Search Documents

By W. B. Morrison

Anderson, King, and Spreadborough present detailed evidence to show what ~aldwin~' has already pointed out, that, over a relatively small grain-size range (Ad"1/2 ^ 10 mm-'I2, d is average grain diameter), yield point data can fit a number of relationships. Part of the difficulty in obtaining data which reflect only the effect of change in grain size on yielding arises from the fact that in varying the grain size, even though great care is taken, other structural changes are almost certain to occur. In iron alloys, these changes may consist of variations in subgrain size, grain boundary ledge density, and degree of carbon and nitrogen segregation at grain boundaries, all of which are difficult to detect and which may affect yielding, primarily through their effect on dislocation generation. Because of the inherent inaccuracy associated with yield point measurements there is little point in using relatively complex equations to fit data, as was done by Anderson et mnl., rather than the simpler, widely used Hall-Petch equation. In compiling their table of data, it is surprising that they did not include results from certain low-carbon steels,31 in which, as illustrated in Fig. 2, the grain-size range is very much larger than in their Armco Iron. The very fine grains in these steels were obtained by a thermomechanical process. Examination by electron microscopy showed that the grains were separated by high-angle boundarie and contained only an occasional subboundary. The data from these steels obeyed the Hall-Petch equation, and it was shown quite conclusively that they did not fit a d-l or (1-lJ3 relationship. Obviously, a much wider range in grain size than used by Anderson et al. is desirable if we are to determine the true relation between lower yield stress and grain size.

Jan 1, 1969

By David A. Summers, Steven McGroarty

The last ten years has witnessed the change in water jet cutting studies, on rock, from laboratory testing to prototype use of field equipment. Unfortunately, while equipment and technological developments have occurred, the understanding of the exact mechanisms of water jet erosion have been less well developed. Commonly, theoretical evaluations have used the uniaxial compressive strength of the target rock as the major parameter of rock erosion resistance . It is considered that the structural properties of the rock, and most particularly, the flaw density and heterogeneity of the rock are much more important parameters. This is demonstrated and discussed. Locating the jet and target under water and pressurizing the containing vessel makes it is possible to induce cavitation in and around the water jet and create a much slower erosion process.

Jan 1, 1982

By A. Lee Barrett

SO commonplace that they are seldom noticed, mining-machinr, bits have a definite and important bearing on the cost of coal production. At the average mine many thousands of bits are used during the year. The actual cost represented by the purchase of the bits used, as well as that of sharpening and handling them, represents a considerable sum of money. From the point of view of indirect costs they are important, as the lack of good bits at a mining machine can seriously impair production. Good bits tend to ensure an adequate supply of coal. Classes OF Bits Mining-machine bits may be divided into three general classes, based on shape and method of use: (I) chisel, (2) pick-point and (3) one-use. The chisel and pick-point bits are shown in Fig. I. The so-called "chisel" bits were made of steel of various sizes and were sharpened to a wide chisel cutting edge. Few of this type of bit are used, except in places where coring is very bad. Sometimes chisel bits are used with standard bits to help cut out the core. The "pick-point" bit is widely used today. Normally it is made from ½ by I-in. steel, is about 4½ in. long when new, has a rake angle of about 25°, a front clearance of about 23O, a side clearance of approximsteji 8".' There are many variations in the shape of this bit, depending on the ideas of the individual that may be dressing the dies of the bit machine. This bit has been generally used for many years and at present, in one form or another, is by far the most popular bit used in coal mines. This bit usually is made from 0.85 carbon steel, although in recent years some alloy-steel bits have made their appearance. At present, carbon-steel bits are frequently tipped in. hard facing materials. A third class of bits might be called the L'one-use" bit; that is, a small bit that is used once and then thrown away. These bits have two or three points, are usually made from 0.85 carbon steel and sometimes from higher alloys. Recently some. of them have been tipped with hard facing material. Most of them were used at first with special

Jan 1, 1942

By A. Lee Barrett

SO commonplace that they are seldom noticed, mining-machinr, bits have a definite and important bearing on the cost of coal production. At the average mine many thousands of bits are used during the year. The actual cost represented by the purchase of the bits used, as well as that of sharpening and handling them, represents a considerable sum of money. From the point of view of indirect costs they are important, as the lack of good bits at a mining machine can seriously impair production. Good bits tend to ensure an adequate supply of coal. Classes OF Bits Mining-machine bits may be divided into three general classes, based on shape and method of use: (I) chisel, (2) pick-point and (3) one-use. The chisel and pick-point bits are shown in Fig. I. The so-called "chisel" bits were made of steel of various sizes and were sharpened to a wide chisel cutting edge. Few of this type of bit are used, except in places where coring is very bad. Sometimes chisel bits are used with standard bits to help cut out the core. The "pick-point" bit is widely used today. Normally it is made from ½ by I-in. steel, is about 4½ in. long when new, has a rake angle of about 25°, a front clearance of about 23O, a side clearance of approximsteji 8".' There are many variations in the shape of this bit, depending on the ideas of the individual that may be dressing the dies of the bit machine. This bit has been generally used for many years and at present, in one form or another, is by far the most popular bit used in coal mines. This bit usually is made from 0.85 carbon steel, although in recent years some alloy-steel bits have made their appearance. At present, carbon-steel bits are frequently tipped in. hard facing materials. A third class of bits might be called the L'one-use" bit; that is, a small bit that is used once and then thrown away. These bits have two or three points, are usually made from 0.85 carbon steel and sometimes from higher alloys. Recently some. of them have been tipped with hard facing material. Most of them were used at first with special

Jan 1, 1942

By Joseph C. Platt

IT is not the object of the present paper to give a description of the minerals found on Mine Hill, in Sussex County, N. J., nor even to touch upon all the forms of the ores named, but to place upon record and call to the attention of the Institute some interesting facts concerning them. In May, 1875, after the Dover meeting, some of the members visited this locality, and, no doubt, it is fresh in their memories, being one of the best known mineralogical points in our country. It will be only necessary to describe it very briefly. Mine Hill and Stirling Hill, in Sussex County, N. J., the former being at the village of Franklin Furnace, and the latter near Ogdensburg,-are the only localities in the State where zinc ores are found in workable quantities.* Mine Hill is the more northerly, and mineralogically differs from its neighbor, chiefly in having no hydrated ores to speak of, while at Stirling this deposit is considerable. At both points Franklinite, red oxide, and silicate of zinc occur in large quantities. Mine Hill lies on the east side of the Wallkill River, above which it rises to an extreme elevation of about 150 feet. On the summit the outcrop of the Franklinite vein appears, while the lowest worked points are perhaps 10 or 15 feet above the level of the stream. Corn¬mencing at the northern end, where the Hamburg Road crosses it, this outcrop runs along the northwestern brow of the hill a distance of about 2000 feet, in a general southwest direction, to a point where is a large, cavern-like opening, called the "Southwest Opening." " Double Rock," about the highest point on the hill, lies near the middle of this 2000 feet of outcrop, and over or near it passes a property line, to which allusion will hereafter be made. At the Southwest Opening the vein bends abruptly towards the east,-the angle between the two parts being perhaps 45°,-and this easterly branch continues some 700 feet. From the northern part of the Stirling Hill deposit to the southern part of the Mine Hill deposit is about two miles, and in this interval the vein carrying Franklinite * See New Jersey State Geology, 1868, p. 669.

Jan 1, 1877

By C. K. Leith

THE outstanding fact of the mineral world today, at home and abroad, is the surplus of current production, and particularly of capacity for production, over current requirements. This is not by Any means a new condition, but never before has it loomed up in such' menacing form. - Those of us who have devoted most of our professional efforts to the discovery and development of 'new mineral supplies now suddenly find ourselves with the job apparently accomplished, waiting for some one else to find an outlet for excess mineral production before we can further. The management of the industry is in much the same boat. The psjrcho16gy of the industry has been so grooved in the direction of acquisition of, minerals that at the present moment the mineral industry confronts the new problem of surplus in more or less of a daze.

Jan 1, 1931

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

R. E. Hoffman and D. Turnbull—The authors have presented evidence which they have interpreted as indicating that the rate of self diffusion is not intrinsically more rapid at grain boundaries than within the grain. Grain-size effects which apparently exist are attributed rather to impurities concentrated at the grain boundaries. In view of our own experiments and the existing evidence, we believe that the support for this hypothesis is not convincing. We have in progress an investigation in which the rate of self diffusion of silver is being measured over an extended temperature range in both single-crystal and polycrystalline specimens. The results of the single-crystal experiments and some preliminary data on fine-grained polycrystalline specimens have already been reported:' and it is anticipated that a complete report will be published in the near future. The self-diffusion coefficient of large-grained polycrystalline silver (1 grain per sq mm) has previously been measured by Johnson" between 730" and 940°C. The diffusion coefficients which we have measured in single crystals (210 plane normal to diffusion direction) agree within experimental error with values calculated from an extrapolation of Johnson's curve down to temperatures as low as 500 °C. However, it has been demonstrated that the overall self-diffusion rate in fine-grained polycrystalline specimens (initial grain size of 0.003 cm) becomes measurably larger than the overall rate in a single crystal at a temperature of 600°C, and the discrepancy between the two rates becomes greater as the temperature is further decreased. In fact, it has been possible to obtain satisfactory penetration curves for polycrystalline specimens using the sectioning technique at temperatures as low as 400°C. At this temperature, the penetration is 50 to 100 times greater in the polycrystalline specimens than in a single crystal. Fisher" has developed an analysis whereby the ratio of the rate of the unit diffusion process at the grain boundary to the corresponding rate within the grain can be calculated from the penetration curves and an assumption as to the width of a grain boundary. This analysis applied to our data indicates that the unit process at the grain boundary is faster by a factor of 10' at 475°C when the grain boundary width is taken to be 5. The silver used in most of these experiments was obtained from the Handy and Harmon Co. and listed as 99.97 pct pure. Preliminary experiments on 99.999 pct silver from the Jarrel-Asch Co. indicate a grain-size effect of the same order of magnitude as in the less pure silver. Nominally, these purities are as good, at least, as that of the carbonyl iron used by the authors, but of course if an impurity effect does exist its magnitude might be very dependent upon the nature of both major and minor constituents. The authors have cited the work of other investigators who have found no grain-size effects. Neither Steigman, Shockley and Nix" nor Maier and Nelson8 were able to correlate self-diffusion coefficients of copper with grain size. However, all their measurements were performed at or above 750°C; and on the basis of our work with silver, no grain-size effect would be expected at temperatures above about 0.7 of the absolute melting temperature unless the grain size were exceedingly small. Likewise, in the investigation of the self diffusion of lead by Seith and Keil,14 the lowest temperature at which the diffusion coefficient was measured in polycrystalline specimens was 207°C, which is still sufficiently high so that the lack of a grain-size effect is not surprising. Finally, in those experiments on iron from which they concluded that there was no grain size effect, Drs. Birchenall and Mehl seem to have no information as to the actual grain sizes immediately prior to and following the diffusion anneal. Without this information, we believe that their own experiments offer little support for their hypothesis. F. S. Buffington, I. D. Bakalar, and M. Cohen—The results given in this paper agree in order of magnitude with those tentatively reported by us.27 However, significant differences exist in the two sets of data, and it may be well to make an explicit comparison. The diffusion studies at M.I.T. were conducted on somewhat higher purity iron (99.98 pct Fe) than the grades used by the authors, but this is undoubtedly not the answer. Fig. 4 shows the diffusion results of both laboratories for the gamma phase, omitting the authors' data on the commercial steels, while fig. 5 presents a similar comparison for the alpha phase. The divergence is much more marked in the latter case than in the former. In connection with the M.I.T. determinations, all of the runs in the gamma range and those above 800 °C in the alpha range were conducted with specimens having a relatively thick (0.002 cm) electrodeposit of radioactive iron. This practice minimizes any possible error due to extraneous diffusion that may occur during the heating to and cooling from the operating temperature. An exact solution of Fick's law for these boundary conditions was used in calculating the diffusion coefficients. At a later time, three runs were made below 800°C, using very thin electrodeposits similar to those of the authors, and the points fell considerably below the values expected from the extrapolation of the results based on the specimens with the thick deposits (compare dash-dot line in fig. 5). However, in the runs with the thin deposits, deviations of 100 pct were found between the individual specimens, whereas the maximum deviation with the thick deposits was less than 25 pct. Accordingly, it is not known at the moment whether the M.I.T. points below 800 °C should be given as much weight as those above 800°C. If this were done, the frequency factor would be of the order of 400 cm2 per sec, which is quite high. In other metals, the frequency factor for self diffusion lies between about 0.1 and 10 cm2 per sec. As the points below

Jan 1, 1951

By Richard H. Willey

Efficient handling of large tonnages in open-pit mining demands, primarily, an abundance of well fragmented rock. To accomplish this, a drilling and blasting department composed of a well-knit, versatile group of workers and supervisors must be established. Some costs will remain relatively on the same level over a period of years, while others can be greatly lowered as will be shown. 'The Utah Copper Division, Kennecott Copper Corp., Bingham Canyon, Utah, has been ever alert for improvements in operating methods and equipment to gain increased efficiency and lower costs. Bingham Canyon MIne The greatest dimension of the mine is 8000 ft northeast-southwest with a width of 5000 ft southeast-northwest. From the lowest level, at an elevation of 6040 ft above sea-level, the mountain rises in 27 benches on the west side to W level (elevation 7800 ft) and 21 benches on the east side to Q level (elevation 7460 ft). At the inception of open-pit mining in 1906, the overcapping of leached porphyry had to be removed to reach a commercial grade of sulphide ore. The overcapping or waste now remaining is quartzite with intercalated limestone beds. The limestones are usually soft in nature except in the south-middle portion of the mine where they have been meta-morphized along the contact zone. This area usually gives drilling and blasting operations a great deal of trouble. Here occurs the greatest amount of secondary blasting, as the well-established fracture planes cause the altered beds to break into large boulders. Several massive quartzite "ribs" occur in the overburden, and as a result, the uniform breakage is difficult to obtain. The major quartzite areas have been subjected to complex folding, fracturing and faulting because of the intrusion of the underlying stock. The monzonite porphyry, which carries the commercial values, presents no serious drilling problem because of its softness and extensive minute fracturing throughout the mass. A series of major slips or faults pass through the ore body which, although of considerable advantage to the drilling and blasting department, sometimes works to the disadvantage of the track department. Drilling an11 blasting of the porphyry apparently becomes easier as depth is attained. but highly siliceous streaks throughout the pit still present difficulties. At no place is the rock of such character as to allow excavation without preparations. On certain higher elevations or levels, old fill material can be dug by the shovels, but only at some risk to equipment because of bank slippage. Past Methods At the outset of shovel operations in 1906, drilling was done with the Ingersoll-Rand F-24 piston drill mounted on an un-

Jan 1, 1949

By Lloyd R. Jackson

In the past 15 years there has been a great deal of interest in the fundamentals of plastic flow and rupture in metals and a number of papers have presented substantial advances toward a fundamental insight into the mechanism of these two processes. This paper is an appraisal of the present position with respect to the following: 1. The relative importance of shear and hydrostatic stresses in controlling the plastic flow of metals. 2. The relative importance of shear and hydrostatic stresses in determining the amount of flow before rupture in metals. 3. The use of generalized strains in determining the effect of plastic flow on the work-hardening of metals. FundamentalS Involved in Plastic Flow In attempting to devise a quantitative description of plastic flow in metals, it has been customary to assume that metals are homogeneous and isotropic. The fact that neither of these assumptions is correct complicates the experimental appraisal of relations developed. Nevertheless, as will be shown, metals are close enough '0 being isotropic and homogeneous so that considerable insight into the mechanism of plastic flow can be obtained. The assumptions of isotropy and homogeneity allow both the elastic and plastic behavior of metals to be described in terms of 12 variables—six being stress variables, and six being strain variables. From this viewpoint, it should be possible to represent the stress-strain relations in the plastic range for metals by a surface in 12 dimensions. One boundary of this surface would be the surface of transition from elastic to plastic behavior; the other would be the surface of rupture. These two surfaces would be joined by the surface of plastic flow. The shape of this composite surface would depend on the test temperature and speed of straining This paper is concerned only with results obtained at constant temperature and constant speed of straining. While such a representation is conceivable, the demonstration of such a surface would present almost insurmountable obstacles. The most fruitful simplification of this concept has been the recognition that the behavior of metals in the plastic region is primarily a result of shear stresses and strains. Based on this viewpoint, it is possible to utilize stress and strain invariants that are independent of hydrostatic components to define an effective stress and strain. In effect, this amounts to reducing the task of representing stresses and strains in 12 dimensions to one of representation in two dimensions. The two invariants (one for stresses and one for strains) that have received most attention are the following: q2 = ½[(Txx= - Tyy)2 + (Tyy - Tzz)2 + (Tzz - Txx)2 + 3(Txy2 + Tyz2 + 7xx2) [1]

Jan 1, 1947

By Lloyd R. Jackson

In the past 15 years there has been a great deal of interest in the fundamentals of plastic flow and rupture in metals and a number of papers have presented substantial advances toward a fundamental insight into the mechanism of these two processes. This paper is an appraisal of the present position with respect to the following: 1. The relative importance of shear and hydrostatic stresses in controlling the plastic flow of metals. 2. The relative importance of shear and hydrostatic stresses in determining the amount of flow before rupture in metals. 3. The use of generalized strains in determining the effect of plastic flow on the work-hardening of metals. FundamentalS Involved in Plastic Flow In attempting to devise a quantitative description of plastic flow in metals, it has been customary to assume that metals are homogeneous and isotropic. The fact that neither of these assumptions is correct complicates the experimental appraisal of relations developed. Nevertheless, as will be shown, metals are close enough '0 being isotropic and homogeneous so that considerable insight into the mechanism of plastic flow can be obtained. The assumptions of isotropy and homogeneity allow both the elastic and plastic behavior of metals to be described in terms of 12 variables—six being stress variables, and six being strain variables. From this viewpoint, it should be possible to represent the stress-strain relations in the plastic range for metals by a surface in 12 dimensions. One boundary of this surface would be the surface of transition from elastic to plastic behavior; the other would be the surface of rupture. These two surfaces would be joined by the surface of plastic flow. The shape of this composite surface would depend on the test temperature and speed of straining This paper is concerned only with results obtained at constant temperature and constant speed of straining. While such a representation is conceivable, the demonstration of such a surface would present almost insurmountable obstacles. The most fruitful simplification of this concept has been the recognition that the behavior of metals in the plastic region is primarily a result of shear stresses and strains. Based on this viewpoint, it is possible to utilize stress and strain invariants that are independent of hydrostatic components to define an effective stress and strain. In effect, this amounts to reducing the task of representing stresses and strains in 12 dimensions to one of representation in two dimensions. The two invariants (one for stresses and one for strains) that have received most attention are the following: q2 = ½[(Txx= - Tyy)2 + (Tyy - Tzz)2 + (Tzz - Txx)2 + 3(Txy2 + Tyz2 + 7xx2) [1]

Jan 1, 1947

By H. J. Modi, P. L. De Bruyn

IN recent years interest has been aroused in flotation rate studies both from a technical and a more practical aspect. With increasing fineness of grind becoming a necessity in treatment of low grade ores, difference:; in flotation rates of various size ranges will assume importance in the evaluation of overall recovery results. Theoretical analysis of flotation kinetics was initiated by Schuhmann,' who sought to define flotation rate of a given mineral and specified size range in terms of certain physical variables of the flotation system. Using as a basis for his analysis the bubble-particle encounter hypothesis previously advanced by Gaudin,' Schuhmann writes for the rate of flotation (R,.) of particles of average size x, Rx = PcPa(x) V F. [1] In this relation Pc and Pa represent, respectively, the probability of collision between particle and gas bubble in a given time interval and the probability of adhesion of particle to the bubble after collision. Rigorously speaking, the term PC does not have the significance of a probability factor, since it depends on the time interval and therefore can be numerically greater than unity. The term c(x) expresses the concentration of particles of an average size x in the flotation cell in weight per unit volume of pulp, and V denotes the total volume of pulp in the cell. The product, P,c(x)V, defines the frequency of particle-bubble collisl.on, and when it is multiplied by P,, the number of collisions per unit time resulting in successful adherence is obtained. The factor, F, measures the froth stability and is introduced because after fruitful bubble-particle contact some particles may still riot reach the froth launder. Coalescence of bubbles in the froth column or too short a bubble life could account for this effect. Schuhmann also introduced the concept of "specific flotation rate" (Q) to allow for the relative abundance of different mineral species in the flotation pulp. The specific flotation rate, having the dimension of reciprocal time, is defined as Eq. 2: Qx =Rx/c(x)v [2] and it also follows from Eq. 1 that Qx = PcPaF. [31 The theoretical aspects of flotation kinetics were also considered by Sutherland,3 who tried to improve Eq. 1 by expressing the probability factors in terms of such physical variables as particle radius (x), bubble radius (X), velocity of bubble relative to particle (v), the number of bubbles per unit volume of pulp (N) and the induction period (A) necessary for air-mineral adhesion. According to Sutherland's treatment, the rate equation, Eq. 1, transforms to R, = [3pX x v N] [sech2 (3 v ?/4 X) ] ?c(x) V [4] where the first term in brackets on the right-hand

Jan 1, 1957

By E. W. Felegy

THE need for improved mine communication to increase efficiency and to insure greater safety has long been recognized. General and unrestricted communication between all points underground, and between the surface and all points underground, is probably the least advanced phase of the mining industry. An ideal system of mine communication must re- quire no fixed wire installations. The equipment must be small, lightweight, and readily portable, and the power requirements low. A system that can be used not only under normal circumstances but also in an emergency, when the continuity of wires, tracks, and pipelines may be disrupted, must function independently of any aid furnished by standard installations.

Jan 5, 1953

By AIME AIME

MORE than thirty members of the Coal Division attended the Coal Land Valuations Round Table on Monday morning. Chairman Dilworth stated that the Committee had been appointed to take up the question and, after reading the list of members of the Committee, pointed out that the object of the meeting was to formulate a plan of action rather than to discuss any phases of valuation, per se. To this end he presented a tentative outline of points to be considered in the future by the Committee. After a lively discussion on the desirability of inclusion of some questions in the agenda of the Committee, the following outline was adopted :

Jan 1, 1931

By W. C. Ellis, E. S. Greiner

METALLIC titanium has been prepared in small quantities since the beginning of the century. Hunter1 reported in 1910 that he obtained a malleable product of 99.9 pct purity by the reduction of the tetrachloride by sodium in a closed container. Later Van Arkel2 and Fast3 prepared small quantities of malleable titanium by thermal decomposition of titanium iodide. Another method for producing malleable titanium from tetrachloride was reported by Kroll4 who used magnesium as the reducing agent. More recently Dean, Long, Wartman, and Anderson5 working at the U.S. Bureau of Mines have reported the preparation of the metal on a pilot plant scale by the reduction of titanium tetrachloride by magnesium in an atmosphere of helium. Their product, which is malleable, was used in the present investigation. Early in 1948 after the work of this paper: was completed Campbell, Jaffee, Blocher, Gurland, and Gonser6 described the strength and working characteristics of pure titanium which was prepared by the iodide method on a scale producing 300 to 600 g per run, in the form of 0.3- to 0.4-in. diam rods. Their product is characterized by low hardness and large capacity for cold work which they attribute to a high degree of purity with respect to oxygen, nitrogen, and carbon. Titanium has a melting point of about 1725°C5 it may be classed as a light metal since the specific gravity is 4.5 g per cc-1. The crystal structure is close-packed hexagonal from room temperature t0 885°C. Above this temperature the structure is reported7 as body-centered cubic. The change in crystal structure has been associated with discontinuities in specific heat8 electric resistance9 and thermoelectric force10 at temperatures near 890°C. It is reported11 that annealed titanium has a tensile strength 0f 78,700 psi which can be increased by cold-work to 123,000 psi. In the present investigation, the lattice constants at room temperature, the thermal expansivity between 30 and 800°C, as well as the electrical resistivity and thermoelectric force against platinum between - 200 and 1000°C have been determined. MATERIALS For the measurements, two series of specimens were prepared from titanium furnished by the U. S. Bureau of Mines. The first was lade from an annealed sintered compact, 0.38 in. thick. Sections of the compact were cold-swaged with intermediate anneals in vacuum to the sizes used. Sizes over 0.25-in. diam were annealed at 1000°C and smaller sizes at 800°C. Specimens originating from the sintered compact are designated in this paper as A. The second series of specimens was lade from a rod of titanium, 0.19 in. in dial, which was cold-swaged with the necessary intermediate anneals to the required sizes. This series of specimens is designated B. The impurities in the specimens of titanium, determined by chemical analysis, are given in Table I. Oxygen and nitrogen which were not determined by analysis, are probably present although in small quantities in view of the ductility of the material.

Jan 1, 1948

By J. B. Conway

RECENT studies of first-stage creep data have led to a special least-squares procedure for use in calculating the Andrade creep-equation constants. This procedure is easy to apply, uses only experimental data, and yields results which do not vary with the individual making the analysis. Taking logarithms of the Andrade equation I = lo(1 +ßl1/3)ekt leads to In l = In lo + In(1 + ßl1/3) + kt A residual can then be defined as the difference between the logarithm of an experimental length value and the logarithm of a calculated length value. Following the usual least-squares approach differentiation with respect to 10 and k of the expression for the sum of the squares of the residuals leads to two equations which cannot be solved directly for the three constants involved. However, values of ß can be assumed and corresponding values of lo and k can then be calculated. Then the sum of the squares of the residuals can be calculated. For a certain value of ß this sum will exhibit a minimum value to identify the least-squares values for ß, lo, and k. An illustration of the application of the above least-squares approach is obtained by employing the creep data for lead originally presented by Andrade' in the development of the one-third creep law. A plot of the sum of the squares of the residuals as a function of ß is shown in Fig. 1 along with the corresponding lo and k values. The minimum is seen to occur at ß = 0.0143 from which lo = 39.149 and k = 7.27 x 10-5. Based on these results the Andrade equation for these lead data is 1 = 39.149(1 + 0.0143 t1/3)e7.27 x 10-5t compared to the equation I = 39.13(1 + 0.01457/l/3)e6.95 X 10-5t developed by Andrade (calculation procedure not given but was probably a graphical solution). Calculating length values using the above equations and comparing with the experimental length values, residuals corresponding to the difference between experimental and calculated length values can be obtained. The sum of the squares of the residuals can then be calculated. For the case of the least-squares approach a value for this sum was found to be 2.37 x 10-3 compared to a value of 3.47 x 10" for the equation originally proposed by Andrade. In other words, while the constants proposed by Andrade provide an excellent fit for the lead data, a still better representation is afforded by applying the least-squares approach discussed above. A similar result was obtained for the lead data at 162oc.l The least-squares approach led to 1 = 9.866(1 + 0.0497 t1/3)el.011 x 10-2t compared to the equation I = 9.94(1 + 0.0433 l1/3)e1.06 X 10-2t given by Andrade. In this case, too, the sum of the squares of the residuals is slightly smaller for the equation based on the least-squares approach. It should be pointed out that a double trial and er-

Jan 1, 1965

By R. Taggart, R. H. Ericksen, D. H. Polonis

Transmission electron microscopy techniques hare been used to study the spontaneous marfensite phase that forms during the thinning of Ti-Cr alloys. The structure of this phase has been found to differ. from the hcp martensite and has been identified as a clisforted fcc lattice. The spordaneous marlensile in this system is interpreted as a metastable isomorph of the equilibriunz TiCr, phase. WHEN thin-foil specimens for transmission electron microscopy were prepared from metastable alloys of the Ti-Cr system, a spontaneous transformation occurred' when the foils contained the untrans-formed 0 phase or two-phase mixtures of the 0 and w phases. The purpose of this paper is to examine the relationship that exists between the crystal structure of the spontaneous product and that of the matrix. The differences between the martensite transformation that occurs in the bulk material and the spontaneous reaction that occurs during the preparation of thin foils are compared with the observations that have been reported for similar phenomena in a commercial titanium alloy.' A spontaneous reaction that exhibits characteristics similar to a martensite transformation has been reported to occur in thin foils prepared from the retained metastable structures of several alloy systems.1'3"7 ~ull~ observed such a spontaneous reaction in 0 brass and attributed the apparent increase in the martensite transformation temperature to a decrease in the non-chemical free energy associated with bulk strain energy. He also showed that the spontaneous product did not have a specific habit plane, but that its orientation relationships to the parent matrix were dependen on the thickness of the transforming region. It has also been pointed out by Breedis6 that in thin films the absence of the constraints imposed by a bulk matrix can cause different requirements for the martensite plate interface and lattice distortion which is reflected bv a dependence of the transformation mechanism on the specimen geometry. In the case of the spontaneous reaction reported for Au-Zn alloys7 a definite habit plane was determined and shown to correspond with the habit plane calculated on the basis of the Bowles and Mackenzie crystallographic theory of the martensite transformation.'- lo EXPERIMENTAL PROCEDURE A series of titanium alloys containing 5.5, 5.9, 6.4: 7.6, 8.0, 11.3, and 18.7 at. pct Cr were prepared from high-purity (iochrome) chromium and iodide-grade titanium by levitation melting. The experimental procedure used for sectioning the alloys and for thin-foil preparation has been reported in an earlier paper.' X-ray diffraction patterns were obtained using a 114-mm Debye-Scherrer camera and Cu-Ka radiation. In order to minimize fluorescent radiation from the specimen, a strip of aluminum foil 0.002 in. thick was placed in contact with the X-ray film. After a specimen was removed from the camera: an additional X-ray experiment was performed, to insure that no spurious lines were obtained due to the presence of the aluminum foil. The interstitial impurity analysis for the alloys used in this study was as follows: oxygen, 100 ppm: hydrogen, 30 ppm: nitrogen, 28 ppm. EXPERIMENTAL RESULTS Electron diffraction patterns were obtained from several individual crystals of the spontaneous marten-

Jan 1, 1970

By Dale A. Vaughan, Oliver M. Stewart, Charles M. Schwartz

A. U. Seybolt (General Electric Research Laboratory)—The authors should be commended for adding some important information to our knowledge of the solubility of interstitial elements in metals. It is becoming increasingly evident that the effect of even traces of such elements have very far-reaching effects upon the mechanical properties of the body centered cubic metals. Those who have worked in this area know that the accurate determination of the small solid solubility limits in systems of the type reported by the authors is a quite difficult task, and it is therefore not surprising that frequently the results of different workers are not in agreement. It is instructive, and usually helpful, to plot the solubility results on log weight or atomic percent -1/T coordinates to find out if a straight line is obtained. A straight line is expected because in systems displaying solubilities of the order of 1 to 3 at. pet or less, Henry's law is usually obeyed—or at least well enough obeyed so that the deviation from linearity is not very appreciable. If Henry's law is obeyed, one canthen use the Van't Hoff Equation in the form In N = ?H/RT + C, where N is mole fraction, at. pet, or wt pet for small values, and AH is the partial molal heat of solution of the solute. R and T have the usual significance, and C is an integration constant. If one plots the reported nitrogen solubility values as indicated above, the three points fall reasonably well on a straight line. The oxygen values for the two upper temperatures fall very closely to the nitrogen values as shown in the authors' Fig. 15. However, the value at 500°C departs widely from the straight line established by the data at 1500" and 1000°C. It is, of course, true that one cannot place too much emphasis on the significance of a line established by only three points, but in the absence of reasons for anticipating deviations, data exhibiting wide departures from linearity should at least be examined closely. Fig. 16 shows the log at. pct -1/T plots for the authors Ta-O and Ta-Ndata including a solid circle point at 500°C and 1.8 at. pet for Ta-O, which is simply extrapolated from the two higher temperature points. In addition, the data of R. P. Elliott9 for Nb-O are shown. These points were picked off his curve and are not very exact, but as can be seen they line up well on a straight line. It is interesting, and probably significant, that the slope of Elliott's results is not far from those of Vaughn, et al. This is probably to be expected because one would anticipate that the partial molal heats of solution of oxyten in these two very similar metals should be not too far apart. AH for Ta-O is about -1900 cal per mol, while for Nb-O it is near -2300 cal per mol. Hence, this lends some support to the thesis that the point at 500°C for Ta-O is much too high. The data of Gebhardt and Preisedanz10 are also plotted, and it is seen that their data while lying on a linear plot, have an appreciably steeper slope. The possible reasons for this will not be discussed here except to point out that their pressure-composition data show anomalies which suggest that they may have been dealing with a different equilibrium from that being discussed. There is another consideration which would also suggest that the solubility at 500°C is lower than shown. The solubility values were obtained by the classic method of first establishing a lattice parameter-composition curve. This the authors did, and there is probably little doubt that it is quite accurate. Such a plot is generally almost error-free because it has a self-correcting feature in that any deviation from linearity makes a data point immediately suspect, and subject to confirmation. Unfortunately, this is not true with respect to the actual solubility values. These are obtained ordinarily by taking an alloy containing more solute than is soluble at some temperature and then thermally

Jan 1, 1962

By L. O. Bacon

IN the spring of 1952 Calumet and Hecla Inc. began a geophysical program near Shullsburg, Wis., in the Wisconsin-Illinois lead-zinc district, to assist the geological and drilling exploration programs. Sphalerite, the ore mineral in this area, occurs with a considerable amount of marcasite. In general the higher the percentage of sphalerite in the ore, the higher the percentage of marcasite; however, there may be mineralized zones high in marcasite but low in sphalerite. Orebodies in general are relatively narrow and elongated. Reconnaissance exploration of virgin areas consisted of drilling along lines at 500 to 1000-ft intervals. Whenever a mineralized zone was intersected additional drilling was done to determine whether or not the zone carried zinc percentages of ore grade and, if so, to delineate the body. Calumet and Hecla Inc. was interested particularly in a method that would show the direction and position in which to drill from the original discovery hole. This suggested a method of contacting the orebody, which occurs at depths ranging from 100 to 200 ft, with one electrode. After a number of procedures had been considered it was decided to use equipotential line methods. Instrumentation and Field Procedure: The power source used was a 400-cycle Signal Corps motor-generator having a rated output of 1200 w at 115 v. The detection unit consisted of test probes, a two-stage amplifier, and &apos;head phones for determining the equipotential line by audio null. Field procedure consisted of contacting the sulfide body in the hole by a specially built spring-loaded expanding electrode which would be lowered into the hole, in the closed. position, until it reached the mineralized zone. At that point the mechanism was released so that the arms would make contact with the walls of the hole in the same manner that a well-bore caliper does. This electrode was then connected to the generator, the other terminal of which was connected to the surface electrode. The surface electrode was either a point, a straight line, or a circular line electrode. The point surface electrode was placed at a considerable distance from the hole, that is, 2500 to 5000 ft, depending somewhat upon the depth to the sulfide zone and the distance from the hole containing the subsurface electrode to which exploration was considered. A higher voltage output from the power source would have been desirable, although no difficulty was encountered in determining null points to a distance of 500 ft. Straight line electrodes used were approximately 1000 ft in length at a distance of approximately 1000 ft from the hole containing the subsurface electrode. The circular line electrode used consisted of 4400 ft of bare No. 10 copper wire, which provided a circle of 700-ft radius. All line electrodes were fastened to the ground at 20-ft intervals with copper staples 4 in. long. Equipotential points were determined at 25 to 100-ft intervals. Location of the points was made by plane table and stadia. In open country with a three-man crew, the points were plotted as they were determined. With a two-man crew, pegs were placed at equal potential points and surveyed in after several equipotential lines were determined. Although interpretation of results given in this paper is qualitative, the paper as a whole would not be complete without a discussion of the theoretical distribution of potential due to a circular line electrode. The theoretical distribution would be required if a quantitative interpretation of the measured potential distribution were to be made. The theoretical potential distribution due to a circular line electrode can be obtained by means of Legendre polynomials. Using the method as developed by Weber,&apos; the potential for a circular line electrode in a semi-infinite, homogeneous, isotropic medium can be expressed, using the spherical coordinate system, as: V(r,n) = pi/2pR[S(r/R)nPn(cos?)Pn(cosa)]r<R [1] er V(r,a) =pI/2pr[S(r/R)Pn(cos?) Pn(cosa)]r>R [2] where: 0 is the angle at the origin, taken on the axis of the circular electrode between the axis and the line drawn to the circumference of the circular electrode. a is the angle between the axis and the radius, r.

Jan 1, 1957

By T. F. Witherbee

ON the 22d of November, „1879, white iron unexpectedly appeared while working the Cedar Point Furnace, Port Henry, N Y., on the following burden, calculated to turn out mill and foundry iron: Anthracite coal, - 3000 pounds. Connellsville coke, - 1500 pounds. Total, - 4500 pounds. Old Bed ore, - 3750 pounds. New Bed fine ore, - 2000 pounds. New Bed chunk ore, - 1000 pounds. Kearnev hematite ore, - 750 pounds. Total, - 7500 pounds. Magnesian limestone, - 1865 pounds. Common limestone, - 885 pounds. Total, - 2500 pounds. The production per week since making mill iron-from September 1st, 1879, to date, seven weeks-was 412 gross tons. Ore was not immediately taken off, as nothing serious was looked for. The iron for the next week graded from No. 4 to white, and in. six days the make was 274 1/2 tons. At 10 P.M., Friday, the 28th, a slip of-..4 feet occurred, and on Saturday, at 5 A.M., another of 3 feet on the south side and. 7- feet on the north side took place. At this time it was found that the south side had been hanging for over a week--a fact which had not been reported. Throwing off the wind, to produce slips. and reduce pressure, had been tried with no effect. The stock, as seen through the tuyeres, seemed to consist almost entirely of coal, with just enough infusible cinder to cement it into a mass through which the blast could not be forced. At 3.50 A.M., Sunday, the 30th, the first cinder seen in seventeen hours came into tuyeres Nos. 1, 2, 3, and 6, At 9.30 A.M. No. 3 was taken out to see if the stock

Jan 1, 1881

By F. C. Langenberg

DURING the course of some magnetic investigations which the authors have under way, six bars of 0.43-carbon steel were tested, a permeameter designed after the Hopkinson yoke type being used. The results obtained were of some interest and although far from complete serve at least to show the necessity for a careful investigation of the previous history of the samples under study as well as the chemical composition. A steel of given chemical composition may assume a great variety of structures, depending on its treatment. Professor Sauveur has devised a very clear and effective means of illustrating this point: The accompanying microphotographs show some of the possible structures assumed by a 0.30 carbon steel (Fig. 1). It is now a well-established fact that a structural change is accompanied by changes in the tensile strength, elastic limit, hardness, etc., and it seems reasonable to assume also, a change in the magnetic properties. Six bars of a 0.43-carbon steel were used, all the bars being taken from the same rod and treated as follows: Bar 1. Heated to 1,100° and cooled in the furnace. Bar 2. Heated to 1,000° and cooled in the furnace. Bar 3. Heated to 900° and cooled in the furnace. Bar 4. Heated to 1,000° and cooled in air. Bar 5. Heated to 900° and cooled in air. Bar 6. Untreated. The bars were then turned to 13 mm. diameter and tested by the Hopkinson yoke method. After testing, three specimens were taken from each bar, one from each end and one from the middle. The homogeneity of the. bars was tested in this manner and in no instance could any difference in structure be detected between the three specimens.1

Jan 2, 1915