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By Leendert de Witte

A review is given of the principles on which recently proposed methods of electric log interpretation in shaly sands are based and of the evidence brought up in support of the theoretical derivations. It is. pointed out that the qualitative techniques suggested to date have a tendency to be too pessimistic in the prediction of the presence of commercial hydrocarbon accumulations. In the quantitative treatment, a new concept is introduced, namely that of strongly reduced activity of the double layer counter ions which are present near the negatively charged rock surfaces. This lemmu when applied to the calculation of the equilibrium concentratiotls of interstitial waters yields a set of very simple relations. The resulting expressions for electrochemical potentials across rock samples appear in satisfactory agreement with laboratory experiments. The formulae obtained for the electrical conductivity of shaly formatioris are of the same form as those arrived at empirirally by previous workers. Combination of the expres.riorls for potentia1s and conductivities gives a direct proof of the Tixier relation which states that for shaly water sands the product of apparent formation water resistivity and apparent formation factor equals the resistivity of the sand 100 per cent .saturated with formalion water and which was verified by the work of Wyllie and Perkins and their co-workers. The relations for the resistivities and spontaneous porer11inI.s have been extended to the case of hydrocarbon hearing shaly formations, thus laying a formal basis for the quantitative interpretation of electric logs in shaly oil sands. INTRODUCTION The presence of disseminated clays in porous rocks saturated with electrolytic solutions has a strong influence on the transference of ions taking place under electrical or chemical potential gradients. Both the electrochemical emf's in evidence on the SP curves of electric logs and the electrical conductivity measured on resistivity logs arc directly dependent on the ionic transference in the interstitial waters of the formations traversed by boreholes. A large number of researches have been carried out on the nature and magnitude of the effects of clays on ionic transference. The most recent of these have been described in papers by McCardell and Winsauer,1 2 Wyllie and Southwick,3 poupon, Loy, and Tixier,4 and by Perkins et al.5 Most of these authors consider the effects of the clays as due to the fixed negative charges on the clay lattice. These charges cause the formation of diffuse surface layers with a high concentration of positive ions. The internal solution of the shaly reservoir rock has therefore a different ionic composition and concentration than the electrolyte with which it is in equilibrium (connate water produced from the formation or mud filtrate by which the formation is invaded). To calculate the equilibrium concentration of the internal solution, use is made of the Donnan6 relation, which states that the mean ionic activities of the internal solution and of the external electrolyte must be equal. From this and the

Jan 1, 1956

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

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

Jan 1, 1963

By J. G. Thompson

PROJECT 8411 of the U. S. Bureau of Standards, sponsored by the Iron and Steel Division of the A.I.M.E., is an attempt to define more concisely than has been possible heretofore the accuracy and the Limits ' of usefulness of the ' various methods now in use for the determination of oxygen as it exists in ferrous materials. It originated in correspondence between John Johnston and other metallurgists, and was brought to the attention of the Iron and Steel Division of the Institute at the Annual Meeting in February, 1933. As reported in MINING AND MET,ALLURGY, Vol. 14, page 152, March, 1933, "Dr. Johnston introduced, and those present adopted, a resolution that the Iron and Steel Division of the A.I.M.E., believing that a careful comparison of the several methods now in use for the analysis of steel for nonmetallic elements such as oxygen is highly desirable, heartily endorses the proposal that the U. S. Bureau of Standards act as a clearing house " in this matter, undertaking the final preparation and allocation of identical samples to those laboratories willing to collaborate in this important question, and collate the results re- ported back to the Bureau.'"

Jan 1, 1934

By AIME AIME

The American Society of Mechanical Engineers.-The semi-annual meeting of the American Society of Mechanical Engineers will be held in Detroit, Mich., June 23-26. A session will be devoted to hoisting- and conveying-machinery; and many other subjects will be treated in professional papers, among which are . Clutches (with special reference to automobile clutches); The Thermal Properties of Superheated Steam; The Horse-Power, Friction-Losses, and Efficiency of Gas- and Oil-Engines; A Journal-Friction Measuring-Machine; A Simple Method of Checking Conical Pistons for Stress, and The By-Product Coke-Oven. The usual receptions will be held and excursions will be made to manufacturing plants, the slip-building yards, and various points of interest in and around Detroit. Among the excursions' planned is one to the University of Michigan at Ann Arbor. The Gas-Power Section of the Society will hold a session, and the Society for the Promotion of Engineering Education and the Society of Automobile Engineers will hold meet-

Jan 5, 1908

By McHenry Mosier

SUMMARY MERCURY is one of the strategic metals of which the supply has been raised from critical uncertainty to more than enough for essential demands. Work by the Bureau of Mines has contributed substantially to increased production of mercury in the United States and to consequent accumulation of Government stocks. Other contributing factors have been higher prices for mercury and Government loans to operators. The Bureau has undertaken 13 exploration projects, 10 of which have been completed. This work has comprised 28,376 ft. of several types of drilling and 23,798 lin. ft. of surface trenching, and has indicated commercial ore containing 34,800 flasks of mercury and marginal ore containing 26,200 flasks, a total of 61,000 flasks; equivalent, respectively, to domestic production for 8 months, 6 months, and 14 months. As Government stocks are now adequate, domestic production (currently at the rate of 50,000 flasks per year) is gradually being curtailed through Government control of labor and operating supplies.

Jan 1, 1944

By John Johnston

THIS necessarily brief sketch will attempt to summarize the high lights of perhaps the best meeting so far held by the Iron and Steel Division. All sessions were well attended and the discussion was vigorous and of a high order. The technical sessions opened. on Tuesday morning. "Precipitation Hardening of Copper Steels" was discussed by Cyril S. Smith and Earl W. Palmer, and dealt with steel with a 1 per cent copper content. Discussion brought out that there were no fabricating difficulties, but that the surface might be somewhat checked due to intergranular penetration of copper which could be easily taken care of. Probable advantages of steels of this type for high temperatures were pointed out. "An Improved Nickel-chromium Hardened Chilled Cast Iron," by J. S. Vanick, described a wear-resistant cast iron and evoked a lively discussion.

Jan 1, 1933

By William E. Ford, Edward Salisbury Dana

1. Normal Class (25) Barite Type 2. Hemimorphic Class (26) Calamine Type 3. Sphenoidal Class (27) Epsomite Type Mathematical Relations of the Orthorhombic System Crystallographic Axes. - The orthmhombic system includes all the forms which are referred to three axes at right angles to each other, all of different lengths. 296 Any one of the three axes may be taken as the vertical axis, c. Of the two horizontal axes the longer is always taken as the b or macro-axis * and when orientated is parallel to the observer. The a or brachy-axis is the shorter of the two horizontal axes and is perpendicular to the observer. The length of the b axis is taken as unity and the lengths of the other axes are expressed in terms of it. The axial ratio for barite, for instance, is a : b : c = 0'815 : 10 : 131. Fig. 296 shows the crystallographic axes for barite.

Jan 1, 1922

By G. A. Savanick

Borehole (slurry) mining, where a tool incorporating a water-jet cutter and a downhole slurry pump mines phosphate through a borehole, was field tested in northeastern Florida as part of a US Bureau of Mines program to increase the domestic availability of critical minerals. About 1.5 kt (1700 st) of phosphate ore were mined at 23.6 t/h (26 stph) from a depth of 76 m (250 ft). The borehole was filled with water during mining for roof support and to assist slurry pumping. Underwater cutting was enhanced with an air-shrouded water jet. Mined cavities were backfilled to prevent subsidence after abandonment. Roof subsidence during mining was avoided only when the cavity was filled with water. Environmental monitoring before, during, and after mining included hydrological studies and measurements of water quality. Significant water quality changes occurred only in the zone being mined and were confined to the immediate area of the borehole.

Jan 1, 1986

By George C. Stone

Since the Troy meeting I have received several additional results of analysis of the same sample of spiegel, which I give below: P. I know only by correspondence. His methods are : for results Nos. 47, 48 (13.03, 13.26) dissolve In hydrochloric acid, evaporate, oxidize with nitric arid, filter from silica, separate iron as basic acetate, precipitate manganese as sulphide, dissolve in hydrochloric acid; and precipitate as carbonate. No. 49 (13.72) was obtained by Eggertz's method. Nos. 50, 51 (13.10, 13.10) were dissolved and oxitfized as before, the iron precipitated by oxide of zinc, filtered and washed four times with cold water; and the manganese titered hot with permanganate. P. regards these two results as low. Nos. 52, 53 (13.75, 13.69) were dissolved and treated like the last two, the precipitated iron was again dissolved, separated, and titered as before; the results are the sum of the manganese joined in both

Jan 1, 1884

By Charles E. Lees

The Globe Mining District is in the southeast central part of Arizona, in Gila County. Globe, with a population of about 7000, is the terminus of the Arizona Eastern R.R., a branch line 130 miles long that connects with the Southern Pacific R.R. at Bowie. In 1874, prospectors crossing the Pinal Mountains from the west located what is generally known as the Old Dominion mine. For several years, it attracted little attention, because of the greater interest aroused by the discovery of high-grade silver ores in some of the foothills northeast of Globe. About six years later, the prospector turned his attention to the abundant copper ore revealed by surface workings along the Old Dominion vein, and, in 1884, the Old Dominion company erected two 30-ton furnaces. From 1888 to 1893, the Old Dominion company is said to have maintained an average annual production of about 8,000,000 Ib. of copper. Until Dec. 1, 1898, all supplies had to be freighted into Globe by wagons and the mines of the district operated intermittently because of high expenses, but with the advent of the railroad the Old Dominion company continued to be a large and steady producer. In the Globe district, the production of copper far exceeds in importance that of any other metal. There are four operating companies along the Old Dominion vein and the total annual product of these properties for 1923 was about 45,000,000 lb. of copper. The unit size of the mineral tracts in the district is the regulation mining claim, 600 ft. wide by 1500 ft. long, and all ownerships are held in fee. Globe is 3600 ft. above sea level, and lies between the Apache MOUntains to the east and the Pinal Mountains to the west. The principal drainage of the district is northward through Pinal creek into the Salt River. The general slope from the high point along the vein, where the Superior & Boston mine is, to Pinal creek, where the Old Dominion mines are, is about 250 ft. to the mile. Geology The oldest rocks in the district are pre-Cambrian crystalline schists known as the Pinal schist, which are the basement upon which all the later rocks were deposited. These latter rocks comprise shale, con-

Jan 1, 1925

By J. B. Austin

It is now well established, chiefly through the work of Davenport and Bain,' that the influence of temperature upon the rate of transformation of austenite to ferrite at constant temperature is represented by a curve of the type shown in Fig. 5 on page 295 and the reasons for this general shape have been discussed by them in a qualitative way. Thus, the upper part, or nose, of the curve is the resultant of two factors of which the rate of change with temperature is not the same, and by analogy with other like cases it is almost certain that these factors are: (1) the chemical potential, or driving force, of the transformation, which is zero at the equilibrium temperature and increases rapidly as the temperature falls below this point; and (2) a factor analogous to viscosity, or resistance of the crystal lattice to a change in structure, which also increases as the temperature is lowered. Just below the equilibrium temperature this virtual "viscosity" of the metal is relatively low—that is, the metal offers little resistance to a change in lattice—but the driving force is also small, and the net result is that the reaction proceeds slowly. As the temperature is lowered the magnitude of both factors increases; but at first the driving force increases more rapidly than the resistance and the reaction is observed to proceed more rapidly. At lower temperatures, however, the resistance begins to increase faster than the driving force, and eventually, at the nose of the curve, overbalances it, causing the reaction to proceed more and more slowly thereafter. This concept is somewhat, though not completely, analogous to that employed in certain electrical cases where the precise factors are known and are separately measurable. The current I (in amperes or coulombs per second) flowing through a given wire is proportional to the impressed potential, or driving force E, and is inversely proportional to the resistance R of the wire; that is, I = E/R. Stated in a slightly different way, the time required for one coulomb to pass a given point (1/I) is equal to R/E. If the temperature of the whole circuit is changed, the resultant change in 1/I will depend on the relative rates of change of R and of E,

Jan 1, 1935

By J. B. Austin

It is now well established, chiefly through the work of Davenport and Bain,' that the influence of temperature upon the rate of transformation of austenite to ferrite at constant temperature is represented by a curve of the type shown in Fig. 5 on page 295 and the reasons for this general shape have been discussed by them in a qualitative way. Thus, the upper part, or nose, of the curve is the resultant of two factors of which the rate of change with temperature is not the same, and by analogy with other like cases it is almost certain that these factors are: (1) the chemical potential, or driving force, of the transformation, which is zero at the equilibrium temperature and increases rapidly as the temperature falls below this point; and (2) a factor analogous to viscosity, or resistance of the crystal lattice to a change in structure, which also increases as the temperature is lowered. Just below the equilibrium temperature this virtual "viscosity" of the metal is relatively low—that is, the metal offers little resistance to a change in lattice—but the driving force is also small, and the net result is that the reaction proceeds slowly. As the temperature is lowered the magnitude of both factors increases; but at first the driving force increases more rapidly than the resistance and the reaction is observed to proceed more rapidly. At lower temperatures, however, the resistance begins to increase faster than the driving force, and eventually, at the nose of the curve, overbalances it, causing the reaction to proceed more and more slowly thereafter. This concept is somewhat, though not completely, analogous to that employed in certain electrical cases where the precise factors are known and are separately measurable. The current I (in amperes or coulombs per second) flowing through a given wire is proportional to the impressed potential, or driving force E, and is inversely proportional to the resistance R of the wire; that is, I = E/R. Stated in a slightly different way, the time required for one coulomb to pass a given point (1/I) is equal to R/E. If the temperature of the whole circuit is changed, the resultant change in 1/I will depend on the relative rates of change of R and of E,

Jan 1, 1935

By Harold B. Janzen, M. A. Nobles

Campbell and Martin1 described a new exploratory logging tool which was developed as the result of a new concept of the phenomenon that takes place when a porous formation containing mobile hydrocarbons and irreducible interstitial water is invaded by mud filtrate. They postulate that invasion will create a bank of interstitial water between the flushed zone and the undisturbed formation. This postulate was confirmed by Wyllie.' Thus, if R,, is greater than R, and mobile hydrocarbons are present, the resistivity profile with increasing radii from the borehole is high:low:high, as shown in Fig. 1. If mobile hydrocarbons are absent, the bank of interstitial water is indistinguishable from the undisturbed formation and the resistivity profile, when R is greater than R,, is high:low, as shown in Fig. 2. The zone containing the bank of interstitial water and residual oil was named the "low zone". Campbell and Martin conducted extensive electrolytic wedge and resistivity analog model studies to select a logging system that would reflect the presence or absence of the low zone. The system they selected was that of a family of lateral curves. The model studies indicated that the presence of a low zone could be detected in approximately 60 to 70 per cent of the producing sand reservoirs with a family of lateral curves provided that the sonde effectively occupies 90 per cent of the diameter of the hole. These studies were conducted with D, = 5d. The presence or absence of the low zone is best determined by a plot of the apparent resistivity vs spacing as shown in Figs. 3 and 4. A dip or inflection in the profile that repeats at successive depth intervals is considered diagnostic. To reduce the shunting effect of the hole and mud, a sonde of insulating material that is surrounded by a series of flexible rubber bumpers was designed. The bumper efficiency is considered to be the ratio of the bumper diameter to the hole diameter. Field tests conducted by Campbell and Martin on 10 wells with a tool that provided for station readings indicated that dips or inflections could be detected in 19 out of 25 known producing zones. INSTRUMENT DEVELOPMENT Halliburton developed a logging system to simultaneously and continuously record eight lateral curves. The instrumentation is described in the literature.' The original logs made

ENGINEERS AVAILABLE (Under this heading will be published notes sent to the Secretary of the Institute by members or other persons introduced by members.) Technical graduate, aged-31, with experience as surveyor, chemist with a sulphur company, practical miner, and as chief engineer of an iron mining company, desires a position as mining engineer or superintendent. Speaks French and German. No. 165. Member, aged 31, married, graduate Yale and Massachusetts Institute of Technology, six years' experience in coal and iron mining, from engineer to general superintendent, desires position with large coal or iron company. Will go anywhere. References. . No. 167. Member, technical graduate, with experience as machinist, chemist, construction engineer, and manager-of mines in the United States and Mexico, desires position .as mine superintendent or manager. Speaks Spanish. No. 168. Member, technical graduate, aged 26, with experience as engineer, mine foreman, assistant superintendent for a pyrite mining company. Experience includes diamond drilling, shaft sinking, underground work, milling of pyrites, and mine accounting. No. 169.

Jan 12, 1914

By S. H. Penn

One of the more challenging aspects of the unfolding age of space travel centers about the opportunity for man to use the natural resources of other worlds. The first of the extraterrestrial worlds to be exploited will be the moon. After only a scant few thousand years of scratching the earth's crust, man will embark upon a venture that for centuries has excited the imagination of many (while staggering that of most) and may become a reality within the next decade. There has never been a time when so much money and effort will have been expended to exploit an area about which so little is known. Paradoxically, this effort combines much of the detached objectivity so typical of our analytical time with the proverbial optimism of the indefatigable prospector. As the earliest manned lunar missions will be brief and exploratory in nature, astronauts will not be expected to attempt to exploit any of the possible lunar natural resources. In later missions, with a more extended period of time available for the astronauts to stay on the moon, it may be desirable or even necessary to "live off the land". The resulting exploitation of lunar resources will be intended primarily to reduce the dependence of manned missions upon terrestrial logistic support and to reduce the cost of maintaining lunar bases.

Jan 3, 1966

By ROBERT. RICHARDS

I. INTRODUCTION The object of this paper is to enlarge the field of settling velocities treated by me in my former papers, Close Sizing Before Jigging, and Sorting Before Sizing.' There seemed need of work both on coarser and on finer sizes. Messrs. A. Sidney Warren and M. L. Nagel undertook the investigation for the coarser sizes, from 12.85 mm. down to 2.05 mm. diameter. Their work, because of the closer spacing and because of the increased number of observations and consequent stronger averages, called for a revision of the former work. Messrs. G., A. Barnaby and Ralph Hayden undertook this part of the work, from 2.49 mm. down to 0.28 mm., which is near the limit of sifting. Their work covers the ground much more minutely and comprehensively than the former papers. There remained to be covered the portion of the field too fine for investigation with the sieves. This part, covering the range of grains from 0.48 to 0.03 mm., was undertaken by Mr. E. S. Bardwell. For it he used the elutriation method. II. THE FIRST, OR COARSEST, SECTION OF THE FIELD. The first desideratum in this investigation was a series of sieves for sizing the sands preparatory to making the tests. It became necessary, therefore, to decide on a sieve-scale for this purpose. A sieve-scale is a series of sieves in which the dimensions of the holes of the successive members form a series increasing by a. definite ratio. There are three natural sieve-scales : 1, progressing by doubling the width of the hole for each suc-

May 1, 1907

By David A. Keys

The actual procedure in estimating depth of overburden from magnetic observations made on the surface will vary with the form of the deposit and any theoretical discussion will apply only so far as the form of the deposit conforms to the mathematical premises on which the theory is based. Since the shapes of natural deposits in the field cannot be expressed rigorously in mathematical form, the best that can be done is to assume some simple form and deduce results. Fortunately many small variations in form produce only slight changes in the estimated depth of overburden, therefore the methods have a definite practical value. For the theoretical treatment, magnetic ore deposits may be divided roughly into three classes, depending upon whether the magnetic anomalies may be considered to arise from (1) a single magnetic pole, (2) a dike or (3) a magnetic doublet. Particular cases, falling under one or other of these classes, have been discussed by different authors.1"4 In general, it may be stated that when the magnetic effects as measured on the surface are due only to one pole of the body, the other pole being so remote that its effect may be neglected, the resultant anomaly F at any point will vary as the inverse square of the distance r of the point from the pole, which may be expressed mathematically by F = k/r2, where k is a constant. When the deposit occurs in the form of a long, thin dike, the resultant anomaly will be of the form F = k'/r and when the deposit is in the shape of a lens, so that both poles have an appreciable effect on the surface, the result will be similar to that caused by a magnetic doublet, and the form will be F = k'/r3. The particular class under which a deposit falls may be deduced from the results of the magnetic survey. The second class is readily found, but there may be difficulty in deciding between the first and third. Isody-namic contours of both the vertical and horizontal anomalies will often be a good guide in making a correct decision. The correctness of the theoretical calculations may be checked in two ways. The first is to make laboratory models of various known shapes and pole distributions, to calculate the anomalies to be expected

Jan 1, 1940

By David A. Keys

The actual procedure in estimating depth of overburden from magnetic observations made on the surface will vary with the form of the deposit and any theoretical discussion will apply only so far as the form of the deposit conforms to the mathematical premises on which the theory is based. Since the shapes of natural deposits in the field cannot be expressed rigorously in mathematical form, the best that can be done is to assume some simple form and deduce results. Fortunately many small variations in form produce only slight changes in the estimated depth of overburden, therefore the methods have a definite practical value. For the theoretical treatment, magnetic ore deposits may be divided roughly into three classes, depending upon whether the magnetic anomalies may be considered to arise from (1) a single magnetic pole, (2) a dike or (3) a magnetic doublet. Particular cases, falling under one or other of these classes, have been discussed by different authors.1"4 In general, it may be stated that when the magnetic effects as measured on the surface are due only to one pole of the body, the other pole being so remote that its effect may be neglected, the resultant anomaly F at any point will vary as the inverse square of the distance r of the point from the pole, which may be expressed mathematically by F = k/r2, where k is a constant. When the deposit occurs in the form of a long, thin dike, the resultant anomaly will be of the form F = k'/r and when the deposit is in the shape of a lens, so that both poles have an appreciable effect on the surface, the result will be similar to that caused by a magnetic doublet, and the form will be F = k'/r3. The particular class under which a deposit falls may be deduced from the results of the magnetic survey. The second class is readily found, but there may be difficulty in deciding between the first and third. Isody-namic contours of both the vertical and horizontal anomalies will often be a good guide in making a correct decision. The correctness of the theoretical calculations may be checked in two ways. The first is to make laboratory models of various known shapes and pole distributions, to calculate the anomalies to be expected

Jan 1, 1940

By D. R. THOMAS

GENERALLY speaking, the production of other metals in Mexico fluctuates with that of silver. The first commercial discovery of mineral was in Taxco, Guerrero, in 1552. Five years later, the patio process was introduced at Pachuca, by Bartolome de Medina. In 1884, the main line of the Mexican Central R. R. was completed and a few years later, the National railway. In 1907, the patio process, after 350 years of successful operation, was replaced by cyanidation. Soon after the completion of the railroads, smelters were built at various points and provided means of treating ores that could not be treated by any of the processes existing at that time, such as patio, lixiviation, or pan amalgamation. As a result, a number of mines were developed along the railroads and even far \ out in the mountains. In order to facilitate the shipment of this ore to the smelters, purchasing agencies were established, which for a time were very profitable; most of these agencies are now permanently closed.

Jan 1, 1921

By J. J. Kramer, G. W. Wiener, K. Foster

The effects of the primary grain size and sheet thickness on the secondary growth rates of grains with (100) surface planes were studied in 3 pct Si-Fe sheets. This secondary grain growth was carried out under conditions in which the {100} plane had the lowest surface free energy. The value of the surface energy difference, between the (100) plane and the random matrix planes was found to he only about 3 pct of the grain boundary energy, indicating that most of the driving force for secondary growth is supplzed by grain boundary energy. A method for obtaining cube texture in 3 pct Si-Fe sheets by a secondary recrystallization process has been reported.' It has been demonstrated that a difference in surface free energy between the (100) plane and other planes is responsible for this growth, where the (100) plane has the lowest surface energy. A semiquantitative relation has been derived for secondary grain growth in sheets where primary grain growth has proceeded until the grains have grown through the sheet and the average grain diameter in the plane of the sheet is from one to two times the sheet thickness. Then, the linear growth rate, G, for the secondary grains can be given by where M is the grain boundary mobility, is the grain boundary free energy, is the average primary grain radius, A is the average difference in surface free energy between the (100) plane and planes of other orientations, t is the sheet thickness, and C is a term first proposed by zener6 which acts as a negative driving force, the effect of inclusions in holding up grain boundary motion. Since the problem of grain growth being discussed is under conditions where the matrix grain size is at least equal to the sheet thickness, the radius r is, of course, a function of the sheet thickness. The term B/r is the grain boundary driving force normally associated with inclusion inhibited or texture inhibited secondary recrystallization. Here, however, the term is modified to account for the fact that growth occurs in thin sheets. The term is the additional driving force available because of the difference in surface free energy. The purpose of the present work has been to evaluate the driving force terms of the growth equation by studying growth rates of (100) secondary grains as a function of sheet thickness and primary grain size. From these data it has been possible to determine the relative values of grain boundary energy, surface energy difference, and the inclusion term, C. EXPERIMENTAL PROCEDURE A 3 pct Si-Fe alloy was melted and cast under a helium atmosphere using electrolytic iron and a pure commercial grade of silicon as raw materials. The alloy was hot and cold rolled to a thickness of 0.6 mm, and samples approximately 5 in. long by 1 1/4 in. wide were cut from the cold-rolled sheets. Four different primary grain sizes were obtained

Jan 1, 1963