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By J. B. Clark, A. J. McEvily, R. L. Snyder

The nonuniform distribution of precipitate particles has been recognized as a leading factor contributing to the relatively low fatigue resistance of aluminum alloys. The structure of many of these alloys is characterized by narrow precipitate-free zones adjacent to the grain boundaries. Alloys with such zones exhibit a tendency for brittle inter crystalline fracture. The interrelation between this type of structure and mechanical properties was investigated in an Al-10 wt pct Mg alloy. It was found that deformation during fatigue occurs preferentially along these zones and cracks initiate there. In Al-10wt pct Mg, the zones were found to be supersaturated even after extensive general precipitation and are due to the absence of proper precipitate nuclei in the region near the grain boundaries. Cold working the alloy prior to aging improves the mechanical properties by inducing precipitation within the zones and also by jogging of grain boundaries. The mode of fracture is changed from brittle inter crystalline to more ductile trans granular fracture. THE process of fatigue is highly structure sensitive, with the strength of the whole often dependent upon some localized discontinuity, either geometrical or metallurgical in nature. Much has been learned about the role of geometrical discontinuities, e.g., notches, in fatigue, but with the exception of the effects of inclusions or the shapes of carbides, relatively little is known about the specific effects of discontinuities in metallurgical structure such as nonuniform precipitation. In most age-hardening aluminum alloys, metallo-graphic studies have shown that the extent of precipitation adjacent to grain boundaries is much less than that which occurs in the interior of the grains. The width of these almost precipitate-free regions, which are sometimes called denuded zones, and the extent of solute depletion within them, are dependent upon the particular alloy and its aging treatment. It has been observed1 that these zones are relatively soft with the result that plastic deformation takes place preferentially within them. It has also been shown 2-4 that there exists a tendency for intercrys- talline cracking in fatigue when such zones are present. It is of interest to note that Broom et al.2,3 were able to reduce the incidence of this type of failure in an A1-4 wt pct Cu alloy by stretching the material 10 pct prior to aging. In the present study, the effects of precipitate-free regions on the fatigue properties of an A1-10 wt pct Mg alloy were studied in detail, and the effects of deformation prior to aging on the nature of the precipitation process as well as on fatigue properties were also investigated. MATERIAL AND PROCESSING An A1-10 wt pct Mg alloy was selected for this study, because it was known that well-defined precipitate-free regions along the grain boundaries are readily obtained in this alloy after aging at 200oC.5 The starting materials were 99.998 pct A1 and singly sublimed magnesium of about 99.9 pct purity. The aluminum was induction melted in a graphite crucible, and then the magnesium addition was immersed until dissolved. Chlorine gas was then bubbled through the molten alloy for 4 min to degas the melt, after which the melt was cast at a pouring temperature of 730" to 760°C into a cold, graphite-coated, tapered steel mold. Since A1-Mg alloys are difficult to homogenize,5 special care was taken to obtain a uniform composition. Two-in. cubes were cut from the ingot and heated at 446°C for 30 min. These cubes were then hot forged approximately 35 pct in each of the three cube directions and homogenized for 16 hr at 446°C. Sheet specimens were then obtained by pressing 40 pct and rolling 35 pct per pass with reheating between reduction steps to a final thickness of approximately 0.10 in. The sheet was then solution treated for 16 hr at 446°C and water quenched. The age hardening behavior of this material at 200°C was then determined, and the results are shown in Fig. 1. The age hardening of this alloy when subjected to cold work prior to aging is also shown in this figure. Preliminary work indicated that extensive deformation after quenching was required to affect drastically the precipitate-free regions in this alloy, and a rolling reduction of 50 pct was chosen. For purposes of comparison the following three conditions were studied: a) Solution treated, quenched, and aged 20 hr at 200°C

Jan 1, 1963

By G. D. Monk, W. C. Krumbein

The relation between permeability and the size parameters of unconsolidated sand is approached by considering sands as logarithmic frequency distributions having the basic parameters mean size and standard deviation. Sieve separates were mixed in accordance with the normal logarithmic probability law, so that the mean and standard deviation could be varied at will. Experiments were conducted in which one parameter was kept fixed and the other varied; in this manner the dependence of permeability on the individual parameters was evaluated. It was found that permeability can he expressed as the product of a power function of the mean size and an exponential function of the standard deviation. Earlier studies of the effect of size of particles on the permeability of uncon-solidated sand have shown that the permeability varies with the square of some average diameter. This was first pointed out by Hazenl in 1892 and verified by Slichter2 in 1898. Hazen's mean size was defined as the 10 percentile of the cumulative curve (i.e., size that is smaller than 90 pel cent of the distribution and larger than 10 per cent). Slichter's effective size, on the other hand, was found by Wilsey3,4 to agree with the 31 percentile. Fair and Hatch6 found that the geometric mean size of sieve separates yielded the same power function; Hulbert and Feben6 found that the permeability of sieve separates varied as the 1.89 power of the median diameter (i.e., the size associated with the 50 percentile of the cumulative curve). Relatively few studies included the effect of the "sorting" of the sediment on the permeability. It was recognized that the nature of the size distribution, in terms of the spread of the particles about the mean, affects the permeability, but no systematic investigations of this effect are known to the writers. Cloud7 demonstrated that the effect of the grain-size distribution on permeability is definitely measurable. In the present paper the authors investigate this relation analytically, and show that the effects of the size parameters on permeability may be predicted for at least a restricted set of conditions. Properties OF Sediments Recent investigations have shown that essentially all the geologically important characteristics of sediments may be expressed in terms of six measurable quanti-tities possessed by each clastic sedimentary particle. These attributes are: (I) size, (2) shape (sphericity), (3) roundness (angularity) , (4) mineralogical composition (density), (5) surface texture, (6) orientation. Each of these characteristics may be defined in several manners. Size may be expressed in terms of sieve mesh, settling velocity, volume, etc. Sphericity is a shape concept introduced by Wadell;8 it is essentially a measure of the ratio of the surface area of an equivalent sphere to the surface area of the particle. The same

Jan 1, 1943

By G. D. Monk, W. C. Krumbein

The relation between permeability and the size parameters of unconsolidated sand is approached by considering sands as logarithmic frequency distributions having the basic parameters mean size and standard deviation. Sieve separates were mixed in accordance with the normal logarithmic probability law, so that the mean and standard deviation could be varied at will. Experiments were conducted in which one parameter was kept fixed and the other varied; in this manner the dependence of permeability on the individual parameters was evaluated. It was found that permeability can he expressed as the product of a power function of the mean size and an exponential function of the standard deviation. Earlier studies of the effect of size of particles on the permeability of uncon-solidated sand have shown that the permeability varies with the square of some average diameter. This was first pointed out by Hazenl in 1892 and verified by Slichter2 in 1898. Hazen's mean size was defined as the 10 percentile of the cumulative curve (i.e., size that is smaller than 90 pel cent of the distribution and larger than 10 per cent). Slichter's effective size, on the other hand, was found by Wilsey3,4 to agree with the 31 percentile. Fair and Hatch6 found that the geometric mean size of sieve separates yielded the same power function; Hulbert and Feben6 found that the permeability of sieve separates varied as the 1.89 power of the median diameter (i.e., the size associated with the 50 percentile of the cumulative curve). Relatively few studies included the effect of the "sorting" of the sediment on the permeability. It was recognized that the nature of the size distribution, in terms of the spread of the particles about the mean, affects the permeability, but no systematic investigations of this effect are known to the writers. Cloud7 demonstrated that the effect of the grain-size distribution on permeability is definitely measurable. In the present paper the authors investigate this relation analytically, and show that the effects of the size parameters on permeability may be predicted for at least a restricted set of conditions. Properties OF Sediments Recent investigations have shown that essentially all the geologically important characteristics of sediments may be expressed in terms of six measurable quanti-tities possessed by each clastic sedimentary particle. These attributes are: (I) size, (2) shape (sphericity), (3) roundness (angularity) , (4) mineralogical composition (density), (5) surface texture, (6) orientation. Each of these characteristics may be defined in several manners. Size may be expressed in terms of sieve mesh, settling velocity, volume, etc. Sphericity is a shape concept introduced by Wadell;8 it is essentially a measure of the ratio of the surface area of an equivalent sphere to the surface area of the particle. The same

Jan 1, 1943

By H. R. Stahl

The disseminated lead district of Southeast Missouri lies 70 miles south of St. Louis. The only metal of economic importance in the ore is lead, but minor amounts occur of iron, zinc, copper, cobalt, nickel, silver and cadmium. These minor metals, as might be expected, tend to concentrate in both the flotation and table middlings. In the past, some zinc has been recovered by differential flotation. The silver and cadmium tend to associate with the zinc, and some recovery is made of these two metals at the smelter. The lead occurs as galena, or lead sulphide. The minor metals are also present as sulphides. The presence of oxidized lead is suspected, but has not been definitely proved. The gangue is chiefly dolomitic limestone, with small amounts of sandstone and shaly glauconitic and chloritic minerals. The ore contains about 3.25 per cent lead, occurring as galena disseminated through the gangue. Some of the galena is very finely disseminated, and the mineral in the gravity tailings, or chat; is seldom or never in the free state. The method of treatment of the ore has been evolved over a period of 75 years; hence probably is not far from correct. The milling processes have tended toward simplification during the past 15 years, but recoveries have never been sacrificed for the sake of simplicity. In many cases, simplification of flowsheets has led to better recoveries and operating economies. A simplified flowsheet is shown in Fig. I. The St. Joseph Lead Co. operates four mills in the Flat River district, with a normal total capacity of about 21,000 tons per day, divided as follows: Federal mill, 11,000 tons; Leadwood mill, 4500 tons; Desloge mill, 3400 tons and Bonne Terre mill 2400 tons. The methods of concentration used at these plants are similar in principle; they differ mainly in details and in the type and size of the equipment used. The process of concentration may be divided into five main steps; i.e., dry crushing, wet grinding, classification with its attendant desliming, tabling and flotation. A brief description of these processes will be given, noting important differences in the various plants, and also noting the more important changes or developments of the past few years. Dry Crushing The run-of-mine ore is hoisted in skips, the capacity of these skips ranging from 23/4 tons to 81/4 tons. At the Desloge plant, the ore is hoisted in 2-ton mine cars on self-dumping cages. All ore is hoisted at shafts adjacent to the various crushing plants, no ore being transported on the surface. Primary breaking at all the mills is accomplished with 9E Telsmith breakers. Preliminary screening is provided ahead of most of these crushers, either by station-

Jan 1, 1943

By H. R. Stahl

The disseminated lead district of Southeast Missouri lies 70 miles south of St. Louis. The only metal of economic importance in the ore is lead, but minor amounts occur of iron, zinc, copper, cobalt, nickel, silver and cadmium. These minor metals, as might be expected, tend to concentrate in both the flotation and table middlings. In the past, some zinc has been recovered by differential flotation. The silver and cadmium tend to associate with the zinc, and some recovery is made of these two metals at the smelter. The lead occurs as galena, or lead sulphide. The minor metals are also present as sulphides. The presence of oxidized lead is suspected, but has not been definitely proved. The gangue is chiefly dolomitic limestone, with small amounts of sandstone and shaly glauconitic and chloritic minerals. The ore contains about 3.25 per cent lead, occurring as galena disseminated through the gangue. Some of the galena is very finely disseminated, and the mineral in the gravity tailings, or chat; is seldom or never in the free state. The method of treatment of the ore has been evolved over a period of 75 years; hence probably is not far from correct. The milling processes have tended toward simplification during the past 15 years, but recoveries have never been sacrificed for the sake of simplicity. In many cases, simplification of flowsheets has led to better recoveries and operating economies. A simplified flowsheet is shown in Fig. I. The St. Joseph Lead Co. operates four mills in the Flat River district, with a normal total capacity of about 21,000 tons per day, divided as follows: Federal mill, 11,000 tons; Leadwood mill, 4500 tons; Desloge mill, 3400 tons and Bonne Terre mill 2400 tons. The methods of concentration used at these plants are similar in principle; they differ mainly in details and in the type and size of the equipment used. The process of concentration may be divided into five main steps; i.e., dry crushing, wet grinding, classification with its attendant desliming, tabling and flotation. A brief description of these processes will be given, noting important differences in the various plants, and also noting the more important changes or developments of the past few years. Dry Crushing The run-of-mine ore is hoisted in skips, the capacity of these skips ranging from 23/4 tons to 81/4 tons. At the Desloge plant, the ore is hoisted in 2-ton mine cars on self-dumping cages. All ore is hoisted at shafts adjacent to the various crushing plants, no ore being transported on the surface. Primary breaking at all the mills is accomplished with 9E Telsmith breakers. Preliminary screening is provided ahead of most of these crushers, either by station-

Jan 1, 1943

By L. T. Lloyd, H. H. Chiswik

The operative deformation elements in a-uranium single crystals under compression at room temperature have been determined as a function of the compression directions. The deformation mechanisms noted may be arranged with respect to their frequency of occurrence and ease of operation in the following order: 1 — (010)-[I001 slip, 2—{130} twinning, 3—{~172} twinning, and 4bunder special conditions of stress application, kinking, cross-slip, {.-176) twinning, and (011) slip. The composition planes of the (172) and (176) systems were found to be irrational. Cross-slip was shown to be associated with the major (010) slip system, coupled with localized interaction of slip on the (001) planes. The mechanism of kinking was found to be similar to that observed in other metals in that it occurred chiefly when the compression direction was, nearly parallel to the principal slip direction [loo] and was associated with a lattice rotation about an axis contained in the slip plane and normal to the slip direction: the [001] in the uranium lattice. The resolved critical shear stress for slip on the (010)-[100] system was found to be 0.34 kg per mm2 In a single test it was shown that under compression in suitable directions twinning on the (130) also occurs at 600°C. DEFORMATION mechanisms of large grained polycrystalline orthorhombic a-uranium have been studied by Cahn.1 A major slip system identified as the (010) with a probable [loo] slip direction and a minor slip system on the (110) planes were reported; the slip direction of the minor system was not determined. The twinning systems that were identified experimentally included the (130) and the irrational (172) composition planes; observations of other traces which were not as frequent and which did not lend themselves to positive experimental identification led Cahn to postulate on the basis of indirect evidence that twinning also occurred on (112) and (121) planes. In addition to the foregoing slip and twinning mechanisms, Cahn also observed kinking and cross-slip in conjunction with the major (010) system; the cooperative cross-slip plane was not identified. The availability of single crystals to the present authors has enabled them to check these results, particularly with reference to the doubtful mechanisms and the preference of operation of any one mechanism in relation to the direction of stress application. The tests were confined to compression only, primarily because of experimental limitations imposed by the size and shape of the available crystals. The tests were performed at room temperature except for one crystal compressed at 600°C. The compression directions were chosen to obtain a representative coverage of one quadrant of the stereo-graphic projection. To test the existence of some of the deformation elements that were reported by Cahn, but were not found in the present study, several additional crystals were compressed in specifically chosen directions considered most ideal for their operation. Experimental Techniques The single crystals were obtained by the grain coarsening technique described by Fisher? They grinding and polishing on rotating laps, with final surface preparation performed in a H3PO4-HNO3 electropolishing bath. A typical crystal readied for compression is shown in Fig. 1; their dimensions were rather small and depended upon the testing direction. Crystals isolated for compression in a direction close to the [010] axis, which lay roughly parallel to the longitudinal axis of the polycrystalline rod, were about 3 to 4 mm long and 5 mm2 in cross-section, while those prepared for compression in other directions were smaller. Most of the crystals were free from twin markings and showed no evidence of Laue asterism. Several crystals, however, contained twin traces prior to compression; these were identified prior to compression so as to clearly distinguish them from those initiated during deformation. The origin of the twin markings prior to deformation may be ascribed to two sources: thermal stresses and specimen handling during isolation and preparation. Two other types of imperfections in the crystals should be mentioned: inclusions, which were probably oxides or carbides. and three of the crystals contained a small number of spherical included grains (<0.01 mm diam), which were remnants of unabsorbed grains from the coarsening treatment. The volume represented by these imperfections was small, and their presence presented no difficulties in the interpretation of the macrodeformation processes during subsequent compression. Two compression fixtures were employed: crystals A, B, C, E, and G were compressed in a hand-operated screw-driven jig whose compression platens were designed to minimize axial rotation;

Jan 1, 1956

By L. W. Kempf

THE thermal expansion characteristics of aluminum alloys have been examined by several investigators, among whom may be mentioned Shakespear,1 Schulz,2 Hidnert,3 Hidnert and Sweeney4 and McCullough.5 Shakespear compared the expansion of a series of aluminum alloys containing 14 per cent copper, with separate additions of about 1 per cent each of manganese, tin and zinc with that of pure copper. Schulz examined the expansion of aluminum and zinc and some aluminum-zinc alloys. Hidnert determined with a high degree of precision the expansion characteristics of pure aluminum, some aluminum-copper, aluminum-zinc, aluminum-silicon and some commercial alloys. Hidnert and Sweeney examined the expansion characteristics of aluminum-beryllium alloys. McCullough, by an interferometer method, determined the expansivity of some aluminum-copper, aluminum-magnesium, aluminum-iron, aluminum-nickel, aluminum-silicon and aluminum-manganese alloys. Incidental to an investigation carried out during the past six years and leading to the development and exploitation of an aluminum piston alloy of relatively low thermal expansivity, the expansion characteristics of a wide variety of alloys were examined. Some of the data which might be of general interest are gathered in this paper.

Jan 1, 1933

By E. J. Rapperport, E. D. Levine

The boundaries of the (a +ß) field in the Al-Li system were determined between 150°and 550°C utilizing quantitative metallography and lattice-parameter measurements. The solubility of lithium in aluminum decreases from 12.0at. pct Li at 550°C to 5.5 at. pct Li at 150°C. P Al-Li is saturated with aluminum at 45.8 at. pct Li and has this boundary value constant over the temperature range 150°to 550°C. THE solid solubility of lithium in aluminum has been determined by several investigators, 1-6 but, as shown in Fig. 1, there is little agreement among the various determinations. The earliest investiga-tions&apos;-&apos; are suspect because of the use of impure materials. Although high-purity materials were employed in more recent work,4&apos;5 the experimental techniques may have led to contamination of the specimens. Probably the best work has been that of Costas and Marshall,6 who obtained close agreement between results obtained by two independent phase-boundary techniques: electrical resistivity and mi-crohardness. No detailed studies of the solubility of aluminum in the bcc ß phase, Al-Li, have been reported. Cursory investigations1,2,6 have indicated only that the (a+ß) -p boundary lies between 40 and 50 at. pct Li and is relatively independent of temperature. The present work was undertaken in order to provide an independent check on Costas and Marshall&apos;s determination of the solubility of lithium in aluminum, to extend knowledge of this solubility limit to temperatures below 225°C, and to make an accurate determination of the solubility of aluminum in Al-Li. EXPEFUMENTAL Alloy Preparation. In view of the difficulties encountered in previous investigations of the A1-Li system, close attention was paid to the use of methods of alloy preparation and treatment that would minimize contamination. Aluminum sheet (99.99 + pct Al) was vacuum-induction melted in a beryllia crucible to remove hydrogen. Lithium (99.9 pct Li) was charged with pre-melted aluminum into a beryllia crucible, in a helium-filled drybox. The crucible was sealed in a Vycor tube and transferred from the drybox to an induction furnace. Melting of alloys was performed by induction heating in a helium atmosphere. Solidification was accomplished by means of a suction apparatus, shown in Fig. 2, in which the alloy was forced by changes of pressure into a 3/16-in. inside diam closed-end beryllia tube. This technique produced rapid solidification of a small portion of the melt, resulting in alloys with a high degree of homogeneity. Typical lithium distributions are presented in Table I. Transverse sections 1/8 in. long were cut from the alloy rods, and each section was split in half longitudinally. One half of each section was analyzed for lithium, and the opposing halves were employed for phase-boundary determinations. Lithium contents were determined by flame photometry with an accuracy of 1 pct of the amount of lithium present. Thermal Treatments. Homogenization and equilibration heat treatments were performed in electrical-resistance furnaces with temperatures controlled to ± 2OC. Calibrated chromel-alumel thermocouples were employed to measure temperature. Homogenization was performed in helium-filled l?yrex tubes for 1 hr at 565°C. The encapsulated specimens were then transferred directly to furnaces maintained at lower temperatures for equilibration. Equilibration times were 2 hr at 550°C, 8 hr at 450°C, 27 hr at 350°c, 90 hr at 250°c, and 285 hr at 150"~. These times were chosen on the basis of conditions employed by previous investigators. Alloys were quenched from the equilibration temperatures by breaking the capsules into a silicone oil bath. By performing all possible operations either in sealed capsules or in a helium-filled drybox, the specimens were given minimum exposure to the atmosphere. Quantitative Metallography. Metallography of Al-Li alloys is difficult because of the atmospheric reactivity of the ß phase. It was found possible, however, to prepare surfaces of good metallographic quality by preventing contact with moisture during preparation. Grinding through 4/0 paper was performed in the drybox. The specimens were then transferred under kerosene to the polishing wheel. Three polishing stages were employed: 25-p alundum with kerosene lubricant on billiard cloth, 1-µ diamond paste on Microcloth, and 1/4-p diamond paste on Microcloth. Between stages the samples were cleaned by rinsing in trichloroethylene and buffing

Jan 1, 1963

By Herbert H. Kellogg

In 1930, Taggart, Taylor and Knoll1 found that addition of various electrolytes to suspensions of ground minerals resulted in the stopping or starting of Brownian movement of the suspended particles. On the basis of the many new facts found, they rejected the " classical"† theory of Brownian movement and proposed an "ioniza-tion " theory. This new theory was further supported in later publications by Taggart.3,4 The acceptance of the ionization theory by men in the field of flotation may be judged by the mention given this theory in Gaudin&apos;s "Principles of Mineral Dressing,&apos;16 Wark&apos;s "Principles of Flotation,"8 as well as in a recent paper by Fitt, Thomas and Taggart.7 The proponents of the ionization theory have gone further than the mere statement of the new theory. A parallelism between the Brownian movement of mineral particles and their behavior in flotation was reported.1,3,4 Likewise, the correlation between flocculation-dispersion of mineral particles and the Brownian movement of these particles has been investigated.&apos; Bankoffl5 has suggested that "slime-coating" can also be directly correlated with the Brownian movement of the slime particles. In each of the instances mentioned it is the ionization theory of Brownian movement that has been used to "explain" the correlations that were found. The essential conflict between the kinetic theory and the ionization theory can be understood best by a brief description of each. The kinetic theory* proposes that Brownian movement is caused by the impacts of liquid molecules against the solid particles. At any instant of time, the molecular impacts on all sides of the solid particle will not balance, and the particle will receive a push in some direction. According to this theory, dl particles suspended in a liquid are in Brownian movement. However, if the particle is very large, the impacts on all sides will very nearly balance and the motion will not be noticeable. Another factor, besides the size of the particle, that affects the magnitude of the Brownian movement is the viscosity of the liquid—the greater the viscosity, the less the displacement of particles by Brownian movement. This theory has been verified experimentally by measurement of the velocity of Brownian movement, and by measurement of the compacting of suspensoid particles under the influence of gravity.2 The originators of the ionization theory found that he addition of various electrolytes to slime pulps caused cessation or commencement of Brownian movement, depending upon the chemical nature of the particle and the electrolyte. The Brownian movement of quartz particles was observed to stop upon the addition of Certain electrolytes, where the conditions of the experiment prevented flocculation

Jan 1, 1947

By Herbert H. Kellogg

In 1930, Taggart, Taylor and Knoll1 found that addition of various electrolytes to suspensions of ground minerals resulted in the stopping or starting of Brownian movement of the suspended particles. On the basis of the many new facts found, they rejected the " classical"† theory of Brownian movement and proposed an "ioniza-tion " theory. This new theory was further supported in later publications by Taggart.3,4 The acceptance of the ionization theory by men in the field of flotation may be judged by the mention given this theory in Gaudin&apos;s "Principles of Mineral Dressing,&apos;16 Wark&apos;s "Principles of Flotation,"8 as well as in a recent paper by Fitt, Thomas and Taggart.7 The proponents of the ionization theory have gone further than the mere statement of the new theory. A parallelism between the Brownian movement of mineral particles and their behavior in flotation was reported.1,3,4 Likewise, the correlation between flocculation-dispersion of mineral particles and the Brownian movement of these particles has been investigated.&apos; Bankoffl5 has suggested that "slime-coating" can also be directly correlated with the Brownian movement of the slime particles. In each of the instances mentioned it is the ionization theory of Brownian movement that has been used to "explain" the correlations that were found. The essential conflict between the kinetic theory and the ionization theory can be understood best by a brief description of each. The kinetic theory* proposes that Brownian movement is caused by the impacts of liquid molecules against the solid particles. At any instant of time, the molecular impacts on all sides of the solid particle will not balance, and the particle will receive a push in some direction. According to this theory, dl particles suspended in a liquid are in Brownian movement. However, if the particle is very large, the impacts on all sides will very nearly balance and the motion will not be noticeable. Another factor, besides the size of the particle, that affects the magnitude of the Brownian movement is the viscosity of the liquid—the greater the viscosity, the less the displacement of particles by Brownian movement. This theory has been verified experimentally by measurement of the velocity of Brownian movement, and by measurement of the compacting of suspensoid particles under the influence of gravity.2 The originators of the ionization theory found that he addition of various electrolytes to slime pulps caused cessation or commencement of Brownian movement, depending upon the chemical nature of the particle and the electrolyte. The Brownian movement of quartz particles was observed to stop upon the addition of Certain electrolytes, where the conditions of the experiment prevented flocculation

Jan 1, 1947

By Eugene P. Pfleider, Claus Freyberger

Generally, the different methods of financing new mining projects are not well understood by the engineers and supervisory personnel. Nor are the effects of these alternatives on depletion, taxes and profitability readily apparent to even the sophisticated management personnel without the aid of cash flow studies. Fortunately, with the advent of the computer it is possible now to simulate many different combinations of 1) equity, 2) loan and 3) production payment financing with little effort. A general computer program for cash flow analysis of mining ventures has been developed and applied as a case example to a 1967 feasibility study of the Underground Mining of Minnesota Taconite. The effects on profitability as measured both in rates-of-return and present value are presented for various financing combinations. In addition, percentage depletion rates were altered so as to measure the impact of this statuatory allowance. Based on the cost data as presented in the aforementioned 1967 feasibility study, and assuming 7% loans, the rates-of-return vary from 9. 9% to [00] % on equity variations and from 9. 9% to 11.4% on total invested funds.

Jan 1, 1969

By K. H. Hiller

A rotational viscometer has been designed which perrnits the measurement of the rheological properties of drilling muds and other non-Newtonian fluids under conditions equivalent to those in a deep borehole (350F, 10,000 psi). The important mechanical features of this instrument are described, and its design criteria are discussed. The flow equations for the novel configuration of the viscometer are derived and the calibration procedures are described. The data and their interpretation, resulting from measurement of the flow properties and static gel strengths of homoionic montmorillonite suspensiom at high temperatures and pressures, are presented. Data are also presented for the flow behavier of typical drilling fluids at high temperatures and pressures. The pressure losses in the drill pipe and the annulus depend critically upon the flow parameters of the drilling fluid. This work demonstrates the need to measure these parameters under bottom-hole conditions in order to obtain a reliable estimate of the pressure losses in the mud system. INTRODUCTION The rheological properties of drilling fluids are affected by temperature and pressure, but the extent of these effects on the dynamic flow properties is not well known. Measurements of changes of the flow properties of clay-water drilling muds with temperature have been reported by Srini-Vasan and Gatlin.1 The temperatures reported did not exceed 200F, a limitation imposed by the apparatus used by these authors. The rheological properties of clay suspensions were measured at temperatures up to 100C by Gurdzhinian.&apos; Neither the nature of the exchange ions in the clay suspensions nor the degree of purity were defined in his work, nor were the measurements extended to currently used drilling fluids. The lack of systematic measurements of dynamic flow properties at high temperatures and pressures seems the more surprising since during the last decade the importance of the control of the hydraulic properties of drilling fluids has come to be widely recognized. Very good mathematical treatments of the friction losses in drill pipe and annulus have been developed.3 4 These treatments are based on the assumption that drilling fluids behave as Bingham plastic fluids. Quite often this assumption is justified, while in other cases a power law equation pro- duces better fit than the Bingham model does. For convenience in applying viscometer data to pressure-drop calculations, the Bingham plastic flow equation is preferable and, therefore, has been applied to the data reported in this paper, although other equations may fit these data more accurately. In a Bingham plastic fluid the relationship between the shearing stress 7 and the rate of shear D is given by the following equation: where is the plastic viscosity and 4 the yield point. If 4 = 0, the equation for simple Newtonian flow, 7 = pD, is obtained. Two empirical constants are required for the description of laminar flow of a Bingham plastic fluid, and calculations of the flow behavior at high temperatures and pressures cannot be better than is permitted by the accuracy with which these constants are known. For this reason a high-pressure, high-temperature rhe-ometer has been designed to measure the plastic viscosity the yield point +, and the static gel strength S, at pressures up to 10,000 psi and temperatures up to 350F. The important features of its design will be described. The results of measurements on homoionic clay slurries will be discussed insofar as they are relevant to an understanding of the general flow behavior of clay-water drilling fluids. The results of measurements on some typical drilling fluids will be presented also, and their practical implications will be briefly discussed. DESCRIPTION OF EQUIPMENT MECHANICAL FEATURES A viscometer designed to measure the plastic viscosity, yield point and gel strength of non-Newtonian fluids must permit the measurement of the shearing stress t at any given rate of shear D. This is possible only if t and D are approximately uniform throughout the entire sheared sample. A Couette apparatus is the most convenient method of realizing this condition, as has been pointed out by Grodde." The "high-pressure, high-temperature rheometer" described in this paper is basically a rotational Couette viscometer that is immersed in a cell in which pressure and temperature can be controlled over the range of interest. Fig. 1 shows schematically the important features of the pressure cell and associated equipment. The heart of the instrument is the rotating cup. It is shown more clearly in Fie. 2. which revresents the lower one-third of the pressure cell (below the input drive shaft shown in Fig. 1), and it is shown in detail in Fig. 3. For measurements of dynamic flow properties, the rotating cup is driven by a 1/2-hp electric motor, which operates through a Vickers

Inflation, tight money and keen competition spur companies to consider advanced material handling systems capable of reducing cost per ton of moving ore, waste or men and supplies. Since transportation charges account for an average of about 25% of the total delivered price of a product, then this cost center may actually determine the economic value of a new deposit. This being so, it is interesting to note that of the 1.4 billion tons of revenue freight carried by all Class I carriers of the nation in 1967, over 247 million tons or 17.5% were industrial minerals or products dependent on industrial minerals, i.e., glass, gypsum board, brick, etc. Because most bulk commodities have a comparatively low market value and are usually classified for lower than normal freight rates, railroads rely on large volumes and better equipment utilization to effect an equitable return. It is for this reason that the unit and shuttle train concept came into being. The average rate per ton-mile of all materials hauled by rail in 1968 was 1.31 cents. The low rates existing for industrial minerals contributed to this low average as did unit and shuttle train rates.

Jan 10, 1969

By Heinrich Siemes, Christa Hennig-Michaeli

The effect of temperature and orientation on the plastic behaviour of an impure titaniferous magnetite from Palabora (South Africa) has been investigated. Prismatic specimens were axially compressed along [001], [110] and [111]. The strain rate was about 3.10-6 s-1. Trace analyses of glide lines revealed a plastic anisotropy due to glide on several non-equivalent crystallographic planes. At 200 °C {111}<112> twinning, {111}<110> slip and {100}<011> slip have been operative. At 400 °C {111}<110> slip and {100}<011> slip are primary glide modes. {110}<110> slip seems to be a secondary glide mode in the [001] specimens at 400 °C. {III}<112> twin glide generates isolated sharp lamellae. {111}<110> slip produces smooth surface striae. {100}<011> slip is characterized by coarse and partially wavy slip bands. {I10}<110> slip displays faint remarkably equidistant glide lines. The critical resolved shear stresses (CRSS) decrease with rise of temperature. The CRSS ratio of slip on [100) to slip on {lll} increases from 1.1 at 200 °C to 1.4 at 400 °C giving rise to a distinct flow anisotropy of the magnetite at 400 °C.

Jan 1, 1982

By Charles A. Ashburner

A very limited development has been made of the coal-fields of this Territory. This is to be accounted for by the fact that a number of the coal-fields lack railroad transportation, by the distance of other fields from the consumers (due to restricted settlements), and finally by the poorer quality of a number of coals which have been mined as compared to others which can be economically imported into the Territory. The consumption of coal in Utah during 1886, outside of that used by the railway companies, was: Tons. Utah coal,..........110,000 Wyoming coal,. .....19,000 Colorado coal,........* 4,945 Total,........... 133,945 It is estimated that there are 1100 miles of railroads in the Territory which use coal for fuel. The consumption of these roads for the year is estimated at 100,000 tons, making an aggregate consumption in the Territory of 223,945 tons. The consumption of coal in Salt Lake City duriug the year was as follows: Tone. From Grass Creek mines,.......21,000 " Pleasant Valley Company&apos;s mines,.. 12,700 " Utah Central Company&apos;s mines,.9,000 " Bock Spring mines,.6,500 " Almy mines .. ., .. .. . 6,000 " Miscellaneous sources,..5,800 Total ,.........60,000

Jan 1, 1888

By Larry D. Patts

Section 317(e) of the Federal Coal Mine Health & Safety Act of 1969 directed the Secretary of the Interior to prepare standards under which all working places in a mine shall be illuminated by permissible lighting while persons are working in such places. Section 317(e) further provides that such working places shall be illuminated within 18 months after such standards are promulgated. In accordance with this section of the Act, there was published in the Federal Register for December 31, 1970, a notice of proposed rulemaking which prescribed the illumination to be provided in the working places of underground coal mines. In light of written comments, suggestions, and objections to this proposed rulemaking, the proposed standards were withdrawn and reproposed in the Federal Register for Wednesday, October 27, 1971. In light of further comments, suggestions, and objections, a public hearing was held on April 4, 1974, and standards were again reproposed and published in the Federal Register for April 1, 1976. Promulgation of the final lighting-standards &k place on October 1, 1976, which means that the underground coal mining, industry must comply with face illumination requirements by April 1, 1978.

Jan 3, 1978

By David Turnbull

IN isothermal recrystallization processes, new crystals generally grow into the matrix until they impinge upon other new crystals or an external surface, at constant linear rates G. Before impingement the perceptible course of growth can be described by the equation: 1 = G(t-7) C1I where, G = dl/dt, 1 is a crystal dimension measured in a constant direction, t is the time, and 7, the nucleation period, is a positive intercept on the time axis. Fig. 1 is a schematic representation of I as a function of time for a recrystallizing grain. G is dependent upon temperature, driving energy (strain or surface energy), relative grain and boundary orientations, but is generally independent of time. The frequency of nucleation, fi, (time" volume") can be defined by the equation: N = 1/fV [2] where ? is the mean nucleation period and V is the volume of the specimen that has not recrystallized. The kinetics of primary and secondary recrystallization generally can be described satisfactorily in terms of the parameters N and G only.&apos;-" After recrystallization is complete the average grain size 7 increases with time by "normal grain growth;" didt, the average rate of grain growth, is strongly time dependent and has not yet been precisely related to G for the motion of the individual grain boundaries constituting the system. It has been suggested4* " that the elementary act in grain boundary migration is closely related to the elementary act in grain boundary self-diffusion. Although the distance of atom movement in the two processes may be somewhat different, there is reason to expect that the activated states may be very similar, so that the free energy of activation for grain boundary migration should be of the same order of magnitude as for grain boundary self-diffusion. Therefore, it is desirable to develop a satisfactory basis for comparing data on self-diffusion and grain boundary migration and to make such comparisons where possible. Theory The formal theory of grain boundary migration rates is analogous to the theory for the rate of growth of crystals into supercooled liquids reviewed elsewhere 6-8. Boreliuss has shown that the latter theory describes, within the theoretical uncertainty, the growth of selenium crystals into supercooled liquid selenium. Motto and more recently Smolu-chowski" have derived expressions for the rate of boundary migration in recrystallization. The treatment to be presented is similar to Mott&apos;s excepting that the formalism of the absolute reaction rate theory will be used. The atomic mobility, M, in grain boundary migration is defined by: G = -M6p/6x where p is the chemical potential per atom and x is the coordinate measured in the direction of grain boundary movement. Let AF be the free energy difference per gram atom on the two sides of the boundary and k the thickness of the boundary. For RT>>AF the potential gradient across the boundary (6p/6x) is essentially linear and it follows that: SF/8x = - aF/N\ [4] where N is Avogadro&apos;s number. According to the Nernst-Einstein equation, M is related to a diffusion coefficient, Do, for matter transport in grain boundary migration by the equation: M = Da/kT [5] Substituting eqs 4 and 5 into eq 3 gives the basic relation between Do and G: G = DoaF/\RT [6] Do values may be calculated from experimental values of G from eq 6 and directly compared with the coefficient of self-diffusion within the crystal, DL, or the grain boundary self-diffusion coefficient D,. However, a more convenient, though equivalent, basis for comparing atomic mobility in grain boundary migration and self-diffusion is through the constants of the absolute reaction rate theory. According to this theory diffusion coefficients may be written:" D = k2(kT/h) exp [-AF,/RT] 171 aFa, the free energy of activation, is related to the measured energy of activation, Q, by the equation: AFA = Q - T aSx - RT [8] where aSa is the entropy of activation. Substituting eqs 8 and 7 into eq 6 gives: G = ek(kT/h) (aF/RT) exp [(AS,,)C/R] exp C-Qc/RTI C91 where the subscript G refers to boundary migration. The relationship between the driving free energy and the free energy of activation in boundary migration is indicated schematically in Fig. 2. Experience indicates that the variation of G with temperature can be described by: G= Go exp [- Qc/RT] [10] where Go and Qc are generally temperature independent over wide ranges of temperature. Comparison of eq 9 with eq 10 gives:

Jan 1, 1952

By Charles L. Mantell, James E. Hoffmann

Mechanical inclusion, electrophoretic deposition, and adsorption were studied as mechanisms for code-position of aluminas present in copper-plating electrolytes as an insoluble disperse phase. Mechanical inclusion was not a significant factor. That codeposi-tzon of aluminas by an electrophoretic mechanism was unlikely was substantiated by measurements of the potential of the aluminas. The alumina content of the deposits was studied as a function of the pH of the bath. These tests in conjunction with sedimentation studies demonstrated the absence of an isoelectric point for the alutninas over the pH range examined. Thiourea in the electrolyte (a substance known to be adsorbed on a copper cathode during electrodeposition) affected the amount of alumina in the electrodeposit. However, no adsorption of thiourea on aluminas in aqueous dispersions was detected. If it were possible to produce a dispersion-hardened alloy of copper and alumina by electrodeposition, an alloy possessing both strength and high conductivity at elevated temperatures might be anticipated. Investigation of the mechanism of codeposition of aluminas with copper was undertaken with the hope that knowledge of the mechanism would aid in the development of such an alloy. The word "codeposit" here does not necessarily imply an electrolytic phenomenon but rather that the materials codepositing, the various aluminas, are transported to and embedded in the electrodeposited copper by some means. Mechanical inclusion in electrodeposition implies a mechanism of codeposition which is wholly mechanical in nature; the only forces acting on a particle are gravity and contact forces. Such a particle is presumed to be electrically inert and incapable of any electrical interaction with electrodes in an electrolytic plating bath. Processes for matrices containing a codeposited phase by electrodeposition from a bath containing a disperse insoluble phase frequently state that code-position is caused by mechanical inclusion.10,2,12 If settling, i.e., gravity, be the controlling mechanism for codeposition of aluminas, then assumptions may be made that 1) the content of alumina in the electrodeposit should be enhanced by increasing the particle size, 2) the geometry of the system, that is, the disposition of the cathode surfaces relative to the di- rection of the falling particles, should affect the alumina content of the electrodeposit, 3) in geometrically identical systems the chemical composition of the electrolyte employed should exercise no effect on the alumina content of the deposit, that is, the alumina content should be the same in all cathode deposits irrespective of bath composition. A bent cathode19 evaluates the clarity of filter effluent in electroplating baths by comparing the roughness of the deposit on the vertical surface with that on the horizontal surface. Two difficulties are inherent in this technique: 1) the current density on the horizontal portion of the cathode would be substantially greater than that on the vertical surface; 2) should the deposit obtained be rough, projections on the vertical face could act as horizontal planes and vitiate the relationship between the vertical and horizontal surfaces. Bath composition should have no substantial effect on the alumina content of the deposit. Two different electrolytic baths were employed. They possessed variant specific conductances and substantially different pH ranges. The experimental tanks were rectangular Pyrex battery jars 6 in. wide by 3 1/4 in. long by 9 3/4 in. deep. The cathodes were stainless steel 316 sheet of 0.030 in. thickness, cut to 7.5 by 1.75 in. and bent at right angles to form an L-shaped cathode whose horizontal surfaces measured 1.75 by 3.0 in. All edges and vertical surfaces were masked with Scotch Elec-troplaters Tape No. 470. The anodes were electrolytic cathode copper 9 in. high by 2.25 in. wide by 0.5 in. thick. To eliminate inordinately high current densities on the projecting edge of the cathode, the anode was masked 1 in. above and below the projected line of intersection of the cathode with the anode. The exposed area of the anode was equal to that of the cathode, providing both with equal average current densities. The agitator in the cell was of Pyrex glass and positioned so its center line was equidistant from cathode and anode, and a plane passed horizontally through the center of the blade would be located equidistant from the bottom of the cathode and the bottom of the deposition tank. The assembled apparatus is depicted in Fig. 1. Hatched areas on anode and cathode represent the area of the electrodes wrapped with electroplaters tape. MATERIALS The chemicals were copper sulfate—CuSO4 • 5H2O— technical powder (Fisher Scientific Co.). Spectro-graphic analysis showed substantial freedom from antimony, arsenic, and iron. Traces of nickel were present.

Jan 1, 1967

By Gerhard Bockstiegel

Kuczynski&apos;s formula has been derived for the case of nonspherical particles. TWO formulae of Kuczynski&apos;s type have been derived, one describing the increase in tensile strength, the other describing the progress of shrinkage of a powder compact. It has been strength,shown that the exponents of all three formulae each contain two magnitudes of different physical characters, viz, the geometrical factor a and the kinetic factor ß. The interrelationships between the three exponents are stated. SOME years ago Kuczynski1 experimentally showed that the radius, x, of the area of contact between very small spherical metal particles and a metallic block is related to the time of sintering, t, by the following equation x = constant tk [11 where k has the value 1/5 or 1/7. Assuming that the metal particles were perfect spheres and the metallic block was perfectly flat, he derived the foregoing equation from theoretical considerations of the process of material transport in metals, and he showed that exponent k is different for different mechanisms of transport, e.g., k = 1/2 for viscous flow (according to Frenkel2), k = 1/3 for evaporation and condensation, k = 1/5 for volume diffusion, and k = 1/7 for surface diffusion. From this Kuczynski concluded that the mechanism of transport was either volume diffusion or surface diffusion, depending on whether the value of k, as found in his experiments, was 1/5 or 1/7. Subsequently. Cabrera8 corrected Kuczynski&apos;s calculations with regard to surface diffusion, showing that the theoretical value of exponent k is 1/5 for both volume and surface diffusion. He supposed that the different experimental values of k were due to slight differences in the shape of the metal particles. An exponential relationship similar to the aforementioned was found by Okamura, Masuda, and Kikuta,4 Masuda and Kikuta, and Takasaki8 when studying the rate of shrinkage on powder compacts during sintering. The authors measured the shrinkage by means of the fraction w = Vp — V./Vp — V,,,, where V,, is the volume of the green compact, V, is the volume of the sintered compact, and V,,, is the volume of the compact in its densest state. This fraction, w, they found, is related to the time of sintering, t, by the equation w == constant tm. [21 Further, Bockstiegel, Masing, and Zapf7 observed that the tensile strength, s, of sintering iron powder compacts can also be related to the time of sintering, t, by an equation of the foregoing type, i.e., s = constant tn. [3] For exponent n the values 0.28 (S=2/7) and 0.35 ( 2/5) were obtained, and the authors pointed out that there might exist a simple interrelation between exponent n as found in their experiments and exponent k in Kuczynski&apos;s equation. The authors supposed that 2k = n, since the strength of adhesion between a metal sphere and a block (as in Kuczyn-ski&apos;s experiments) must approximately be proportional to their contact area, p. x2. Theoretical Considerations This paper is an attempt to correlate the fundamental experiments of Kuczynski&apos;s type with the results obtained with powder compacts as represented by Egs. 2 and 3. In particular, the paper is to show how the rate of sintering is influenced by the geometry of the sintering particles and by the type of material transport. As the geometry of particles conglomerating in a powder compact is very complex, some simplifying assumption has to be made, of course, in order to adapt the problem to mathematical treatment. In the following paragraph a suitable simplification is introduced, and Kuczynski&apos;s formula is derived for the case of nonsphcrical particles. Relation Between Area of Contact and Sintering Time—As the face of contact between two particles in a sintering powder compact is not necessarily a circle (as in the case of spheres sintering to a block), Kuczynski&apos;s formula is modified as follows: Let the perimeter of the face of contact be described by means of polar coordinates R, 4, as shown in Fig. la, so the area of contact, f, is determined by f= 1/2 . S112p[R(Æ) ]2 dÆ [4] Then, let the two particles be intersected by a plane perpendicular to area f. The intersection is shown in Fig. lb. According to the nomenclature in this figure, the distance, h, between the surfaces of the two particles is a function of T and Æ: h = h(r,Æ). For the particular case of spherical particles, as in Kuczynski&apos;s theory, this function becomes: h = constant r2. It shall be assumed here that in the close neighborhood of their

Jan 1, 1957

By D. G. Westlake

The electrical resistance of a series of V-H alloys (0 to 3.5 at. pct H) has been measured over the temperature range G° to 360°. Interstitial impurities made contributions to the residual resistivity, but not the ideal resistivity. The contribution of hydrogen in solid solution is expressed by Ap = 1.12 microhm-cm per at. pct H; but the contribution of precipitated hydride was negligible. A portion of the so1vu.s for the V-H phase diagram is presented. The solubility limit is given by In N (at. pct H) = (5.828 i 0.009) - (2933 i 44)/RT. Comparison of critical temperatures joy hydride precipitation and published critical temperatures for hydrogen embrittlement suggests the two are related. ThiS study was initiated as part of an investigation of the mechanism by which small concentrations of hydrogen embrittle the hydride-forming metals at low temperatures. It has already been shown that, in the case of hcp zirconium, a reduction in ductility accompanies the strengthening resulting from precipitation of a finely dispersed hydride phase.&apos;&apos;&apos; Our attempts to detect a similar precipitation of a second phase at low temperatures in V-H alloys by transmission electron microscopy have been thwarted because we have been unable to prepare thin foils that are representative of the bulk material with respect to hydrogen concentrati~n.~&apos;~ The present investigation establishes the solvus of the V-H system at subambient temperatures. Subsequently, we hope to be able to determine whether the embrittlement temperature is related to the critical temperature for precipitation of the hydride in a given V-H alloy. veleckis5 has proposed a partial phase diagram for the V-H system based on extrapolations of the pressure-composition relations he measured at higher temperatures. Kofstad and wallace&apos; conducted a similar study of single-phase alloys but did not attempt to establish the phase diagram. Zanowick and wallace&apos; and ~aeland&apos; have studied a portion of the phase diagram by X-ray diffraction, but they investigated no alloys in the hydrogen concentration range 0 to 3 at. pct, the range of interest to us. EXPERIMENTAL PROCEDURE The vanadium was obtained from the Bureau of Mines, Boulder City, Nev., in the form of electrolytic crystals. The analyses supplied with them listed 230 ppm by weight metallic impurities, 20 ppm C, 100 ppm N, and 290 ppm 0. The crystals were electron-beam-melted into an ingot that was rolled to 0.64 mm. Strips, 60 mm long and 4.2 mm wide, were cut from the sheet, and both rolled surfaces were ground on wet 600-grit Sic paper to produce specimens 0.4 mm thick. They were wrapped in molybdenum foil, vacuum-encapsulated in quartz, and annealed 4 hr at 1273°K. The specimens were annealed in a dynamic vacuum of 2X lo-&apos; Torr for 30 min at 1073°K for dehydrogenation, and charged with the desired quantity of hydrogen by allowing reaction with hydrogen gas at 1073°K for 2 hr and cooling at 100°K per hr. Purified hydrogen was obtained by thermal decomposition of UH3. Sixteen specimens were studied: two contained no hydrogen and the others had hydrogen concentrations between 0.5 and 3.5 at. pct (hydrogen analyses were done by vacuum extraction at 1073°K). Electrical resistances were measured by the four-terminal-resistor method on an apparatus similar to the one described by Horak.~ The specimen holder was designed so that both current and potential leads made spring-loaded mechanical contact with the specimen. The potential leads were 30 mm apart, and the current leads were 55 mm apart. The current was 0.10000 amp. We used the following baths for the indicated temperature ranges: liquid nitrogen, 77°K; Freon 12, 120" to 230°K; Freon 11, 230" to 290°K; and ethanol, 290" to 340°K. Temperatures lower than 77°K were achieved by allowing the specimen to warm up after removal from liquid helium. Temperatures above 77°K were measured by a calibrated copper-constantan thermocouple (soldered to the specimen holder) and below 77°K by a calibrated carbon resistor. The temperature of the bath changed less than 0.l0K between duplicate measurements of the resistance. RESULTS AND DISCUSSION Typical plots of resistivity p vs temperature T are shown in Fig. 1. In the interest of clarity, only five curves are presented and the data points have been

Jan 1, 1968