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By Leland L. Mink, Roy E. Williams, Lewis M. McNay, Alfred T. Wallace

In 1968 the metal-mining industry of northern Idaho installed tailings ponds as a means of handling and treating mine wastes, metallurgical process wastes and domestic wastes. The installation of the ponds constituted a crash program to minimize pollution of the Coeur d'Alene River. The ponds provided an opportunity to investigate which combinations of wastes tailings ponds can be treated. The research data pertaining to tailings pond discharge lends insight into compliance with the recent EPA guideline for effluent quality.

Jan 7, 1973

By Fred W. Gordon

The heading of this paper was prompted by the knowledge that experience, up to this time, seemed to indicate that smaller furnaces were preferable for smelting the material of this section. Since the reasonable success thus far achieved by the first furnace of this plant tends to change the above opinion, and unsettle the generally-accepted views of furnace-men as to "weak " coke, a few words as to the design of the plant and the mode of operation adopted may prove interesting.

Jan 1, 1889

By William E. Ford, Edward Salisbury Dana

Normal phosphoric acid is H3P04, and consequently normal phosphates have the formulas R3PO4, R3(P04)2 and RPO4, and similarly for the arsenates, etc. Only a comparatively small number of species conform to this simple formula. Most species contain more than one metallic element, and in the prominent Apatite Group the radical (CaF), (CaCI) or (PbCI) enters; in in the Wagnerite Group we have similarly (RF) or (ROH).

Jan 1, 1922

By J. R. Low, A. M. Turkalo

ManY qualitative observations have been made concerning the relationship of the carbide dispersion and the mechanical properties of steel. With reference to the strength and hardness we know that for a given composition a steel having a fine pearlitic structure is stronger than that having a coarse pearlite. The martensitic structure tempered at a relatively low temperature and having finely dispersed carbides gives greater strength than that given by the martensitic structure tempered at a relatively higher temperature and having a coarser

Jan 1, 1959

By M. M. Austin

PURE metallic tantalum, from a practical standpoint, is one of the newer developments in the metal field. Although it was used as filament in incandescent lamps in 1906, only within the last five years has the metal been available in sufficient quantity and suitable form for more general application. In addition to corrosion-resisting properties and high melting point, the metal has an ability to withstand unusual amounts of cold working. It affords some striking demonstrations of block movement during plastic flow.

Jan 1, 1930

Nominating Committee.-On the recommendation of the President, the Board of Directors, at their meeting on Apr. 25,1913, appointed the following Nominating, Committee to nominate officers and directors for next year: John Hays Hammond (Ex-President), Chairman. Robert H. Richards Chairman of Boston Local Section. Richard S. McCaffery, . . . . Chairman of Spokane Local Section. Chester F. Lee Chairman of Puget Sound Local Section. Frederick G. Cottrell, . . . . San Francisco, Cal. Charles W. Goodale Butte, Mont. James W. Maleolmson, . . . . Kansas City, Mo.

Jan 5, 1913

By V. C. Allen

THE Tri-State Zinc, Inc., Galena, Ill., was confronted with the problem of securing ore from a deposit because the hoisting shaft was several thousand feet from the mill. The orebody is several thousand feet long, averaging 200 ft in width and 60 ft in height and opened up by vertical shafts some 300 ft deep. Mining is by the room-and-pillar method. During the initial operation the ore was loaded by conventional electric 1/2-yd boom-and-dipper shovels and hauled to the shaft by 8-ton diesel trucks. This underground ore loading and hauling was well adapted to the conditions and productive of low costs per ton. However, with the mill situated as mentioned, a triple handling of all broken rock was necessary: l—from the stope to the shaft by truck, 2—up the shaft by skip br can into the surface hopper, and 3—by truck from the surface hopper to the crushing plant at the mill. In addition to the repeated handling, serious troubles were encountered during the winter because of freezing in the shaft hopper. Consideration was given to either moving the mill to the new orebody or to the construction of a second mill. The presence of other orebodies to be mined at a later date made the first alternative impractical while the capital outlay for a second mill, when the present plant of approximately 850 tons per day was deemed sufficiently large for the total reserves, made the second alternative also unwise. It was decided to retain the mill in the originals location and continue to move the ore to it. The idea of driving an inclined adit from the surface to the bottom of the orebody suitable for truck haulage and big enough to allow the passage of all mechanical equipment was conceived. Among the apparent advantages of such an incline were: 1— Direct haulage from the stope to the mill without rehandling. 2—Elimination of virtually all grizzlies. Trucking from underground to the mill would do away with all hoppers, chutes, gates, and skips and make the maximum rock size dependent solely on the size of the shovel dipper at the mine and the crusher opening at the mill. 3—Less secondary blasting would be needed. 4—Ease of transporting equipment and supplies underground. Shovels and trucks could be taken through the incline intact. 5—Equipment could be brought to the surface for repairs and servicing without loss of time. The same advantages of ease in moving would be present in the handling of men, steel, powder, and supplies. 6—There would be far less difficulty in increasing the amount of tonnage that could be moved by truck up an incline than would be found in attempting to increase the capacity of a shaft. 7—All the broken ore in the stopes would serve as bin capacity, as it would take the breakdown of all of the loading and hauling equipment to have the same effect as a delay in shaft hoisting. 8—All danger of men being trapped in the mine as a result of shaft fire or power stoppage would be eliminated. 9— Virtually all trouble from severe winter conditions would be eliminated by the direct haul underground to the mill. The decision was made to proceed with the driving of an inclined adit. The topography of the surface between the orebody and the mill was such that it was possible to locate the portal at a point 170 ft above the mine floor and 1800 ft horizontally from the central point of the orebody to the south and 2500 ft from the mill to the north. A grade of 10 pct was found to be optimum for continuous truck haulage when the various factors of speed, safety, and truck maintenance were all considered. The incline as driven was consequently 1700 ft long on 10 pct grade and 12 ft high by 17 ft wide in cross section. The tunnel-driving equipment was chosen so that it could be used in mining after the completion of the tunnel. Drilling was done with a jumbo with two Joy jibs mounting 3-in. drills, loading with an Allis-Chalmers diesel-powered, front-end loader of approximately 11/4-yd capacity, and hauling by Koehring Dumptor trucks of 8-ton capacity, diesel-powered. The width of the tunnel allowed the end loader and Dumptor to be placed abreast. Since the Dumptors can be driven either forward or backward with equal facility, loading was accomplished without turning around either machine throughout the loading operation. The crew in addition to the tunnel foreman was comprised of three men per shift at the start and in the later work, four men. Each crew could perform any part of the working cycle. If the drilling was completed and the round blasted in the middle of a shift, the same men would proceed with the loading and hauling. Since the mine already had been drained to the bottom levels, no water was encountered. At the halfway point the tunnel was widened for approximately 100 ft to permit trucks to pass. The total cost of the tunnel excluding the capital outlay for equipment, which was all continued in use in the subsequent mine operation, was $60,363.00 or $35.50 per ft. The tunnel was completed at the end of June, 1949 and has been in continuous use since that time. In the five months from July to November inclusive, 106,049 tons have been transported to the mill or an average of 835 tons per day. No unforeseen disadvantages have been encountered and the advantages which had been predicated before the adit's construction have been more than realized. As previously mentioned, the deposit is worked by the room-and-pillar system with occasional faces up to 125 ft high. Except in driving development drifts when diesel-powered, front-end loaders such as were used in the tunnel are employed, all shoveling is done by Yz-yd boom-dipper type shovels electrically driven. These units need a width of 25 ft and a height of 14 ft in which to operate. All hauling is by diesel trucks, mainly Koehring Dump-tors. Roads are maintained with caterpillar tractors and a road grader. The tonnage output from the

Jan 1, 1952

By A. Gemperle

Electron diffraction and transmission electron microscopy on foils at room temperature were used to investigate the ordering of Fe-Si alloys containing 10 to 23 at. pct Si. A certain degree of DO3 order was found in all alloys. With the exception of the lowest silicon concentration for which the antiphase domains could not be clearly resolved, the alloys have a domain structure of two-domain type with boundaries having 1/4a01<111> displacement vectors for less than 12.3 at. pct Si and with boundaries having 1/2 a0<100> displacement vectors for more than 12.3 at. pct Si. The alloys with 12.3 at. pct Si have a domain structure consisting of fine domains with 1/2a&apos;o<100> boundaries within much larger domains with 1/4a&apos;o<111> boundaries. The development of these structures can be explained by transition of the alloy from the disordered state into the B2-type order and then into the D03-type order by the mechanism proposed previously for the FeSAl alloys. The existence of the B2 structure in the lower part of the investigated concentration range reported in some articles can be explained by fine domains with 1/2a&apos;o<100> boundaries formed by several disordered planes within large domains with 1/4a&apos;o<111> boundaries. The ordered structure predicted by the theory —with practically no domain boundaries —is found in the alloys having 12.3 at. pct Si where it develops in the B2 structure region. ORDERING in Fe-Si alloys was first studied by phragmenl who found that beginning with 13 at. pct Si the DO3 (Fe3Si) superlattice reflections appear in the diffraction patterns. The equilibrium diagrams constructed later by corson2 and Haughton3 from various measurements proposed the existence of a homogeneous solid solution (a phase) in the range from 0 to 25 at. pct Si. Jette and Greiner4 and Farquhar et al.5 measured the relation between lattice parameter and composition and they considered the break in the curve at 9 to 10 at. pct Si to be caused by the ordered solution a"(Fe3Si). Glaser and Ivanick6 Determined critical ordering temperatures of the alloys containing from 10.9 to 27.9 at. pct Si from the measurement of the electric resistivity of quenched samples. In all cases the critical temperature was lower than the melting point and it was highest for 25 at. pct Si. Lihl and Ebel7 measured the lattice parameter curves at various temperatures up to 1000°C. The region between two breaks on these curves, corresponding to 10 to 12.5 at. pct Si at room temperature, was considered by them to be two-phase (a + a"). They concluded by extrapolation of the measured values that a" in the alloy having 25 at. pct Si is stable up to the melting point. Davies8 studied superlattice reflections in the X-ray diffraction patterns of an alloy containing 8.7 at. pct Si. He found the B2 structure and short-range order in the slowly cooled samples and the DO3 A. GEMPERLE is Research Scientist, Institute of PhysicS, Czechoslovak Academy of Sciences, Prague, Czechoslovakia. __Manuscript submitted January 2, 1968. IMD structure in the quenched and annealed samples. This investigation first reports the presence of the B2 structure, phase a&apos;: in Fe-Si alloys. Meinhardt and krisement9,10 also found its existence in Fe-Si alloys by neutron diffraction. No order was detected by them in the alloy containing 8 at. pct Si. The onset of B2 order was observed at a composition of 9.2 at. pct Si. They found almost perfect B2-type order with partial DO3-type order at room temperature in the 10 to 12.5 at. pct Si range and almost perfect DO3-type order in the 12.5 to 25 at. pct Si range. They established the critical temperatures Tc of both the structures through measurement at higher temperatures. The critical temperature for the B2 structure was found to be always higher than the critical temperature for the DO3 structure of the same alloy. They extrapolated the curves of the critical temperatures and concluded that the alloys with more than 17 at. pct Si have the B2 structure up to the melting point and the alloys with more than 23 at. pct Si have the DO3 structure up to the melting point. The results of Meinhardt and krisement9,10 were confirmed by Dokken&apos;s measurement" of the temperature dependence of the electrical resistivity in the 10.8 to 15 at. pct Si range. On the other hand chessin12 detected by X-ray diffraction a considerably lower degree of order in the 12.7 at. pct Si alloy. ANTIPHASE DOMAIN STRUCTURE IN ALLOYS WITH B2- AND DO$-TYPE ORDER The ordered structures B2 and DO3 can be described in terms of a subdivision of the bcc lattice into four fcc sublattices with a parameter double that of the bcc lattice. Following Marcinkowski13 we will label them I. 11, 111, IV. The B2 structure in the AB alloy is formed by placing A atoms on sublattices I and II and B atoms on sublattices III and IV. In a non-stoichiometric perfectly ordered alloy having concentration (A) > (B), A atoms occupy sublattices I and 11. and A and B atoms distributed at random occupy sublattices III and IV. The DO3 structure in an A3B alloy is formed by placing A atoms on sublattices I, 11, and 111, and B atoms on sublattice IV. In a nonstoichiometric, perfectly ordered alloy having concentration (A)/3 > (B), A atoms occupy sublattices I, 11, and 111, and A and B atoms distributed at random occupy sublattice IV. As further shown in Ref. 13, two types of domains are possible in the B2 superlattice and the antiphase domain structure has associated with it boundaries with displacement vectors 1/4 a&apos;o<ll1> only. Four types of domains are possible in the DO3 superlattice and the antiphase domain structure has associated with it boundaries with displacement vectors 1/4a&apos;o<111> and 1/2a&apos;o<l00>. Bethe14 suggested on the basis of theoretical considerations that in a structure with two sublattices at low temperatures only one domain should be present in the whole crystal at equilibrium. Similarly Bragg15 concluded that at low temperatures the domain struc-

Jan 1, 1969

By T. V. Philip, Paul A. Beck

IN a previous note1 it was pointed out that the available information suggests a distinct correlation between the occurrence of the CsCl-type ordered structures formed in equi-atomic binary alloys of transition elements and the location of the components in the periodic table. A definite increase in the bond strength between unlike atoms, as compared with that between like atoms, is indicated when, in binary alloys of iron group elements, the other component is changed from chromium to vanadium or tantalum, to titanium. Laves and Wallbaum,2 eported a CsCl-type ordered structure for the stable intermediate phase at the equi-atomic composition in the Ti-Fe system (and also in the Ti-Ru and Ti-Os systems). On the other hand, Tagaya, Nenno, and Nishiyama8 found no ordering of this kind in the body-centered-cubic solid solutions in the Cr-Fe system. It was concluded&apos; that the occurrence of a CsC1-type ordered phase of intermediate stability may be expected in the V-Fe system. Preliminary results were described: suggesting that at least some degree of order does exist in the equi-atomic alloy VFe, annealed at 1200° C and quenched in cold water. Using CrK radiation, at least one weak superlattice line was found in the X-ray diffraction pattern which could be indexed as (100). and which disappeared, as expected, when FeK radiation was used. It was found more recently that the impurity phase (presumably VN), previously giving rise to additional X-ray diffraction lines and thus preventing definite indentification of the (111) superlattice line,&apos; can be eliminated by preparing the alloy by arc melting in a helium atmosphere. The alloy specimen melted in this manner had clean surfaces and showed very littte, if any, nitride phase in the microstructure after annealing in vacuum at 1250°C and quenching. The relative intensity of the (100). superlattice line with CrK radiation was greatly increased and, in addition, a fairly strong (Ill) , superlattice line and even a detectable (210) , super- lattice line was obtained, when the powder produced by filing from the 1250°C annealed and quenched specimen was reannealed in vacuum at 625°C for 1 hr. By using a cellulose acetate film as a filter in front of the photographic film in order to absorb the soft radiation resulting from air fluorescence, the background intensity could be reduced considerably in relation to the intensity of the diffraction lines. All three superlattice lines, (100),, (111)., and (210)a, disappeared, as expected, when a radiation other than CrK, was used.1 For the powder reannealed at 625ºC, the strongest lines of the s pattern also appeared weakly, indicating that during an: nealing at 625°C a small amount of transformation took place from the body-centered-cubic to the u phase. However, since all superlattice lines to be expected in the 0 angle range used were actually very clearly present, it was evident that the high temperature body-centered-cubic phase had transformed into a CsCl-type ordered structure before much s phase could form. Reannealing filings for 1 hr at 700°C resulted in complete transformation into the u phase. After 1 hr at 650°C the transformation into IT was not quite complete, the strongest body-centered-cubic diffraction lines were still present, although fairly weak, and only the (100), super-lattice line was detectable (extremely weak). These findings not only confirm the previous conclusionsL as to the existence of a CsCl-type ordered structure in the Fe-V system, but they also indicate that this metastable ordered structure forms at about 600°C preceding the formation of the stable s phase, while at 1250°C the disordered body-centered-cubic phase is stable. The faint (loo) , super-lattice line previously observed in specimens quenched from 1200°C was probably due to the fact that the quenching of the powder in an evacuated fuse:! quartz capsule was not fast enough to prevent completely the ordering reaction on cooling. The present results conform with the suggestion that the A-B bond, in relation to the A-A and B-B bonds, increases in strength from CrFe to VFe to TiFc. It is, therefore, of interest to compare the measured values of the average atomic diameter for these three alloys with the corresponding average atomic diameters calculated from the atomic radii of the elements concerned. ASSUming A-B contacts

Jan 1, 1958

By Pol Duwez

IN the course of an investigation of the V-CO system, two intermediate phases were found. One of these phases corresponds approximately to the stoichiometric composition VCo and is isomorphous with the sigma phase in the Fe-Cr system.&apos; The second phase has the composition V3Co; its crystal structure is described in the present note. The alloys were prepared by mixing the two metals in the powder form, pressing a small disk weighing about 5 g at 80,000 psi, and arc melting this disk on a water-cooled copper plate in an atmosphere of pure helium. The details of this technique have been described.&apos; The vanadium powder was obtained from Westinghouse Electric Corp., Bloomfield, N. J. This powder is probably of very high purity, since when it is properly sintered or melted in the above-mentioned arc furnace, ductile specimens are obtained. The cobalt powder, from Charles Hardy, Inc., New York, contained 0.5 pct Ni, 0.1 pct Cr, and traces of Si and Fe. After melting, the V,Co samples were sealed in evacuated quartz tubes and homogenized for ten days at 800°C. Powder diffraction patterns were obtained with a 14.32 cm diam camera, using Ka copper radiation. The patterns were readily indexed on the basis of a primitive cubic lattice with a parameter equal to 4.675A. The density, determined by the immersion method, was 6.71 g per cu cm; hence the number of molecules per unit cell is approximately 1.95; i.e., 2. At this point, the possibility that the structure might be that of beta tungstena became apparent. The beta tungsten structure is described as follows: Space group 03,, — Pm3n 2 Co in (a) : 000; ?4lhYZ (hhl) reflection present only if 1 = 2n. Assuming this structure to be the correct one, intensities were computed by means of the usual eauation: 1 + cos220 I oc p F sin 0 cos 6 where F is the structure factor, 0 the Bragg angle, and p the multiplicity factor. The observed and calculated values of sin 0 and the intensities are given in Table I. The agreement between the observed and the calculated sin 0 is good and there are no flagrant discrepancies between the calculated intensities and those estimated visually. The (hhl) reflections for which 1 is odd are not observed, as required by the space group. In addition, the (410), (430), and (531) reflections are missing as expected, because of the special (a) and (c) positions in0%. However, six reflections—(llo), (220), (310), (411), (422), and (510)—which have very weak computed intensities were not observed. For these reflections, the structure factor is proportional to the difference between the scattering factors of the two atoms in the structure. Since the scattering factors of vanadium and cobalt are not very different, these reflections are weak. However, by using Ka chromium radiation, whose wavelength is just above the absorption edge of vanadium, the effective scattering factor of vanadium may be decreased by one or two units; consequently the difference between the cobalt and vanadium scattering factors is increased. It was, indeed, found that in a powder pattern taken with chromium Ka radiation, the three reflections (110), (220), and (310) were actually present. The three other reflections (411), (422), and (510), with spacings smaller than half the wavelength of chromium Ka, were obviously not obtainable with chromium radiation. All the experimental results appear to confirm the beta tungsten structure for V,Co. In this structure, each cobalt atom is surrounded by twelve vanadium atoms at 2.61A; each vanadium atom is surrounded by two vanadium atoms at 2.34A, four cobalt atoms at 2.61 A, and eight vanadium atoms at 2.86A. Acknowledgment This work was done at the Jet Propulsion Laboratory, California Institute of Technology, under contract number W-04-200-ORD-455 with the Army Ordnance Department, Washington, D. C. The author wishes to thank this agency for the permission to publish the results of this investigation. References &apos;P. Duwez and S. R. Baen: X-Ray Study of the Sigma Phase in Various Alloy Systems. Symposium on the Nature, Occurrence, and Effect of Sigma Phase. ASTM Special Tech. Pub. No. 110, pp. 48-54. Philadelphia, 1951. 2 C. H. Schramm, P. Gordon, and A. R. Kaufmann: The Alloy Systems Uranium-Tungsten, Uranium-Tantalum, and Tungsten-Tantalum. Trans. AIME (1950) 188, pp. 195-204; Journal of Metals (January 1950). 3 M. C. Neuburger: The Crystal Structure and Lattice Constants of Alpha and Beta Tungsten. Ztsch. fiir Krist. (1933) 85, pp. 232-237.

Jan 1, 1952

By S. S. Cole, H. Sigurdson

The melting points of mixtures of titanium dioxide and other titanates have been reported to a limited extent as binary systems and some results have been reported in conjunction with silicon dioxide. The limited data indicated that a low melting zone might exist in a ternary or quarternary system of CaO-MgO-TiO2-Al2O3, since the eutectics reported in the binary systems of MgO.TiO2-TiO2, Al2O3TiO2-TiO2 and CaO.TiO2-TiO2 were of about equivalent composition of TiO2. The importance of a low melting region with a high titanium oxide value in the developing of high titanium slags is fully appreciated by metallurgists. A comprehensive study was undertaken to establish basic information on low melting titanate mixtures. Compounds in the System CaO-MgO-TiO2 -Al2O3 Preparation of the titanates of CaO, MgO and Al2O3 confirmed reported data that the following compounds could be formed under oxidizing conditions in solid state reactions: CaO.TiO2, 2MgO.TiO2, MgO.TiO2, MgO-2TiO2 and Al2O3.TiO2. Under oxidizing conditions it was not possible to react MgO with TiO2 in mol ratios higher than 1:2 without having unreacted TiO2 in the product, nor was it possible to form calcium or aluminum titanates with a higher mol ratio of CaO and A12O3 to TiO2 than 1:1. By fusing mixtures of Al2O3-TiO2 and MgO-2TiO2 together a series of solid solution products were obtained, which showed an MgO-2TiO2 X ray diffraction pattern shifted to smaller inter-planar spacings. Range of Investigation Data in the literature1 indicated that these titanates had melting points which ranged from 1645 to 1860°C. Since the purpose of the study was primarily to provide useful data for smelting titaniferous ores, the work was restricted to the zone of the system which would include the crystalline phases present in the slags. The explored limits were bounded by CaO.-TiO2-MgO.TiO2-TiO2in the base plane. The system was extended to a fourth component Al2O3-TiO2 since many titaniferous ores contain appreciable amounts of A12O3. In the quarternary system CaO-TiO2-MgOTiO2-TiO2-Al2O3TiO2, a tetrahedron was used to represent graphically the components, with one component at each point of the tetrahedron. In the base plane, mixtures were pre- pared to represent fairly uniform changes of composition over the desired range expressed on a mol percent basis. Al2O3-TiO2 was brought into the system in increments of 10 mol pct up to 40 pct. Mixtures were then made up for each of the Al2O3-TiO2 planes. The ranges employed were then represented by five planes cutting the tetrahedron at 10 mol pct Al2O3-TiO2 intervals. Choice of Equipment Although it was necessary for all smelting work to be done in a strongly reducing atmosphere, it was decided that all melting point determinations should be done under oxidizing conditions. This decision was prompted by the fact that TiO2 reduced to lower oxides in a reducing atmosphere with consequent changes in melting points. The use of a micropyrometer and a platinum strip furnace for work of this type is adequately described in the literature.2 With modifications, equipment was selected which provided a fairly rapid method of determining melting points of refractory oxides. The final assembly, which was used, consisted of a platinum strip furnace and a Leeds and Northrup disappearing filament optical pyrometer attached to a special telescope which magnified the sample about 20 diam. The furnace assembly consisted of a platinum strip 0.005 X 0.3 X 2.2 in. mounted on brass posts on a refractory base. This was enclosed in a black steel shell which had a 2-in. opening at the top for purposes of sighting the telescope. The platinum strip was in series with two 0.04 ohm nichrome resistors connected to the secondary of a 2 kw transformer which supplied 17 volts. The current to the primary was varied

Jan 1, 1950

By David A. Thomas, David N. French

The lrnrdness of WC crystals has been measured with the Knoop indenter at loads of 100 and 500 g on the (0001) and (1070) planes. The hardness as tneasitred on the basal plane is 2400 kg per sq mm and shows little anisotropy. The hardness on the prism plane, however, shows a marked orientation dependence, with a low value of 1000 kg -per sq mm when the long axis of the Knoop indenter is oriented parallel to the c axis and a high value of 2400 kg per sq mm when the indenter is perpendicular to the c axis. Slip lines (Ire observed surrounding the microhardness indentations and they show slip on (1010) planes, probably in [0001] and (1120) directions. This slip behavior can be explained by the crystal structure of TVC, which is simple hexagonal with a c/a ralio of 0.976. The hardness anisotropy call be explained by [0001]{1010} and (1130) {10l0] slii) and the resolved shear-stress analysis of Daniels and Dunn. HARDNESS anisotropy is a well-known phenomenon and has been reported for many metals, with both cubic and hexagonal structure.1-6 For hexagonal tungsten carbide, WC, a wide range of hardness values is reported in the literature. For example, Schwarzkopf and Kieffer7 give a hardness of 2400 kg per sq mm and report a value of 2500 kg per sq mm by Hinnüber. Foster and coworkerss give the average Knoop microhardness as 1307 kg per sq mm with a maximum value of 2105 kg per sq mm. Although these values and the structure of WC suggest the likelihood of hardness anisotropy, no such measurements have been made. We first detected a large apparent hardness anisotropy in WC crystals about 75 p large, in over-sintered cemented tungsten carbide. Prominent slip lines also occurred around many indentations. This report presents further observations and interpretations of hardness anisotropy and slip in WC crystals obtained from Kennametal, Inc. Both Knoop and diamond pyramid indenters were used on a Wilson microhardness tester with loads of 100 and 500 g. EXPERIMENTAL RESULTS The carbide crystals tended to be triangular plates parallel to the (0001) basal plane of the hexagonal structure. The side faces were parallel to the ( 1010) prism planes. Specimens were mounted approximately parallel to these two types of faces and metallographically polished. Laue back-reflection X-ray patterns were used to orient the specimens, which werethen ground to within ±1 deg of the (0001) and (1010) planes. The Knoop hardness values measured on the basal plane are plotted in Fig. 1. There is only a small anisotropy, with a hardness range of 2240 to 2510 kg per sq mm. The additional points at angles from 52.5 to 67.5 deg confirm the sharp minimum hardness at 60-deg intervals, consistent with the sixfold hexagonal symmetry. The average hardness of all values obtained on the basal plane is 2400 kg per sq mm. While the basal plane shows only slight anisotropy, the (1010) plane exhibits marked hardness anisotropy, from 1000 to 2400 kg per sq mm. Fig. 2 shows the hardness as a function of the angle between the long axis of the indenter and the hexagonal c axis, the [0001] direction. The minimum and maximum occur when the indenter is oriented parallel and perpendicular to the [0001] direction, respectively. The anisotropy of the prism plane is contrary to that reported for hexagonal zinc and hard- However, the basal-plane anisotropy is similar to these two metals.1&apos;2 To check the accuracy and reproducibility of the measurements, a series of fifteen impressions was made at 100-g load in the same orientation in the same area of the specimen surface. The average for all was 2040 kg per sq mm, with a range of 1950 to 2130 kg per sq mm, giving an accuracy of about ± 5 pct. Thus the slight anisotropy on the basal plane is almost within experimental error. Fig. 3 shows slip lines around the Knoop indentations on the basal plane. The slip traces are in directions of the type (1130). The presence of slip steps on the basal plane indicates that the slip direction lies out of the (0001) plane. Because WC has a c/a ratio of 0.976,&apos; the shortest slip vector is [0001], which suggests slip systems of the type [0001] (1010). Fig. 4 shows slip lines around the Knoop intentations on the (1010) plane. These slip lines are inconsistent with [0001] slip but can be

Jan 1, 1965

By C. G. Dunn, M. Sharp

IN twinned crystals of the face-centered cubic metals the lattice of one twin is a mirror image of the other in a common twin boundary. When several twins appear within large grain in a sheet specimen, the twin one boundaries form a set of lines at the surface of the specimen which coincide with (111) planes of the large grain. Furthermore, for twins of the same orientation, these lines are parallel. Generally, the presence of identically oriented regions with straight parallel boundaries coinciding with a (111) plane of the surrounding crystal is strong evidence for identifying the island regions as twins of the parent crystal. However, Fig. 1, which shows the macrostructure of a large grain of copper with island regions that satisfy these conditions. is not an illustration of (111) twins. Since the reverse side of the specimen has much the same appearance, it was thought at first that these regions, which appear dark in the macrograph, actually were twins. According to X-ray data, however, these regions are second-order twins of the large crystal. With regard to their formation, these second-order twins formed by secondary recrystallization in a cube texture matrix. Growth occurred in the direction of the arrow (see Fig. 1) as the specimen moved slowly into a gradient temperature furnace as described previously.&apos; Nucleation of the second-order twins occurred, therefore, on the ends facing opposite the arrow. If the origin of the second-order twins were due to repeated twinning, some first-order twin structure should be visible on these ends. This proved to be the case, as very small twins were readily found with the aid of a microscope, and probably could have been seen, in some instances, under ideal lighting conditions without aid of a microscope. Fig. 2 shows a cross-section view taken perpendicular to both the surface and the (111) trace of the parent crystal (visible as a straight boundary in Fig. 1) at the beginning point of growth of a second-order twin and where one first-order twin was relatively thick. In the micrograph, A is the large parent grain; B is the first-order twin of A; and C, which is a first-order twin of B; is a second-order twin of A. Between A and B and between B and C the major straight portions are traces of common (111) twin boundaries. The straight portion of boundary between A and C, however, is not a common crystallographic plane to the two lattices; it is a (111) plane of A and a (115) plane of C. Without considering the mechanism of twinning itself, the origin of the second-order twins may be accounted for in terms of repeated twinning and special growth characteristics. After each nucleation, a selective growth process can be thought of as favoring growth of the first-order twin in local spots only and favoring growth of the second-order twin to an extent comparable with that of the parent grain over relatively large areas in a way similar to that described for twinning in aluminum.&apos; It has already been pointed out that the boundary between the large grain (A) and the second-order twin (C), which is responsible for the straight boundary portions in Fig. 1, involves a (111) plane of A and a (115) plane of C. The same combination of planes is not only possible in first-order twins, but actually appears quite frequently.3 Their prevalence in first-order twins and their presence here in second-order twins, together with the necessary occurrence of a large number of common lattice sites at the boundary, is an indication that this combination produces an "energy cusp"&apos; boundary. (Energy cusp boundaries have been described by Shockley and Read.") The configuration of atoms near a {Ill), (115) boundary in first-order twins is of course different from the configuration near the same type of boundary in second-order twins. References 1 M. Sharp and C. G. Dunn: Secondary Recrystallization Texture in Copper. Journal of Metals (January 1952) Trans. AIME, p. 42. 2W. G. Burgers and W. May: Stimulated Crystals and Twinning in Recrystallized Aluminum. Recueil des travaux chimiques des Pays-Bas (1945) 64, p. 5. aD. Whitwham, M. Mouflard, and P. Lacombe: Discussion of W. C. Ellis and R. G. Treuting, "Atomic Relationships in the Cubic Twinned State." Trans. AIME (1951) 191, p. 1070; Journal of Metals (October 1951). 4 W. Shockley and W. T. Read: Dislocation Models of Crystal Grain Boundaries. Physical Review (1950) 78, p. 275.

Jan 1, 1953

By Herman Dykstra, R. L. Parsons

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.&apos; THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy&apos;s Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. &apos;Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If&apos; .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By N. A. Gokcen, J. Chipman

A revised treatment of the authors&apos; published data eliminates the complex relation previously proposed between concentration of silicon and activity coefficient of oxygen in liquid iron. Revised values of the thermodynamic properties of the liquid solution are presented. IN a recent experimental study of the reaction SiO2 (s) = Si+ 2O; Kf, = [% Si] [% O]² [1] the authors&apos; found a substantially constant equilibrium product in liquid iron at 1600°C of 2.8x10-5 They also reported extensive data on the reactions: SiO2 (s) + 2H2 (8) = Si- + 2H2O (g); K&apos;2= [% Si] (H2O/H2 [2] and H, (g) + 0 = H2O (g); K&apos;3 =( H2 O [31 (H2) [%O] From the results on reaction 3 and earlier data of Dastur² on this same reaction in the absence of silicon, they determined the activity coefficient of oxygen, f0, on the basis of the definition K3 = (H2O)/ (H2)f0 [% 0] where K, is the equilibrium constant and f0, is taken as unity in the pure Fe-0 system. Similarly values of fsi were deduced from results on reaction 2. In a more recent study" of analogous reactions in the system Fe-A1-0, it was found impossible to reconcile the results on reaction 3 with Dastur&apos;s data; accordingly the latter were ignored and the equilibrium results were extrapolated to find a value of K, at zero concentration of aluminum. This procedure failed to locate the cause of the discrepancy but it did yield reasonable values of activity coefficients. It also avoided introduction of the complex empirical relation between the oxygen activity coefficient and the concentration of the added element. The same type of discrepancy exists for system Fe-Si-0.&apos; In the earlier paper an attempt was made to fit both sets of data by a single curved line (Fig. 6 of ref. l), the form of which is contrary to the theoretical requirement of a finite slope at infinite dilution. In the light of experience on the Fe-A1-0 system the discrepancy must be recognized as one which can be resolved only by more refined measurements. Accordingly Figs. 6 and 10 are retracted. It is pointed out also that until the discrepancy is resolved Figs. 7, 8, and 11 are subject to some uncertainty. Qualitatively the following conclusions still appear valid: 1—The activity coefficient of oxygen is reduced by addition of silicon. 2—In dilute solutions the activity coefficient of silicon increases with its concentration. 3—With respect to equilibrium in reaction 1, the above effects are approximately compensating. The discussion of K&apos;1 in the previous paper requires no revision. It was pointed out that the constancy of the product [% Si] [% 0]² ndicated a compensating effect of the activity coefficients of silicon and oxygen. Therefore, as a very good approximation, K1 = K&apos;1 and the following average values are suggested both for K, and K&apos;, at the temperatures 1550°, 1600°, and 1650", respectively, 1.0x10-", 2.8~10-" and 5.5 ~lo-&apos;. Revision of the thermodynamic treatment is necessitated by the recent appearance of new data, based on a combination of combustion and solution calorimetry,&apos; which yields for the heat of formation of low-cristobalite from the elements, the value —209,330 ±250 cal per mol at 25°C. This is about 4000 cal larger than the value previously accepted. The new value for cristobalite is used, together with Kelley&apos;s tables of high-temperature heat contents" and entropies and with Korber and Oelsen&apos;s&apos; heat of fusion of silicon to obtain the following equation for the standard free energy of cristobalite in the temperature range 1700" to 2000°K: Si (1) + 02 (g) = Si02 (crist.); ?F° = -217,700 + 47.OT [4] The free energy of solution of 0, in liquid iron is:8 O2 (g) = 20 (in Fe); AF° = -55,860 - 1.14T [5] and these two equations are combined to give: Si (1) + 20 = SiO, (crist.); AF° = -161,840 + 48.14T [6] ?F°1873 = -71,700 cal. From the experimental value of K, = 2.8x10-5, Si + 20 = SiO2 (crist.); ?F°1873 = -39,000 cal. [7] The combination of Eqs. 6 and 7 yields the free energy change when liquid silicon dissolves in iron to form the dilute solution of unit activity (1 pct). Si (1) = Si; ?F°1873 = -32,700 cal. [8] The heat effect in this process according to Korber and Oelsen&apos; is an evolution of 28,500 cal per gram

Jan 1, 1954

By J. J. Gilman

The data presented indicate that the critical shear stress and strain-hardening Thedatapresentedrate of a zinc monocrystal depend on the orientation of its slip direction with respect to its external boundaries. The tendency of a crystal to form deformation bands also depends on its shape. THE plastic behavior of pairs of zinc monocrystals in which both members of the respective pairs had the same orientation with respect to the longitudinal axis, but each had different orientations with respect to their rectangular external shapes, were compared in this investigation. The purpose of the investigation was to see what influence the shape or surface of a zinc crystal has on its mechanical properties. In a previous investigation of triangular zinc monocrystals,1 anomalous axial twisting was observed which seemed to be related to the triangular shape of the crystals. Wolff,&apos; in 400°C tensile tests of rectangular rock-salt crystals bounded by cubic cleavage planes, found that, of the four equivalent slip systems, the two with the "shorter" slip directions yielded and produced slip lines at lower stresses than the other two. This observation and the work of Dommerich³ as formulated by Smekal4 as a "new slip condition" for rock-salt: "among two or more slip systems permitted by the shear stress law, with reference to the formation of visible slip lines by large individual glides, that slip system is preferred which has the shortest effective slip direction." More recently, Wu and Smoluchowski5 reported essentially the same effect for ribbon-like (20x2x0.2 mm) aluminum crystals at room temperature. Experimental Chemically pure zinc (99.999 pct Zn), purchased from the New Jersey Zinc Co., was the raw material. Glass envelopes, containing graphite molds and zinc, were evacuated while hot enough to outgas the graphite but not melt the zinc. At a vacuum of about 0.2 micron the envelopes were sealed off and then lowered through a furnace at 1 in. per hr so as to melt and resolidify the zinc and produce mono-crystals. One-half of one of the molds is shown in Fig. la. Each mold consisted of four pieces from a cylindrical graphite rod that was split longitudinally and transversely at its midpoints. Rectangular milled grooves 0.050 in. deep and % in. wide formed the mold cavity when the split halves were assembled with twisted wires. Fig. lb shows the specimen shape obtained when the top and bottom mold-halves were rotated 90" with respect to each other. Good fits prevented leakage and excess zinc was necessary to provide enough liquid head to fill the mold completely. In removing soft crystals from the molds it was impossible to avoid small amounts of bending. However, manipulations were carried out whenever possible with the crystals protected by grooved brass blocks. All specimens were annealed prior to testing. From the top and bottom sections of each crystal, X-ray specimens and tensile specimens 7 to 8 cm long were sawed. The tensile specimens were annealed inside evacuated tubes for 1 hr at 375°C. Next the crystals were cleaned and polished by 2-min dips in a solution of 22 pct chromic acid, 74 pct water, 2.5 pct sulphuric acid, and 1.5 pct glacial acetic acid.&apos; Cleaning was followed by a 10-sec dip in a 10 pct caustic solution, then washed in water and alcohol, and dried. This treatment results in a bright surface covered by an invisible oxide film. The testing grips were a slotted type with set screws and were supported in a V-block during the mounting operations in order to avoid bending the crystals. A schematic diagram of the recording tensile-testing machine is shown in Fig. 2. The machine has been described elsewhere.&apos; The head speed was 0.3 mm per sec for all tests. The crystal orientations were determined by the Greninger X-ray back-reflection method with an estimated accuracy of 1. Description of Crystal Geometry A schematic picture of a rectangular zinc mono-crystal is shown in Fig. 3. ABD designates the front edge of a basal plane (0001) of the crystal, the only active slip plane for zinc at room temperature. Of the three possible (2110) slip directions, the active one is indicated by an arrow. Cartesian coordinates are taken parallel to the specimen edges. The normal, n, to the basal plane (n is parallel to the hexagonal axis) has the direction cosines a, ß and ?. X0 = 90 — y is the angle between the longitudinal axis and

Jan 1, 1954

By W. O. Philbrook, K. Natesan

The oxidation kinetics of spherical pellets of zinc sulfide made from Santander concentrates were studied using a thermogravimetric technique. The experiments covered a temperature range-. of 740" to 102O°C, 0-N mixtures varying from 20 to LOO pct O2, and pellet diameters between 0.4 and 1.6 cm. Mathematical models were formulated to Predict the reaction rate on the assumption that a single transport or interface reaction step was rate -controlling. Analysis of the data indicated that the process of oxidation was predominantly controlled by transport through the zinc oxide reaction-Product layer. ROASTING processes, which are reactions between solids and gases, are very important because they are employed in the production of a number of basic metals. These processes are highly complicated, and one needs to consider the transport phenomena of heat and mass between the solids and gases in addition to the kinetics of various chemical reactions involved. Because of such complications there is a lack of knowledge concerning the rate-limiting factors, which may strongly depend on temperature, particle size, gas composition, and solid structure. The oxidation of zinc sulfide, which is of commercial importance in zinc production, falls into this class of reactions. The major goal of this work was to elucidate the roles played by different process variables, such as reaction temperature, gas composition, pellet size, and pellet porosity, on the kinetics of oxidation of single pellets of zinc sulfide. Roasting of zinc sulfide single particles has been a subject of both experimental and theoretical investigations.&apos;-&apos; The reaction is exothermic and may be considered to be irreversible. Such a reaction has been found to proceed in a topochemical manner. In other words, as the reaction proceeds, a progressively thicker outer shell of zinc oxide is formed, while the inner core of unreacted sulfide decreases. It has been found experimentally, both in the present work and in the previous investigations,1-9 that the particle retains its original dimensions and the process requires transport of gaseous oxygen across the porous product layer for continued reaction. The reaction may be represented by ZnS(s) + 3/2 O2(g) = ZnO(s) + SO2(g) [1] The solid product considered here is only zinc oxide, since the diffraction patterns of zinc sulfide pellets oxidized partially at &apos;798" and 960°C showed K. NATESAN, Junior Member AIME, formerly St. Joseph Lead Fellow, Department of Metallurgy and Materials Science, Carnegie-Mellon University, Pittsburgh, Pa., is now at Argonne National Laboratory, Argonne, Ill. W. 0. PHILBROOK, Member AIME, is Professor of Metallurgy and Materials Science, Carnegie-Mellon University. This paper is based on a them submitted by K. NATESAN in partial fulfillment of the requirements for the Ph.D. degree in Metallurgy and Materials Science at Carnegie-Mellon University. Manuscript submitted December 2, 1968. EMD lines corresponding to original zinc sulfide and the newly formed zinc oxide. OXIDATION MODEL The generalized model for gaseous oxidation of zinc sulfide is illustrated in Fig. 1. This depicts a partially oxidized sphere of zinc sulfide in a gas stream surrounded by a laminar film of gas. The spherical sample of zinc sulfide of unchanging external radius r0 is suspended in a flowing gas stream of total pressure PT and composition specified by the partial pressures of the individual components. Partial pressures of the gaseous species in the bulk gas phase, at the exterior surface of the pellet, at the ZnS/ZnO interface, and at equilibrium for Reaction [I] are identified by the superscripts b, o, i, and eq, respectively. The overall reaction involves the following ~te~s:&apos;~&apos;~&apos; Step 1. Transfer of reactant gas (oxygen) from the bulk gas stream across the gas boundary layer to the exterior surface of the pellet and the reverse transfer of the product gas (sulfur dioxide). Step 2. Diffusion and bulk flow of oxygen from the pellet surface through the product shell (ZnO) onto the ZnS/ZnO interface and the reverse transfer of sulfur dioxide. Step 3. Chemical reaction at the interface, which results in consumption of oxygen gas and generation of sulfur dioxide gas and heat; at the same time the _________ PARTICLE SURFACE / x^^^^n^X / MOVING INTERFACE core-----/ sJSNxy " /T^T^02 \ V\V$\ ^NWX/ "*/— GAS BOUNDARY x. \\ZnO SHELLV/ / \^ . / &apos; ^ BULK GAS --------N_______ _____,------p£ w \ P« / (f> \ / a \ <i) / <----------------- _(o) ^^--------------(b) °- pso, pso2 ro ri 0 ri ro RADIAL POSITION Fig. 1—Generalized model for oxidation of a sphere of zinc sulfide.

Jan 1, 1970

By J. M. W. Mackenzie, C. J. Wood

In attempting to describe the size classification performance of a hydrocyclone, most workers have elected to use either an equilibrium orbit theory or an non-equilibrium orbit theory. The equilibrium orbit theory has been used by the majority of workers including Lilge,&apos; Bradley; and Yoshioka and Hotta. In applying this theory, it is argued that particles in the body of a hydrocyclone attain an equilibrium radial position where the drag force on the particle resulting from the inward radial fluid velocity is balanced by the outward centrifugal force caused by the tangential component of fluid flow. When considered over the full height of the hydrocy-clone, attainment of this radial equilibrium orbit results in the particle following a conical equilibrium envelope. It is then argued that if this envelope lies outside the envelope of "zero vertical velocity," the particle will report to the underflow, while if the equilibrium envelope lies inside the envelope of "zero vertical velocity," the particle will report to the overflow or vortex finder product. The d50-sized particle which reports in equal quantities to the underflow and overflow is assumed to correspond to particles whose equilibrium envelope is coincident with the envelope of "zero vertical velocity." In considering the equilibrium orbit theory, it is apparent that the horizontal position of the particles in the feed inlet pipe should have no effect on their ultimate destination on the hydrocyclone. Each particle should attain an equilibrium position which depends on the density, size, and shape of the particle; the density and viscosity of the fluid; and the flow patterns within the hydrocy-clone. The nonequilibrium orbit or unsteady state theory has been largely developed by Rietema4 and Mizrahi.6 Mizrahi has listed four main objections to the equilibrium orbit theory. These objections center on the short residence time in the hydrocyclone, the fact that the experimental classification curve is much less sharp than is theoretically predicted, and the absence of negative efficiency conditions in hydro cyclones operating on a feed material which is much finer in size than d50. Proponents of the nonequilibrium orbit theory argue that for a particle to discharge with the underflow it must have sufficient outward radial velocity to reach the downward-flowing region close to the hydrocyclone wall in which the flow lines are parallel to the wall and the ratio of vertical to radial velocity is constant. It is then postulated that a d50 particle entering the cyclone at the center of the feed inlet will just reach this downward-flowing region as it reaches the apex. Thus for uniform distribution of particles across the feed inlet, half the d50 particles—that is, those injected in the half of the inlet area nearest the cyclone wall —will report to the underflow while those injected in the other half will not reach the downward-flowing region and will be carried inward to the center of the cyclone and thus report in the overflow. The exact thickness of the down-ward-flowing region of fluid adjacent to the outer wall of the hydrocyclone is uncertain but Mizrahi considers it to be equal to the apex radius minus the air core radius. Particles larger than d50 have a greater outward centrifugal force acting on them than the d50 particles and may reach the wall even if injected at a distance from the wall greater than Di/2 (Di is inlet diameter). Conversely, particles smaller than d50 may not reach the wall even if injected at a distance less than Di/2 from the cyclone wall. Since the equations put forward by the proponents of both theories yield approximately the same values of d50, it is not possible to decide between these theories by measurement of d50. It should be possible however to examine the theories by injecting a small stream of solids into the feed inlet of a hydrocyclone running on clear water. If the efficiency or classification curve is measured for various horizontal injection positions, then the curves should be coincident if the equilibrium orbit theory holds. If, however, the unsteady state theory describes the cyclone operation, then the classification curves should show finer d50 sizes for particles injected close to the cyclone wall. Experimental A 6-in.-diam hydrocyclone with geometry as in Figs. 1 and 2 was used. Quartz particles were injected as a 50% by wt pulp via an 1/8-in. steel probe. For each in-

Jan 1, 1971

By R. A. Oriani

The partial molal volume of hydrogen is one of the parameters that describe the elastic interaction between the solute and the stress fields about inclusions, dislocations, and cracks. As such the partial molal volume is probably of importance in the elucidation of phenomena such as hydrogen embrittlement and hydrogen yield point. A knowledge of this quantity would also be helpful in thinking about the state of dissolved hydrogen in iron. However, because of the very low lattice solubility of hydrogen in iron the usual ways of determining the lattice expansion are not practicable. It is therefore of interest to apply the thermodynamics of stressed bodies to two sets of measurements of the effect of elastic stress upon the permeability of hydrogen in order to deduce a value of the partial molal volume, VH, of hydrogen dissolved in a iron. Beck ..&apos; and previously de Kazinczy, observed that a uniaxial tensile stress increases the permeability of hydrogen in iron and in various steels. Beck et 01. employed Armco iron and A.I.S.I. 4340 steel, whereas de Kazinczy used a steel the composition of which was 0.13 C, 0.23 Si, 0.46 Mn, 0.006 P, and 0.038 S. Upon releasing the stress the permeability increment disappeared if the stress was below the elastic limit. Both investigators employed cathodic charging to introduce the hydrogen. de Kazinczy measured the permeation through a thin-walled tube by collecting the gas, whereas Beck et al. measured the permeation through sheets of various thicknesses by a very sensitive electrochemical technique. Both investigators measured the steady-state permeation at constant rate of hydrogen ion discharge, and Beck measured in addition the hydrogen diffusivity by a time-lag technique which is independent of the boundary conditions. Beck et al. and de Kazinczy found a linear relationship between log (J,/Jo) and the stress, where Ju/Jo is the ratio of the flux of hydrogen when the metal is under uniaxial tensile stress, a, to the flux under zero stress, for the same temperature and charging current. Beck et al. found in addition that the diffusivity of hydrogen is not changed by stress. Both investigators concluded that the observed change in permeability is due to an increase in hydrogen concentration, and furthermore that the increase in concentration is due directly to the thermodynamic effect of stress upon concentration. Accepting this assessment of the situation for reasons given below, one may use the equation3j4 in order to evaluate I/H, the partial molal volume of hydrogen. This equation is valid for the domain of a/E «¦ 1 (where E is the Young&apos;s modulus) and under the assumption that hydrogen expands the lattice isotrop-ically. From the data of Beck el al, one calculates V7H - 2.0 cu cm per g-atom, and from those of de Kazinczy one obtains 1.8 cu cm per g-atom. That the increase of concentration with stress is indeed of thermodynamic origin is attested to by the facts that the experimental results conform to the thermodynamic relation, Eq. [I], and that the results are the same whether a pure iron1 or each of two different steels172 is used. Neither of these facts wou1.d necessarily be expected if the effect of stress were, rather, to increase the ratio kn/k, of the kinetic factors of the following competing reactions: H(ads) — H (dissolved) Such a change of kinetics at the surface could be an alternative explanation of the effect of stress on the permeability. Although this writer does not deem this explanation to be the correct one for the reasons given above, it must be admitted that unambiguous proof that the phenomenon has a thermodynamic origin does not yet exist. Two kinds of experiments may be suggested. One is to plate a variety of metals on the input surface of the steel and repeat the stress experiment at a variety of hydrogen charging currents. The other is to employ somewhat thicker specimens in order to be able to apply uniaxial compressive stress. Eq. [I] shows that ln(c,/c,) depends on the sign of the stress, but it is difficult to see a physical basis for which k2/kl would depend on the sign of a. The present value of V^ in a iron agrees with phragmen&apos;s5 estimate, which he based on comparisons with the lattice expansion by hydrogen of titanium, zir-

Jan 1, 1967

By R. E. Reed-Hill

The lattice reorientations in (1011) and (1013) twins of pure magnesium have been investigated using polarized light. Both forms (Ire subject 20 almost complete second-order twinning on the (1012) plane of the first-order twin. The observed deviations of composition planes by 6 and 3 deg, respectively, from coherent twinning planes are caused by second-order twinning. The experimental data indicate that (1011) and (1013) are reciprocal twins with a twinning shear 0.136. In a previous paper1 it was shown that the primary fracture mechanism in single crystals of magnesium strained in tension parallel to the basal plane is parting or fracture inside twins. In the temperature interval 25oto286oC, the observed twinning form, dominant in fracture, was a very small twin which formed in bands. Because these twins were very small and appeared in extensively deformed regions they did not lend themselves to X-ray analysis. Lacking Cou-ling and Pearsall&apos;s2 recently reported polarized light technique for magnesium, the twinning plane indices (K1) were originally determined by two surface composition plane measurements. This plane fell in a major zone (axis < 1120>) at an angle of 55.75 deg to the parent crystal basal plane. Because its habit deviated by 6 deg from{l0ll), 61.9 deg, the experimental data per se were not consistent with simple (1011) twinning and, for expedience, the twin was designated with habit plane indices (30341, 54.5 deg, representing the lowest set of indices corresponding to measured angles. Couling, Pashak, and sturkey3 have also found bands of reoriented lattice with a similar habit in polycrystalline specimens of magnesium and certain dilute magnesium alloys. These bands are significant because their formation in large numbers during plastic flow permit specific magnesium alloys to undergo very extensive deformation by cold rolling. Using polarized light2 they showed that the basal plane in the reoriented material was nearly parallel to the band habit and, as a result, proposed a mechanism for band formation involving a double twinning process in which (1011) twins form and then retwin according to (1012). Because of the obvious similarity between the twin bands observed in single crystals and in polycrystalline specimens, it was decided to investigate if the two phenomena were not identical and, if possible, to verify the retwinning hypothesis. The present paper is a report of this investigation and shows that the twins with the (3034) habit correspond closely to retwinned (l011) twins. Evi- dence is also given for an analogous retwinning process in (1013) twins. EXPERIMENTAL PROCEDURE Rectangular single-crystal specimen deformed in tension (stress axis in the basal plane parallel to [1010], as previously described,4 were polished electrolytically by Jacquet&apos;s method5 and etched in acetic picral.2 All twins studied in this investigation belong to a major zone, whose axis, [1210], was perpendicular to both stress axis and two sides of each specimen [(1210) surfaces]. These latter contain the plane of shear of the twins and measurements of the basal plane trace of twins on these surfaces determines the lattice orientations of the twins. The position of the basal plane in each case was determined with a polarizing microscope using a modification of the technique of Couling and Pearsall.2 For each twin the four positions of maximum extinction were measured, the data averaged, and then the pair of extinctions corresponding to the basal plane was determined by rotating the microscope stage and observing the position at which the color changed from orange to blue with a gypsum red, first-order plate inserted between the crossed Nicol prisms. EXPERIMENTAL RESULTS (1013) Twins—In general, especially in speci-mens deformed at 150°C, (1073) twins appear in greater numbers and larger sizes than (1011) twins, and the lattice reorientation inside these twins is therefore easier to study and measure. Fig. 1 shows an area of an unetched and unpolished (1210) crystal surface containing a number of (1073) twins sloping upward to the right at about 29 deg with the basal plane of the original crystal (horizontal direction). Slip line segments may be seen in both the parent crystal (running horizontally) and in the twins (sloping downward to the right at approximately -22 deg with the horizontal). As may be seen in Fig. 2, the slip lines in the twin are not at the proper angle (64 deg from basal plane of the

Jan 1, 1961