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By R. J. Charles

SEARCH for a consistent theory to explain the relationship between energy input and size reduction in a comminution process has accumulated, over the years, an enormous amount of plant and laboratory data. Although some correlation of these data has been possible for purposes of engineering design and for the advancement of research in fracture, there is still great need of a means of predicting behaviour of a solid when it is reduced in size by mechanical forces. The best known hypotheses proposed to describe the energy-size reduction relationships in crushing and grinding stem from a common origin. The present article analyzes problems of comminution in the light of the precepts of this origin. Its object is to reconcile points of difference between these well known hypotheses and to present relationships more widely applicable to comminution studies. Theoretical Considerations: Most existing relationships between energy and size reduction of a brittle solid stem from a single, simple, empirical proposition.&apos; Although this proposition can be demonstrated by observation and experiment, no theoretical derivation is yet possible. Mathematically, the proposition may be stated as follows: dE = -Cdx/xn [1] where dE = infinitesimal energy change, C = a constant, dx = infinitesimal size change, x = object size, and n = a constant. Eq. 1 states that the energy required to make a small change in the size of an object is proportional to the size change and inversely proportional to the object size to some power n. No stipulations are placed on the exponent n in either magnitude or sign. In 1867 Rittinger2 postulated that the energy required for size reduction of a solid would be proportional to the new surface area created during the size reduction. As far as can be determined there is as yet no physical basis for Rittinger&apos;s hypothesis. Rittinger&apos;s hypothesis can be stated mathematically as follows: E, = K(oa-a-0 . [2] Er = energy input per unit volume, K = a constant, <ti = initial specific surface, and o2 = final specific surface. In the size reduction of particles of size x, to particles of another smaller size, x2, Eq. 2 becomes the well known relation: ET = K&apos; {l/x2-l/xx) [3] where K&apos; is a constant. Eq. 3 may be arrived at from the proposition given in Eq. 1 by integrating and by assigning a value of 2 to the exponent n. J dE = J - C dx/x2 E = Kt (1x - 1x) where K&apos; = C. In 1885 Kick3 proposed the theory that equivalent amounts of energy should result in equivalent geometrical changes in the sizes of the pieces of a solid. For example, if one unit of energy reduced a number of equal-sized particles to particles of one half the size, then the same amount of energy applied to the particles resulting from the first test should result again in a size reduction of one half or a final size one quarter the original size. The Kick concept may be expressed as follows: Ek = K" log x1/x2 [41 K" = a constant and E, = energy per unit volume. The expression for Kick&apos;s law may be arrived at by again integrating Eq. 1 and in this case assigning a value of 1 to the exponent n. dE= J - C dx/x Eh = - C In {x/x2) = K" log (x,/x,) where K" = 2.3 C. Application of Kick&apos;s and Rittinger&apos;s laws to comminution has met with varied success. Gross and Zimmerley4 and Piret5 have shown that Rittinger&apos;s equation applies under certain conditions of experimentation. Walker and Shaw6 express the belief that in metal turning and shaping and in grinding of both metals and minerals the production of very fine particles (less than lP) follows Kick&apos;s hypothesis, whereas Rittinger&apos;s concept is valid for the size reduction of coarse particles. For the practical case of crushing and grinding, however, neither of the above hypotheses has received general acceptance. Bond&apos; has lately proposed that since neither Kick&apos;s nor Rittinger&apos;s hypotheses seem correct for plant design work, an energy-size reduction relationship somewhere between the two would be more applicable. The fundamental statement of Bond&apos;s work

Jan 1, 1958

By K. Mukherjee

A quasi-thermodynamic calculation is presented for estirt~ating vacancy Parameters in fcc metals. For fcc metals the equilibrium vacancy concentration at the melting point can be approximated by a constant mole fraction. The Gibbs free energy of formation of the vacancies can then be expressed as a simple function of the absolute melting temperature alone. From this description the formation energy Ef, the vibrational entropy Sv, and the formation volume of a vacancy can be calculated in terms of known thermodynamic parameters. The calculated values are in good agree-rnent with available experimental results. IT appears that many of the physical parameters associated with lattice defects can be empirically related to thermodynamic melting parameters.&apos;-7 Besides the implicit correlations between melting phenomenon and point defects, the melting temperature itself at atmospheric pressure can be used as a reference temperature for the purpose of comparison of vacancy concentrations in a given crystal class. The concentration at the melting point then corresponds to the maximum vacancy super saturation in the crystalline state at a fixed pressure. For pure fcc metals such as Au, Cu, Al, Ag, Pb, and Pt the mole fraction of vacancies at the melting point8 is of the order of 10*"3 to 10"1. The equation expressing the equilibrium vacancy concentration at the melting point contains three parameters: the formation energy, the vibrational entropy, and the absolute melting temperature, see Eq. [2]. Since these three parameters cover a wide range of values8 in the above-mentioned metals, it can be assumed that in other fcc metals, for which no reliable data are available, the mole fraction of vacancies at the melting point most likely lies in the range 10~3 to lO"4. This is then the basis of the calculations described in this article. Within this range the mixing entropy can be linearized and the vibrational entropy, the formation energy, and the vacancy formation volume can be calculated in terms of known thermodynamic constants. 1} LINEARIZATION OF MIXING ENTROPY The Helmholtz free energy of a crystal containing n vacancies at the melting point can be writteng as where Ef, T,, k, and S, are the formation energy of a vacancy, the absolute melting temperature, Boltz-mann&apos;s constant, and the vacancy formation entropy, respectively. After applying Stirling&apos;s approximation in Eq. [l] and minimizing with respect to n where (n/N), is the equilibrium vacancy concentration in mole fraction at the melting temperature at 1 atm pressure. If instead of setting (6~/6n) = 0 immediately after Stirling&apos;s approximation in Eq. [I], the configurational partition function is simplified, then some useful and significant results can be obtained by utilizing the experimental inforrnation After applying Stirling&apos;s approximation and rearranging is plotted as a function of (n/N) in Fig. 1. The points, not all of which are shown, are fitted by a straight line substituting from Eq. [5] into Eq. [I] and minimizing with respect to n combining Eqs. [6] and [2] It must be emphasized that Eq. [7] is only a crude approximation based on an oversimplified model of

Jan 1, 1967

By H. Herman, C. Chiou, M. E. Fine

From variation in Young&apos;s modulus and Vicker&apos;s hardness during GPl zone formation in A1-2 at. pct Cu the following was observed: 1) the presence of grain boundaries does not have any perceptible? effect on the aging reaction; 2) the modulus charge is orientation dependent; 3) the activation energy for zone growth is confirmed to be 11 * 1 kcal per mole; 4) reaging after reversion is preceded by an incubation time that varies with temperature. An analysis is applied to the present data and to data of other workers and kinetic laws dependent on the quenching rate are determined. In Al-base Cu alloys the decomposition product of a supersaturated solid solution at low temperatures (for example 25°C) and the first product at moderate temperatures (for example 150oC) are Guinier-Preston zones of the first kind (GPI).&apos; These zones are nonideal and are thought Jo &apos;Onsist roughly of sheets of Cu atoms up to 150A in diam and one or two atoms thick.&apos; The kinetics of the reaction, ass — a2

Jan 1, 1961

By W. H. Triplett

DISCUSSION John G. Barry (Mexico)—"The Nerinea limestone," writes W. H. Triplett, p. 584, "is ... medium-bedded (0.5 to 1.0 m)...." This is the Zuloaga formation. It has always been described as thick-bedded (1.0 to 3.0 m). "Whether the marls and shales were less amenable to replacement," he goes on to say, ". . . is a matter of opinion." In general, it is probable that the thinner-bedded formations were less competent than the nearby thicker-bedded, so that the latter produced pre-mineral breccias when all were subjected to flexing stresses. With reference to Mr. Triplett&apos;s analysis, p. 584, under Lower Cretaceous, in the Taraises and Cupido formations some few horizons should be considered as possibly containing hidden orebodies. In the Potrero camp, shown on the general map in the northwestern part of Fig. 4, p. 587, several mineralized beds are known; they are found throughout the whole thickness of the Cuesta del Cura formation. With regard to intrusive rocks, p. 585, the general map, Fig. 4, shows that the Potrero and Noche Buena camps are near a third, monzonitic intrusive. It seems doubtful that the Aranzazu was any hotter than the Providencia camp. However, the former does contain large deposits of exogenetic silicates, which in large part occur within the Zuloaga limestone, as shown by Bergeats in a stereogram. At the Aranzazti camp the La Caja formation was only slightly changed, whereas it was altered highly at the Providencia, possibly en-dogenetically. That the temperatures at the Providencia camp were relatively high at one time is also shown by the tourmaline veinlets and lenses in the monzonite and by the garnets on Temeroso peak; high temperature mineralization has possibly been eroded. Maps and sections show that the Concepcion del Oro —Temeroso stock occupies the original locus of some 40 kms of sedimentary rocks. The remains of large roof pendants at Carmen and Animas indicate that stoping was active. Whether all the sedimentaries were stoped and assimilated presents a lively problem, a correlative of which would be an estimate of the original constitution of the invading instrusive rock. As to extrusive rocks, see p. 585, there is also a large thick area of the extrusives left near Noche Buena in the "La Caja" intramontane valley of the La Caja range. This place gave its name to the range. The volcanics are also said to occur in considerable amount in the Mazapil valley.&apos;&apos; Turning now to the remarks under Regional Structure, p. 586, as partly indicated on the general map, Fig. 4, the Mazapil Mountains of the Mazapil region are a continuous, U-shaped range including a northern leg of some 24 km, a southern leg of similar length, and a uniting base which lies to the East and which measures some 10 km in a S 20 E direction. Thus the U-shaped mountains are continuous through a length of 58 km and also contain one continuous anticline, the adjacent valleys being synclinal. The northern leg of the U is called the La Caja range, the base is called the Concepcion del Oro range, and the southern leg the Santa Rosa range. The ranges in northeastern Zacatecas and southern Coahuila contain anticlines and the valleys contain synclines, which where thin are necessarily highly compressed isoclines with very steep dips. Many of the anticlines also have isoclinal components which are overturned, original mushroom tops being indicated. The anticline in the base of the U of the Mazapil Region, Concepcion del Oro range, is a recumbent anticline, over to the ENE, with a necessarily subjacent recumbent syncline.

Jan 1, 1953

By W. H. Triplett

DISCUSSION John G. Barry (Mexico)—"The Nerinea limestone," writes W. H. Triplett, p. 584, "is ... medium-bedded (0.5 to 1.0 m)...." This is the Zuloaga formation. It has always been described as thick-bedded (1.0 to 3.0 m). "Whether the marls and shales were less amenable to replacement," he goes on to say, ". . . is a matter of opinion." In general, it is probable that the thinner-bedded formations were less competent than the nearby thicker-bedded, so that the latter produced pre-mineral breccias when all were subjected to flexing stresses. With reference to Mr. Triplett&apos;s analysis, p. 584, under Lower Cretaceous, in the Taraises and Cupido formations some few horizons should be considered as possibly containing hidden orebodies. In the Potrero camp, shown on the general map in the northwestern part of Fig. 4, p. 587, several mineralized beds are known; they are found throughout the whole thickness of the Cuesta del Cura formation. With regard to intrusive rocks, p. 585, the general map, Fig. 4, shows that the Potrero and Noche Buena camps are near a third, monzonitic intrusive. It seems doubtful that the Aranzazu was any hotter than the Providencia camp. However, the former does contain large deposits of exogenetic silicates, which in large part occur within the Zuloaga limestone, as shown by Bergeats in a stereogram. At the Aranzazti camp the La Caja formation was only slightly changed, whereas it was altered highly at the Providencia, possibly en-dogenetically. That the temperatures at the Providencia camp were relatively high at one time is also shown by the tourmaline veinlets and lenses in the monzonite and by the garnets on Temeroso peak; high temperature mineralization has possibly been eroded. Maps and sections show that the Concepcion del Oro —Temeroso stock occupies the original locus of some 40 kms of sedimentary rocks. The remains of large roof pendants at Carmen and Animas indicate that stoping was active. Whether all the sedimentaries were stoped and assimilated presents a lively problem, a correlative of which would be an estimate of the original constitution of the invading instrusive rock. As to extrusive rocks, see p. 585, there is also a large thick area of the extrusives left near Noche Buena in the "La Caja" intramontane valley of the La Caja range. This place gave its name to the range. The volcanics are also said to occur in considerable amount in the Mazapil valley.&apos;&apos; Turning now to the remarks under Regional Structure, p. 586, as partly indicated on the general map, Fig. 4, the Mazapil Mountains of the Mazapil region are a continuous, U-shaped range including a northern leg of some 24 km, a southern leg of similar length, and a uniting base which lies to the East and which measures some 10 km in a S 20 E direction. Thus the U-shaped mountains are continuous through a length of 58 km and also contain one continuous anticline, the adjacent valleys being synclinal. The northern leg of the U is called the La Caja range, the base is called the Concepcion del Oro range, and the southern leg the Santa Rosa range. The ranges in northeastern Zacatecas and southern Coahuila contain anticlines and the valleys contain synclines, which where thin are necessarily highly compressed isoclines with very steep dips. Many of the anticlines also have isoclinal components which are overturned, original mushroom tops being indicated. The anticline in the base of the U of the Mazapil Region, Concepcion del Oro range, is a recumbent anticline, over to the ENE, with a necessarily subjacent recumbent syncline.

Jan 1, 1953

By Michel Elle, John Chipman

The equilibrium of gaseous H20-H2 mixtures with liquid iron-columbium alloys in the range 0.2 to 2.4 pct Cb shows that the activity coefficient of oxygen is strongly diminished by Cb. The oxide in equilibvium with the melt is identified as CbO2. The equi-librium constant at 1600 deg C is [%Cb][fo. % 0]2 = 2.9 x 10-4 where log fo= —0.14 [%Cb]. The deoxidizing power is comparable to that of vanadium, COLUMBIUM (niobium) is finding increasing use as an alloying element in steel. It forms several stable oxides and is removed from the steel bath by oxidizing slags. The specific oxide formed in steel-making is not known although Sazanov snd Shvarts-man,&apos; in their study of its partition between slag and metal, have assumed this to be Cb2O5 It is the purpose of this study to determine its deoxidation equilibrium at 1600°c, the nature of the oxide formed and the interaction between columbium and oxygen in the melt. The investigation was based on the reaction H2 + O=H2O; Kl=ph2o/(pH2[%O]) [1] in which 0 signifies oxygen dissolved in the liquid Fe-Cb alloy. The method and equipment of recent studies2,3 were utilized. In brief, the molten alloy, contained in a small crucible, is held in a controlled mixture of steam, hydrogen, and argon until equilibrium is reached. It is then cooled quickly in a stream of helium and analyzed for columbium and oxygen, the latter by vacuum fusion.4 The solubility of the oxide in liquid iron is determined by visual observation of scum formation on the surface of the melt. Crucibles of MgO proved unsatisfactory because of partial reduction at the metal interface. Pure A12O3 crucibles were heavily blackened by the melt and could not be used at high concentrations of columbium. Silica crucibles were more satisfactory but these introduced some silicon into the melt thus necessitating an uncertain but small correction for its effect on the activities of the other solutes. In silica it was possible to observe the scum formation when the melt became saturated and there was no apparent reaction between scum and crucible. The procedure for saturated melts was as follows. The alloy charge composed of electrolytic iron and columbium grain was melted and held at constant temperature. The gas ratio H2O:H2 was progressively increased by raising the saturator temperature until a point was reached at which a bright film appeared on the surface and covered it completely. This film could be dissolved by raising the temperature of the melt and it reappeared when the temperature was lowered. Under a partial film covering, utilizing bare areas for temperature measurement, the melt was brought to equilibrium with the atmosphere by holding at temperature for about 1 hr as suggested by Dastur.5 INTERACTION IN THE MELT Several experiments were made without columbium to establish a base in silica crucibles. The results are shown in Table I. Except for one run, they agreed well with Floridis1 comparable results in other crucibles. The value of log K1 is taken from Table I as 0.58. This is slightly larger than Floridis&apos; result, probably because of less elaborate safeguards against thermal diffusion. Results obtained in the Fe-Cb-0 series in which no scum formed are shown in Table 11. The equilibrium ratio Kl is defined as ph2o/(ph2[%O]). It is related to the equilibrium constant K1 as follows:

Jan 1, 1962

By Harry V. Warren

During the past few years the author has had an opportunity to examine a number of base-metal mines in the western United States, France and Spain. Nearly all of these mines produced some silver, and laboratory studies of the relationship between the silver and the various base-metal minerals in the ore have given some interesting and, it is to be hoped, enlightening facts. As this work was undertaken primarily to ascertain the amount of silver chemically associated with, not controlled by, the various base-metal minerals, the laborious and not always satisfactory method of picking out "pure" samples of each mineral from many localities was employed. However, the results obtained have justified the time that has been spent. Not only have the conclusions arrived at in different mining areas been in accordance with one another but in many instances they have afforded scientific support or explanations for much of the knowledge that operators in the various camps have acquired by practical experience. Although many of the conclusions are not new, many of the facts are, and the results, if they do nothing else, serve to confirm the findings of some of the other workers in this field, particularly the work of Nissen and Hoyt1 and of F. N. Guild2. Dr. S. G. Lasky3 has suggested a novel method for determining from a series of algebraic equations the amount of silver controlled by each of the base-metal minerals but I doubt very much whether his method can be justified, chiefly because there appear to be more variables to be considered than the few that appear in his equations. Typical Examples of Irregular Silver Distribution Combination Mine, New Mexico, U.S.A.—In this mine an examination of the assay plans either of the mine or of the average mill feed or products

Jan 1, 1935

By Harry V. Warren

During the past few years the author has had an opportunity to examine a number of base-metal mines in the western United States, France and Spain. Nearly all of these mines produced some silver, and laboratory studies of the relationship between the silver and the various base-metal minerals in the ore have given some interesting and, it is to be hoped, enlightening facts. As this work was undertaken primarily to ascertain the amount of silver chemically associated with, not controlled by, the various base-metal minerals, the laborious and not always satisfactory method of picking out "pure" samples of each mineral from many localities was employed. However, the results obtained have justified the time that has been spent. Not only have the conclusions arrived at in different mining areas been in accordance with one another but in many instances they have afforded scientific support or explanations for much of the knowledge that operators in the various camps have acquired by practical experience. Although many of the conclusions are not new, many of the facts are, and the results, if they do nothing else, serve to confirm the findings of some of the other workers in this field, particularly the work of Nissen and Hoyt1 and of F. N. Guild2. Dr. S. G. Lasky3 has suggested a novel method for determining from a series of algebraic equations the amount of silver controlled by each of the base-metal minerals but I doubt very much whether his method can be justified, chiefly because there appear to be more variables to be considered than the few that appear in his equations. Typical Examples of Irregular Silver Distribution Combination Mine, New Mexico, U.S.A.—In this mine an examination of the assay plans either of the mine or of the average mill feed or products

Jan 1, 1935

During the past few years the author has had an opportunity to examine a number of base-metal mines in the western United States, France and Spain. Nearly all of these mines produced some silver, and laboratory studies of the relationship between the silver and the various base-metal minerals in the ore have given some interesting and, it is to be hoped, enlightening facts. As this work was undertaken primarily to ascertain the amount of silver chemically associated with, not controlled by, the various base-metal minerals, the laborious and not always satisfactory method of picking out "pure" samples of each mineral from many localities was employed. However, the results obtained have justified the time that has been spent. Not only have the conclusions arrived at in different mining areas been in accordance with one another but in many instances they have afforded scientific support or explanations for much of the knowledge that operators in the various camps have acquired by practical experience. Although many of the conclusions are not new, many of the facts are, and the results, if they do nothing else, serve to confirm the findings of some of the other workers in this field, particularly the work of Nissen and Hoyt1 and of F. N. Guild2. Dr. S. G. Lasky3 has suggested a novel method for determining from a series of algebraic equations the amount of silver controlled by each of the base-metal minerals but I doubt very much whether his method can be justified, chiefly because there appear to be more variables to be considered than the few that appear in his equations. Typical Examples of Irregular Silver Distribution Combination Mine, New Mexico, U.S.A.—In this mine an examination of the assay plans either of the mine or of the average mill feed or products

Jan 1, 1935

By Harry V. Warren

During the past few years the author has had an opportunity to examine a number of base-metal mines in the western United States, France and Spain. Nearly all of these mines produced some silver, and laboratory studies of the relationship between the silver and the various base-metal minerals in the ore have given some interesting and, it is to be hoped, enlightening facts. As this work was undertaken primarily to ascertain the amount of silver chemically associated with, not controlled by, the various base-metal minerals, the laborious and not always satisfactory method of picking out "pure" samples of each mineral from many localities was employed. However, the results obtained have justified the time that has been spent. Not only have the conclusions arrived at in different mining areas been in accordance with one another but in many instances they have afforded scientific support or explanations for much of the knowledge that operators in the various camps have acquired by practical experience. Although many of the conclusions are not new, many of the facts are, and the results, if they do nothing else, serve to confirm the findings of some of the other workers in this field, particularly the work of Nissen and Hoyt1 and of F. N. Guild2. Dr. S. G. Lasky3 has suggested a novel method for determining from a series of algebraic equations the amount of silver controlled by each of the base-metal minerals but I doubt very much whether his method can be justified, chiefly because there appear to be more variables to be considered than the few that appear in his equations. Typical Examples of Irregular Silver Distribution Combination Mine, New Mexico, U.S.A.—In this mine an examination of the assay plans either of the mine or of the average mill feed or products

Jan 1, 1935

By J. L. Gregg

A STUDY of copper and silver base alloys was made with the object of finding, if possible, useful alloys subject to dispersion hardening. These studies led to the discovery of several alloys showing considerable dispersion hardening, the most important of which, the alloys of copper with iron, nickel, cobalt and chromium silicides, have since been very ably reported by M. G. Corson.1 This paper is offered as a few notes covering alloys other than those described by Corson and some further data on the silicide alloys.

Jan 1, 1929

By C. E. Lundin

The Ce-H system was investigated in the temperature range, 573° to 1023°K, and the pressure range, 10-3 to 630 Torr, as a function of &apos;composition up to 72 at. pct H. Families of isothermal arid isopleth curves were plotted from the pressure-terr~perature-composition relationships. From these curves the solubility relationships were determined for the system. The isopleths are analytically represented by equilibrium dissociation pressure equations. The relative partial molal enthalpzes and entropies of solution of hydvogen in the systerrz were calculated fronz the dissociation pressure equulions and are tabulated. The integral free energies, enthalpies, and entropies of mixing in the Ce-H system were determined from the relative partial quantities and are also tabulated. The standard free energy, enthelpy, and entvopy of reaction of the dihydride phase at kcal per kcal per mole H2, and ?S° = -34. 1 cal per deg mole H2, respectively. The equilibrium dissociation pressure equation in the two-phase region is: UNTIL recently very little was known of the detailed solubility and thermodynamic relationships of the Ce-H system. Two previous investigations1,2 are noteworthy. However, significant discrepancies and omissions exist on analyzing them. The work of Mulford and Holley1 on cerium did not clearly delineate the boundaries of the two-phase region, Cess - CeH2-x. The plateau partial pressures were not thoroughly defined and were considerably displaced in pressure compared to those from the work of Warf and Korst.2 These latter authors concentrated their studies primarily from 823° to 1023°K in the pressure range of 1 to 760 Torr. No data were determined to outline the regions of primary solid solubility and the hydride phase. Also the establishment of the plateau partial pressures was rather limited in scope. In neither work was a treatment conducted of the relative partial molal enthalpies and entropies of solution of hydrogen in the single-phase regions and the integral thermodynamic quantities of mixing throughout the system. Therefore, it was the objective of this research to determine the complete equilibrium solubility relationships and thermodynamic data for the system by pressure-temperature-composition studies. EXPERIMENTAL PROCEDURE The cerium metal for this study was donated by the Reno Metallurgy Research Center of the Bureau of Mines. Total impurity content was 0.13 pct with only 60 ppm O. The metal was checked metallographically and contained only minor amounts of second phase compared to cerium from other sources. Specimen preparation was done in a dry box flushed with argon gas. The surface of a small rectangular piece of cerium (about 0.2 g) was filed with a clean, mill file. Final weighing was done in a tared enclosed vial containing argon gas. The specimen was then loaded quickly into the reaction chamber which was purged several times with high-purity hydrogen gas and then allowed to pump to about 10-6 Torr. The furnace was heated to the reaction temperature and the run started. The equipment used to conduct the hydriding was a Sievert&apos;s-type apparatus. Basically it consisted of a source for pure hydrogen, a precision gas-measuring burette, a heated reaction chamber, a McLeod gage, and a mercury manometer. Pure hydrogen was supplied by the thermal decomposition of uranium hydride. The 100-ml precision gas burette was graduated to 0.1-ml divisions and was used to measure the quantity of gas and admit it to the chamber. The reaction chamber was a quartz tube. Prior to each run, the cerium specimen was wrapped in a tungsten foil capsule to prevent reaction of the cerium with the quartz. Control of the temperature was achieved within ±1°K. Pressures in the manometer range were measured to ±0.5 Torr and in the McLeod range (10-3 to 5 Torr) to ±3 pct. The compositions of hydrogen in cerium were calculated in terms of hydrogen to cerium atomic ratio. These compositions were estimated to be ±0.01 H/Ce ratio. The technique used to study the equilibrium pressure-temperature-composition relationships of the Ce-H system was to develop experimentally a family of isothermal curves of composition vs pressure. The range of pressure through which each isotherm was developed was from 10-9 to about 630 Torr in the temperature interval, 573° to 1023°K. RESULTS AND DISCUSSION The hydriding characteristics of cerium are iso-morphous with those of the elements of the light-rare-earth group (lanthanum, cerium, praseodymium, and neodymium) wherein the region from the dihydride to trihydride is continuously single phase.&apos; The structure of this phase is fcc.3 The heavy rare earths form a trihydride,2 which is hcp, separated by a two-phase region from the fcc dihydride phase. The Ce-H system is represented by the family of experimental isotherms in Fig. 1. Due to the small scale required to draw the curves, the experimental points are omitted; however, a total of 240 experimental data points were taken to prepare these curves. The solubility relationships can be deduced therefrom. Three distinct regions of partial pressure and composition can be seen. The region of cerium solid solution is represented by the rapidly rising isotherms in the dilute composition range. In accordance with Gibbs Phase Rule only one solid phase, the cerium solid so-

Jan 1, 1967

By M. L. Rudee, R. A. Huggins

Samples of iron containing nitrogen or carbon have been given treatments similar to those used in cold-work peak (CWP) measurements and examined by transmission electron microscopy. It was observed that the unusual and nonreproducible behavior of the carbon CWP can be explained by a strong tendency for carbon to form grain boundary precipitates at temperatures below those used for CWP measurements. These precipitates dissolved at the temperatures used in the CWP measurements. There was no evidence for nitrogen precipitation at grain boundaries. There was no indication of precipitation along dislocations in either carburized or nitrided samples given treatments similar to those of CWP measurements. Although it is possible that subelectron-microscopic clustering had occurred, this observation supports the theories of the CWP that are based on continuous atmospheres rather than on individual precipitates. In an earlier paper,&apos; the present authors developed a new distribution function to predict the occupation of sites for interstitial impurity atoms around a dislocation. When this distribution was applied to the case of carbon and nitrogen in iron, it predicted that, if the temperature dependence of the concentration of solute atoms in the matrix was controlled by the presence of equilibrium carbide or nitride precipitates, the tendency for nitrogen to segregate to dislocations would be greater than that for carbon even though their binding energies to dislocations are identical. The cold-work internal-friction peak (CWP) is considered by most authors to be produced by the interaction of interstitial impurities with dislocations. Many investigators have studied the CWP in iron containing carbon and nitrogen and have observed a significant difference between its behavior in the two cases. In this paper a series of experiments will be reported that were initiated to determine whether the application of the new distribution function would explain the observed differences between the carbon and nitrogen CWP. Although it was found that the distribution function, pev se, did not explain the differences, the differences became clear, and some insight into the mechanism of the CWP was realized. Before reporting the present experiments, the literature pertaining to the differences between the carbon and nitrogen CWP in iron and the various mechanisms proposed for the CWP will be reviewed. LITERATURE REVIEW Snoek2 first observed the CWP in iron specimens containing nitrogen, but also reported a weak and unreliable peak in carburized samples. Later, Ke3 established that the CWP height was proportional to the degree of deformation. The presence of nitrogen alone would produce a peak of the same size as found in a sample containing both nitrogen and carbon, and KG concluded that the CWP was caused by nitrogen. In a discussion of G&apos;s paper it was reported that Dijkstra had investigated the CWP in samples that contained only carbon. He found it to be much smaller than the nitrogen peak and "unstable". KG et al.4 charged specimens of iron with both carbon and nitrogen. They observed that the carbon CWP was much smaller than that observed in nitrided samples, but that aging at 300°C caused the carbon peak to increase. A similar treatment produced no change in a nitrogen peak. Annealing at higher temperatures caused the height of the CWP in both the nitrogen and carbon samples to decrease. This behavior was also observed by Kamber et al. 5 who found that the activation energy for the annealing of the CWP was identical with the activation energy for the self-diffusion of iron. They concluded that the annihilation of dislocations by climb caused the reduction in the CWP height. Kamber et al. studied the "unstable" carbon peak in detail. They measured both the Snoek and CWP during various aging treatments. In carburized samples, aging at 100°C caused the Snoek peak to disappear, although the CWP peak remained small. However, a subsequent treatment for 5 hr at 240°C caused the CWP to reach a maximum. They proposed that an additional location for the carbon, other than whatever site produced the CWP, is present. In nitrided samples the CWP was completely developed as soon as a measurement was made; additional sites are not present. No explanation of either the additional site or the difference in the behavior of carbon and nitrogen was offered. petarra5 performed a systematic study of the effect of composition on the CWP. Using three kinds of "pure" iron, he showed that there was a residual CWP when the carbon and nitrogen concentrations had been reduced to less than that detectable by Snoek-peak measurements. He observed the same general annealing behavior and composition dependence as previous investigators, with the following exceptions. On first measuring the carbon CWP, it was found to be identical with the residual peak, and essentially independent of the carbon content. If the CWP was measured a second time in the same sample, it increased in size, but was still only about one-fourth the size of a CWP in a sample of the same iron nitrided to the same composition. On the other hand, a series of annealing experiments showed that the nitrogen CWP was not al-

Jan 1, 1967

By Gene Long

10.4-1. Load Design and Construction. Surface mine haulage roads are used for transporting raw products to the mine site, preparation plant, or loading facilities, and to provide personnel and equipment an access to the pits and mine area. All of the aspects of highway engineering, including minimum slope inclines, properly banked curves, and adequate drainage, must be followed to facilitate construction of safe and efficient haulage roads for fast and economical transportation of the mined product to its destination. By maintaining good haulage roads, both truck and equipment maintenance will be kept to a minimum, resulting in reduced mining costs and subsequently higher profits. [ ] There are several basic considerations in haulage road planning. Most important, one must follow all safety procedures in both design and construction of the roadway. A maximum effort should be made to follow current mining plans when laying out and planning haulage roads (aerial photographs can be extremely useful in planning and routing of roadways). Grades, road widths, and curves must be maintained within limits of present and/or planned haulage equipment specifications, since all these factors can limit speed, and hence production (Table 10.4-1). Grades in most mining operations are adverse (against the loaded haul), which increases haul cost per mile. Operators must balance these increased

Jan 1, 1968

By G. H. Lair, B. J. Langford, S. H. Rockwood

Volumetric reservoir analysis is dependent upon a firm relationship between porosity, connate water, and net pay. Capillary presswe data on core samples interrelate these three factors. It is shown that other reservoir problems may be resolved: (I) whether water production is indigenous or extraneous to the oil producing interval, (2) an oil-water contact is being approached, and (3) whether the oil-water contact is remotely situated. INTRODUCTION Volumetric analysis of carbonate reservoirs challenges the ingenuity of the reservoir engineer due to an absence of data on the minimum oil-bearing and oil-producing pores of a given reservoir rock. Many studies with this as the ultimate objective are available on the physical characteristics and fluid-flow behaviors of the carbonate reservoir. Some of these publications are: Hassler, Brunner and Deahl&apos;s1 study of the role of capillarity in oil production; Jan Law&apos;s&apos; and A. C. Bulnes3 statistical treatment of core analysis data; Chalkley&apos;s method4,5 or estimating specific surface areas and porosity; Walter Rose&apos;s9 report on porosity, reserves, and recovery; Archie&apos;s78 tex-tural classification of carbonate rocks; Stewart and Spurlock&apos;s9 large core analysis; Purcell&apos;sl0 mercury injection method in studying capillary pressure phenomena; Stewart, Craig, and Morse&apos;s" model multiple-phase flow test in investigating the relative permeability effect; and Fatt&apos;s12 illumi-nating network model of porous me-dia. The present study shows that the static reservoir parameters of porosity, connate water, and net productive thickness may be interrelated by utilizing a statistical arrangement of mercury capillary pressure data in addition to routine core analysis. This report summarizes the techniques that are followed to obtain these relations which are applicable to carbonate and sandstone reservoirs that do not contain clays. Capillary pressure statistical studies may be extended to include clay-bearing rocks by utilizing water capillary pressure data. POROSITY It is necessary that the laboratory determine the porosity value that includes the pores that are filled with hydrocarbons and water in the reservoir. This is the reservoir&apos;s total porosity. When true total porosity values are not available, correlations between porosity and capillary pressure characteristics lose their significance since they cannot be related through oil-base mud core data to the porosity and connate water values found in reservoirs. Methods used to obtain reliable porosity data will not be discussed; however, care should be exercised in selecting samples for measurement. In homogeneously porous formations, small core plugs sampled frequently will furnish adequate information. Where heterogeneity, particularly vugginess, is present, large-core porosity data may be required; in such reservoirs a suite of capillary pressure samples may be selected from small plugs. CAPILLARY PRESSURE Capillary pressure data provide a method for relating two carbonate reservoir parameters, porosity and connate water saturation, which in turn permit delineation of productive rock types necessary for selecting the third parameter, productive thickness. Specific applications of capillary pressure data to petroleum reservoirs were suggested by Archie8 and Pur-cell."&apos; Their work demonstrated that in preferentially water-wet rock, porc

Jan 1, 1958

By W. A. Wood, H. L. Wain, R. I. Garrod

The mechanical behavior of recrystallized chromil~m of high purity has been studied, principally in torsion and to a lesser extent in tension, at temperatures between —196oand 350oC. Depending upon the conditions of test, the material may show brittle or ductile behavior or an intermediate or subduc-tile state having some of the characteristics of each. This latter state existed at temperatures between approximately ±50°C and was characterized by a) extensive creep at stresses well below the normal fracture stress, b) nonelastic loading/unloading effects during creep, c) strain softening under cyclic loading, and d) final failure of a brittle type. Suggestions are made on the dislocation processes and interactions which give rise to subductile behavior The ductile-brittle transition in bee metals has been studied mainly by tension and bend tests. These methods, however, favor crack propagation which may follow too closely on initiation for detailed study of the transition itself. For work of this nature, therefore, other modes of deformation less favorable to crack propagation may be preferable. This paper describes a study of the ductile-brittle transition in chromium which is based mainly on torsional testing although a few subsidiary experiments were made in tension. It appears to reveal at the transition an intermediate state that cannot properly be described as either brittle or ductile. Torsional tests on chromium have been made by other workers1 but not, as here, primarily for study of this intermediate state. EXPERIMENTAL The chromium, in the form of swaged rod, was prepared by techniques already described.&apos; The particular material used was one in which the main impurities were 0.03 wt pet 0 and 0.006 wt pet N and one in which transition from ductile to brittle states in torsion conveniently fell at about room temperature. For torsion, test specimens were from 5/16-in.-diam rod to provide test portions 1-1/4 in. long by 7/32 in. diam, a twist of 1 deg thereby corresponding throughout this paper to 0.0015 surface shear. The specimens before test were annealed for 2 hr at 1200°C in vacuo, which left them with a re-crystallized grain size of about 0.01 mm, and then electropolished. They were tested under dead-weight loading in an apparatus in which they could be surrounded by a furnace or cooling chamber, tests in practice being made at various temperatures between -196" and +350°C. For tension tests, cylindrical specimens were prepared in a similar manner and tested at room temperature under dead-weight loading. RESULTS (TORSION) Subductile State. The state described above as intermediate between brittle and ductile may be perhaps best defined by reference to torque/twist curves at various temperatures. These are grouped in Fig. 1. Below about -50°C the material was brittle, in the sense that it exhibited little plastic deformation under stress and fractured by cleavage along planes of maximum resolved tension, which in torsion produces the well-known helical type of fracture. The deformation is typified by the curves for -196" and -150°C in Fig. 1; it shows a slight but progressive deviation from linearity above a certain torque, here about 50 lb-in., until fracture occurs at about 95 lb-in. A feature to which it is desired specially to call attention is that under none of the loads did the specimens show significant creep.

Jan 1, 1964

By Eldon C. Pattee

Variations of a very reliable geochemical field test for beryllium developed by Patten and Ward, have been adapted by the U.S. Bureau of Mines to facilitate rapid testing of reconnaissance samples and to aid in rapid examination of known occurrences. Although several qualitative tests for detecting beryllium have been described in the literature,1,2,3, the Patten-Ward4 morin geochemical field method has the advantages of being rapid and being quantitative for minute amounts of beryllium. In addition to the morin field method, Patten, in cooperation with Griffitts, have developed a contact- print method for determining beryllium in hand specimens.5 The semiquantitative method can be used for rapid screening of samples in exploration or reconnaissance work. The use of beads for fusing samples provides a more rapid test, but gives less accurate results than the method developed by Patten and Ward. The semiquantitative method, however, requires less equipment and combines three stock solutions into one reagent for easy application. Estimates of samples in the range from 3 to 1000 ppm varied from about 0.25 to 5 times the actual beryllium content.

Jan 5, 1965

By O. A. Cheadle, F. E. Lane

ThE computer program for arbitrary crystal systems reported by Camp and Clum&apos; has been modified to make it more convenient for hexagonal crystals. The program&apos; uses the Miller indexes (hkl) which can be confusing for hexagonal crystals while the modified program uses the Miller-Bravais indexes with four axes; e.g., the angles between the (110) planes, Fig. 1, are 0 and 90 deg but in the (hkil) system the angles between the (1150) planes are 0 and 60 deg. If a Laue photograph is taken of a crystal oriented with the prismatic planes nearly parallel to the film then the spots on the stereo graphic projection will be from high-index planes. The probable positions of the low-index planes, e.g., (0001) plane, can only be obtained from the intersection of zones and this is not accurate to 1 or 2 deg. The number of planes considered by the program (card 1)&apos; has to be limited to the ones of low index or the program time is excessive but a solution will not be obtained if one of the spots has an index that is not being considered. To overcome this problem the program1 was modified so that if no fit was obtained at *1 deg (card 3) of the tabulated angles then ±2 or ±3 deg was tried. If still no solution was obtained either due to one of the angles not being measured correctly to ±3 deg or because one of the spots was from a high-index plane, then the last spot was discounted and a fit tried for the remaining spots at i1 deg, and so forth. The minimum number of spots that the program will try to fit is five. If the limit on any individual index is 4 (card 1) and (h + k + l + 1) is six then twenty-three planes are considered and there are over 1000 interplanar angles. Many pairs of planes have very similar interplanar angles and with the errors previously mentioned the program will often produce several alternative solutions to a group of spots particularly at ±2 or ±3 deg. However without the program the alternative solutions would probably not have been found. If a large number of spots are used the number of possible fits is reduced. In the example shown in Fig. 2, if only spots which are on the film are used (case 1) the program gives six possible solutions, Table I. However if points 7 and 8 are also used (case 2) the program gives only one fit which also agrees with a standard projection of the crystal. In addition to time-saving the program ensures that a correct solution is obtained since it is unlikely that all the alternatives would have been gound manually; the first would probably be assumed to be the correct solution. The program has been used for zirconium crystals but is equally suitable for other hexagonal materials.

Jan 1, 1969

By F. E. Bash

PREVIOUS to the war, this country depended on Europe for its supply of a number of alloys of great importance in the manufacture of electrical apparatus and equipment. When this source was cut off shortly after the beginning of hostilities and the small stocks in the United States were exhausted, either inferior substitutes had to be used or the manufacture of the apparatus suspended. Since electrical equipment was of primary importance in the prosecution of the war, the substitutes had to be used until the composition and processes of manufacture of the alloys could be determined. Included among these alloys was one generally known as manganin, which is composed chiefly of copper and manganese and which, beside having a low-temperature coefficient of resistance, has a low thermal electromotive force against copper. These qualities make it valuable for the manufacture of electrical instruments and machines in which it is used in the shape of wire, rod, and strip. As a result of these circumstances, an investigation was started to deter mine how manganin could be made on a commercial basis so that a product of uniform quality and the necessary electrical characteristics could be produced. The object was to procure an alloy with temperature coefficient of resistance not greater than T 1 X 10-5 per ° C. and a thermal e.m.f. against copper no greater than that of the imported material. It is characteristic of manganin that the temperature-resistance curve is not a straight line but has a peak, which varies in position with different samples; it is most desirable, however, to have it at a temperature of 25° C. if possible. The coefficients of manganin from all records available ranged from a large negative to a large positive value. The composition as reported by different authorities is given in Table 1. Prof. Matthew A. Hunter, of Rensselaer Polytechnic Institute, made up a number of small melts of manganin in a graphite crucible and the one that he reported as having the best coefficient gave the following analysis: Copper, 83.6 per cent.; nickel 2.5 per cent.; manganese,-13.6 per cent.; iron, 0.3 per cent. An analysis of a sample of German manganin gave the following: Copper, 82.6 per cent.; nickel, 3.8 per cent.; manganese, 12.8 per cent.; iron 0.7 per cent.

Jan 9, 1919

By F. E. Bash

Previous to the war, this country depended on Europe for its supply of a number of alloys of great importance in the manufacture of electrical apparatus and equipment. When this source was cut off shortly after the beginning of hostilities and the small stocks in the United States were exhausted, either inferior substitutes had to be used or the manufacture of the apparatus suspended. Since electrical equipment was of primary importance in the prosecution of the war, the substitutes had to be used until the composition and processes of manufacture of the alloys could be determined. Included among these alloys was one generally known as manganin, which is composed chiefly of copper and manganese and which, beside having a low-temperature coefficient of resistance, has a low thermal electromotive force against copper. These qualities make it valuable for the manufacture of electrical instruments and machines in which it is used in the shape of wire, rod, and strip. As a result of these circumstances, an investigation was started to determine how manganin could be made on a commercial basis so that a product of uniform quality and the necessary electrical characteristics could be produced. The object was to procure an alloy with temperature coefficient of resistance not greater than 1 X 1X per " C. and a thermal e.m.f. against copper no greater than that of the imported material. It is characteristic of manganin that the temperature-resistance curve is not a straight line but has a peak, which varies in position with different samples; it is most desirable, however, to have it at a temperature of 25&apos; C. if possible. The coefficients of manganin from all records available ranged from a large negative to a large positive value. The composition as reported by different authorities is given in Table I. Prof. Matthew A. Hunter, of Rensselaer Polytechnic Institute, made up a number of small melts of manganin in a graphite crucible and the one that he reported as having the best cocfficient gave the following analysis: Copper, 83.6 per cent.; nickel 2.5 per cent.; manganese, 13.6 per cent.; iron, 0.3 per cent. An analysis of a sample of German manganin gave the following: Copper, 82.6 per cent.; nickel, 3.8 pcr cent.; manganese, 12.8 per cent.; iron 0.7 per cent.

Jan 1, 1921