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By C. H. P. Lupis, Henri Gaye

There are m -I conditions for the stability of a solution of m components with respect to infinitesinzal flucturations. However, in most cases, only one of these conditions has to be considered to determine the domain of instability and the existence of this more restrictive condition greatly simplifies the calculations. It may be used advantageously for the prediction of miscibility gaps and the method is illustrated in details for the case of the Ag-Pb-Zn system. THE thermodynamic conditions for the formation of a miscibility gap may be viewed as a necessary consequence of the conditions for spinodal decomposition. A previous article1 has examined in detail the form of these conditions for multicomponent systems. There is only one condition for the stability of a binary system (with respect to infinitesimal fluctuations), but there are two conditions for a ternary system, and m — 1 conditions for an m-component system. The probability of violating a stability condition, and thus forming a miscibility gap, obviously increases with the number of components, a result which is rather intuitive since the atoms of the solution have now many more ways of redistributing themselves and introducing complexities in the form of the free energy hy-persurface. It is of interest to take advantage of this possibility of precipitating new phases and to examine which stability condition is the likeliest to be violated, that is, which stability condition is thermodynamically the most restrictive. The finding of such a condition would greatly simplify the application of the stability criteria since only one condition could then be considered, instead of m - 1. In Ref. 1, coherency strain energy terms were neglected, thus restricting the applications of the treatment to solutions where they are negligible, such as liquid alloys. In the following study the same assumption will be made. To generalize the treatment to systems where the strain energy terms are sizable, the reader is referred to Cahn's classical article on spinodal decomposition.2 Let us designate by Gij the second derivative of the Gibbs free energy with respect to the number of moles ni and n j. There are several equivalent sets of m — 1 stability conditions.' The one considered here expresses that the successive diagonal determinants of order 1, 2, ... m — 1, associated with the symmetric Gij matrix (for 2 5 i, j 5 m) are positive.' For a binary solution 1-2, the condition for stability is: O(u=G22^0 [1] For a ternary system 1-2-3, the condition [I.] is re- tained (the value of G22 will differ, of course, according to the concentration of 3) and another condition is introduced: £>(21 = G22G33 - Gl3 ^ 0 [2] In a composition diagram, these two conditions define two domains of instability. Starting at a point where the solution is stable (for instance at a point where the solution is very dilute) we gradually change the composition until the condition [I] or [2] is violated. As already noted in the literature, e.g., in the work of Prigogine and Defay,3 it is the boundary of the domain (2) which is first crossed. For if we assume that the boundary of the domain (1) is reached first, at this point G22 = 0 and the second condition is necessarily violated (D(2) = -& 5 0), in contradiction with our original assumption. An exhaustive study of the ternary regular solution case may be found in the work of Meijering.4 Moreover if the boundaries of the two domains have a common point, they also have a common tangent. For if the two lines were to cross each other as is illustrated in Fig. 1(a) any point M in the line QP would be such that £> = 0 and 0"' > 0 which, as shown above, are incompatible results. Thus, the two lines must be tangent at their common point Q as illustrated in the example of Fig. l(b). The reasoning of Fig. l(a) implies that the point Q is not a "singular" point for either boundary line. This singularity may be of two types. First, the lines meet without crossing each other and without being tangent. Second, the tangent at Q for D"' or 0"' is not single-valued. Other types of singularity are unlikely because of the usual analytical forms of D"' and 0"'. The exception to the common tangent requirement due to the first type of singularity was pointed out by John Morral;5 it occurs when the common point, Q' or (3" in Fig. l(b), is located at a boundary of the composition diagram, e.g., at the line X3 = 0. It may also be noted that at the common nonsingular point Q of D(1) and D(2), Fig. 1(b), G23 is necessarily equal to zero, whereas at a point such as Q' or Q", this conclusion is no longer valid because the product G22G33 is now indefinite (of the form 0. a). The exception to the common tangent requirement due to the second type of singularity occurs when two branches of the same boundary line intersect, for example when D(1)or D(2) decomposes into a product of functions, at a point which belongs to the boundary of the other condition. It is possible to show by a simple analytical calculation that, in this case, if Q is a singular point of D(1), then it is necessarily a singular point of D(2), and that the reciprocal is true except if G33 = 0 at Q. For the present article, however, more elaboration on these singularities appears to be unwarranted. To generalize the previous results to an m -component system, we use the mathematical theorem stating that if the diagonal determinant D(r) = 0, then

Jan 1, 1970

By H. H. Pentz

This paper gives the derivation of a practical formula for the calculation of slopes in seismic reflection prospecting. The derived formula is an approximation and can be used where the slope of the reflecting horizon is less than 250 ft. per 1000 and the depth to the reflecting horizon is greater than 2500 ft. The slope of sediments in oil regions is generally considerably less than 250 ft. per 1000. This is particularly true of the Gulf Coast, with the exception of the salt domes, which usually have the sediments at a greater slope than 260 ft. per 1000. Derivation In Fig. 1, o represents the image of the shot point a. Then the length of the path acb is equal to ob and ae'd is equal to od. In the triangle aob, p is equal to ob, x is equal to , and c is equal to ao. The angle u is the apparent dip of the reflecting horizon. Angle oab is equal to (90" - u). The quantity m is the slope of a line tangent to the curve, defined by equation 1, at the point (p, x). The quantity m' is the slope of the line tangent to the curve at the point (p', 2').

Jan 1, 1940

By H. H. Pentz

This paper gives the derivation of a practical formula for the calculation of slopes in seismic reflection prospecting. The derived formula is an approximation and can be used where the slope of the reflecting horizon is less than 250 ft. per 1000 and the depth to the reflecting horizon is greater than 2500 ft. The slope of sediments in oil regions is generally considerably less than 250 ft. per 1000. This is particularly true of the Gulf Coast, with the exception of the salt domes, which usually have the sediments at a greater slope than 260 ft. per 1000. Derivation In Fig. 1, o represents the image of the shot point a. Then the length of the path acb is equal to ob and ae'd is equal to od. In the triangle aob, p is equal to ob, x is equal to , and c is equal to ao. The angle u is the apparent dip of the reflecting horizon. Angle oab is equal to (90" - u). The quantity m is the slope of a line tangent to the curve, defined by equation 1, at the point (p, x). The quantity m' is the slope of the line tangent to the curve at the point (p', 2').

Jan 1, 1940

By A. G. Jordan, W. Jeitschko, Paul A. Beck

The occurrence qf the V phase structure /Zr,Co,Ge, type) in ternary syste7ns (titanium, zivconium, niobium, lanta1urn) -(nickel, cobalt, iron)-(silicon, germanium) was incestigated. Nine V silicides and four V gertrlanides were found and their lattice constants are reporled. The lattice constants of twenty-one preri-ously identified E phases (TiNiSi type) are given. The average atomic volumes of these phases are discussed in relation to similar binary phases. ThE occurrence of a phase Ti4Ni4Si7 was first reported by Westbrook. DiCerbo, and peat' who gave it the name "V phase". They also reported the existence of an E phase TiNiSi. Subsequently a systematic study was undertaken in this laboratory to explore the occurrence of E' and V phases3 in related ternary systems. In the meantime the crystal structure of the E phase TiNiSi 4 and of the V phase Zr4CO4Ge 75,6 was determined. In the present paper the details of the V phase investigation and the lattice constants of the E and V phases are presented. V PHASES Alloy specimens of approximately 10 to 15 g were prepared by arc melting under argon (99.996 pct Ar) atmosphere. The starting materials were all of purity higher than 99.9 pct, with the exception of cobalt. which contained 0.14 pct Fe as the only major impurity. The weight losses were in all cases less than 2 pct, in most cases less than 1 pct. The samples were encapsulated in fused silica tubes with sufficient argon to yield about 1 atm pressure at the annealing temperature. After the homogenization anneal. Table I. the specimens were water-quenched. A representative portion of each specimen was then examined metallographically (etchant: 20 pct HNO,. 10 pct HF. 25 pct glycerine, 45 pct H20). Only minor amounts of second- and third-phase particles were observed in the specimens listed in Table I, with the exception of alloys Zr4Fe4Si7 and Ta,Fe,Si,. which contained an estimated 10 pct by volume of foreign phases. X-ray powder photographs were taken with a Seeman-Bohlin type focusing camera and Fe-KO radiation. Of the thirty possible combinations of elements in the ternary systems (titanium, zirconium. vanadium. niobium. tantalum)-(iron. cobalt, nickel)-(silicon. germanium) thirteen V phases could be identified. In the remaining seventeen ternary systems and also in the systems Cr-Ni-Si and (M0.W)-(Ni.Co)-Si no V phase was found at the composition 4:4:7 after annealing at temperatures between 900" and 1200'C. For the determination of the lattice constants of the V phases Debye-Scherrer photographs were taken using the asymmetric film arrangement and CrKcr radiation (ka1, = 2.28962A). Using the positional parameters, as determined6 for Zr,Co,Ge,. Table 11. intensity calculations were carried out for each of the V phases with the aid of a computer program.: Thus unequivocal indexing of the diffraction patterns was greatly facilitated. The lattice constants. Table I. were then computed by a least-squares fit of the high-angle lines with f (0) = cos2 Q as extrapolation function. Only few. if any. very weak impurity lines were observed, with the exception of the three iron alloys Zr,Fe,Si7. Zr4Fe,Ge7. and Ta,Fe,Si7. The agreement

Jan 1, 1970

By D. Krammer, E. S. Machlin

The effect of a brior high-temperature creep strain on the low-temperature ductility of commercially pure nickel has been evaluated. The low-temperature (-196°C) ductility decreases linearly with an increase in prior high-temperature (920°C) creep strain. The effect is experimentally correlated to the formation of inter crystalline cracks and voids during the prior high-temperature creep strain. The magnitude of the effect is also believed to be a function of the notch sensitivity of the material. SEVERAL mechanisms have been presented to explain the process of inter crystalline cracking in metals undergoing high-temperature creep. zenerl has suggested that grain boundary relaxation of shear stresses could build up high stresses at ob- stacles to grain boundary shear and thereby nucleate a crack. Chang and rant' have experimentally demonstrated that cracks do form at obstacles to grain boundary shear such as lines where three grains meet. The role of vacancies in the mechanism of high-temperature inter crystalline cracking has been explored by Machlt with the conclusion that the nu-cleation of voids by vacancy condensation is almost

Jan 1, 1960

By H. Yoshida, B. G. Liebmann, R. E. Green

In recent years considerable work has been undertaken in order to gain an understanding of the mechanisms responsible for the generation of recrystal- lization textures in face-centered-cubic metals. Two theories have been proposed, that of oriented growth1 and that of oriented nucleation,' and several attempts have been made to check these theories directly by recrystallizing deformed single crystals.3-5 Two groups, Graham-Cahn and Liebmann-Liicke-Masing, studied the orientation of recrystallized grains and their rate of growth, both using strained aluminum single crystals of commercial purity (Graham et al., 99.6 pct, Liebmann et al., 99.8 pct). Surprisingly, the results obtained by the two groups were completely

Jan 1, 1960

By Hsun Hu, R. S. Cline

In an earlier publication1 it was shown that a single crystal of Cu-4 wt pct Al cold-rolled in the (110)[112] orientation was stable up to 95 pct reduction, although the orientation spread was considerable larger than in a similarly oriented and cold-rolled copper single crystal. When rolled to 99 pct reduction, the copper crystal retained its initial orientation and a high degree of sharpness of texture, whereas the Cu-4 pct

Jan 1, 1969

By Gary E. McIntosh

This paper will discuss a US Bureau of Mines project designed to assess and predict the impacts which surface coal mining will have on the regional shallow groundwater systems in the Powder River Basin. The primary objective will be met through the accomplishment of the following: (1) The design and establishment of a regional network for monitoring shallow groundwater systems in the basin; (2) monitoring the direction and rate of flow, water quality, and aquifer characteristics of the shallow groundwater systems; and (3) development of a regional groundwater simulation model, with appurtenant subroutines to determine local effects.

Jan 1, 1980

By Robert B. Kistler, Ward C. Smith

The borate industry is one of the few sectors of the mining and mineral-processing industry which the United States still dominates. Since about 1927, the United States has supplied over half of the world's total boron and borate raw materials, and many of the chemical derivatives as well. Chiefly responsible for this record are companies producing sodium borates from two large deposits in southern California, at Boron (Kramer) and Searles Lake. The sodium borates, or products derived from borax and borax-containing brines, are the preferred borates for industry because they are soluble in water and combine readily with most other chemicals. Calcium borates are required for certain end uses, and these are produced from smaller colemanite-ulexite-probertite bodies. Sodium-free borate compounds also are produced from boric acid, which can be manufactured from either sodium or nonsodium borate minerals. During the past hundred years, the use of boron compounds throughout the world has risen from a few tons per year to the equivalent of over a million tons of B2O3. Leadership in supplying borates shifted from country to country and from region to region during this period, generally as the result of the development of newly discovered deposits that were better in quality, more accessible, or more economically exploitable than previous sources (Table 1). Primary Products and End Uses The principal borate products offered by primary producers in the United States are listed in Table 2. In general, these products are utilized worldwide by almost all consumers, regardless of the original source of the primary borates, In the United States, the primary borates all originate in southern California. Colemanite is produced as crude or processed crude ore from the Death Valley area and is utilized by the fiber glass and ceramic industries without further treatment. Production from Searles Lake, CA is from brines that are processed in chemical plants where borax and other compounds are recovered and the principal borate products are produced. At Boron, CA, the world's leading producer is mining a deposit of mineral borax and operating a chemical refinery. The mineral borax is mined together with included clay, and refined borax or "10-mol" is one of the refinery products. The mineral and the chemical compound are identical, Na2B4O7 • 10H2O. In addition to ship¬ping all major refined borate products from [ ]

Jan 1, 1983

By N. E. Rogen, N. J. Grant

AGE-hardening in nickel-chromium-titanium-aluminum alloys in the composition range characterized by the Nimonic alloys, is dependent upon the precipitation of the Ni3(AI,Ti) (y') phase.1 This phase is found to precipitate at about 700°C.1 Ni,Al is a face-centered-cubic ordered structure with a lattice parameter of 3.560 A. The atomic configuration is such that the aluminum atoms occupy the cube corners and nickel occupies the cube faces with titanium substituting for the aluminum preferentially. A maximum of three out of every five aluminum atoms can be replaced by titanium atoms in the -y 'phase.' When the solubility of the y'-phase is exceeded for titanium the T(Ni,Ti) phase is formed. The T-phase is an ordered close-packed hexagonal intermetallic structure which shows little solubility for the other elements in these alloys. The lattice parameter for T-phase is a - 2.5454 kr and c = 8.2900 kx units."

Jan 1, 1959

By W. O. Philbrook, R. H. Spitzer, F. S. Manning

The steady-state operation of an isothermal, counter-current reactor in which a mouing bed of hematite particles is reduced by hydrogen has been modeled mathematically using a generalized single-particle kinetic formulation for topochemical reduction with formation of the intermediate oxides, wustite and magnetite. Reduction prof iles have been generated for various oper- REDUCTION of iron ore, as practiced industrially, approaches counter current, granular-bed operation. The total process is extremely complex. Quite under- ating conditions selected to demonstrate the influence of major variables such as gas and solid flow rates, bed length, and particle size. These profiles illustrate , among other things, that the reducing-gas requirement in a countercurrent bed hinges upon the iron-wüstite equilibrium or 'pinch-point" in much the same way as in a staged reactor. standably, nearly all research has been focused on reduction of single particles of oxide under controlled conditions. While this approach simplifies the problem by eliminating interparticle interactions, the remaining intraparticle transport and kinetic processes still constitute a most formidable challenge. Only within the last few years has knowledge of single-particle reactions been developed sufficiently to make modeling of counter current-bed reduction a realistic and useful study of process behavior. The authors have analyzed1"3 extensive laboratory

Jan 1, 1969

By Hsun Hu

C. G. Dunn (Geneva1 Electvic Reseavclz Labo,vatory)-Dr. Hu16 has obtained a number of rolling and annealing texture results that partly agree with those of Dunn17 and Dunn and Kohl8 for experiments of a similar nature. I would like to discuss some of the points of agreement as well as some of disagreement and then present some unpublished data as a contribution to the work on textures. Firstly, there is agreement on the components produced during a 70 pct cold-rolling reduction of a (110) [001 ] single crystal; there is agreement on the forma- tion of a (110) [001] recrystallization texture provided recrystallization occurs at 800°C or higher; and there is agreement on the formation of (120) [001] components provided recrystallization occurs below 600°C. There is some disagreement on the low-temperature recrystallization since I also obtained a substantial amount of a (110) [001] component while the author obtained only (120) [001] components. I also discussed the differences between low- and high-temperature recrystallization (which included further annealing changes in the samples on long

Jan 1, 1962

By Richard Klimpel

This paper describes the effects of slurry viscosity on the selection-for-breakage and breakage distribution parameters in the wet grinding of ores. A series of experimental tests were run on laboratory scale ball mills. Slurry viscosities were modified by varying the solids/water ratio with and without the presence of selected chemicals. Very consistent and predictable correlations are shown to exist. The grinding parameters were calculated using a computerized back-calculation technique developed by Klimpel and Austin. Industrial scale circuit calculations and preliminary plant trial data suggest that considerable increases in throughput and/or fineness of grind can be achieved through the judicious use of chemical additives.

Jan 1, 1977

By Robin P. Gardner

Prior work by the author has established that closedform analytic solutions can be obtained for certain steady-state and transient types of operation of open circuit, continuous ball mills. This is possible when the tanks-in-series concept is used with the segregated flow or lumped parameter milling models. Such models should be useful (whenever they apply) in any calculational application since they are efficient and simple to program for digital computation. For example, they might be used within a computer program such as that developed by Herbst et al. for the calculation of model

Jan 1, 1975

By O. T. Marzke, Robert F. Mehl

A study of the structures arising from the decomposition of the ß solid solutions in the Cu-Zn and the Cu-A1 systems is of peculiar interest in the study of the mechanism of precipitation from solid solutions. It is possible in these alloys, by varying the composition within the ß field, to precipitate from the same basic lattice phases having different lattice structures. It has been rather generally assumed heretofore that the type of structure originating from the decomposition of a solid solution— the Widmanstätten structure—-is determined by the lattice structure of the parent solid solution alone. In the first paper of this series1 evidence was advanced which threw doubt upon this hypothesis; but definite proof of the correctness or incorrectness of the hypothesis should be forthcoming from a study of these alloys, for if the structures originating, for example, from the precipitation of the a phase from ß and of the ? phase from the ß in the Cu-Zn system should be shown to be crystallographically different, the hypothesis would necessarily be held as definitely disproved. Furthermore, the newer proposal enunciated in the first paper of this series—that the origin of the Widmanstätten structure lies in a cooperation between the lattice of the parent solid solution and that of the precipitate-—which at present seems the only a1ternative hypothesis, would in such an event be given added weight. The work here reported shows that the Widmanstätten structures originating in the precipitation of the a phase from the ß and in the precipit'at.ion of the y phase from the y in the Cu-Zn system are indeed crystallographically different; and incidentally presents some new descriptive information on the Widmanstätten structure from a more general point, of view.

Jan 1, 1931

CONTRARY to the natural order of art, it has been discovered how to cast in moist earth in order to avoid labor and expense. This is truly a thing that many desire and few practice because it is not as smooth a way nor as easy to effect as it apparently seems. To do this, one part of fine-grained yellow tuff is taken, or some very

Jan 1, 1942

By Robert Mehl

A STUDY of the structures arising from the decomposition of the a solid solutions in the Cu-Zn and the Cu-Al systems is of peculiar interest in the study of the mechanism of precipitation from solid solutions. It is possible in these alloys, by varying the composition within the ß field, to precipitate from the same basic lattice phases having different lattice structures. It has been rather generally assumed heretofore that the type of structure originating from the decomposition of a solid solution-the Widmanstätten structure-is determined by the lattice structure of the parent solid solution alone. In the first paper of this series1 evidence was advanced which threw doubt upon this hypothesis; but definite proof of the correctness or incorrectness of the hypothesis should be forthcoming from a study of these alloys, for if the structures originating, for example, from the precipitation of the a phase from ß and of the -y phase from the ß in the Cu-Zn system should be shown to be crystallographically different, the hypothesis would necessarily be held as definitely disproved. Furthermore, the newer proposal enunciated in the first paper of this series-that the origin of the Widmanstätten structure lies in a cooperation between the lattice of the parent solid solution and that of the precipitate-which at present seems the only alternative hypothesis, would in such an event be given added weight. The work here reported shows that the Widmanstätten structures originating in the precipitation of the a phase from the a and in the precipitation of the -y phase from the ß in the Cu-Zn system are indeed crystallographically different; and incidentally presents some new descriptive information on the Widmanstätten structure from a more general point of view.

Jan 1, 1931

By Charles S. Barrett, Robert F. Mehl

A study of the structures arising from the decomposition of the ß solid solutions in the Cu-Zn and the Cu-A1 systems is of peculiar interest in the study of the mechanism of precipitation from solid solutions. It is possible in these alloys, by varying the composition within the ß field, to precipitate from the same basic lattice phases having different lattice structures. It has been rather generally assumed heretofore that the type of structure originating from the decomposition of a solid solution— the Widmanstätten structure—-is determined by the lattice structure of the parent solid solution alone. In the first paper of this series1 evidence was advanced which threw doubt upon this hypothesis; but definite proof of the correctness or incorrectness of the hypothesis should be forthcoming from a study of these alloys, for if the structures originating, for example, from the precipitation of the a phase from ß and of the ? phase from the ß in the Cu-Zn system should be shown to be crystallographically different, the hypothesis would necessarily be held as definitely disproved. Furthermore, the newer proposal enunciated in the first paper of this series—that the origin of the Widmanstätten structure lies in a cooperation between the lattice of the parent solid solution and that of the precipitate-—which at present seems the only a1ternative hypothesis, would in such an event be given added weight. The work here reported shows that the Widmanstätten structures originating in the precipitation of the a phase from the ß and in the precipit'at.ion of the y phase from the y in the Cu-Zn system are indeed crystallographically different; and incidentally presents some new descriptive information on the Widmanstätten structure from a more general point, of view.

Jan 1, 1931

William Metcalf, Pittsburg, Pa. (communication to the Secretary*): I am greatly pleased that some one has at last reached what I have long regarded as the only rational explanation yet given of the reasons why steel hardens. Mr. Field claims originality; and doubtless he is entitled to it, but not to priority, mhich must be granted to Prof. John W. Langley.' The difference between them is that Langley says " Tension, probably molecular," and Field says " Tension, probably atomic "; in either case the vital thing after solution is tension. Mr. Field's argument carries with it the idea of increase of density with hardness; if he mill study the facts farther he will observe that the case is just the reverse; that is, the greater the hardness the less the specific gravity; it was just this fact that led Langley to his conclusion, in mhich I have always concurred. Field agrees with Langley that the first requisite for perfect hardening is complete solution of the carbon, not combination; and all of the facts agree with this conclusion. The fact that increase of hardness causes reduction of density was first brought to my notice some 40 years ago, when Major William Wade was testing Jones & Laughlin's cold-rolled iron, and I mas his assistant. We found the well-known increase of tenacity, compressive strength, torsional resistance, and hardness. Specific-gravity tests showed that the cold-rolled iron was less dense than the hot-rolled bars. Major Wade was so surprised at this result that he gave me a lot of samples to weigh, saying that he was not satisfied with

Jan 1, 1904

By G. W. Powell

ACCORDING to crank,' the accumulation equations for inter diffusion in a binary system whose molal volume is a function of concentration are

Jan 1, 1965