Search Documents

By H. M. Stewart, R. A. Grange

MANY steel parts may crack if quenched directly into a bath near room temperature, but not if quenched at a temperature just above the range where martensite forms and then allowed to cool slowly to room temperature. This latter procedure, which is the basis for such modern hardening techniques as "martempering " and "isothermal quenching," may entail some sacrifice in depth of hardening but very little, if any, in intensity of hardening. In planning such treatments, it is necessary to know the upper limit of the martensite range, and often desirable to know the proportion of martensite that would form on cooling to any lower temperature; furthermore, the tendency of a particular steel to crack when quenched is unquestionably associated with the temperature range of martensite formation, and consequently knowledge of this range aids in selecting the optimum composition for a given application. Certain puzzling phenomena associated with the properties of quenched and tempered steel may be at least partly clarified as the manner in which martensite forms is more fully under- stood. Information on the temperature range of martensite formation, particularly with respect to how much martensite results from quenching to a given temperature, is lacking for most commercial types of carbon and low-alloy steel. These considerations led us to study martensite formation in 14 carbon and low-alloy steels. The resultant data may be directly used in the following ways: (I) for selecting the lowest quenching temperature at which no martensite will form; (2) for selecting the highest quenching temperature at which virtually dl marten- site will form, thereby avoiding quenching to an unnecessarily lower temperature with attendant danger of cracking; and (3) in producing a mixture of tempered marten- site and bainite, which in high-carbon steels has been found to possess somewhat better ductility than tempered martensite, yet does not require the full transformation time necessary for a completely bainitic (austempered) structure. PART I. OBSERVATIONS OF MARTEN- SITE FORMATION IN FOURTEEN CARBON AND LOW-ALLOY STEELS Transformation of austenite to pearlite or bainite can be conveniently studied by observing the change that occurs over a period of time at constant temperature; such studies are the basis of the isothermal transformation diagram (S-curve). This isothermal technique is not applicable to martensite formation, which occurs within a time interval too small to measure, at least by any ordinary means. For all practical purposes, therefore, martensite may be regarded as forming only during cooling and not during a period of time at constant temperature. As austenite is cooled below

Jan 1, 1946

By Charles T. Holland

In connection with the problems of bumps in coal mines, much has been written concerning the manner in which roof action and methods of mining enter into the pressure effects observed but little has been written upon the relationship between the physical properties of coal and associated rocks and the cause of bumps. The question of the strength of bituminous coal, of its elasticity, and the energy it can absorb and store has been neglected to a considerable extent in connection with this problem. It is generally agreed that one of the necessary conditions for bumps is a strong coal.' Therefore, since the strength of coal is an important factor, a study of this property should be made. several investigators have conducted laboratory experiments upon the strength of coal, using small cubical or rectangular test pieces. An attempt will not be made to go into all of these investigations, but they are briefly summarized in Table I. Experiments of the U. S. Bureau of Mines and of Lawall and Holland (pp. 27 and 34 of ref. 9), however, indicate that regardless of whether the coal is a soft and weak semihituminous (Pocahontas No 3) or a hard and strong bituminous (Stockton) coal, the maximum ultimate unit stress developed in laboratory tests is higher in small cubes than in larger cubes of the Same coal.

Jan 1, 1942

By Charles T. Holland

In connection with the problems of bumps in coal mines, much has been written concerning the manner in which roof action and methods of mining enter into the pressure effects observed but little has been written upon the relationship between the physical properties of coal and associated rocks and the cause of bumps. The question of the strength of bituminous coal, of its elasticity, and the energy it can absorb and store has been neglected to a considerable extent in connection with this problem. It is generally agreed that one of the necessary conditions for bumps is a strong coal.' Therefore, since the strength of coal is an important factor, a study of this property should be made. several investigators have conducted laboratory experiments upon the strength of coal, using small cubical or rectangular test pieces. An attempt will not be made to go into all of these investigations, but they are briefly summarized in Table I. Experiments of the U. S. Bureau of Mines and of Lawall and Holland (pp. 27 and 34 of ref. 9), however, indicate that regardless of whether the coal is a soft and weak semihituminous (Pocahontas No 3) or a hard and strong bituminous (Stockton) coal, the maximum ultimate unit stress developed in laboratory tests is higher in small cubes than in larger cubes of the Same coal.

Jan 1, 1942

By H. D. Hoskold

I. Instrument-Parts and Implements. Cross-hairs ; Stadia-measurement; Fineness of Graduation ; Cylindrical Gradu ation ; Nonius; Vernier ; One Vernier or two ; Leveling-Screws ; Troughton & Simms' Shifting Tripod-Head ; Hoskold's Shifting Tripod-Head; Hoskold's Extensible Tripod ; Electric Lamp ; Plumb-lines; Chain. II. Instruments. Compass (Mine-compaes of 1518, Compass of 1541, and Agricolals of 1556, Voig tel's Setz-compass, Circumferentor, Stanley's Hedley Dial, Compass on Tele scope, Hanging Compass, Lack of Precision) ; Plane-table; Octant and Quadrant; Theodolite and Transit (Evolution of the Theodolite, Scott's Tachymeter, Hoskold's Engineer's Theodolite, Angleometer, Precision of Mine-Theodolites). I. Instrument-Parts and Implements. Cross-Hairs.—Mr. Scott‡ says Lean's dial " might also have been provided with a diaphragm and cross-hairs; for Huygene discovered that any object placed in the common focus of the two lenses of a Kepler telescope (1611)- appeared as distinct and well defined as any distant body. Following this established theory, in 1669 Jean Picard, Marquis Malvasia and others crossed silken fibers in the mutual focus of their astronomical instruments." If by this Mr. Scott means that Huygens and Picard first devised and applied cross-hairs to the focus of the telescope, the writer cannot agree with him. Huygens did not describe " his telescope without tubes until 1684, in his Astroscopia Compendiaria."§ Moreover, it is recorded that the English astronomer, Gascoigne,?

Jan 1, 1902

By Robert E. Sorenson

EXPLORATION for deep-seated orebodies in the Silver Belt area of the Coeur d'Alene mining district is complicated by meager surface expressions of diagnostic criteria, lack of knowledge of the significance of specific alteration phenomena, and the great expense involved in the exploration for ore shoots, the tops of which often occur near sea level elevation or below and as much as 4000 ft or more below the surface. Except for the early studies of Ransome and Calkins in 1903 and 1904,[1] little geological work was done in the Coeur d'Alene district for many years, and it is only during the last 15 to 20 years that complete and careful geological mapping has been applied to most of the mines in the area. Much early information, which now would prove invaluable, is lost in hundreds of miles of caved and inaccessible mine openings not mapped by mining geologists. In more recent years mining geology has become a tool of greater use in the district, and some measurable progress is being made in the accumulation of observations that are adding gradually to the knowledge of ore deposits in the district.

Jan 7, 1951

By M. Prats

This paper presents a method for obtaining the correct values of the breakthrough sweep efficiency of the staggered line drive, taking into account the proper shape of the breakthrough streamline. Results obtained were different from those previously published, which were obtained by using an inexact shape of the breakrhrough streamline. INTRODUCTION In Section 9.31 of Muskat's' The Flow of Hotnogeticous Fluids Through Porous Media, it is stated that in a staggered line drive flood "the streamline of highest average velocity [is] the line of centers between input and output wells" (see Fig. I). Muskat used this concept to determine the relationship between the breakthrough sweep efficiency and the geometry of the staggered line drive pattern. Although it is clear from symmetry considerations that the breakthrough streamline passes through the midpoint between input and output wells, it is equally clear, as shown in Fig. 239 of Ref. 1, that the breakthrough streamline is not represented very well by the straight line joining the input and output wells. Therefore, it is desirable to determine the proper relationship between the breakthrough sweep efficiency and the pattern geometry by using the proper shape of the breakthrough streamline. METHOD OF SOLUTION It was found that the effect of the geometry of the staggered line drive on the breakthrough sweep efficiency can be investigated easily by making use of the method developed in Ref. 2. With this method, it can be shown that the general complex potential for the staggered line drive, which can be considered as a rectangular five-spot, is given in the coordinate system of Fig. 1, by O(z) = In cn(z\m) = +(x,y) + i $(x, y) . (1) where z = x + iy, +(x, y) is the potential distribution and $(x, y) is the stream function. The function cn (zm) is a Jacobian elliptic function of parameter m and has simple zeros at z,. = (2n + 1) K + 21iK and simple poles at z, = 2nK + (21 + 1)iK. Thus, the complex potential behaves like a(z) = ln(z - zr.) in the neighborhood of the production wells and behaves like a(z) = - ln(z - Z,) in the neighborhood of the injection wells. Since (z - z1.v) = rll.ei, we note that the potential + has the proper logarithmic behavior near the two wells, while the stream function $ varies with the angle, decreasing clockwise around the production well and increasing clockwise around the injection well. The functions K(m) and K'(tn), related by K(m) = K'(m,), where m + m, = 1, are known as the complete elliptic integrals of the first kind. By use of other properties of the Jacobian elliptic functions, the general stream function distribution for the staggered line drive can be obtained from Eq. 1: From the Jacobian elliptic function values, sn(0lm) = 0 dn(O(m) = cn(0jm) = 1, and f[K'(m)Iml = 03, it follows that the stream function given by Eq. 2 satisfies the proper symmetry conditions near a production well P located at [K(m), 01 and an injection well I located at [0, K' (m)]. That is, the line IOP in Fig. 1 is a streamline with value G (0. 0) = -0. and the straight lines connecting I and P to the point [K(m), K' (m)] is a streamline of value $[K(m), K' (m)] = -7/2. Similar symmetry conditions are obtained near other wells. It should be nuled that for m = m1, = 0.5, Eq. 2 reduces to the stream function distribution of the regular five-spot given in Ref. 7. SHAPE OF THE BREAKTHROUGH STREAMLINE It is apparent, from symmetry considerations, that the breakthrough streamline ($,) passes through the point [K(m)/2, K' (m)/2]. Its value there is so that the shape of the breakthrough streamline $,, is given by

Jan 1, 1957

By John S. Alexander

By ARTHUR S. DWIGH

Discussion of the paper of W. W. NORTON, presented at the Salt Lake meeting, August, 1914, and printed in Bulletin No. 92, August., 1914, pp. 1993 to 1999. ARTHUR S. DWIGHT, New York, N. Y.-Mr. Norton's chief argument is directed against the idea that the D. & L. sinter is any better material for the blast furnace than the H. & H. product. He supports this by citing two experimental furnace runs. Reducibility.-To discuss a furnace record like that quoted by Mr. Norton for the five days' run in August, 1912, is manifestly difficult for an outsider, but a possible explanation for the poor reduction on Furnace No. 5, smelting D. & L. sinter, may lie in the fact that both sets of furnaces carried the same fuel charges. Other things being equal, if 11 ½ per cent. coke was right for the furnaces smelting H. & H. product, it Was too much for the furnace smelting D. & L. product, as I shall endeavor to show later, and incipient overfire, accompanied by higher leads in slag and matte, was induced. It may sound like a paradox to say that excessive fuel sometimes produces poor reduction, but it is a sad fact. In certain plants where practically the entire charge to the blast furnaces receives a preliminary treatment by being sintered on the D. & L. machines the peculiarities of this problem have had to be very carefully studied, for serious metallurgical difficulties presented themselves when the change was first made to D. & L. sinter in large quantities. Some of these plants had blast pots before they had D. & L. machines, and many opportunities were afforded for comparative study of this very point. There is reason to believe that, clue to the long period of blowing and the higher temperatures developed in the pots from greater mass action, the iron in the H. & H. product is present chiefly as Fe203, perhaps in the form of ferrites, while in the D. & L. product the iron is present as FeO. The fuel charge in the blast furnace must be so proportioned as to exactly meet the chemical and thermic requirements of reduction and melting. If ally of these functions have been performed before the material enters the furnace, a corresponding allowance should be made or the fuel balance will be disturbed and bad work will result. One of the functions of the coke is to reduce enough metallic Fe for the matte requirements, leaving the remainder of the iron as FeO to go into the slag. In smelting almost any other material than D. & L. sinter the iron must-be reduced from the higher oxides, Fe203 or Fe304, to the protoxide, FeO, before a true comparative basis is reached. Experience has shown that with about one-half D. & L. sinter on the charge the coke should-be cut about 10 per cent. This theoretical benefit is borne out by the practical blast-furnace results on a large scale in numerous plants. In fact, wherever this very important factor is ignored the evil symptoms of excessive fuel will be indicated,

Jan 11, 1914

By Z. F. Oszter, D. Vincent, W. K. Behrands

With the expansion of open pit operations, belt conveyors are going to be used in the 13 608 to 18 144 t/h (15,000 to 20,000 stph) capacity range, which calls for a review of some of the horsepower calculation methods. This paper presents methods (based on German research data, field tests and theoretical considerations) for the evaluation of the Ky factor in the CEMA formula for belt conveyors of large carrying capacity, which fall beyond the limits of the data given in tables in the CEMA book. (The CEMA limits are 407 N\\m (300 lb ft) and Tave = 7.3 Mg (16,000 lb). At these large loads, the impression resistance of the belting on the idlers plays a major role, which in turn influences the magnitude of the drive horse power required. An example will illustrate the order of magnitude difference of the horsepower values obtained by using a conventional calculation method and the suggested method, as well as the beneficcia1 influence of the 4-roll idler in comparison to the standard 3-roll unit for a large caving capacity belt conveyor. This paper concerns itself with the analysis of the resistance to motion of belt conveyors, emphasizing the evaluation of the frictional resistance to motion due to load and belt pressure on the idlers and the flexing resistance of the belt and material when passing over the idlers. In the case of long and heavily loaded belt conveyors, the aforementioned resistances reach extremely high values calling for close analysis of the phenomena, presently not calculable with normally used formulas. This paper establishes correlation between experimental and empirical data presenting practical formulas a tool for the designer of high-capacity belt conveyors. The application of the formula is illustrated in an example in the Appendix.

Jan 1, 1981

By AIME AIME

THAT neither the Reconstruction Finance Corp. nor its subsidiary, the Metals Reserve Corp., are in competition with private enterprise was stressed by Charles B. Henderson in an informal talk before the N. Y. Section, A.I.M.E., on Sept. 23. Among other things, the speaker stated that the R.F.C., since its establishment, had authorized loans of $12,000,000, of which over $8,775,000 has actually been distributed. Of this amount, over $6,600,000 has been repaid. None of this money was appropriated by Congress, the sole assistance from that body being the initial authorization of $500,000,000 capital stock.

Jan 1, 1941

By Walter Miller

During the second year of America's active ia in the war the inain objectives of the petroleum-refining industry were again to provide the four most important product needs for war: 100-octane aviation gasoline, toluene for T.N.T. production, high-quality lubricating oils for the needs of aviation and the armed forces, and petroleum chemicals for synthetic rubber manufacture. All other materials supplied by the petroleum industry took an inferior priority ranking, depending on the degree of essentiality. To accomplish the above objectives the industry initiated and carried on a building program during 1942 and 1943 which will put those two years down in petroleum-refining history as the greatest construction years of all time, a record which will hold for decades to come. Led by an estimated total of $ 900,000,000 going into 100-octane and contributory plant investment, it is easy to picture a total of two billion dollars and more going into additional refining-industry plant investment during 1942 and 1943, most of it privately paid for, but a substantial part covered by R.F.C. Government money financing. Some of the new plants will not be completed until 1944, but a large proportion of the program was finished and put into operation, adding substantially to the output of the four principal products during 1943- lne most important and spectacuiar activity of the refining industry is of course the 100-octane gasoline program necessitated by the fact that nearly 90 per cent of the requirements of the United Nations is being furnished by the United States. Recent P.A.W. figures mention $goo,-ooo,ooo as the cost of the construction looking to increasing the output of this all-important munition. Thirty-four major plants have been completed, 11 of them during the last quarter of the year. Thirty-eight more will be completed and put into operation during the first four or five months of 1944. Twenty-two additional plants authorized during 1943 are already well under way and scheduled for production late in 1944. Early in 1942 the aim was to treble the capacity for making 100-octane gasoline then existing; later, plans were to make it five times as great, to match the increased warplane building program; and toward the end of the year the sights had been set at a still higher but unannounced target, representing six to seven times the early 1942 figure. Comparative figures issued at the end of 1943 enable one to guess a program by the middle of 1944 of eight to nine times the former production, with an ultimate production in 1944 of eleven or more times the early 1942 output. It became obvious in 1943 that building of new units would be materially slowed because of delay in getting construction materials and that they would reach operation at considerably later dates than

Jan 1, 1944

By Walter Miller

During the second year of America's active ia in the war the inain objectives of the petroleum-refining industry were again to provide the four most important product needs for war: 100-octane aviation gasoline, toluene for T.N.T. production, high-quality lubricating oils for the needs of aviation and the armed forces, and petroleum chemicals for synthetic rubber manufacture. All other materials supplied by the petroleum industry took an inferior priority ranking, depending on the degree of essentiality. To accomplish the above objectives the industry initiated and carried on a building program during 1942 and 1943 which will put those two years down in petroleum-refining history as the greatest construction years of all time, a record which will hold for decades to come. Led by an estimated total of $ 900,000,000 going into 100-octane and contributory plant investment, it is easy to picture a total of two billion dollars and more going into additional refining-industry plant investment during 1942 and 1943, most of it privately paid for, but a substantial part covered by R.F.C. Government money financing. Some of the new plants will not be completed until 1944, but a large proportion of the program was finished and put into operation, adding substantially to the output of the four principal products during 1943- lne most important and spectacuiar activity of the refining industry is of course the 100-octane gasoline program necessitated by the fact that nearly 90 per cent of the requirements of the United Nations is being furnished by the United States. Recent P.A.W. figures mention $goo,-ooo,ooo as the cost of the construction looking to increasing the output of this all-important munition. Thirty-four major plants have been completed, 11 of them during the last quarter of the year. Thirty-eight more will be completed and put into operation during the first four or five months of 1944. Twenty-two additional plants authorized during 1943 are already well under way and scheduled for production late in 1944. Early in 1942 the aim was to treble the capacity for making 100-octane gasoline then existing; later, plans were to make it five times as great, to match the increased warplane building program; and toward the end of the year the sights had been set at a still higher but unannounced target, representing six to seven times the early 1942 figure. Comparative figures issued at the end of 1943 enable one to guess a program by the middle of 1944 of eight to nine times the former production, with an ultimate production in 1944 of eleven or more times the early 1942 output. It became obvious in 1943 that building of new units would be materially slowed because of delay in getting construction materials and that they would reach operation at considerably later dates than

Jan 1, 1944

By E. J. Dulis, G. V. Smith

AS reported several years ago,' nitrogen may be taken up from the atmosphere by austenitic Cr-Ni steels during creep or creep-rupture tests. This was indicated by chemical analysis and by the appearance of a new microstructural phase, or phases, tentatively identified as chromium nitride (S), at the surface or at the intergranular cracks associated with fracture. The nitrogen pickup was observed to be dependent on time, temperature, and deformation. In a more recent investigation, a sample was obtained in which there was sufficient of the precipitate to suggest that it could be readily identified by X-ray diffraction. This sample had been taken from a 1/4 in. diam creep-rupture specimen of annealed, type 304L stainless steel of the following initial composition: C, 0.03 pct; Mn, 0.65; P, 0.010; S, 0.019; Si, 0.54; Cr, 19.50; Ni, 12.02; N, 0.031; and Al, 0.005. The specimen had ruptured after 10,470 hr at 1500°F (2000 psi). In this case nitrides were distributed across the whole section of the sample, Fig. 1. The precipitate occurred both at the grain boundaries and within the grains; the latter precipitate had in some cases the appearance of pearl-ite, and in others was distinctly Widmanstatten. Chemical analysis of the sample after test showed 0.64 pct "soluble" nitrogen (soluble in 1:1 hydrochloric acid: water) and 0.18 pct "insoluble7' nitrogen (insoluble in the hydrochloric acid solution but dissolved by fuming sulphuric acid). For identification of the precipitate by X-ray diffraction, the matrix in the surface layer of the specimen was dissolved by prolonged attack in an alcoholic solution of picric and hydrochloric acids. The appearance of the specimen surface after such etching is shown in Fig. 1c. The diffraction pattern of the surface-concentrated precipitate was obtained with a recording spectrometer in both the forward and back-reflection regions (the latter by adapting a special fixture to the conventional X-ray unit). The observed X-ray diffraction lines, Table I, show the presence of Cr,N and CrN; the agreement with interplanar spacings calculated from reported data2,3 is quite good. Since it has been suggested' that CrN dissolves only in concentrated sulphuric acid, whereas Cr2N dissolves in dilute hydrochloric or sulphuric acids, an effort was made to distinguish between the two nitrides. This proved possible, inasmuch as etching in a dilute solution of hydrochloric acid gave a sample in which microscopic examination showed that much of the Widmanstatten-pearlitic precipitate within the grains had been eaten out, leaving the grain boundary precipitate in relief, and which, when examined by X-ray diffrac-

Jan 1, 1953

By B. E. Eakin, A. L. Lee

Atmospheric pressure viscosity values For light hydrocarbons were calculated by a simple mixing rule based on the Sutherland constants for pure components. This method was further extended so that the atmospheric pressure viscosity of a mixture may be calculated based on the molecular weight information only. INTRODUCTION A proven method for estimating the gas-phase viscosity of a mixture is the one by Herning and zipperer.l This mixing rule has the following form: One method for calculating the pure component viscosity i is the Sutherland equation,2 which has the following form: The Sutherland constants B and S are determined from experimental data. A set of Sutherland constants for light hydrocarbons based on the data of several investigators3-5 is presented in Table 1. APPLICATION The Herning-Zipperer equation and the Sutherland equation were used to obtain an equation for calculating the gas-phase viscosity of light hydrocarbons. This equation has the form, Eq. 3 was used successfully in the study of methane-n-butane mixtures.6 Further analysis indicated that the Sutherland constants are a function of molecular weight.7 The gas-phase viscosity may be calculated based on molecular weight information only. The following equation was developed: The atmospheric pressure viscosity of ethane, propane, n-butaneand four methane-propane mixtures calculated on the basis of Eq. 6 are compared with the data of other investigators in Tables 2, 3, 4 and 5, respectively. A plot of atmospheric pressure viscosity vs molecular weight based on Eq. 6 is presented in Fig. 1.

Jan 1, 1965

By Lawrence Adler

MINE hoist ropes have hitherto been selected by successive approximation, a process both tedious and inexact. The proposed expression is a readily solved synthesis of existing data and the following standard equation:' [ W + Wr + (W + Wr) -a 9 (W + W)f + b] n=T [1] For convenience, a glossary of all terms appears on page 564. Since rope weight (W,) and bending load (B) are functions of unit rope weight (Wv), which in turn is a function of rope strength (T), W, and B can be expressed in terms of T. W, as a Function of T: A study of the curve in Fig. 1, unit rope weight vs strength, yields Eq. 2: W. = -f- [2] Therefore Wr = WvL = T. [3] iv B as a Function of T: From Fig. 2, unit rope weight vs diameter, Eq. 4 is obtained: W, = 1.6d2 [4] B is related2 to d and D, and d has been expressed in terms of W, by Eq. 4, so the curve B vs W, (Fig. 3) gives Eq. 5: 177,000 177,000 This may readily be checked from the expression3 for a 6x19 rope, i.e., d3 B = 288,000D Since d2 = 0.625 W, and N = substituting d into the above expression gives Ea. 6: 180,000 180,000 B T, which will be used. [6] Into Eq. 1 substitute Eq. 3 and Eq. 6, noting that f=0.02: W + T 1.02+=T. [7]

Jan 1, 1958

By R. F. Mehl, B. Lustman

The formation of intermediate phase layers in cementation processes has been subjected to extensive qualitative investigation though to relatively little quantitative study; this work has recently been fully summarized by F. N. Rhines.' It is necessary here only to cnumerate the general conclusions drawn concerning the kinetic laws governing the growth of intermediate layers and to state what is known concerning the structural changes accompanying the generation of phase layers. I. When the intermediate phase is protective in type—i.e., when its density is less than that of the base metal, so that a continuous coating is formed and maintained—the isothermal growth of the phase follows a simple parabolic equation: X2 = kt [i] where X is the thickness of the alloy layer, k thc reaction rate constant, and t the time. The applicability of this equation to diffusion processes is tested by plotting the square of the thickness versus time, or by plotting the thickness versus the square root of time; the resultant achievement of a straight line in such a plot has been considered sufficient proof of the validity of this equation. Exceptions have been found where liquid phases are involved in the reaction, where the diffusion layer is cracked,2 and where thin semimetallic oxide and sulphide coatings are formed on metals.$ In the first two cases the thickness increases linearly with time, and in the latter it is a logarithmic function of time. 2. The rate of thickening varics with temperature according to the Arrhenius equation: k = Ae-Q/RT [2] where k is the parabolic rate constant of Eq. I, or some other rate-descriptive function, A is the action constant, e the base of natural logarithms, Q the heat of activation, R the gas constant, and T absolute temperature. This equation has been found to be generally valid except when transformations occur during reaction in either the base metal or in the reaction layer; in such instances Eq. 2 is still applicable with different values for the constants A and Q above and below the transformation temperature. 3. Ali phases that are stable at the temperature at which diffusion occurs will appear in the interdiffusion of two components. In some cases certain of the phases may be too thin to be observed and identified easily. Nonequilibrium phases have never been noted in thick reaction layers; i.e., layers of a thickness that may be discerned microscopically. The relative thickness of each phase in a diffusion layer is proportional to the concentration gradient and to the rate of diffusion in that phase.4 The reaction layers tend to have a

Jan 1, 1942

By R. F. Mehl, B. Lustman

The formation of intermediate phase layers in cementation processes has been subjected to extensive qualitative investigation though to relatively little quantitative study; this work has recently been fully summarized by F. N. Rhines.' It is necessary here only to cnumerate the general conclusions drawn concerning the kinetic laws governing the growth of intermediate layers and to state what is known concerning the structural changes accompanying the generation of phase layers. I. When the intermediate phase is protective in type—i.e., when its density is less than that of the base metal, so that a continuous coating is formed and maintained—the isothermal growth of the phase follows a simple parabolic equation: X2 = kt [i] where X is the thickness of the alloy layer, k thc reaction rate constant, and t the time. The applicability of this equation to diffusion processes is tested by plotting the square of the thickness versus time, or by plotting the thickness versus the square root of time; the resultant achievement of a straight line in such a plot has been considered sufficient proof of the validity of this equation. Exceptions have been found where liquid phases are involved in the reaction, where the diffusion layer is cracked,2 and where thin semimetallic oxide and sulphide coatings are formed on metals.$ In the first two cases the thickness increases linearly with time, and in the latter it is a logarithmic function of time. 2. The rate of thickening varics with temperature according to the Arrhenius equation: k = Ae-Q/RT [2] where k is the parabolic rate constant of Eq. I, or some other rate-descriptive function, A is the action constant, e the base of natural logarithms, Q the heat of activation, R the gas constant, and T absolute temperature. This equation has been found to be generally valid except when transformations occur during reaction in either the base metal or in the reaction layer; in such instances Eq. 2 is still applicable with different values for the constants A and Q above and below the transformation temperature. 3. Ali phases that are stable at the temperature at which diffusion occurs will appear in the interdiffusion of two components. In some cases certain of the phases may be too thin to be observed and identified easily. Nonequilibrium phases have never been noted in thick reaction layers; i.e., layers of a thickness that may be discerned microscopically. The relative thickness of each phase in a diffusion layer is proportional to the concentration gradient and to the rate of diffusion in that phase.4 The reaction layers tend to have a

Jan 1, 1942

By Clyde Williams

IF you would allow me some liberties, I would restate the title of this talk as "Scientific Research, Our Greatest Resource," because that title would represent more clearly a present-day conception of the metals and minerals situation. It is a subject worthy of careful consideration. Canada and the United States are so similar and interdependent in their national economies that, in the following discussion, examples of conditions in the United States may be interpreted to apply to Canada as well. Moreover, it is a striking fact that the per capita value of mineral production in Canada and the United States in 1940 was almost the same. Therefore, in the consideration of this subject, I have made no attempt to differentiate between the two countries. Consumption of the world's mineral resources in the last few decades. and particularly during World War II, has been so enormous as to require some form of magic to ensure the continued progress of civilization in the face of a diminishing supply of these resources which are so critically essential. As C. K. Leith pointed out, in 1941, indus-

Jan 1, 1947

By M. S. Azun

I do not at all agree with the basic points of the author's conclusion. The use of lognormal or normal model to respond to the attribute distribution function should be carefully questioned. If fitting a distribution function of regionalized variables is the main purpose, one may employ one of certain well-known families of distributions, such as Tukey's lambda functions. For instance, the distribution function of gold assay values studied by Krige (Krige, 1978) may fit the lognormal model well, but one should not exclude that the basic idea of using the distribution function of observed data is to have insight of the physical mechanism that gives rise to the regionalized variables. In Applied Geostatistics, there are many examples considering only lognormal or normal model for the distribution function of geostatistical data even if the observed distribution function has more than one mode. Of course, using lognormal or normal model always brings easy computation for the statistical properties of attribute under investigation. Still, I object to adopting any of those models without having any "statistical inference." As seen from the author's paper, lognormal and normal model produce the same average grade (0.746% copper) and almost the same sample variance. Therefore, which model explains the probabilistic behavior of ore deposit is always an important question that should be replied by the geostatistician using not the common sense but the statistical and probabilistic methods. For kriging procedures, such as linear kriging, one should describe either second order stationary properties or bivariate properties of regionalized variables. Second order properties, such as correlogram function or semivariogram function, are the inputs of the so-called kriging equations. Selecting one of any useable models for the observed second order properties, such as spherical model, is not easy since the models are not based on the correlations structure of the regionalized variables. How those models being used in Applied Geostatistics can be distinguished is another important problem. One may develop many fitting models to respond to the observed second order properties of regionalized variables. However, I suggest that the model should be based on the probabilistic behavior of geologic process. The author used spherical model for copper, wolfram, and silver grades from isotropic sector (Fig. 2, 4, 3b) and exponential model for silver grades obtained along raises in isotropic sector (Fig. 3a). It seems that those semivariograms given in Fig. 3b for isotropic sector and Fig. 4 may be described by the random model implying that regionalized variables do belong to renewal process (Azun, 1983). If I knew the total number of data points used in estimation, may prove that my conclusion is correct. Recalling the test for the first order sample correlogram value, the test procedure is introduced such that the independence is rejected if [Ir(1) I > Za/2 N1/2] where Za/2 is the a/2 percentile of standard normal random variable and N is the total number of samples used in estimation (Azun, 1983). For the other observed semivariogram functions I suggest the author might try to use the so-called "Markovian model" describing not only the correlation structure of regionalized variables, but also the physical mechanism that produces the regionalized variables. The Markovian model for correlogram function is, [p (h) = T 1ih , h>1 ,] The Markovian model for the other second order properties of ReV are also derived. [T veß], in the above equation, show, for example, structural change and mineralizational variation in a considered deposit, respectively (Azun, 1983). In selecting any model, it is not easy to search for the "best" response to the observed second order properties of ReV's. The Markovian model, based on a theoretical understanding of underlying mechanism, gives more information about the occurrence of regionalized variables and respond to all properties. Random model and the so-called hole effect structure can be easily defined as a special form of the Markovian model (Azun, 1983). An estimation of any second order properties of regionalized variables may be computed through (N-1) lag. However, the dependency between the regionalized variables may be deemed to have "died out" after the so-called stationarity width (range). In practice, the estimation is carried out through 25% of the total number samples available. Therefore, the large fluctuations around the zero level and variance for correlogram or covariogram function and semivariogram function, respectively, cannot be observed. Since the number of pairs involved in the estimation of higher second order properties is small, the estimation variance at those lags is large. There is no need to show higher order estimated second order properties. After using one of any kriging procedure for block estimation, the distribution function of average grades has the same mean as the drilling sample grades but

Jan 1, 1986

By A. Keith Brewer

RECENT advances in the fields of chemistry, biology, and metallurgy have confronted the analytical chemist with an entirely new set of problems. Development of plastics and synthetics has brought about a need, not only for adequate methods for their analysis but also for the various raw materials entering into their manufacture. The remarkable advance made in biochemical and agricultural research resulting from the use of isotopes as tracers or "tagged atoms" has established the necessity for the development of methods for the concentration of natural isotopes and for a means for their analysis. Similarly the advent of new and complex alloys calls for accurate analytical methods. Fortunately the analytical chemist has been able to meet some of these new demands by adapting to his purposes an instrument which has long been the most exclusive toy of the physicists. Solubility and the chemical properties of the atoms, which have always served as the basis for chemical analysis, do not enter into this new technique. Instead, momentum, defined as mass times velocity, is utilized as the means for the separation of atoms or mass groups.

Jan 1, 1946