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By O. D. Sherby, J. L. Lytton, C. R. Barrett

Randomly oriented polycryslalline copper of 99.995 pcl was tested in tension at temperatures of 626o, 496o, and 406o. The gvain-size mnge investigated was from 0.03 to 0.7 mm. Grain sizes were produced by two techniques: 1) varying the amount of prior cold work and the amealing time at constant annealing temperature so as to obtain various vecrystallized grain sizes with minimum grain growth, and 4 holding the prior cold work constant while varying the annealing time or temperature so as to obtain varying grain sizes by grain growth. Polycrystalline samples (grain size of 0.03 mm) with a strong. [001](100) texture were also studied. The relationship between the steady-state creep rate, Es, and pain size was found to be the same indepentent of the technique used to prepare the various grain sizes. For specimens with grain diameters above about 0.1 mm ea zuas esse)ztiallj~ independent of grain size, while for smaller grain diameters Cs increased slightly with decreasing grain size. Strongly textured polycrystalline copper, which contained low-angle grain boundaries, exhibited steady-state creep rates that were slightly lower than those observed in randomly oriented copper, of the same gain size. The results are explained by conside?%ng- the contribution of grain boundary shearing to the total strain and the effect of grain size on the resulting creep substructure. EXPERIMENTAL observations concerning the influence of grain size on steady-state creep rates are varied and oftentimes conflicting. Numerous early investigators found that an increase in the grain size resulted in a decrease in the high-temperature steady-state creep rate, i,.'-" Other workers have foundthat ef decreases with increasing grain size up to some optimum grain size and then increases with a further increase in grain size.'- '' It has been suggested that es, decreases with an increase in grain size only because the range of grain sizes studied normally lies to the left of the grain size for optimum creep resistance. However, sherbyl2 and Feltham and his co-worker13, 14 have found that even for small grain sizes 2, does not always decrease with an increase in grain diameter but may be proportional to the square of the grain diameter. A possible explanation for the different creep rate-grain size relationships which have been observed is that in most experimental studies different grain sizes have been prepared by annealing at various temperatures. For metals in which the impurity concentration is high (greater than about 0.1 at. pct) this type of

Jan 1, 1968

By S. Jana, C. M. Wayman

The reverse transformation of bcc martensite to the fcc phase was studied in an Fe-33.95 wl pct Ni alloy by nzeans oj dilatometry, melallography, and electron microscopy. Upon "slozc" heating (-1°C per min) length cJmnge us temperature plots showed u gradual contracLion over the temperature range 200" to 280"C ,followed by a more abrupt contraction beginning a1 -280°C. Howet,ev, zchen the heating rate was increased -4°C per tnin, no gradual contraction was observed and only the abrupt contraction starting at -2BO"C was found. Thus on slower heating- the AS "temperature" for the subject alloy, unlike the MS temperature, is better defined as a range of temperatures. Both optical and transmissiorl electron microscope observations showed that some of the martensite plates exizibited a partial loss of transformation twins during reversal. The midvib region of the martensite plates disappeaved relatively early duirng the reversal. Metallographic observations slowed that the earliest detectable stage of the rezlerse tvansforrvration begins (axd Moues inulardly) at The Martensens i te - parent interface. At higher temperatirres, the. formation of martensitically reversed jcc plates within the bcc martensite plales was observed. It is concluded that the reverse transformation consists of a diffusion less process (martensitic); but this is ps-obably aided by a prior or simultaneous dijjusiorz-comltvolled process, at leasl in the case of slower heat-ing' experiments. ALTHOUGH numerous investigations have dealt with the parent-to-martensite ("forward") transformation (fcc — bcc) in Fe-Ni alloys, comparatively little is reported on the ("reverse7') martensite-to-parent transformation.'-4 Even though such reverse transformations have been studied in detail in some nonferrous systems, one of the difficulties of studying the reverse transformation in most ferrous mar-tensites is that the martensite decomposes by tempering during heating. However, carbonless Fe-Ni alloys do not exhibit this difficulty since the transformation in these alloys is completely reversible. The present investigation represents an attempt to shed more light on the nature and mechanism of the martensite-to-parent transformation. 1) EXPERIMENTAL PROCEDURE 1.1) Alloy Prepatation. Fe-Ni alloys of compositions near 34 wt pct Ni were prepared from zone-refined iron (99.994 wt pct Fe) and high-purity nickel (99.999 wt pct Ni) by induction melting in recrystallized alumina crucibles in an argon atmosphere, with prior vacuum evacuation to 10"3 mm Hg. The alloys were homogenized by induction stirring in the molten state for 5 min. After solidification, the alloys were further homogenized in evacuated quartz capsules for 96 hr at 1230°C. 1.2) Dilatometry. Slices of the ingot were hot-forged (750°C in air) into approximate rod form and these specimens were then hot-swaged (750°C in air) into long cylindrical rods 0.55 mm diam. From the rods, specimens about 1 in. long were cut. These were then vacuum-annealed for 24 hr at 1200°C, cooled to room temperature, and subsequently transformed to martensite in liquid nitrogen (whereby about 40 pct transformation was obtained). Dilatation measurements were made by observing length changes in a vacuum dilatometer with an externally mounted LVDT sensing element. 1. 3) Preparation of Electron Microscope Specimens. Slices of the ingots were cold-rolled (with intermediate vacuum anneals) to -0.020 in. Out of these rolled sheets, specimens (about 1 by 1 in.) were cut. These were then vacuum-annealed, transformed to martensite by cooling in liquid nitrogen, and subsequently heated from room temperature to various temperatures to effect either partial or complete reverse transformation. These specimens were then chemically polished to 0.002 in. in l:l HsOz (30 pct) and &PO4 (85 pct) solution, and thinned to electron transparency in an electrolyte consisting of 150 g CraOs, 750 ml glacial acetic acid, and 30 ml ~~0.~ Observations were made with a 100-kv Hitachi HU-11 electron microscope equipped with an HK-2A tilting device. 1.4) Optical Microscopy. Metallographic observations were made with a Leitz MM5 metallograph on the same 0.020-in. sheet specimens as were used for electron microscopy and on bulk specimens which were 0.2 in. or more on a side. The chemical thinning solution when cooled below 20°C also served as an etchant for this alloy. Observations of surface relief were made with a Zeiss interference microscope employing a Thallium light source of wavelength 0.54 p. Specimens for interference studies were prepared by two-stage polishing on Buehler vibromet polishers using 0.3 and 0.05 p alumina abrasives. 2) EXPERIMENTAL RESULTS 2.1) Comparison of the MS,AS, and Af Tempera-tures wTth Previous Re sults. The AS aLd Af tempera -tures of several Fe-Ni alloys were determined dila-tometrically. The MS temperatures of the same alloys were determined by continuously lowering the temperature using a mixture of isopentane and liquid nitrogen and observing the highest temperature at which a prepolished specimen showed surface upheavals. For the present the As temperature is defined as the temperature at which an abrupt decrease in length occurs in the dilatation plot. The Ms,As7 and A determinations in the present investigation and those of Kaufman

Jan 1, 1968

By M. J. Blackburn

The ordering reaction and its effect on dislocation awangements in alloys based on Mg3Cd has been studied by transmission electron microscopy. Ordering occurs by the growth of ordered domains until they impinge, thus producing an antiphase domain boundary (APB) network. In the disordered alloy, slip is confined to the basal plane while in the ordered condition slip occurs on the basal, prism, and pyramidal planes. Superdislocations have been identuied on these planes and their origin and expected spacings are discussed and compared with the observations. The APBs between the dislocation pairs have been resolved and have proved useful in the identification of superdislocations. Observed slip structures are related to the changes in mechanical properties produced by ordering. At high temperatures magnesium and cadmium form a continuous series of disordered hexagonal solid solutions. At lower temperatures three ordering reactions occur; two based on the compositions Mg3Cd and MgCd3 are transformations to DO19-type superlattices while alloys based on the composition MgCd transform to a B19 lattice. The ordering process in alloys near the composition Mg3Cd has been studied by several workers'-4 and it has been shown to be a first-order type transformation. The variation of mechanical properties with the degree of order and temperature have been reported in some detail by Stoloff and Davies.5 It was shown that the disordered alloy was stronger and less ductile than the ordered alloy, the differences being attributed to changes in the number of active slip planes and to the presence of short-range order in the disordered alloy. In this investigation the ordering reaction has been qualitatively followed by transmission electron microscopy. The effect of this ordering transformation on the dislocation arrangements in deformed specimens has been studied in some detail. EXPERIMENTAL Alloys were melted in a stainless-steel crucible under a flux and chill cast; both melting and casting were performed in an argon atmosphere. The ingots were hot-rolled and tensile specimens cut from the resultant strips. Some large-grained specimens were grown by the strain-anneal method. Heat treatment was carried out in inert atmosphere furnaces and in oil baths at the lower temperatures. Thin foils for transmission electron microscopy were produced by electropolishing in a cooled solution (temp = -40°C) containing 50 cu cm of nitric acid and 180 cu cm of methanol at a potential of 10 v. The ordering reaction was followed by transmission electron microscopy, X-ray, and electrical resistivity measurements but this paper will be concerned chiefly with the electron-microscopy results. Much of the work described in this paper was performed on an alloy containing 26.10 at. pct Cd although two of the micrographs are taken from work on a 25.55 at. pct Cd alloy. RESULTS i) The Quenched Solid Solution. Specimens which were quenched from above the critical temperature showed diffuse superlattice reflections. sark-field analysis on these reflections failed to reveal the presence of ordered domains and thus the superlattice reflections were assumed to arise from regions of short-range order. Quenching from temperatures of 400" to 450°C results in the formation of dislocation loops and helical dislocations. Such defects have been observed and analyzed in detail in several hexagonal metals6-' and as the crystallography and interactions of such loops appear similar in this alloy they will not be reported in detail. Fig. 1 shows a high density of loops

Jan 1, 1968

By John A. Emery

The Pea Ridge iron ore deposit near Sullivan, Missouri, is a dike-like mass of magnetite enclosed in Precambrian porphyries. The ore body tops at the Precambrian surface at a depth of 1300 feet below the present surface and extends to an unknown depth. It dips nearly vertically, intersecting the dip and strike of the enclosing porphyries at an extremely sharp angle. Faulting, both pre- and post-ore, appears to be of minor consequence, and present knowledge indicates that no preferred structural conditions existed prior to emplacement. The ore body is composed of magnetite with specular hematite, quartz, apatite, and pyrite occurring as accessory primary minerals. Specular hematite in appreciable quantities occurs on parts of the cap and the footwall of the ore body. Fresh porphyry breccia is enclosed in the magnetite along the hanging wall and in the western portion of the ore body. Hanging-wall quartz-amphibole and footwall quartz-hematite occur as replacements of certain porphyries. Further alteration has caused sericitization of parts of these zones. The ore deposit is interpreted as having been formed essentially by a single injection of a magmatic differentiate with hydrothermal end phases forming the quartz-amphibole and quartz-hematite portions of the deposit.

Jan 1, 1968

By J. J. Tietjen, D. Richman

Single-crystal Gap lms been epitaxially grow from the vapor phase at a rate oJ 3 p per nzin without encountering a7Zy low-ang-le grain boundaries or debwading- the electrical properties of the material. This growth rate exceeds any value previol~sly reported for the vapor phase growth of Gap. In pure material, mObilities ns high as 175 sq cm per U-sec at room tenzperature and 1450 sq cm per v-sec at 77°K have been obtained. These values are anLong the highest that have been attai)led for this material. For the first time, Gap possesses a number of important properties which make it well-suited for use in electro-optic modulators. First, the transverse electro-optic effect is operable in this material, which makes it possible to increase the path length of the modulated iron doping of Gap has been achieved; this results i?z resistivities of approximately 10" ohm-cm. The problelrls of residual strain and isolated shorting paths in these crystals have been partially solved. Electro-optic modulation of visible radiation has been demonstrated with this material. It is anticipated that further improvement with regard to the probleins of strain and shorting paths will result in a practical Gap electro-optic modulator. radiation without increasing the applied voltage. In addition, this permits the use of thin crystals so that relatively small voltages are needed to provide the requisite high electric fields. Second, GaP is a cubic crystal and therefore does not introduce critical optical-alignment problems associated with birefrin-gent crystals, such as ammonium dihydrogen phosphate (ADP), and potassium dihydrogen phosphate

Jan 1, 1968

By R. K. Ham, M. L. Wayman

TD-Nickel has been broken in tension and in fatigue at voom temperature. Rod specimens failed in tension by necking, with axial cracks attributed to voids elongated in the extrusion direction. Fatigue specimens failed in shear. Thin-film electron microscopy showed that the subgrain structure of TD-Nickel was very stable, and that particle-matrix detachment was very difficult, in tension and fatigue. TD-Nickel softened slightly during fatigue but had a high fatigue ratio (0.5at 10' cycles). Fractography suggested that Stage I fatigue crack propagation is greatly extended in TD-Nickel. Td-NICKEL* is a dispersion of 2 pct by volume of thoria (ThO2) in nickel, produced by powder-metallurgical methods including compaction, sintering, and extrusion. The spherical thoria particles, which may have a mean diameter of a few hundred angstroms, are dispersed with a mean planar spacing of a few thousand angstroms. By a combination of cold working and annealing, a subgrain or cell structure of dislocations intimately associated with the dispersion can be produced.' This gives the material useful tensile properties which are extremely resistant to exposure to high temperatures.'-= At the same time, the material shows considerable ductility.3'4 At the beginning of the present work, it was considered of great interest to investigate the mechanical stability of TD-Nickel under conditions of fatigue. On the one hand, materials which derive strength from a cold-worked structure are unstable in that they are susceptible to fatigue softening: in addition, the presence of discontinuities such as the particle-matrix interfaces might be expected to assist in the initiation and propagation of fatigue cracks, in that they may provide local concentrations of internal stress and sites for the initiation of voids." On the other hand, the substantial ductility of TD-Nickel suggests that if it obeys Coffin's relation8 (or the more refined form proposed by Manson9) it should have good fatigue resistance. The initial purpose of this investigation was to assess the importance of these factors. Also, relatively little fundamental work has been done on the mechanism of fatigue in dispersion-strengthened materials. Work on overaged A1-4 pct CU10-12 revealed a very large Bauschinger effect indicative of internal stresses at the particles, and very great fatigue hardening1' presumably due to the multiple slip stimulated by these internal stresses, followed by softening which was initially due to softening in the matrix, but later might have arisen from cracking at the particle-matrix interfaces. The study of overaged Al-4 pct Cu could not settle this latter point by the electron microscopy of thin films, since the dispersion is too coarse. A previous study of the fatigue of internally oxidized copper13 was complicated by inter granular failure, attributed to oxide particles at grain bouhdaries; internal oxidation of single crystals, however, improved their fatigue properties.'3 Investigations of SAP (sintered aluminum powder) are complicated by the complex particle shapes, and the possibility of continuous internal oxide films.14 It was hoped to avoid these difficulties with TD-Nickel, which had the further advantages that it was commercially available and suitable for study by the thin-film technique. 1) MATERIALS AND EXPERIMENTAL PROCEDURE TD-Nickel was purchased from the Driver-Harris Co. as 3/9-in.-diam rod which had been extruded, swaged, and "stress-relieved" (normally at 1010°C for 1 hr). Continuous-radius fatigue specimens with a minimum diameter of -0.1 in. were ground to shape and electropolished in 40 pct phosphoric, 35 pct sul-furic, 25 pct water at 25oC, with a stainless-steel cathode, at -6 v. Fatigue tests were carried out at room temperature with a Sonntag SF-1-U machine operating in push-pull at 1800 cycles per min, and in an Instron TT-C-L modified for reversed stressing at 26 cycles per min as described elsewhere.10 Round tensile specimens were ground with 0.85-in. gage lengths of 0.135 in, diam, electropolished, and tested in a Tinius Olsen hydraulic machine. The surfaces of fatigue specimens were examined with a Reichert metallograph. Discs for electron microscopy with a Siemens Elmiskop I were spark-cut 0.01 in. thick with a modified Servomet 11 employing a tool of moving molybdenum wire, cleaned in 50 pct acetic, 30 pct nitric, 10 pct phosphoric, and 10pctsul-furic at 85oC, and thinned by the window method in the electropolishing solution at -20°C and -6 v. Two-stage replicas (parlodion, then Pt-50 pct C self-shadowed at 40 deg) were taken from fatigue fracture surfaces for electron microscopy. Plane sections parallel to the specimen axis and containing the direction of fatigue crack propagation were polished, etched with Carapella's reagent, and examined optically. Transmission Laue X-ray photographs of as-received material electropolished to a point were used to determine preferred orientation. 2) RESULTS 2.1) The Structure of As-Received Material. Grains -1 µ diam and elongated 20 to 30 u in the direction of the rod axis were observed, With' elongated "intergran-ular" voids (-4 p diam and -90 µ long and identified as such using longitudinal and transverse sections and

Jan 1, 1968

By J. E. Spruiell, F. H. Patterson, B. F. Shuler

The microstructures and textures developed by the working of high-purzly thermochemically deposited tungstem sheet have been inuesligated. Greater than 60 pct reduction was required to deslroy the columnar grain structure which existed in the as-deposited sheet. With increasing reductions the texture gradu-ally charged from the initial as-deposited orientation with (100) parallel to the sheet normal to a (100}(011) ideal ovienlation with some spread about the rolling direction. This texture was retained after recrystalli-zation a1 2000°C. THE processes for depositing tungsten by hydrogen reduction of tungsten hexafluoride have been under development for the past several years.1,2 The nature of the deposition process is such that the as-deposited material contains a highly oriented columnar grain structure perpendicular to the deposition substrate. This well-defined columnar structure may be useful in certain applications293 but a wrought or equiaxed structure may be desired for some components such as tubing. Knowledge of the effects of working ther-mochemically deposited (TCD) tungsten is therefore necessary in order to establish the feasibility of obtaining worked and recrystallized microstructures and textures. The details of a recently developed technique for thermochemically depositing flat, uniformly thick tungsten sheet are presented with emphasis on the effects of deformation by rolling on the microstructure and texture. Although no work has been previously reported on the rolling and the annealing textures of TCD tungsten, there have been some determinations of textures for cold-rolled tungsten foil prepared from powder-metal -lurgy billets.4-8 The general description is that of a predominantly lurgy{100}(011) texture, with some spread about the rolling direction as an axis. pugh5 reports data both for cold-rolled and for annealed foil having about 96 pct initial cold work. He observed no change in texture, except for a decrease in the spread, for annealing treatments of 30 min at temperatures up to 1800°C. On annealing at 1900°C, both the low-temperature components plus new components which were described alternately as {001}(320) plus {001)(230) or as {100}(011) ± 12 deg about the sheet normal were observed. Above 1900°C, the new orientation existed alone, and it was stable up to 2500°C, the highest temperature that Pugh investigated. THERMOCHEMICAL DEPOSITION OF TUNGSTEN SHEET High-purity tungsten sheet was reproducibly deposited on the inner walls of a molybdenum mandrel by the thermochemical reaction WFs(g) + 3H2(g) - W(s) + 6HF(g). The mandrel was heated by a five-zone tube furnace which afforded a controllable fixed-temperature profile. Sheets measuring 1+ by 12 in. have been deposited with uniform thicknesses of up to 0.145 m. As shown schematically in Fig. 1, the purified reaction gases were metered into a mixing chamber at a Hz-to-WF6 ratio of 15 and preheated to 350°C. The flow rate of the WF6 was 300 cu cm per min at stp. These gases were directed through a conical injector into the deposition chamber. Inside this chamber hydrogen reduction of the WF6 to pure tungsten metal occurred on the hot walls of the molybdenum mandrel at a total pressure of 5 Torr. Typical temperatures for the five zones in the chamber were, respectively, 565", 540", 550°, 570°, and 590°C. The hydrogen fluorlde generated from the reaction, the excess hydrogen, and some un-reacted WF6 were pumped on through the scavenger

Jan 1, 1968

By A. J. Ardell, O. D. Sherby

The elevated-temperature steady-state creep behavior of polycrystalline a Zr was studied in vacuo under constant tensile stress. The experiments were conducted from 660° to 845°C over the stress range 870 to 5400 psi. The steady-state creep rate, is, of a Zr was found to be related to the applied stress, a, and temperature, T, by the equation where C is a constant. Two interpretations of the data are considered, each requiring different values of the parameters ß, Q, and . It is shown that this formula can be derived using Gilman's phenomeno logical equation relating dislocation velocity to the shear stress for the case where dislocation mobility is limited by the nucleation of kink motion. From the fundamental dependence of strain rate on dislocation velocity and the density of mobile dislocations, the factor exp(ßo) can be related to the stress dependence of the dislocation density, and Q to the energy of kink formation. The two interpretations considered are as follows: Case I—the parameters are adjusted so that the equation above describes the data over the entire range of stress and temperature, implying that creep is controlled exclusively by dislocation glide; Case IIthe parameters are adjusted to allow for the possibility that creep is diffusion-controlled at high stresses but glide-controlled at low stresses. For both cases the values of the parameters are within the spread permitted by the data. Factors favorable to the observation of the unusual stress -dependence of i, for a Zr are discussed and it is shown that the anomalously rapid rates of self-diffusion and the low modulus on the principal glide system are primarily responsible for the anomalous creep behavior. Metal-lograflhic observations are presented and discussed with reference to the overall creep behavior. PREVIOUS investigations of the creep behavior of a Zr have been conducted from room temperature to about 500C The results of these investigations are primarily of engineering significance because of the variety of conditions under which they were carried out, and the low testing temperatures employed. Little information is available concerning the fundamental nature of the elevated-temperature creep behavior of a Zr. This investigation of the creep behavior of a Zr above half the melting temperature (the melting temperature, T,, of a Zr is estimated to be about 1860"K was initiated because there are two significant anomalies of the physical properties of a Zr: a) the rate of self-diffusion in polycrystalline a Zr is anomalously rapid: b) both Young's modulus for polycrystalline a Zr and the shear modylus as-sociated with the prismatic slip system { 1010)( 1120) (the principal slip system in a Zr 7) have anomalously large temperature variations The importance of these quantities to the understanding of creep behavior has been demonstrated, and it was hoped that this investigation would provide a critical test of the predictions based upon the analysis of creep data for other pure metals. However, as the investigation progressed it became increasingly clear that the unusual creep behavior of a Zr could not be analyzed in a conventional manner. 1) EXPERIMENTAL EQUIPMENT AND PROCEDURES Two grades of zirconium, designated A and B, were used in this investigation. The analyses, as supplied by the vendors, are presented in Table I. Material A, with a nominal purity of 99.84 pct, was supplied by the Wah Chang Corp. in the form of cold-rolled sheet from which specimens were machined without further fabrication. Material B, with a nominal purity of 99.95 pct, was purchased from the Nuclear Materials and Equipment Corp. in the form of iodide crystal bar.

Jan 1, 1968

By J. M. Woodall

GuAs crystals which have been grown in quartz boats by the horizontal Bridgman method in the pvesence of Ga20 vapov have beetz found to have carrier and donor distributions which do not correspound to those expected from simple dopant seg-vegation during directional freezing; Instead, the carrier distribution is determined by the heat-trentnzent history of the crystal, while the donor distribution, zohiclz is principally due to silicon, is fixed by the pozuth rate, the geo)tlet.ry of the crystal growth vessel, and tlze initial Ga20 pressure. WHEN semiconducting materials are made into doped crystals by the normal freezing method,&apos; they usually exhibit doping variations along the growth axis. If a) there is no dopant diffusion in the solid, b) the dopant is distributed uniformly in the melt, and c) the distribution coefficient, k, does not vary with composition, then the doping variation along the growth axis is represented by the equation: where C is the doping level in the solid at a point where a fraction g of the original liquid has frozen, and Co is the mean concentration. When the dopant is either a singly ionized shallow donor or shallow acceptor, C also represents the carrier concentration. Even though this equation accurately describes the dcping profiles of a large number of normal freeze systems, there are several special systems for which Eq. [I] does not apply. One such system is the horizontal Bridgman method for preparing oxygen-grown GaAs crystals using quartz vessels. Several workers2"* have shown that GaAs crystals grown by the horizontal Bridglnan method using quartz vessels are generally contaminated with silicon in concentrations in excess of 5 < 10lG atoms per cu cm. This contamination is ascribed to a reaction: occurring at the walls of the crystal-growth vessel which liberates silicon into the melt and Ga2O vapor. It has been shown4 that this reaction, and, hence, the silicon contamination, can be suppressed by the addition of oxygen to the crystal-growth apparatus. It is the purpose of this paper to describe a special apparatus capable of yielding single crystals of GaAs grown in the presence of oxygen and to describe both the kinetics of silicon suppression in this system and the relationship between the carrier concentration profile and the silicon concentration profile. EXPERIMENTAL-CRYSTAL GROWTH A schematic diagram of the apparatus used in the oxygen addition experiments is shown in Fig. 1. The most important features of this apparatus are: a) the use of a sand blasted quartz boat, h) a quartz rod of length 1, with a hole of cross section A, that is placed near the boat to limit the free space volume V, over the melt during the growth, and c) the temperature gradient at and near the solid-liquid interface. Sand blasting the boat is necessary to prevent wetting of the melt. The quartz rod retards the diffusion of the GazO vapor away from the melt to the colder portions of the ampoule. A crystal is prepared by first loading a 5.5-in. boat, which has been cleaned in aqua regia, with 40 g of 99.9999 pct Ga along with 1 to 8 mg of Ga203 powder. GazO3 is a convenient source of oxygen since it reacts with gallium at the melt temperature to form Ga20 vapor, the species which apparently controls the suppression of silicon contamination. The loaded boat, the quartz rod, and the 99.9999 pct As are placed in the ampoule as shown in Fig. 1. Generally, GaAs seeds were not used since most of the unseeded growths resulted in monocrys-tals. The ampoule is evacuated to 10-5 Torr and sealed off. The GaAs melt is synthesized by placing the ampoule into a two-zone horizontal Bridgman furnace. The two zones are separated by several sandwiched layers of -in. Fibre-Fax board drilled with holes slightly larger than the OD of the ampoule. This causes a very large temperature gradient between the two zones, which is necessary for single-crystal growth. The two-zone furnace is mounted on a stand fitted with a roller bearing which allows uniform motion of the furnace in a horizontal direction. A uniform velocity of the stand is achieved by the use of a windlass device which winds up a wire attached to the stand. Movement of the solid-liquid interface is accomplished by fixing the position of the ampoule and moving the stand. Growth rates investigated in this experiment were between 0.4 and 1.2 in. per hr. The composition of the melt is fixed by maintaining an arsenic reservoir at 618°C. The stand is moved away

Jan 1, 1968

By Henry M. Otte, Ralph P. I. Adler

The changes of line position and integral line breadth in the X-ray diffraction pattern of a polycvys-talline Cu-30Zn tensile test piece, incrementally loaded (and unloaded) up to fracture, have been an-alyzed in detail. The stacking-fault probahility, cv, increased linearly with increasing strain, E, wheveas the effective domain size, De(hkl), decreased with decreasing E-1 Over the greater part of the stress-strain curve the rate of work hardening was essentially constant (about 86 kg per sq mwz), and could be correlated with the slope of stage II of the single-crystal stress-strain curve. Consequently the theories of work hal-dening (particularly those parts relating to stage 11) as developed by Mott and Hivsch and others could be applied to the observations made on the polycrystalline brass. A relationship of the form Aa = Aao - MhklEhkl between the change, Aa, in the extrapolated lattice pararneter and the rvns strain, Ehkl, was derived and found to fit the results acceptably well. From this and other relationships developed in the papev it was estimated that the equilibrium stacking-fault energy of Cu-30Zn was between 8.4 and 12.5 ergs per sq cm, in fuirly close agreement with the (corvected) value obtained by Howie and Swann (1961)43 using transmission electron microscopy. The theory of work hardening in the jorm developed and recently presented by Hirsch (1964)3 successfully described all the pvesent observations. In order to test certain aspects of the theories of work hardening, as developed by Mott,1 Hirsch,2,3 Seeger et el,4-7 and others (for review see Nabarro, Basinski, and Holt8), several recent investigations have been concerned with relating the dislocation density, p, with the shear stress, 7 (and strain, y), applied to the specimen. The results of these investigations have shown that the square root of the dislocation density appears to be linearly related to the applied shear (or flow) stress for fcc as well as bcc metals and alloys. Furthermore, the relationship appeared to apply not only to the deformation of poly-crystalline specimens, but also to stages I and I1 of the deformation of single crystals. An expression of the form has thus come into wide use. Here b is the Burgers vector for a total dislocation, G is the shear modulus, and 70 and q are constants. A review9 of available values of q shows it to have values (at room temperature) in general between 0.3 and 0.6. Forms of Eq. [1] can be deduced from, or predicted by, the current theories, and the various constants adjusted so that they are compatible with the experimentally found value of q . No unique relationship has yet been found between the dislocation density and the applied shear strain. There are several serious objections to the use of Eq. 11]. In the first place, it relates the shear stress to the density of the dislocations without regard to their arrangement, type, or distribution; the significance of the relation may therefore be justly questioned.5 In the second place, the values of the experimental quantities usually substituted into Eq. [11 are those of the applied shear stress and the total dislocation density measured after unloaditzg. The dislocation density value that should in fact be used is that for the mobile dislocations present in the specimen when under the applied load.* Finally, in cases where the values used for p, the dislocation density, are those obtained by electron microscopy, p is subject to considerable error,&apos; both systematic and random. The corrections to be applied are still controversial. Dislocation densities can also be measured by etch-pit and other techniques,&apos;&apos; each having their specific limitations. An objective of the present investigation has been to obtain information about the dislocation configyration and distribution by analyzing the changes in the position and shape of X-ray diffraction profiles as a function of deformation. The X-ray techniques employed, also open to criticism, have certain advantages, however. Thus, although the X-rays diffract only from the surface layers to an effective depth of about 20 p, the measurements can be made while the specimen is under load. The value of the dislocation density obtained by the X-ray method is also subject to errors, which are different from those of the electron microscope. Though a considerably larger volume of material is sampled by the X-rays, thereby reducing some of the statistical errors inherent in the electron microscope data, the information obtained is less detailed and is dependent on the method of analysis used to obtain a value for the dislocation density. Nevertheless, important observations can be made because the aforementioned advantages outweigh some of the limitations. In the present paper the X-ray method is briefly described and applied to a brass specimens deformed in tension. The results are then discussed in terms of some of the current concepts of work hardening. 1) EXPERIMENTAL PROCEDURE Details have already been extensively published elsewhere11-14 and therefore will only be dealt with briefly here. 1.1) Materials and Specimen Preparation. Commer-

Jan 1, 1968

By W. C. T. Yeh, T. G. Oakwood, A. A. Hendrickson, R. H. Hammar

The objective of the research is to determine whether solid-solution strengthening effects observed in dilute solutions of silver can be accounted for by the influence of the solute addition on the dislocation structure oj- the crystals. The additions of both tin and indium produced only small changes in the dislocation densities and arrangements in silver crystals. However, as found previously, small solute additions have large effects on the tensile properties; the inj-luence of the tin and indium additions on the temperature dependence of the flow stress and the easy-glide range is especially strong; It is concluded that the indirect strengthening effect of the solute due to variations in the dislocation density as proposed by Seeger is of minor importance and that solute atom-dislocation interactions are responsible for the observed strengthenirzg effects. The experimental results were combined with those of Rogausch to test the concenlvatiorz dependence of solute strengthening. Both the first and one-half power dependences of the critical resoleed shear stress on concentratiorz fail in very dilute solutions. THE objective of the research is to determine whether solid-solution strengthening effects observed in dilute solutions of silver can be accounted for, at least in part, by the influence of the solute addition on the dislocation structure of the crystals. It is recognized that the addition of solute atoms may influence the strength properties of a metal through both "direct" and "indirect" effects. The former refer to the strengthening mechanisms that result from the interaction of solute atoms with dislocations; in the latter case, the strengthening effects arise as a result of solute&apos;s influence on quantities such as dislocation density, dislocation arrangement, stacking-fault energy, diffusivities, the elastic constants, and so forth. It is clear that the correct interpretation of solid-solution strengthening phenomena cannot be given until the importance of indirect strengthening effects is properly evaluated. In the particular case of close-packed metal crystals, Seeger showed that solute strengthening effects in dilute solutions of copper and silver might be accounted for by an increase in dislocation density due to the addition of the solute. Seeger&apos;s argument was that the strengthening effects extrapolated from more concentrated solutions indicate that small concentrations of impurities raise the critical resolved shear stress much more than is predicted by a concentration-independent dislocation density. The above idea was a very reasonable one. The dislocation theories of work hardening of Taylor,2 Cot-trell, 3 Mott, 4 and seeger5 had already associated the increased flow stresses with increased dislocation densities in deformed metals; investigations of the dislocation structure of metal crystals had provided a logical basis for expecting an increased dislocation density in crystals containing impurities (see for example, Ref. 6). The numbers involved seem reasonable, too. It can be expected that the flow stress of the crystal would increase as the one-half power of the dislocation density.&apos; Solute additions of 1 at. pct to metal crystals result in strength increases by factors in the range of three to ten. If one assumes that the strengths of the pure metal crystals are determined by their dislocation densities, then dislocation-density increases of one to two orders of magnitude as a result of solute addition would be required to account for the observed strengthening—not an unreasonable expectation. In addition to the effect of the solute addition on dislocation density, one might also anticipate important strengthening contributions to result from the solute&apos;s influence on the dislocation arrangement. Parker and washburns have reviewed a number of experimental evidences which show important strengthening effects due to the presence of subboundaries. Further, lattice strains due to impurity segregation would be expected to influence the distribution as well as the dislocation density of the as-grown crystal. As pointed out in the reviews of Chalmers,6 Elbaum,9 and winegard,lo micro segregation of impurities occurs at all interfaces of crystals in cellular growth; the impurity gradient results in lattice strains which can be reduced with the presence of dislocation arrays in the region of the impurity gradient. Hence, one would expect the presence of a solute to favor the formation of dislocation subgrain structures and that the subgrains would have an important influence on the strength of the crystal. The experimental observations that concern the possibility of an important strengthening contribution through the influence of the solute on the dislocation density or arrangement are not in agreement. Haasen has reviewed the observations of Meakin and Wils-dorf,12 Howie,13 and Bocek 36 and concluded that the solute&apos;s influence on dislocation density is not sufficient to account for strengthening effects in concentrated solutions but might, as seegerl suggested, make an important contribution in very dilute solutions. On the other hand, Hendrickson and Fine 14 concluded that changes in the dislocation density and dislocation width accounted for the solid-solution strengthening effects observed in silver-based aluminum solid solutions. Goss et a 1.I5 observed dislocation arrays in Ge-6 at. pct Si, Ge-0.2 at. pct Sn, and Ge-0.2 at. pct B crystals that were not observed in germanium crystals of

Jan 1, 1968

By John L. Walter

A sintered compact of iron containing 0.007 vol fraction of glass , prepared 6). powder rnetullurgtcal lechniques, was rolled lo foil, 0.001 in. /hick. The foil sullrples were anneuled a1 650° to 850°C in hydrogen. Pri,narj recryslullization prodtnced large grains which Lc3ere highly elongnled in the rolling direclion und which had an unusual prgferred orientation. The glass parlicles assumed a stringerlike dispersiorz on working; llie slrinyers were parallel lo the rolling direction and to the long axis of the grains. The same unusual grain structure, preferred orientation, and stringerlike dispersion of purticles are found in heal-ily rolled and annealed foil of tungsten which has heen doped wilh small amounts of aluminum, silicon, and polassiutvt. Both the proper dispersion of the particles and severe working (reductions in excess of 98 pct) are necessary to produce the elongzcted grain structure. RECENTLY, the author reported on the origin of the elongated or "nonsag" grain structure in tungsten foil which was doped with aluminum, silicon, and potassium.&apos; It was observed that particles, identified as mullite (Al6Si2Ol3), were present in the doped ingot (as sintered) and at all stages of processing from ingot to sheet or wire. It was shown that the particles, being plastic at tungsten working temperatures (up to 1550"C), underwent a "stringing out" parallel to the working di-direction. It was concluded that these strings of particles were responsible for the formation of the highly elongated interlocking grains observed in doped tungsten wire or sheet. To give further credence to this explanation of a long-observed but not understood phenomenon, it was decided to design a new system, one which was analogous to the doped-tungsten system. Thus, a bcc metal, iron, was chosen to be doped with glass which would be plastic at reasonable working temperatures for iron. The glass chosen was a #0080 Corning lime glass which melts at about 810°C. This is approximately the same fraction of the melting point of iron (0.6) as the melting temperature of mullite is of tungsten. It will be shown that all the observed unusual features of the doped tungsten are duplicated in the glass. doped iron, even to the preferred orientation of the grains in the recrystallized sheet. In the tungsten sheet the preferred orientation consists of two components, (1i3)(691) and (013)(362), neither of which has been observed as a component in textures of primary recrystallized bcc metals. EXPERIMENTAL PROCEDURE The glass, in the form of fine powder, was added to high-purity electrolytic iron powder and mixed dry. The particular composition chosen was 0.007 vol fraction of glass. After mixing, the powder was mechanically pressed to a disk 0.5 in. diam and 0.15 in. thick at a pressure of 5000 psi. The pellet was sintered, in pure dry hydrogen, for 2 hr at 8 50°C. The sintered pellet was then heated to 750°C and rolled to 50 pct reduction of thickness in two passes, with reheating between passes. The rolling temperature was then reduced to 600°C and the slab was rolled to a thickness of 0.050 in. Rolling to 0.010 in. was accomplished in several passes at 300°C. Final reductions to 0.003 and 0.001 in. were taken at room temperature. This rolling temperature schedule was similar, in terms of the fraction of the melting point, to that used in the rolling of the doped tungsten. The total reduction of thickness was in excess of 99 pct. Samples of the rolled foil were lightly electro-polished and annealed for 1 to 6 hr at temperatures of 650" to 85O°C in hydrogen. Samples for transmission electron microscopy were thinned on a Disa Electropol using AC-1 electrolyte.

Jan 1, 1968

By D. J. Freeh, W. E. Horst, R. C. Kellner

This paper is concerned with the description of grinding characteristics in a batch grinding system. A mathematical model was developed and used for simulating the system on an analog computer. A general equation describing the change of selected size fractions with respect to time is presented. The empirical verification of the model is discussed. In order to understand the performance of a grinding system, it would be desirable to have a mathematical description of the system&apos;s behavior. The development of a mathematical model to describe the performance of a batch dry-grinding operation was investigated. This is the first step toward reaching the objective of a practical mathematical description of a grinding system that could be employed for process control and optimization of a simple or complex grinding circuit. Although this article is concerned only with batch grinding performance, experimental work is being conducted to extend the model to continuous grinding systems. BASIC PROCESS CONSIDERATIONS In a paper dealing with the probability theory of wet ball milling, Roberts1 correlated the rate of change of oversize material, C, with energy input, E, as follows where the energy input is expressed in power/unit mass and k is a constant for each particle size. Experimental grinding studies were made by Bowdish2 to extend the previous work of Roberts. The work of Bowdish also showed that the rate of breaking of oversize particles in a ball mill is proportional to the concentration of oversize particles present. He further demonstrated that breaking of oversize particles is proportional to the surface area of the balls used for grinding. Rate equations were presented and it was concluded that grinding could be considered as a first order phenomenon according to the rate equation [2] di which is in accordance with Eq. 1. In Eq. 2, the effect of ball area is included in the constant k,. Other rate equations were reported to show the effect of a change in ball area and removal of fines during grinding. Correlation studies made by Arbiter and BhranY indicate a first-order rate equation for quartz; however, their data showed less than first-order rates existed for some of the other materials evaluated. More recently Kelsall4 has shown that the rate of breakage of any narrow size range of quartz could be described by a first-order rate equation. Several other investigators5-7 have described grinding behavior in terms of rate equations or kinetics. In general, the rate equations have been described for each particle size; however, the interactions between sizes and the overall relationships that exist have not been considered, at least not in the form of solving a group of simultaneous differential equations. Extensive work has been conducted by various investigators using a probabilistic approach which has expanded stein&apos;s&apos; earlier work. Selection and breakage matrices are incorporated in the probabilistic model as contrasted with the deterministic method presented here. A batch grinding operation may be considered as an unsteady-state process from the standpoint that the conditions within the mill are a function of time. Therefore, a plot of mass fraction of the i-th size versus time would give a set of curves as shown in Fig. 1. In these curves X , represents the mass fraction of large size material, X2 intermediate size, and X3 small size material. An examination of these curves shows a strong similarity to the curves that would be obtained from a chemical reaction of the type9 A?B?C, [3] where A would be comparable to the largest size material being broken to an intermediate size, 3, and

Jan 1, 1968

By H. E. Cline

Solidification of Pb-Sn alloys ranging in composition from 1.2 to 56 at. pct Pb ws observed with polarized light. Lamellar structures were observed over a larger range of compositions in alloys containing excess tin than excess lead, as expected from constitutional supercooling. The occurrence of pools of supercooled liquid surrounded by lead is explained by the difficulty in nucleating tin. Cells and dendrites weve observed in tin-rich alloys. Evidence was found that the degenerate structure formed at low growth rates, the formation of faults, and abrupt changes in composition and structure can be attributed to non-steady-state growth. The apparent interface shape was observed to have deep grooves at the interphase boundaries. HUNT and Jackson have observed the shape of the interface during growth of organic eutectics. They observed the formation of lamellar faults and shape instabilities upon changes in growth rate. The lamellar structure in these organic eutectics was not restricted to the eutectic composition. Recent work by Mollard and Flemings2 indicated that Pb-Sn alloys from 12 to 26 at. pct Pb could be solidified with a lamellar or rodlike structure if a sufficiently steep temperature gradient was used at a slow growth rate. Observations of the solid liquid interface of the Pb-Sn eutectic were made by Davies3 using polarized light. Photographs were at too low a magnification to determine the interface shape, but he has concluded that tin was the leading phase. In the following experiments, solidification of a range of Pb-Sn alloys from 1.2 to 56 at. pct Pb was observed using polarized light, to determine the factors controlling stability of the lamellar structure. EXPERIMENTAL Procedure. One hundred-gram ingots of alloys prepared from 99.999 pct pure Pb and Sn were cast into graphite molds under argon. The compositions of the alloys were 1.2, 6, 12, 26, 36, 46, and 56 at. pct Pb. Two-gram pieces were melted between two cover glass slides which were squeezed into a 1-mm separation. Samples were then observed under polarized light in a hot stage shown in Fig. 1. A long working distance objective designed for viewing at 500 times was used. Photography was made difficult by the lack of illumination and contrast at these high magnifications. By using an elliptical polarization compensator, as suggested by A. Holik, the contrast and illumination could be optimized. Photographs could be taken only at slow growth rates to avoid excessive interface motion during the 15-sec exposure used. The solidification rate was varied by increasing or decreasing the power to the heater. It was found that insulation was necessary to avoid undesired growth rate fluctuations. The temperature gradient, as measured with two thermocouples 1 cm apart, was 80" ± 20°C per cm during all the experiments reported here. The advantage of this procedure is in being able to observe solidification while it is occurring. However, the observations are restricted to the glass-metal surface and may be influenced by this surface. Also, one has no knowledge of the interior of the sample, in contrast to studies of the freezing of transparent organic eutectics.&apos; Observations. The alloy near the eutectic composition (26 at. pct Pb) solidified in a lamellar structure when the growth rate was uniform. If the growth

Jan 1, 1968

By J. L. O’Brien, M. Suenaga, K. M. Ralls, V. F. Zackay

The effecls of aging a1 400°C on tile resistive transition at 4.2°K of a superconducling 70Zr-30Nb alloy are reporled. Microstrclural changes were studied by critical temperature, resistiue critical field, residual resistiuily, and microhardness measurements and by X-ray diffraction, optical microscoby, ad replication electron microscopy. The result of the aging treat- A defect-free Type 11 superconductor in a magnetic field above Hc1 cannot sustain a transport current runt is a fine array of w-phase pavticles with a mean center to center interparticle spacing of about 800A. At an aging time of 300 hr the maximum onset critical current density is rcached. The particle size at the maximum current density if about 4202. At times longer than 300 hr effective particle impingement leads to lower onset critical current densities. perpendicular to the applied field without power loss in the sample.&apos;-3 This power loss is due to flux line motion caused by the Lorentz force and is manifested by a longitudinal voltage.4-6 When defects are present in the material, flux lines are pinned until the Lorentz force exceeds the "pinning force". That is, it is thought that flux lines reside in free-energy wells existing at the defects, and the critical Lorentz force is that which when integrated over distance will supply the free-energy difference necessary to move the flux

Jan 1, 1968

By John T. Eastlick

The Banner mining district is about 70 miles northeast of Tucson in the southern part of Gila County, Arizona. Production from the district, valued at about $26 million, is chiefly from copper-silver-lead zinc ores. The stratigraphic section consists of Precambrian conglomerates, quartzites, dolomites, and limestones, Cambrian quartzites; Devonian limestones; dolomites, and shales; Mississippian limestones; Pennsylvanian limestones and shales; and Cretaceous volcanic and sedimentary rocks. Deformation of these rocks presumably started near the end of the Cretaceous, and extended into the late Tertiary. The sedimentary rocks were folded, faulted, and intruded by fine grained diorite, quartz mica diorite, and dacite porphyry. At least four distinct stages of mineralization are recognized. In the first stage of contact metamorphism and the second stage of hydrothermal alteration, favorable zones were prepared for ore deposition. Metallization occurred in three of the mineralizing stages. Magnetite, pyrite, and hematite were deposited near the end of the second stage of hydrothermal alteration. The third stage included the main deposition of sphalerite, chalcopyrite, bornite, and galena. In the fourth and final stage, minor amounts of sulfide minerals were deposited with a late anhydrite and quartz gangue. The ore deposits in the form of veins and veinlets, pipes, irregular massive replacements, and bedded replacements are localized by the extent and distribution of metamorphic and hydrothermal alteration, by the proximity to the intrusive contacts, and by the effects of structural development. Oxidized ores of copper, lead, and zinc constituted the principal production of the district prior to 1940, but, for the most part, supergene enrichment was of minor economic importance. The ore bodies of the district are in the mesothermal class of deposits, occurring as normal metasomatic replacement and vein types.

Jan 1, 1968

By R. A. L. Black

Rock mechanics is a very new science. It has been accepted as a recognized discipline for some two decades, but it is only within the last five to ten years that it has been common to include the teaching of rock mechanics as a separate subject in undergraduate curricula at universities. Thus, few senior mining engineers practicing in industry, either men in charge of production or those engaged in mine planning and design, are familiar with the subject. That this unfamiliarity has continued so long is also due in part to the fact that the results of rock mechanics investigations have been published in a large number of different periodicals covering subjects ranging from experimental stress analysis to obscure branches of applied earth sciences. The first really useful textbook &apos; in the English language was published only in 1965, in Canada. It made available to students and to practicing engineers, for the first time in concise form, the essential body of accepted knowledge about rock mechanics and developed the theories on which it is based in a simple, clear and logical manner. Another factor which has resulted in rock mechanics science being slow to be accepted by the mining industry is that research work has often appeared to be esoteric and unpractical. Senior engineers have been reluctant to spend money on the application of new knowledge when the process of application seemed uncertain and ill-defined, and where the cost of field investigations (which is necessarily high) appeared to offer no certainty of economic reward. This is a reasonable attitude on the part of mining engineers; they are responsible to skeptical boards of directors whose chief concern is, very properly, the net return on capital invested. The application of rock mechanics science has not in the past,

Jan 1, 1968

Jan 1, 1968

By A. F. Giamei, E. J. Freise

A discussion of the various factors affecting the accuracy of volume fraction determination by the direct comparison X-ray diffraction method is presented. To minimize errors introduced by nonrandomization effects such as preferred orientation and large grain size, as well as errors introduced by statistical effects, an iterative mathematical analysis is introduced. This analysis is applied to all observable diffractio~ spectra from a given specimen by means of computer techniques and is statistically superior to the standard direct comparison technique which utilizes only one or tm sets of intensity spectra. The computer program also presents a graphical interpretation of- the results which enables the investigator to visualize and readily assess the scatter in volume fraction estimates caused by deviations from randomness. Finally, the iterative analysis is applied to experimental data collected from a series of plain carbon steels in both the as-received and spheroidized conditions to determine the volume fraction of cemen-tite present in each case. The results show markedly good agreement with chemical analyses for all spheroidized specimens. In theory, quantitative X-ray diffraction is a power-ful analytical technique for precise determination of the volume fractions of various phases present in a multiphase poly crystalline aggregate. There are two generally used methods; both utilize the fact that the intensity of a diffraction line of a particular phase is a function of volume fraction of that phase present in the aggregate. The more common method is the so-called internal standard technique where a known amount of standard substance is mixed with the aggregate containing the unknown. The resulting ratio of the intensity of a particular diffraction line of the unknown to the intensity of a diffraction line from the standard is used to find the weight fraction of unknown material by reference to the intensity data obtained from a previously prepared set of standards containing the same amount of standard material. The details of this technique are outlined in standard works on X-ray diffraction.&apos; The disadvantages of the technique are that it requires the use of powder specimens and that the powder mixture must be homogeneous near the surface to the maximum effective beam depth. The alternative technique is the direct comparison method in which the ratio of the intensity of a diffraction line of a phase in the aggregate to the intensity of a second-phase diffraction line yields the ratio of the volume fractions of each phase present. This method has been applied most extensively to the determination of the percentage of retained austenite in martensitic steels and to determining the amounts of hcp and fcc allotropic modifications in pure cobalt5 and the amounts of hexagonal and rhombohedra1 modifications in graphite.8 This method is applicable to bulk as well as powder aggregates and is the technique which will be considered in the following text. It is the purpose of the present communication to show that by combining the results of X-ray diffrac-tometry with the use of high-speed digital computers the results of the direct comparison quantitative X-ray analysis technique can be optimized by using all of the data available on a diffraction pattern. THEORETICAL DISCUSSION In optimizing any quantitative X-ray diffraction experiment, the problem of accuracy vs time to collect and analyze the experimental data arises. For any method to be practical, it is required that both experimental and analytical procedures are reasonably short. In most of the previous work performed by the direct comparison method, intensity data from only one or two sets of peaks were used to calculate the volume fraction of phases present in the aggregate. Consequently, rather long-time experimental measurements are required to assure that the intensity data are sufficiently accurate to justify the use of one or two sets of data. By using computer techniques to analyze the experimental data it becomes feasible to use all of the available data on a diffraction pattern. By so doing, the time spent in measuring any one diffraction maxima can be appreciably reduced. Although this results in poor counting statistics for any one maxima, the number of data points available for analysis is greatly increased. Based on the above discussion, it will be assumed that a continuous scanning counter-diffractometer technique will be used to collect intensity data from a two-phase mixture. The integrated intensity of the ith diffraction line from the a phase in the aggregate is given by:&apos;" where is the volume fraction of the a phase, The various quantities in Eq. [la] are angular independent while those in [lb] depend on the hkl spectrum of a particular phase. The meaning of the individual quantities in Eqs. [la] and [lb] are given in Appendix 1. It is convenient at this point to outline briefly the factors which will affect the measured intensity of any one hkl spectrum. a) Extinction effects arise from two independent experimental conditions. Primary extinction arises from a high degree of crystal perfection and results in spectra having lower intensity than predicted by Eq. [I]. Any treatment, such as powdering, which reduces

Jan 1, 1968

By Pradeep K. Rohatgi, Clyde M. Adams

Dendritic aggregate of ice formed on freezing of aqueous soluitions has been studied. Chlorides of sodium, potassiutn, lithiunz , and hydroget1 were used as solutes. The spacing between ice platelets or den-drites was experimenlally found proportzonal to the square root of freezing time when the freezing rate was constant from beginrting to end of solidification; the constant freezing rates were obtained during freezing of small droplets of aqueous soliitions surrounded by relatively large heat sinks. The transverse growth velocity of the ice platelets is proportional to the square root of the freezing rate. During unidirectional freezing from a constant temperuture chill, the solution at each location is subjected to a spectrum of freezirtg rates. The freezing rate is ini- FREEZING of solutions has been a subject of investigation in many disciplines. Aqueous solutions offer the advantage of transparenty; their study is of special significance due to the increasing interest in freezing processes for desalination. In addition dendritic solidification of aqueous solutions is in many ways analogous to freezing of metallic solutions. Aqueous solutions of most ionic salts freeze with tially low, passes through a maximum, and then decreases until solidificatimz is complete. The den-drite spacing increases linearly with the distance from the chill surface; it is inversely profiortional to the square root of the maximum freezing rate. The dendrite spacings in the two systems (the constanl freezing rate and the varying freezing rate) are equal, when the maximum freezing rate of the varying freezing rate system equals the average freezing vale of the constant freezing rate system. Mass transport in interdendritic liquid duriug solidificatiotz is analyzed; the experimental observations indicate that maximum concentration difference (AC) and supercooling (AT) in the interdendritic liquid are indepexdent of freezing rate. the separation of practically pure ice crystals from the liquid phase; with very few exceptions there is no solid solubility of ionic salts in ice. As an ice crystal grows there is rejection of solute from the moving interface into the liquid. Since the rejected solute moves primarily by diffusion, concentration gradients are established in the liquid. The highest solute concentrations are found in liquid immediately adjacent to liquid-solid interfaces and lowest concentrations farthest from the interface. Two-phase equilibrium obtains only at the solid-liquid interface; at other locations the liquid becomes supercooled because temperature gradients are negligible compared to concentration gradients. This is an immediate consequence of the fact that thermal diffusivities are considerably higher than mass diffusivities.

Jan 1, 1968