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By R. D. Pehlke

THE impending commercial importance of iron-aluminum alloys has served as a stimulus for re- search on the preparation and properties of these alloys. However, the activities of the components of the binary system remain undetermined. The experimental determination of the thermodynamic properties of binary solutions of iron and aluminum has been hindered by the high liquidus temperatures

Jan 1, 1959

By J. O. Betterton, W. M. Spicer

The solubilities of antimony in the a and ß-forms of zirconium were determined between 750" and 1300°C. The a-phase forms by a peritectoid reaction, and the a/(a + ß) and ß/(a + ß) phase boundaries rise in temperature with in- ' creasing antimony. Impurities in the 99.95 pct zirconium were sufficient to influence the phase boundaries and the variation reported is approximate. The restricted solid solubility of the terminal zirconium phases, which is especially characteristic of this system, is thought to result from the low free energy of the Zr2Sb phase. ZIRCONIUM-antimony alloys are important in zirconium alloying studies since antimony is one of the highest valent elements which can be used to make zirconium alloys. The dilute alloys are of further interest as they have somewhat better corrosion resistance' than pure zirconium. The first investigation of the phase diagram was made by Russi and wilhelm2 who found a eutectic reaction, liquid (- 17.5 at. pct Sb) = ß zirconium (- 11 at. pct Sb) + Zr2Sb, at 1430°C'. The Zr2Sb phase was of complicated hexagonal structure, and by thermal analyses of the relatively impure alloys then available, Russi and Wilhelm found evidence for the peritectoid formation of the a-phase. EXPERIMENTAL In the present work, the phase diagram was re-investigated in the region 0 to 5 at. pct Sb and 750" to 1300°C using iodide-zirconium alloys. Details of the procedure have been described earlier. Essentially the alloys were prepared by arc casting and were then examined by the annealing and quenching method. The times of annealing varied from 1 hr at 1300°C to 30 days at 760°C. As in other zirconium phase-diagram studies1"5 the impurities in the zirconium were still sufficient to affect the results, and the experiments will therefore be described in 3 parts. The results from the first 2 parts of the work are shown in Fig. 1. Here the ß/(ß + Zr2Sb) and a/(a + ZrzSb) phase boundaries were determined with alloys made from 99.9 pct zirconium,* and cast under such conditions that the Vickers hardness of a alloys extrapolated to 95 to 110 VPN at 0 at. pct Sb. Such alloys were not suitable for investigations of the (a + ß) region, and the results shown in Fig. 1 near the (a+ ß) and (a +ß + Zr2Sb) regions were determined with purer alloys. These alloys had an extrapolated hardness range of 75 to 85 VPN and were made from 99.95 pct zirconium. A deviation from binary equilibrium occurs in Fig. 1 as indicated by the (a + ß) region of pure

Jan 1, 1959

By G. A. Yuko, J. W. Barton, J. G. Parr

ALTHOUGH previous work1 has shown the compo- sition range of the complex face-centered cubic phase,2 Ti2Ni, to be narrow, no precise limits were established. The purpose of this investigation was to prepare homogeneous alloys on either side of the stoichio-

Jan 1, 1959

By J. Doig, A. A. Bauer, F. A. Rough

AN investigation of the phase relationships between the 6 phases of the uranium-molybdenum and uranium-titanium systems was conducted by studying alloys ranging in composition from uranium-31.5 at. pct Mo to uranium-34 at. pct Ti. A ternary cut showing these phase relationships is presented upon the basis of thermal-analysis data obtained and upon the basis of metallographic and X-ray examination of heat-treated and quenched specimens. Isothermal ternary sections, inferred from phase relationships determined between the two 6 phases, are presented for the uranium-molybdenum-titanium system. In the compositional range investigated, a y-ura-nium solid solution exists at elevated temperatures. At about 900°C the 6-U2Ti phase, with limited molybdenum solubility, forms. Epsilon, a molybdenum-titanium-rich solid solution appears at the same temperature and appears in all phase regions that exist below this temperature except in the terminal 6-phase regions. The y phase is stable to approximately 660°C in titanium-rich alloys; the y and 6-U,Ti phases decompose at this temperature to a uranium in a peritectoid reaction. The y phase in molybdenum-rich alloys of the ternary cut studied decomposes in an apparent eutectoid reaction, at about 593°C, to the 6-uranium-molyb-denum and a-uranium phases. The e phase while present, presumably plays a negligible role in these reactions. Titanium was found to markedly decrease the stability of retained y in these alloys. Age-hardening characteristics developed in titanium-contain ing uranium-molybdenum alloys quenched from 900°C and aged at 500°C are ascribed to decomposition of Y to the a and E phases. INTRODUCTION Alloys of uranium with molybdenum, titanium, and zirconium, respectively, are of great interest because of their potential use as reactor fuels. As a result, this interest extends to the constitution of these alloys, particularly in view of their uniqueness of constitution. In these systems, alone, among known uranium-alloy systems, an intermediate phase forms by direct decomposition of the high-temperature y-uranium phase. As a prelude to possible future alloy development, an investigation has been undertaken of the phase relationships that occur between the intermediate phases of these systems. These phase relationships have already been reported for the intermediate 6 phases of the uranium-zirconium and uranium-titanium systems.' The results of an investigation of the phase relationships between the 6 phases of the uranium-molybdenum and uranium-titanium systems are reported here. The phase relationships that occur in the binary systems pertinent to this investigation are shown in Fig. 1. Phase nomenclature appearing throughout this report is as shown in these diagrams; the crystal structure of the phase is given in Table I. EXPERIMENTAL PROCEDURE Alloys were cast and fabricated to flat plate. Specimens were heat treated and examined metal-

Jan 1, 1959

By A. A. Bauer, F. A. Rough, G. H. Beatty

AS a result of recent studies, the constitution of the zirconium-uranium system has been fairly well defined. A diagram for the system is shown in Fig. 1. However, both oxygen and nitrogen are known1-3 to have a pronounced effect on the limits of both ß- and e -phase regions. It has been shown that small amounts of oxygen severely constrict the compositional limits of these phase regions in the ternary zirconium-uranium-oxygen system. A previously published tentative diagram shown in Fig. 2 illustrates the ß-phase constriction resulting from oxygen additions. Generally, iodide zirconium has been used in constitutional studies of zirconium-uranium alloys. While this is the highest purity material available, cast iodide zirconium-uranium alloys will generally average from 200 to 300 ppm 0 and from 50 to 60 ppm N. Thus, while the constitution of the zirconium-uranium system is fairly well defined, it must be realized that this definition applies to alloys containing in the vicinity of 250 ppm 0 and 50 ppm N. The present investigation was undertaken to accurately determine the boundary between the ß-plus-P and ß phases at a single temperature in the binary zirconium-uranium system by quantitatively

Jan 1, 1959

By B. D. Cullity

AS methods for measuring fiber textures become more exact, it becomes justifiable to scrutinize an observed pole-density curve for evidence of minor texture components. These are disclosed by minor maxima or abnormally broad major maxima. One possible source of these minor components is twinning of the main component. In cubic metals and alloys, there are two kinds of twins: 1) Annealing twins in face-centered cubic metals. These are reflection twins on {Ill), and they can be expected to be present in recrystallization textures. 2) Deformation twins in body-centered cubic metals. These are shear twins on (112). Although usually formed only by impact, they might conceivably be present in the deformation texture of severely cold-drawn wire. Fortunately, both kinds of twinning lead to the same orientation relationships. It thus becomes possible to prepare a single list of angles between various planes in parent crystal and twin, which is helpful in examining pole-density curves for evidence of twinning in any cubic metal or alloy. Such a list of interplanar angles is given in Table I. This table consists of three parts, corresponding to the three major texture components—<100>, <110>, and <111>-most commonly found in the fiber textures of cubic metals. The table lists the angle between the pole of {hkl}, in either the parent crystal P or the twin T, and the fiber axis <uvu>. The crystals with <uvw> parallel to the wire axis are here

Jan 1, 1959

By J. N. Roberts, K. V. Gow

In a recent review of the field of plastic deforrnation of metal single crystals, Maddin and chenl indicated the need for systematic investigations of the crystallography of the slip process with special attention to: a) The effect of the orientation of a crystal on the appearance of slip lines, b) The effect of high temperatures on the slip systems of aluminum, c) The effect of strain rate on the crystallography of slip. The present paper deals with the effect of temperature and strain rate on the mechanism of deformation of aluminum single crystals similarly oriented for single and duplex slip. The work of several investigators has shown that in aluminum at high temperatures other slip systems in addition to the predicted {I l l) <101> may operate. The most generally reported additional systems

Jan 1, 1959

By A. F. Andresen

IN the course of another investigation the lattice parameters were determined for a series of compositions of tin in copper. Ten-gram samples of the alloys were made from spectroscopically pure tin and copper. The metals were weighed and placed in graphite capsules (previously fired at 5500°F) which were then sealed individually in evacuated vycor tubes. The tubes were mounted on a spit, transverse to its axis, which continually rotated the melts in a furnace. After homogenizing, filings were made of one third of each slug by filing off a complete cross section. A 325-mesh sieve was used to obtain the powder for the X-ray determination. The sieved powders were annealed in vacuo at 600°C for 24 hr to remove the cold work, and then quenched. The lattice parameters were determined with a flat-plate back-reflection camera using CuKa radiation (A., = 1.5405A, A,? = - 1.5443A). With this radiation the (331) and (420) reflections appeared close to the focusing region. As reference lines were used the same reflections from pure copper powder, between which the (420) lines of all these alloys are situated. The variation of the systematic error over this angular range was found to be less than the estimated experimental error ±0.0005A which is indicated in Fig. 1 for all but the sample with 8 pct Sn. As a check some of the powders also were examined in a regular Debye-Scherrer camera with the Straumanis film mounting. The parameters were here evaluated by extrapolation against cos2? to ?= 90o. The results are shown in Fig. 1 where the lattice parameters in Angstrom units are plotted as a function of weight percent of tin. The reflection lines for the 8 pct alloy were not clear at first, perhaps due to coring. Several measurements were made after different annealing programs on two separate

Jan 1, 1959

By L. O. Brockway, W. C. Bigelow, J. A. Amy

Specimens of Inconel-X alloy solution-treated at 2050°F and aged for periods of 1, 10, 100, and 1000 hr at 1200°, 1400°, and 1600°F have been examined by electron microscopy and by electron and X-ray diffraction. Four minor phases were identified: titanium nitride, niobium nitride, an M23C6 complex carbide, and the intermetallic ? phase. The two nitrides were found in all of the aged specimens and in the solution-treated alloy, the y&apos; phase formed at all aging temperatures, while the M23C6 carbide formed only on aging at 1200° and 1400°F. Variations in the hardness, rupture strength, creep strength, and yield strength of the alloy have been shown to be related to variation in the size and distribution of the particles of the y&apos; phase within the matrix grains of the alloy, with maximum values of these properties occurring when there is a maximum amount of the phase present and a fine state of dispersion of the particles prevails. THE nickel-chromium alloys containing titanium and aluminum are widely used in applications requiring high strength at elevated temperatures. Studies on relatively simple ternary and quaternary alloys&apos;-4 have indicated that the favorable high-temperature properties of these alloys are related to the precipitation of an intermetallic ?&apos;-phase having a structure based On that of the Ni3A1 phase of the nickel-aluminum system. The present investigation was undertaken to identify the minor phases and to study the microstructural changes occurring in one of the more complex commercial alloys as a result of aging in the service temperature range, with particular emphasis on investigating the role of the ?&apos; -phase. The microstructural changes were studied by electron microscopy and the minor phases were identified by X-ray and electron diffraction. MATERIALS AND METHODS Inconel-X alloy was selected for this investigation because the previous studies of Frey, Freeman, and white6 provided extensive information on the variations in metallurgical properties of this alloy resulting from high-temperature aging treatments. Specimens aged 1, 10, 100, and 1000 hr at 1200°, 1400°, and 1600°F were made available for the present use. These were taken from 1-in. round-bar stock of a commercial heat having the following weight composition: 0.04 C, 0.56 Mn, 6.59 Fe, 0.007 S, 0.38 Si, 0.03 Cu, 73.22 Ni, 14.97 Cr, 0.78 Al, 2.38 Ti, and 1-02 Nb. They were solutjon-treated at 2050 for 4 hr and then water-quenched prior to aging. Powder X-ray diffraction patterns were obtained from insoluble minor phases which were separated from the alloys by digestion in the reagent of Mahla and Nielsen.6 Back-reflection patterns were obtained from electrolytically polished surfaces of the bulk search to detect the ?&apos;-phase&apos; Cu-K a radiation was used in both cases. In the electron-diffraction studies, the general method developed by Heidenreich, Sturkey, and

Jan 1, 1959

By E. H. Rennhack

THE presence of sufficient quantities of the inter- stitial elements, carbon, oxygen, and nitrogen is known to decrease sienificantly the room-temperature impact resistance of titanium. Hydrogen does not appear to affect impact strength unless present

Jan 1, 1959

By M. Metzger, T. A. Read

The strengthening effects of hydroxide and synthetic plastic films in the creep of cadmium crystals were studied. The results were broadly consistent with the naive mechanical model. The dislocation-film reactions and the significance of the macroscopic stresses associated with certain films are discussed in the paper. ALTHOUGH a number of studies have been made of the strengthening of metal single crystals produced by surface films usually less than Ir in thickness, the mechanisms underlying this phenomenon are still not well established. Roscoe&apos; first noted the critical shear stress and the stress-strain curve of cadmium-crystal wires to be raised markedly by the presence of oxide films. Subsequent investigators2-&apos; have confirmed the effect for several metals and films including a number of plated poly-crystalline metal films. Harper and Cottrel1" with a thin film on zinc presumed to have formed as a result of etching and washing treatments) did not detect a strengthening at a rate of extension of 10 &apos; sec-&apos; although at lo-&apos; sec-&apos; the film raised the flow stress by 7 pct at 0.0005 extension and by 22 pct at 0.01. The marked strengthening at moderate strains thus appeared to be the result of a dynamical effect dependent on the rate and amount of plastic flow. Other observations&apos;. " are consistent with this view. The large effects of films on the tensile creep rate of single crystals were demonstrated when the observation of Andrade and Randall," that the creep rate of cadmium crystals increased on immersion in aaueous solutions of certain cadmium salts. was shown&apos; * to hold only when a film was present initially and was explained by the attack of the solution on the film and the removal of its strengthening effect. Changes in the creep rate interpretable in terms of the removal or formation of various films have been observed by other investigators.3,8,10,31 Certain other experiments have been reported in which surface films or liquid environments have affected the plastic behavior of metals, but these are not within the scope of the present work which deals with the effect of solid films on single-crystal slip. Possible Mechanisms—The film does not significantly reduce the load on the crystal in the elastic range (the elastic moduli of film and crystal are not too greatly different and the area of the film is so small that its share of the load is negligible) so that the initial operation of internal Frank-Read sources is not affected. However, as Fisher" has pointed out, a source terminating on the crystal surface requires only half the critical stress for activation as an internal source of the same length and a relatively strong film (even a very thin one) would pin the free ends of the surface sources so that, if surface sources are responsible for plastic flow in a clean crystal. such a film would increase by roughly a factor of 2 the stress necessary for generation of dislocation loops at a given rate. The other general possibility is that the film resists the passage to the crystal surface of internally generated dislocations. If the film is adherent and if the specimen is to exhibit slip of the same general character as a film-free specimen, the film must deform or fail in shear at the active slip planes. The naive mechanical model, where shear-stress relaxation across the active slip plane in the metal transfers load to the film until it deforms and slip can

Jan 1, 1959

By R. C. Hall

In the present work, experiments determined the effect of the order-disorder reaction near the Fe,Al composition on the magnetic anisotropy and magnetostriction of single crystals: A material which is more difficult to magnetize in one direction than in another is anisotropic, that is, the ease with which ferromagnetic materials may be magnetized in different crystallographic directions determines the anisotropy. Two investigators have estimated the anisotropy of the aluminum iron alloys from poly-crystalline data;1,2 however, these estimates should not be considered to be reliable. Siege1 made two accurate measurements of the first anisotropy constant* from single crystals of 4.0 wt pct aluminum sotropy throughout the ferromagnetic aluminum iron system have been described. These results were obtained from single crystals which were slowly cooled and, hence, ordered near the Fe3Al composition.4 Magnetostriction is the change in length per unit length resulting from applying a magnetic field to a ferromagnetic material. For the purpose of this report, the saturation magnetostriction was measured. This is the maximum change in length per unit length resulting from an applied magnetic field large enough to saturate the material in a given direction. This magnetostriction has been determined for single crystals of the ferromagnetic aluminum-iron system.&apos; The crystals near Fe3Al were also ordered. PREPARATION AND TREATMENT OF SINGLE CRYSTALS Single crystal bars were grown from the melt.&apos; The raw materials for these crystals were iron and aluminum of 99.9 and 99.99 pct purity, respectively. From the bars, crystals in the shape of circular

Jan 1, 1959

By M. L. Bleiberg, L. J. Jones

THE changes induced in metals by subjecting them to heavy particle bombardment have received widespread attention in recent years and results of such investigations have been reviewed by Slater, Dienes, Seitz, Siegel, and Seitz and Koehler.1-5 Of particular significance are the property changes that occur in uranium-base alloys due to neutron bombardment. These changes are generally very severe since fission occurs within the sample, resulting in the formation of heavy, highly energetic fission fragments, as well as additional neutrons born in fission, which serve to intensify the damage generally associated with fast neutron bombardment of nonfissionable metals. The property changes in uranium and uranium alloys due to neutron bombardment have been summarized by Paine and Kitte16 and Billington.7 It has also been shown that neutron bombardment of

Jan 1, 1959

By R. H. Hiltz, N. J. Grant

Solid-solution titanium-cerium alloys, cold-rolled to 0.010 in. thickness, and annealed, were internally oxidized to produce a fine dispersion of CeO2 in the titanium matrix. The oxidized alloys were cut into sheet stress-rupture specimens and tested for rupture life at 426°C, 538°C, and 648°C. There was noted an improvement in strength over that of pure titanium, the internally-oxidized alloys showing curves with a much flatter slope on the log stress—log rupture life plot, characteristic of the stable metal-metal oxide class of alloy. DURING the past 3 to 4-year period, considerable interest has been aroused by the potential offered by alloys based on the ultra fine dispersion of a hard insoluble phase in pure metals or solid-solution alloys for use at high temperatures. The impetus to the development and study of such alloys was provided by Irmann.1,2 through the success of the SAP alloy (pure aluminum containing about 12-14 volume pct of A12O3). Subsequent studies have thrown light on the true potential of this class of alloys in the remarkable stability of the structure after long-time exposure at high stresses and high temperatures.a-5 While success has been demonstrated in the special case of the A1-Al2O3 alloys, and more recently

Jan 1, 1959

By J. O. Betterton, W. K. Noyce

I~JTI HE work on the indium-zirconium system is part A of a larger investigation of zirconium-phase diagrams with solute elements, silver, cadmium, indium, tin, and antimony, which is intended to provide information about the metallic valency of zirconium. The system is an ideal example since the sizes of indium and zirconium atoms are nearly the same, and the solute and the solvent occur in the same row of the periodic table. The only solute from Group III B which had previously been added to zirconium was aluminum&apos; and it was of interest to determine whether indium would dissolve appreciably in alpha zirconium and stabilize this phase in the same manner. Experimental Procedure The experimental methods used in the indium-zirconium work are similar to those described earlier for the silver-zirconium system.&apos; Reactor Grade 1 iodide zirconium of 99.95 pct purity* and indium of 99.99 pct purity were arc cast, and then annealed in silica capsules with protective foils of zirconium and molybdenum. Annealing temperatures and times varied from 1 day at 1300°C to 43 days at 550°C. The compositions of the alloys were detcrmined by an individual chemical analysis of the actual metallographic specimens after two or more sides were examined to insure the absence of solute segregation. Calibrated thermocouples were used throughout, and the uncertainty in the temperatures reported, owing to calibration error, furnace control, and measurement of the small temperature gradients near the capsules, is believed to be well within ±2°C. Typical impurities in the alloys were found by a neutron-activation analysis of four different alloys. The results are given in Table I where the ranges of values will be seen to compare favorably with the usual values for iodide zirconium. With respect to oxygen, nitrogen, and carbon the absence of any unusual amount of these elements compared to iodide zirconium was indicated by the alloy hardness values, since hardness is increased sharply by the presence of these elements. The value for 0 pct In, obtained from the alloys by extrapolation, is 58 2 7 VPN which is in the low part3 f the normal range of hardness found in iodide zirconium. Results of the Experiments The zirconium-rich portion of the indium-zirconium phase diagram from the annealing experiments is shown in Fig. 1. Indium was found to

Jan 1, 1959

By C. Feng, C. Elbaum

AN investigation of the fracture plane of titanium, containing 0.5 wt pct to 1 wt pct 0, was recently carried out by fracturing large-grain specimens in a tensile jig at room and liquid air temperature. The experiments were carried out on strip specimens 3 to 5 mm wide, 2 mm thick and about 100 mm long. The specimens consisted of several grains, each occupying the entire cross section of the strip and extending over a length varying from 5 to 20 mm. These specimens were prepared by a method described elsewhere.&apos; The identification of the fracture plane was possible in twelve of approximately thirty crystals investigated. In some cases severe local distortion took place near the fracture and prevented identification of the fracture plane. On, at least, three occasions the fracture propagated in a helicoidal

Jan 1, 1959

By E. Buehler

THE floating zone refining technique&apos;-4 has provided a new experimental approach to the purification of many reactive materials especially those with high melting points. The method avoids the use of a crucible and at the same time it provides a favorable environment at the freezing interface for the growth of single crystals. The physical properties of refractory metals such as molybdenum and tungsten have long been of interest from a fundamental point of view and because of their widespread use in vacuum electronics. Single crystals are often desirable for study. Prior to the introduction of zone melting, single crystals of these metals were usually grown in the solid state at temperatures slightly below the melting point by strain annealing3 or by the application of a moving temperature gradient. Such techniques were mostly successful on wires, ribbons, or rods having small cross-sectional areas. Recently, larger samples of tungsten, molydbenum, tantalum, columbium, and rhenium were melted by a floating zone process which employed electron bombardment heating.10 Single crystals were obtained in many instances

Jan 1, 1959

By D. J. Mack, J. A. Mullendore

MUCH work has been reported in the literature on the separation of individual phases in steels, particularly carbides, for the purpose of structural and chemical analysis. The methods usually involve separation of the particles from the matrix by chemical or electrochemical methods. Another .group of alloys ideally suited for selective removal of one phase is the commercial aluminum bronzes. Al-

Jan 1, 1959

By J. W. Downey, A. E. Dwight, R. A. Conner

THE MgCu2 type Laves phase has been observed in the thorium-osmium and thorium-iridium systems. Two alloys corresponding to ThOs2 and ThIr, were prepared by arc melting a 5-g charge in a water-cooled copper. crucible. Both alloys were very brittle. X-ray diffraction patterns were obtained using filtered Cu and Co radiation with a Straumanis-type DeBye-Scherrer camera. The a,, values as shown in Table I were obtained by a Nelson-Riley extrapolation. The structure belongs to space group Oh7-Fd3m. Relative intensities for each of these compounds were calculated on the assumption that 8 thorium atoms occupy (a) positions and 16 osmium or irid-ium atoms occupy (d) positions. The calculated intensities are the product of the Lorentz-polarization factor, the multiplicity factor and F&apos;, the structure factor, neglecting the absorption and temperature

Jan 1, 1959

By J. Gurland

A method of measuring the degree of contact between grains of 1 phase in multiphase alloys is derived. It is shown that the number and the areas of contacts between grains can be determined by metallographic analysis. Relations between the area of contact, the dihedral angle, and the mean free path of spherical grains are developed. It is often desirable to interpret the mechanical behavior of alloys in terms of structural features observed under the microscope. A quantitative description of microstructures of multi-phase alloys requires consideration of geometrical and topological factors such as the amount, size, and shape of grains and the continuity of the constituent phases. The number and dimensions of grains may be metallographically determined by applying the methods described by Smith and Guttman1 and by Fullman2 in their papers on the measurement of particle size and internal boundaries in opaque bodies. The present work intends to show that the same methods can be used to evaluate some of the parameters of phase continuity; namely, contiguity, number of contacts, and areas of contact of grains of 1 phase. Application of these concepts may be found in such problems as the calculation of electrical conductivity of 2-phase alloys, or the evaluation of the length of fracture path through grains of a brittle phase more or less dispersed in a matrix. I. DEFINITION The following definitions and derivations are based on 2-phase alloys, of which the units of the microstructure are grains. Contiguity is defined as the average fraction of surface area shared by 1 grain of a phase with all neighboring grains of the same phase. In a 2-phase alloy of constituents A and B, the contiguity of phase B is given by: where Cb is the contiguity of phase B aBß is the average area of contact between a grain of phase B and adjacent grains of phase B, aAB is the average area of contact between a grain of phase B and adjacent grains of phase A. The contiguity is a measure of the average degree of contact between grains of phase B in the 2-phase mixture. The ratio varies from 0 to 1 as the distribution of phase B changes from a completely dispersed to a fully agglomerated structure. Smith and Guttman1 have shown that the relative areas of 2 kinds of interfaces in a volume are directly proportional to the number of interfaces of each type intersected by a random line. The lines can be drawn on metallographically prepared surfaces as long as these are random sections through the sample. The contiguity ratio of phase B then becomes: Cb = 2NBB/NAB + 2N BB [2] where: NBB is the number of interfaces between grains of phase B intersected per unit length of random line. Nab is the number of interfaces between grains of phase B and grains of phase A intersected per unit length of random line. The factor 2 arises in Eq. [2] because each interface B-B is associated with 2 grains of B-phase, whereas the interface A-B involves only 1 grain of B-phase. The calculations of contiguity do not require any assumption as to volume fraction, particle size, or particle shape. Fullman2 gives an expression for the determination of the mean free path between particles. The mean free path PB between grains of phase A, i.e., through grains or agglomerates of phase B, may be found from the relationship: PB =2fB/NAB [3] where fB is the volume fraction of phase B. The calculation of the mean free path is independent of grain shape and grain size distribution. The calculation of the number of contacts and of contact area requires assumptions of grain shape, grain size, and contact shape. In the case of uni-

Jan 1, 1959