulting from variations in the pretreatment of the alloy. The material was furnished by the Allegheny-Ludlum Steel Co. in the form of 5/16-in, dia. rod, finished by air cooling from a mill anneal at 1950°F. (1066°C.). It was analyzed only for the elements shown: carbon, 0,07 per cent; chromium, 18.73; nickel, 9.46; manganese, 0.40. Three pretreating temperatures were chosen, the specimens being held for 15 min. in hydrogen at either: (1) 1150°C., to conform to the recom-mended Strauss treatment; (2) 950°C., to compare with the results of previous tests; or (3) 750°C., to initiate precipitation of carbides in the material before testing. As the test cross sections were only 1/8 -in. dia., air cooling followed the annealing treatment. These treatments per-mitted two direct comparisons: (1) between the 1150° and 950°C. treat-ments to indicate the effect of grain size when all carbides were probably in solution at the start of the test; and (2) between the 950° and 750°C. treatments to indicate the effect of carbide "nucleation" for similar grain sizes.

Jan 1, 1940

By Ralph Hultgren

FEW phase diagrams of alloys composed of two transition metals have been adequately studied, probably because of the high melting points involved. Transition metals are the elements that have inner shells incompletely filled with electrons. They comprise groups IIIa to VIIIa of the periodic table, including more than half of all metals. We have chosen to study two systems whose comparatively low melting points allowed the alloys to be melted in a molybdenum resistance furnace. The nickel-palladium system proved to consist of a simple series of solid solutions, but iron-palladium manifested several remarkable features. The main characteristics of the latter diagram were decisively established, but lack of time prevented precise determination of phase boundaries. The gamma to alpha transformation in this system is unusual and warrants further study. Grigorjew1 determined the liquidus and solidus of the iron-palladium system by thermal methods. He found a minimum melting point, but no eutectic. He also found that palladium lowered the gamma to alpha and raised the gamma to delta transformation temperatures of iron, with a complete series of solid solutions existing between gamma iron and palladium. His measurements also indicated a compound or super-lattice near the composition FePd3. Jellinghaus2 found that annealing at 500° C. greatly increased the magnetic coercive force of an alloy of composition FePd. X-ray dif-fraction photographs showed that a tetragonal ordered phase had formed during the anneal.

Jan 1, 1939

By G. H. F. Gardner

The boundary conditions F = 1.0 and 4 = 1.0 (100 per cent) are dictated by the definition of F in the equation 1/F = aFp. These conditions have physical significance as the "limiting conditions" for the observed behavior in systems of dispersed particles. The other boundary conditions, cited by Gardner in his Eq. 3 as applying to this system, have no significance in the systems we studied. Maxwell&apos;s equation (Eq. 2) cited in Gardner&apos;s comments was developed for and limited to a regular, rather than random, dispersion of spheres which are sufficiently removed from each other so that they do not interfere with current flow about their neighbors. These restrictions also apply to Rayleigh&apos;s analysis. The title of Rayleigh&apos;s paper cited by Gardner is "On the Influence of Obstacles Arrayed in Rectangular Order upon the Properties of a Medium". He is not discussing randomly dispersed spheres. It might be inferred from Gardner&apos;s comments that Rayleigh specifically considered the differential equation (Gardner&apos;s Eq. 3). This is not the case. Mathematically, Gardner&apos;s Eq. 3 is exactly true for the system to which it applies, however, as both Rayleigh and Maxwell note that their equation for F in terms of F is not for randomly dispersed spheres. At the time we wrote our paper, we were aware of the work of Wyllie and Gregory as cited by Gardner. We cited their work in Ref. 5 of our paper. Our comment on page 287 of the paper about the validity of an m value of 1.3 for spheres with a porosity of 38 per cent remains as our answer to Gardner&apos;s question on this point. Our data, at 38 per cent porosity, show that the condition a = 1 and m = 1.3 holds for spheres near 40 per cent porosity.

By LESTER W. STRAUSS

OUR early knowledge of history and geography attracted most of us to the mineral resources of South America. The romantic tales of the Spanish activities, which were curiously alluring, and Prescott&apos;s exceptional bi-Conquest histories-Mexico and Peru-no doubt fired our minds with the .then metallic wealth of the Spanish colonies. Later developments, intensified within the past eighty years, have, however, changed its fame which now rests on such metallics as copper and tin, and among the non-metallics on nitrate of soda and petroleum. South America proper, excluding Panama, is made up of thirteen countries, a coincident parity with our original thirteen States. Its area is given as 7,231,300 square miles, or slightly less than North America (8,037,000 square miles), is made up as follows:

Jan 1, 1930

By Owen Thornton

Recently equations have been presented by Rose and Bruce&apos; and by Rose², showing how the relative permeability of a reservoir rock may be determined from the capillary character of the rock. In particular, equations were developed to show the relationship between capillary pressure and the effective permeability to the wetting phase in a poly-phase flow system. The equations are as follows (nomenclature the same as in the Rose and Bruce paper) Rose and Bruce assume that the average length of path (L,), which the wetting fluid follows in flowing through a porous media is independent of the saturation to the wetting phase, so that 1 is a constant dependent only on the k rock, and the permeability to the wetting phase is a function of the saturation and of the capillnry pressure: In measuring the flow of ekctric current through partially saturated core samples, it has been observed that the electrical resistance usually is not a simple linear function of saturation. This fact indicates that the average length of path in the flow of electric current is not independent of saturation, but rather that the tortuosity of the path depends upon the average saturation to the conducting fluid as well as upon the characteristics of the rock. itself. Inasmuch as the flow of fluid and the flow of electric current in many respects are analogous, it may be indicated further that the length of path for fluid also may not be independent of saturation. The following relationship can be derived to express the resistance to flow of electric current through a core sample partially saturated with conductive wetting phase, the non-wetting phase being non-conductive: where L is the average length of path followed by the current in flowing through a length L of partially saturated core, where L is the length of current path when the core is fully saturated, and where Rs and R, are the specific resistivities of the partially saturated and saturated core sample, respectively. It will be noted that R., the specific resistivity of the core sample when S, = 1.0, is equal to the "formation resistivity factor"&apos; multiplied by the specific resistivity of the saturating fluid. If it be assumed that the average lengths of path for fluid flow and for the flow of electric current are the same, then equation (5) may be combined with equations (l), (2) and (3) to give the following relationship: The above equation suggests including a correction for tortuosity when calculating the relative permeability of a reservoir rock to a wetting phase. The correction factor may be obtained from the resistivity-saturation relationship. For instance, the following calcu- lations are obtained for the unconsoli-dated sands described by Leverett Kw Kw Sw R°/Rs Pt/Pc¹ (Calc.) (Obs.) 0.30 0.08 0.88 0.02 0.0 0.40 0.16 0.94 0.06 0.04 0.50 0.27 0.97 0.14 0.11 0.60 0.40 0.98 0.26 0.21 0.70 0.53 0.98 0.39 0.35 0.80 0.68 0.99 0.57 0.54 0.90 0.84 0.99 0.77 0.76 1.00 1.00 1.00 1.00 1.00 It will be noted that the agreement between the calculated points and the observed data is rather good. Further investigation of the above method for obtaining relative permeabilities may be merited. For many sands within specified ranges of saturations the following relationship has been found to hold approximately&apos;: — =SW"......(7) Rs The exponent n in the above equation has been found to equal two for many sands so that equation (6) reduces to the following: The writer acknowledges the permission of The Texas Co. to submit this note for publication. 1. Walter Rose and W. A. Bruce—Jnl. of Pet. Tech., Vol. 1, No. 5, p. 127 (1949). 2. Walter Rose—Jnl. of Petr. Tech., Vol. 1, No. 5, p. 111 (1949). 3. G. E. Archie— -Trans. AIME, 146, 54 (1942). 4. M. C. Leverett— Trans. AIME, 142, 152 (1941). 5. M. C. Leverett—Trans. AIME, 132, 149 (1939).

Jan 1, 1949

By Owen Thornton

Recently equations have been presented by Rose and Bruce&apos; and by Rose², showing how the relative permeability of a reservoir rock may be determined from the capillary character of the rock. In particular, equations were developed to show the relationship between capillary pressure and the effective permeability to the wetting phase in a poly-phase flow system. The equations are as follows (nomenclature the same as in the Rose and Bruce paper) Rose and Bruce assume that the average length of path (L,), which the wetting fluid follows in flowing through a porous media is independent of the saturation to the wetting phase, so that 1 is a constant dependent only on the k rock, and the permeability to the wetting phase is a function of the saturation and of the capillnry pressure: In measuring the flow of ekctric current through partially saturated core samples, it has been observed that the electrical resistance usually is not a simple linear function of saturation. This fact indicates that the average length of path in the flow of electric current is not independent of saturation, but rather that the tortuosity of the path depends upon the average saturation to the conducting fluid as well as upon the characteristics of the rock. itself. Inasmuch as the flow of fluid and the flow of electric current in many respects are analogous, it may be indicated further that the length of path for fluid also may not be independent of saturation. The following relationship can be derived to express the resistance to flow of electric current through a core sample partially saturated with conductive wetting phase, the non-wetting phase being non-conductive: where L is the average length of path followed by the current in flowing through a length L of partially saturated core, where L is the length of current path when the core is fully saturated, and where Rs and R, are the specific resistivities of the partially saturated and saturated core sample, respectively. It will be noted that R., the specific resistivity of the core sample when S, = 1.0, is equal to the "formation resistivity factor"&apos; multiplied by the specific resistivity of the saturating fluid. If it be assumed that the average lengths of path for fluid flow and for the flow of electric current are the same, then equation (5) may be combined with equations (l), (2) and (3) to give the following relationship: The above equation suggests including a correction for tortuosity when calculating the relative permeability of a reservoir rock to a wetting phase. The correction factor may be obtained from the resistivity-saturation relationship. For instance, the following calcu- lations are obtained for the unconsoli-dated sands described by Leverett Kw Kw Sw R°/Rs Pt/Pc¹ (Calc.) (Obs.) 0.30 0.08 0.88 0.02 0.0 0.40 0.16 0.94 0.06 0.04 0.50 0.27 0.97 0.14 0.11 0.60 0.40 0.98 0.26 0.21 0.70 0.53 0.98 0.39 0.35 0.80 0.68 0.99 0.57 0.54 0.90 0.84 0.99 0.77 0.76 1.00 1.00 1.00 1.00 1.00 It will be noted that the agreement between the calculated points and the observed data is rather good. Further investigation of the above method for obtaining relative permeabilities may be merited. For many sands within specified ranges of saturations the following relationship has been found to hold approximately&apos;: — =SW"......(7) Rs The exponent n in the above equation has been found to equal two for many sands so that equation (6) reduces to the following: The writer acknowledges the permission of The Texas Co. to submit this note for publication. 1. Walter Rose and W. A. Bruce—Jnl. of Pet. Tech., Vol. 1, No. 5, p. 127 (1949). 2. Walter Rose—Jnl. of Petr. Tech., Vol. 1, No. 5, p. 111 (1949). 3. G. E. Archie— -Trans. AIME, 146, 54 (1942). 4. M. C. Leverett— Trans. AIME, 142, 152 (1941). 5. M. C. Leverett—Trans. AIME, 132, 149 (1939).

Jan 1, 1949

OF the many categories into which scientific knowledge has been arbitrarily &apos;divided, the one that has proved most. applicable in our attempts to gain an insight into the details of steelmaking processes is physical chemistry. To the young metallurgist who has only recently survived a college course in this subject, the application of its principles to reactions in liquid steel should not be difficult. The many excellent textbooks of physical chemistry provide ample material on the principles of this subject for the student of steelmaking processes. It is the purpose of this chapter to provide a concise review of the principles of physical chemistry that have proved useful in studies of steelmaking and at the same time to present some of the data that are essential to the application of physical chemistry to reactions at high temperatures. Certain parts of physical chemistry require rather formidable mathematics for their complete development, but in the main those applications in which we are here interested can be expressed in fairly simple terms. Many of the equations are logarithmic, and we shall use the symbols In X and log X to represent, respectively the natural and the common logarithm of X. The two are related-by In X = 2.303 log X. Logarithms may, be read from a good slide rule with sufficient accuracy for our purposes. In a few spots a knowledge of the calculus will be helpful. MATTER Innumerable forms of matter may, be recognized, and these may be converted by chemical processes into others, as ore, coke, and air are converted into iron, slag, and gas.. Whenever such a change occurs there is a corresponding change in the amount of energy associated with the matter. The process may require an input of energy, as in the electrolytic production of aluminum, or it may result in an output of energy, as in the combustion of fuel. The basic laws of the conservation of matter and of energy tell us that we cannot change the total amount of matter or the total amour t of energy.. When the fuel pile is used up, we realize that it has simply been converted into other forms of matter; .i.e., ash

Jan 1, 1964

By J. Gurland, A. Gangulee

The cracking of silicon particles embedded in an aluminum matrix occurs progressively over the range of plastic deformation of the composite specimen. The fracture probability of the particles increases with increasing particle size and decreasing silicon contents. The crack orientation tends to be perpendiculay to the direction of the maximum tellsile strain. An example of a direct association between matrix slip and particle cracking is shorn. ALUMINUM-SILICON alloys of commercial compositions fail by ductile fracture in three stages:&apos; I) initiation of cracks in the silicon particles, 2) growth of cracks into cavities, and 3) rupture of the aluminum matrix separating the cavities. The present work is concerned with the first stage: the initiation of cracks in the silicon particles. EXPERIMENTAL PROCEDURE Aluminum samples with 2.8, 6.1, 9.6, and 13.2 vol pet Si, respectively, were cast from commercial al- loys. Machined tensile specimens (2 in. gage length) were annealed in air at 1000°F for 100 hr, and then pulled at a strain rate of 0.025 per min. The grain size (average linear intercept) of the aluminum matrix was 0.24 and 1.6 mm in the 6.1 and 13.2 pet Si alloys, respectively. The particle size of silicon in alloys of one composition (6.1 pet Si) was varied by either modifying the castings with 0.15 pet Na or prolonging the annealing time. The average particle size was measured by linear and planar analysis, assuming spherical particles of uniform size. The particle sizes and compositions of all samples are tabulated in Fig. 8, together with the identifying symbols used in the graphs. The respective numbers of broken and unbroken silicon particles were determined from metallographically prepared longitudinal sections by counting a total of approximately 2000 particles per sample. EXPERIMENTAL RESULTS 1) Crack Initiation During Deformation as Function of Composition. Nominal stress-strain curves of four specimens of different compositions, but approximately equal particle sizes, are presented in Fig. 1. The fraction of broken particles, P (no. of broken particles/ total no. of particles), is shown in Fig. 2 as function of true stress and in Fig. 3 as function of nominal strain. The last point of each composition line in Fig. 2 rep-

Jan 1, 1968

By Paul A. Farrar, Felix Ermains, Harold Margolin

The systems Ti-Crand Ti-Vhave been reinvesti-gated in the region up to 40 wt pct alloying addition using both conventional and rapid quenching techniques. The Ti-Cr eutectoid temperature was determined to be at 667° & 10° C and 14.5 wt pct Cr. The solubility of the Cr in a Ti was found to be less than 1 pctat 700"C. The P transus of the Ti-V system was found to be depressed to 510°C at 40 wt pct V and the solubility of V in a Ti was found to be less than 2 wt pct at 700°C. Investigation by a. d. McQuillan1-3and m. k. McQuillan4 on the systems Ti-Co, Ti-Cr, Ti-Cu, Ti-Fe, Ti-Mn, Ti-Ni, and Ti-V has cast doubt as to the position of the ß/a + ß boundaries in many of these systems. Their investigations were carried out using hydrogen pressure and/or rapid quenching experiments, as opposed to the conventional quartz capsule techniques employed by most other investigator.&apos;" By these methods, the ß/a + ß boundary was found to be lower than that obtained by conventional techniques in all except the Ti-Fe system. In the latter, the ß/a + ß boundary was essentially the same as the boundary obtained by conventional technique.7&apos; On the basis of rapid quenching results in the Ti-Cr system, M. K. McQuillan4 placed the eutectoid temperature below 550°C whereas other investigations using conventional techniques had placed the eutectoid variously as between 650&apos; and 700°C,5 between 675&apos; and 700°C,6 between 650" and 675°C,7 at 670°C,8 and above 625"C.la9l3 In order to check these results, a reinvestigation of four of the systems was undertaken using both conventional and rapid-quenching techniques. The Ti-Fe and Ti-Mn systems will be dealt with in anoth er paper, with only the Ti-Cr and Ti-V systems being discussed here. EXPERIMENTAL TECHNIQUES Alloys employed for the delineation of the systems under investigation were prepared from iodide titanium sheet capsules containing the alloying materials,

Jan 1, 1962