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By J. E. McDonald, J. G. Eberhart

A model is discussed from which the work of adhcslon .tor liquid transition metals on aluminum oxide surfaces can he calculated, A close-packed (00011 oxygen surface on A12O3 is assumed with two different types of surface sites: one type involving metal-oxygen bonds and the other man der Waals into actions. The work of adhesion is thus expressed as the sum of these two bonsding free energies. Calculated works of adhesion for nickel, titanium, chromium, and zirconium on sapphire agree well with the experimentally determined quantities. The model is extentled to the calculation of the work of adhesion and shear stress required to remove a thin metal film from a sapphire substrate and is in good agreement with experimental values. The obsewed dependence of the work of adhesion on the free energy of oxide formation of the metal is shown to also provide an interpretation of the tittle dependence of thin-film adhesion. THIS paper presents a model for the type of bonding which occurs across a metal-A12O3 interface. The model is used to explain the results of two types of experiments in which such an interface exists: 1) the adhesion of thin metal films on Al2O3 substrates and 2) the wetting of A12O3 by liquid metal drops. The adhesion of thin films to various substrates has been the subject of a variety of investigations.'-' Benjamin and weaver3 and Bowie,6 using the scratch test developed by Heavens,10 studied the adhesion of metallic films to glass substrates. Their observations for noble-metal film adhesion agree well with an adhesion model involving a van der Waals type of bonding between the film and the substrate. For films of metals whose free energy of oxide formation. ?F°f, has a negative value. Benjamin and weaver3 and Bowie6 found a time-dependent adhesion with an initial value that can be interpreted in terms of van der Waals interactions but a larger terminal value which was related to ?F°f, Karnow-sky and Estill7 deposited films on sapphire at elevated temperatures and noticed no time dependence of film adhesion but a similar correlation with ?F°f. Because of the kinetic problems associated with thin-film adhesion it is desirable to examine adhesion in an equilibrium system. The wetting behavior of liquid-metal drops on Al2O3 provides such a system. Systems of this metal-ceramic type have been studied extensively.11 Humenik and Kingeryl2 have measured the wetting of A12O3 (and other substrates) by several metals and have pointed out that the wetting ability of these metals increases with increasing values of -?F°f. It is thus seen that thin-film adhesion and metal wetting on A12O3 are both related to the tendency of the metal to react with the surface oxide ions of the Al2O3 substrate and, because of this, both phenomena should be explainable by an appropriate model for the metal-Al2O3 interfacial bonding. In the sections that follow, wetting and adhesion data on A2O3 are reviewed and a model is presented by which these phenomena can be interpreted. ANALYSIS OF WETTING EXPERIMENTS In an equilibrium system involving a liquid-metal drop on a solid Al2O3 substrate, the work of adhesion, WAD, is defined by the Dupre, equation as WAD = ?s + ?L -?sL [1] where ?s and ?L are the surface free energies of the solid substrate and the liquid drop, respectively, and ?sL is the interfacial free energy. The work of adhesion is the work required to separate a unit area of the solid-liquid interface into two surfaces. The work of adhesion is usually determined from a sessile-drop experiment in which yL and the contact angle, ?, are measured. The Young-Dupr6 equation is then used to calculate WAD Wad = ?L (1+ cos ?) [2] The literature of this subject has been examined and Table I shows work of adhesion data for various liquid metals as measured on A12O3 substrates. The standard free energy of oxide formation of the metal at the temperature of the wetting experiment, ?F°f . is also tabulated in kcal per g-atom of oxygen. The data is grouped according to the gaseous atmos-

Jan 1, 1965

By Don M. Jackson

The techniques for the growth and controlled, graded doping of silicon epitaxial overgrowth layers were established. Grading of- impurities such as arsenic or boron in arbitrarily chosen profiles oiler four orders of magnitude (from I X 10Lg to 1 X 10L5 cm) was accomplished. The graded structures were grown in a stepwise manner where in the profiles were approximated by growing many separate layers with small doping-level changes between layers. Masked-area growth of silicon through windows in a SiO2 masking film was acconiplished through the simultaneous injection of HCl gas 102th Sic14 in the epitaxial reactor. The HCl served to inhihit the growth of silicon on the Sz02 surface, and also to control the cross-sectional profile of the silicon mesas. silicon from the substrate was etched out through the windows, and then epitaxial material was used to fill the holes hack in to form planar diodes. Simullaneous HCl injection was adapted to control the cross-section profile of the hack-filled regions. Arsenic-huried regions beneath in te- In recent months, the epitaxial growth process in semiconductor materials technology has evolved into a complex system directed at both material improvement for better monolithic integrated-circuit characteristics and the development of new silicon structures for future integrated-circuit needs. The advent of high-temperature HC1 gas etching1 grated-circuit transistors reduced V(SAT) by slightly more than one third, bringing this parame-ter to that of an isolated component transistor. When arsenic was diffused into the starting sub-stvate, it was necessary to remove any excess arsenic in order to avoid excessive audodoping of the subsequent epitaxial layer. Oxide isolation of single-crystal regions in a substrate provided complete electrical isolation of integrated-circuit components, thereby eliminating parasitic capacitance which is inherent in standard integrated-circuit processing. The process involved the etching of deep mesas on silicon Wafers, the formation of an oxide over the mesa surface, and then the deposition of several mils of polycrystalline silicon over the oxide. The original substrate was lapped and polished allay until the mesas were left isolated in the polycrys-talline matrix. The Final components were fabri-cated in the single-crystal islands. Speed and power-handling capabilities of standard circuits were improved through the process. wherein work-damaged material is removed from the surface of the silicon wafer just prior to the silicon deposition step has made it possible to grow silicon films with structural quality that approaches that of the substrate. HBr used in the same volume ratio as HC1 etches silicon at the same rate and with the same results as HC1. Recent developments in epitaxial materials technology have occurred in the areas of precise doping control, buried prediffused regions between over-

Jan 1, 1965

By George Hallerman, R. J. Gray

In the customary method of studying age hardening, the process of aging is interrupted by cooling the specimen and measuring its room-temperature hardness. However, the aging process may be conveniently measured while it is occurring at an elevated temperature by a series of hardness measurements at suitable time intervals. The latter method gives data void of complications that might result from processes occurring during the quench, and the data may be more indicative of the alloy's properties at elevated temperatures. The elevated-temperature hardness tester1 used in the present study employed a dead-weight loading system with a synthetic sapphire Vickers-type in-denter mounted in a molybdenum holder. The tests were performed in a vacuum of l0 to 10 torr. Hardness impressions were made by applying a 2-kg load for 15 sec. Although the hardness impressions made in the tester at elevated temperatures were measured at room temperature, the correction for thermal contraction during cooling was insignificant and therefore neglected. The two methods of obtaining age-hardening data were compared using eighteen samples of Haynes alloy No. 25* which had been annealed for 2 hr at 2250°F (1232°C). The test surfaces of the 1 by 1 by 1/4-in. samples were ground and then polished on vibratory polishers2 prior to testing. Three groups of five samples were aged at 1400°, 1650°, and 1800°F (760°, 899", and 982°C) for 4, 16, 32, 64, and 100 hr and then water-quenched. Room-temperature hardness as a function of aging time for these samples is shown in the broken lines of Fig. 1. Only one sample for each of the three temperatures was necessary to determine the hardness of the alloy at the aging temperatures with the elevated hardness tester. The specimens were heated isothermally and hardness impressions were made after various time intervals up to 100 hr. The results of these determinations were represented by solid lines in Fig. 1. Comparison of the two sets of curves shows, as expected, the hardness values determined at the aging temperatures are lower than the room-temperature hardness of the quenched specimens and the hot-hardness values reflect a strong tempera-

Jan 1, 1964

By N. Brown, H. Green

The effect of quenching temperature and of aging temperature and time on compression stress-strain curves of ß brass was investigated. Age softening occurs at a rate which decreases with decrease of quenching temperature below the critical temperature for ordering. The activation energy for softening is 15,400 cal per mol. No matter how rapidly brass is quenched or what the temperature from which it is quenched, practically complete order is obtained at room temperature. It has been demonstrated that with respect to the specific heat,',' electrical resistivity," X-ray diffraction, and microstructure, the slowly cooled and rapidly quenched specimens are the same and that complete long range order exists in both cases. However, Smith" showed that the hardness of ß brass depended upon the cooling rate and the temperature from which brass is quenched. Smith showed that the hardness was a maximum for specimens quenched from about 445 °C and that the as-quenched structure softened at room temperature at a rate depending upon the temperature prior to quenching. This softening after quenching is in this paper referred to as age softening. The results of this investigation are qualitatively the same as the findings of Smith. However, a more detailed analysis of these phenomena has been possible since the stress-strain curve offers a more sensitive index of the state of the metal than hardness. It is the purpose of this paper to show how the mechanical properties are related to the ordering of ß brass. A 200-lb ingot made from electrolytic copper and electrolytic zinc was extruded to 1/2in. rod. Chemical analyses at frequent intervals along the rod showed that the alloy contained 51.5 pct Cu with the greatest impurity being iron, at 0.01 to 0.001 pct. To obtain a constant test material, the 1/2in. extruded rod was warm-rolled to % in. diameter at 200°C and then recrystallized to a grain size of 2.0 mm. The specimens for the compression test were % in. high and % in. in diameter. The specimen ends were polished on 600 metallographic paper and coated with Molykote for a lubricant. The compression rig consisted of an anvil resting on the machined table of the Baldwin Southwark testing machine and a plunger fixed to the movable cross

Jan 1, 1954

By G. R. Speich

The age-hardening of Fe-18 to 21 pct Ni marten-sites containing small amounts of titanium, aluminum, copper, or molybdenum has been studied by hardness measurements, transmission electron microscopy, extraction replicas, and X-ray and electron diffraction. Electyon-probe microanaly-sis of the extracted precipitates was also performed. The effects of temperature and composition on the aging kinetics have been studied in detail for Fe-20 pctNi-Ti martensites. All the martensites hardened on aging at 400" to 500 "C with a single aging peak. In the Fe-20 pct Ni-Ti martensites hardening was associated with the formation of a fine dispersion of NisTi. No precipitation was observed in an Fe-21 pct Ni-2.6 pct A1 alloy, although the hardness increased from 327 to 545 Dph during aging at 500°C. Copper was precgitated from an Fe-20 pct Ni-10.7pct Cu alloy, at least during the later stages of age-hardening. Hardening in an Fe-18 pctNi-5pct Mo alloy was associated with the precipitation of an intemzetallic compound tentatively identified as NisMo. The formation of austenite and the recovery of the defect structure of the martensite occur simultaneously with the normal precipitation processes &ring aging of these alloys. THE age-hardening of substitutional iron-base martensites is an important subject for study since age-hardening is one of the principal means of strengthening the substitutional iron-base martensites in precipitation-hardening stainless steels1 and maraging steels.a~4 In contrast to Fe-C martensites, these martensites are relatively soft and ductile in the as-quenched condition, due to the low solid-solution hardening effect of the substitutional elements as compared to carbon. Also, these martensites are hardened by aging at low temperatures in contrast to Fe-C martensites which generally soften on tempering. Titanium and aluminum, singly or in combination, as well as copper and molybdenum, have been the principal alloying additions to stainless steels to obtain an age-hardening reaction.' Ti-A1 or Co-Mo-Ti combinations have been used in the case of maraging steels.3"4 The present work has been confined to a study of the age-hardening characteristics of an Fe-18 to 21 pct Ni martensite to which small amounts of titanium, aluminum, copper, and molybdenum were added in order to study the effects of each alloying element separately. The age-hardening characteristics of these alloys were studied by hardness measurements, transmission electron microscopy, extraction replicas, and X-ray and electron diffraction. Electron-probe micro-analysis of the extracted precipitates was also performed. The types and dispersion of precipitates, the formation of austenite, and the recovery of the defect structure of the martensite all were studied. EXPERIMENTAL PROCEDURE Alloys. The compositions of the alloys studied are listed in Table I. The level of 18 to 21 pct Ni was chosen to assure complete transformation to martensite on quenching and is the same nickel level used in maraging steels. The concentrations of titanium, aluminum, copper, and molybdenum were chosen after a study of the and Fe-Ni-MO' ternary diagrams indicated how much of each alloying element could be dissolved in austenite. Alloys with 2 and 4 pct Cu were also studied, but these did not show precipitation hardening at the nickel levels studied and will not be discussed further. The alloys were prepared from electrolytic iron and high-purity* nickel, titanium, aluminum, copper, and molybdenum by vacuum melting of 20-lb heats. These were vacuum-cast into two 8-lb ingots. The ingots were hot-rolled at 1100°C to 1/2-in. plate and subsequently cut into 3/8-in. cubes. The cubes were sealed in evacuated quartz capsules and solution-treated for 16 hr at 1100°C, except for the Fe-20 pct Ni-10.7 pct Cu alloy and Fe-21 pct Ni-2.6 pct A1 alloys which were solution-treated for 16 hr at 1300" and at 1250"C, respectively. Metallographic examina-

Jan 1, 1963

By J. G. Kura, P. D. Frost, L. W. Eastwood

THE preparation and general properties of mag-nesium-lithium base alloys have been described in earlier papers.l,2 Lithium forms solid solutions with pure magnesium, lowers its density, and improves its formability. The improved isotropy and better formability of these alloys are attributed to the ability of lithium to convert the magnesium lattice from hexagonal (alpha phase) to body-centered-cubic (beta phase) structure. This change in structure is, however, accompanied by some limitations which make it difficult, if not impossible, to combine all the desirable properties in one composition. The most important of these limitations is the tendency of the high-strength alloys to overage and lose strength at temperatures of the order of 150" to 200°F. A study was made of the effects of composition and heat treatment on the age-hardening character- istics of the alloys. Stability of properties was determined by hardness and tensile testing of the alloys at room temperature after various periods of exposure to elevated temperatures. Precipitation-hardening curves are shown for a number of magnesium-lithium-zinc alloys in fig. 1. All the alloys were solution treated at 700°F and aged at 200°F. The reason for using the drastic quench, toluene at —105°F, was to reduce the rapid precipitation of the hardening phase which takes place at room temperature. Previous experience has shown that a hardness of about 90 to 95 Rockwell E is indicative of yield strengths in the range of 35,000 to 40,000 psi. This is a desirable strength level for magnesium-lithium base alloys with specific gravities of the order of 1.65 or less. Although the hardness level is raised by large zinc contents, a corresponding decrease in the cold formability of these alloys occurs with increasing zinc content. Thus, alloys containing up to about 10 pct Zn and having hardnesses of the order of 70 to 75 Rockwell E may be bent over a very small radius; however, the 16 pct Zn alloy requires a bend radius of more than 8T. The hardness relationships illustrated in fig. 1 can be explained by the partial phase diagram shown in fig. 2. The zinc-free magnesium-lithium alloys are entirely body-centered cubic (100 pct beta phase) when the lithium content of the binary is 10.3 pct or higher. When zinc is added, the boundary between the beta and alpha-plus-beta fields at 700°F is shifted to lower lithium contents. In addition, the solubility of zinc at 700°F decreases with decreasing lithium content. It is shown by a study of micro-structures that the limit of solid solubility of zinc in the 6Mg/Li* matrix at 700°F is about 19 pct. It is believed from a study of the aging curves that this limit is about 2 to 3 pct at 200°F. Zinc additions up to about 2 pct increase the hardness and strength of the magnesium-lithium base solid solution. Larger additions of zinc effect further hardness increases, but precipitate during prolonged aging at 200°F. Alloys having 14 to 20 pct Zn precipitation harden extremely rapidly during quenching, even when quenched in toluene at —105° F. The high-zinc alloys overage at 200°F but are capable of maintaining reasonably high hardnesses for periods up to 1000 hr.

Jan 1, 1951

By D. R. Mash

A strong yield point with attendant enhanced mechanical properties was found in commercially pure beryllium under certain conditions of heat treatment. Beryllium specimens also responded to both quench and strain aging treatments. Based on these results, a possible means of obtaining increased normal temperature mechanical properties is suggested. COMMERCIALLY pure beryllium has been found to exhibit the yield point phenomenon and several other aging manifestations under certain conditions of heat treatment. This behavior is not surprising in view of the present accumulation of experience regarding such effects in numerous metals; but in addition to extending this experience to include beryllium, the present study is of interest because aging effects are generally associated with the presence of small amounts of solute elements. The well known lack of tensile ductility in beryllium at normal temperatures is also considered to be due to impurities in some way. In the present investigation, the view was taken that beryllium of commercial purity (greater than 98 pct) should be considered as a dilute alloy and that precipitation phenomena may well exist which could lead to enhanced mechanical properties. In connection with this possibility, published data on the variation of mechanical properties with temperature are of interest. For example, Fig. 1 illustrates the variation of ductility (percentage of elongation) and ultimate strength as a function of temperature for beryllium of various histories.* Although these curves are somewhat schematic in nature, they clearly indicate the possibility that precipitation of an unstable phase and/or aging effects occur during tests in the region 400" to 700°C. The existence of such behavior should be recognized as affecting the properties of the commercial material and perhaps can be employed advantageously. Experimental Method All testing was done at room temperature using a Baldwin universal testing machine. A microformer extensometer was used in conjunction with a micro-former-type stress-strain recorder. All tests were conducted at constant loading rate, the slowest rates being used. This corresponded to 120 lb per min in the 1200 lb full scale range and 300 lb per min in the 6000 lb full scale range. After the rate of loading was set in the elastic range of the material during the early part of the test, no further adjustments were made, allowing the test to proceed at that setting. In the plastic region of the curve above the yield region, strain rates of from 0.002 to 0.006 in. per min were regularly obtained. All experimentation was carried out on specimens machined from the same lot of beryllium, lot No. Y5036BP. Table I shows the chemical analysis as furnished by the supplier, Brush Beryllium Co., as well as the standard specifications to which commercial beryllium is produced. Both 1/4 in. thick hot pressed plate and ½ in. round hot pressed and warm extruded rods were obtained. The history of the material is reported to be as follows: 1—Beryllium metal plates, produced from a standard hot pressed QMV beryllium metal block 4x15x40 in., were cut off and finished machined to 1/4x6x12 in. flat plates. The original hot pressed block was made by hot pressing —200 mesh vacuum cast attri-tioned powder at about 1050°C under vacuum. 2—Beryllium rod was hot pressed and warm extruded. Extrusion billets were machined from the regular hot pressed blocks followed by extrusion at 425°C. The extrusion was done without jacketing, and graphite was used as a lubricant. The rods were then straightened at 720 °C, after which they were annealed at 800°C for 15 min. Both flat tensile specimens and round tensile specimens were tested. The former were machined from the plate stock into standard specimens according to specifications shown in ASTM E8-52T. The nominal cross-section was 0.25x0.500 in. and the gage length was 2 in. The round specimens were

Jan 1, 1956

By Nicholas J. Grant, Robert F. Wilde

TAYLOR and Floyd's"" work in establishing phase diagrams based on the elements Ni-Cr-Ti-A1 has led to an understanding of the precipitation hardening mechanism in alloys based on these elements. Nordheim and Grant4 concluded that in simple alloys, and where the aluminum to titanium atomic ratio was such that less than three out of five aluminum atoms were replaced by titanium, the precipitate on aging is the face-centered-cubic Ni 3A 1 phase, called They further found that increasing amounts of hexagonal ? phase, Ni3Ti, precipitated from these alloys when the titanium content exceeded the solid solubility of both matrix and Ni3A1. For alloys of Ni-Cr-Ti-Al, in which the titanium and aluminum contents each ranged from 0 to 4 wt pct, the titanium-rich was superior for strengthening to either pure ?' or 7. It was also noted that the combined titanium plus aluminum content (atomic pct) was a direct measure of the high temperature strength and overaging temperatures for these alloys.4 The present investigation was undertaken to extend existing data on precipitation hardening in the more complex commercial alloys containing higher titanium plus aluminum, and with significant quantities of cobalt, molybdenum, and carbon. Experimental Procedure Reforging of As-Received Bar Stock—The alloys were received as ground, forged bar stock. Chemical analyses and the as-received bar diameters are shown in Table I along with the ASTM grain size after the various treatments. All stock except the Waspaloy was reforged to % in. diam to gain material and to facilitate machining of stress-rupture specimens. Forging was carried out at 2100°F, and discontinued when the bar temperature fell to 1800°F. Heat Treatments—For experixental simplicity it was desirable to heat treat all of the alloys at, the

Jan 1, 1958

By R. O. Williams

It is shown that Ni3Al precipitates homogeneously from nickel-rich alwminum alloys as plates on the (100) planes. Prior to actual precipitation a process occurs which is believed to be one of increasing short-range order. After precipitating the Ni3Al plates enlarge through competitive growth. Discontinuous precipitation can occur simultaneously with the above processes. Recent ideas of the origin of precipitation strengthening appear adequate to explain the hardness changes. REMARKABLY little appears to be known about the precipitation process in Ni-Al alloys in spite of their technical importance. This investigation originated to supply additional information about precipitation in general, this system in particular. Information on the structures and kinetics have been obtained through the use of hardness, X-rays, microscopy, calorimetry, and resistivity on high-purity alloys. PROCEDURES Six alloys, Table I, were prepared by melting carbonyl nickel and high-purity aluminum in alumina crucibles in vacuum and casting into 1-in. graphite molds. All rods were homogenized at least once at 1300°C for 24 hr prior to swaging and this was repeated on the first three alloys after 75 pct reduction. Alloy 4 could be reduced only 10 pct at 1000°C (probably in two-phase field) prior to fracture but 1/4-in. samples quenched from 1100°C were readily reduced cold. Alloy 5 was reduced 15 pct cold but failed on the next pass while alloy 6 of essentially the same aluminum content failed inter-granularly without apparent flow up to 1000°C. The alloys were heated in hydrogen at the elevated temperatures and formed thin, coherent aluminum oxide coatings which provided excellent oxidation resistance at lower temperatures. However, freshly prepared surfaces showed considerably less resistance at 500"to 700°C in air and apparently resulted in internal oxidation. As a consequence, low-temperature agings were carried out in evacuated tubes. RESULTS The isothermal hardening behavior of these alloys at 500"and 565C is given in Figs. 1 and 2. These results were obtained from samples cold worked 75 pct, recrystallized at 1000°C (1100°C for the 7.8 pct Al) and quenched in water. This recrystallization was used to give smaller grain sizes so as to obtain more uniform hardness values and the points represent an average of five readings. The electrical resistivity was measured on 1/16-in. wires quenched from 1000°C during aging at 495°C to give Fig. 3. The energy release and its rate are given in Fig. 4 for the 6.9 pct Al alloy during aging around 500°C. Inasmuch as this was a single run, its accuracy is not known but certainly the general shape and magnitudes are correct. The method used to obtain these results is described elsewhere.' Data for the aging at 600°, 700°, and 800°C of these alloys cold worked 50 pct are given in Fig. 5. Supplementary information from microscopy and X-ray diffraction have been included to indicate recrystallization, discontinuous precipitation and the appearance of superlattice lines from the Ni3Al. The hardness of these alloys as annealed, aged, cold worked, and cold worked and aged is given vs composition in Fig. 6. Those samples which were isothermally aged, Figs. 1 and 2, were reaged at 532°C and at successively higher temperatures for the indicated times to give the data of Fig. 7. These results as well as certain others, support the idea that the level of hardness reached for temperatures above 600°C are equilibrium values more or less independent of path. This being the case, the breaks in the curves would be the complete solution of the Ni,Al. The electrical resistivity versus temperatures for some of these alloys, both aged and unaged, is given in Fig. 8 along with those data from heating slowly (10 deg per day) to high temperatures. Interesting points include the lowering of the Curie temperature (the change in slope), the lack of any indications of a solubility limit and the large temperature coefficient for the Ni3Al. A slight break for Ni3Al around 100C shows up but this is not a Curie temperature as Ni3Al is not ferromagnetic down to -190°C. Metallographically both the nickel-rich solid solution and the Ni3Al appear very much like pure nickel. Profuse twin boundaries are present both

Jan 1, 1960

By C. E. Nelson, T. E. Leontis

THE properties and casting characteristics of sand-cast Mg-Al-Zn alloys, used commercially in this country and abroad, have been discussed in a number of articles during the past few years.'-" In addition, broad surveys of many compositions in the magnesium corner of the Mg-Al-Zn diagram between 0 and 12 pct A1 and 0 and 6 pct Zn have been presented by Busk and Marande7 and by Fox." The purpose of this paper is to furnish a comprehensive survey of the changes in tensile properties, micro-structure, and dimensional stability of two magnesium alloys, AZ92A and AZ63A,+ as a function of aging time and temperature after solution heat treatment. Rates of precipitation in Mg-Al-Zn alloys are slow enough so that a substantially homogeneous, supersaturated solid solution can be maintained even when these alloys are air-cooled from the heat-treating temperature. Consequently, even though it has been demonstrated9 10 that significantly higher strengths can be developed in some alloys in the aged condition by quenching rather than air cooling from the heat-treating temperature, general practice is to air-cool magnesium alloys. All the work discussed in this paper is based, therefore, on aging studies performed on material air-cooled from the heat-treating temperature. This investigation was intended to be a study of commercially practical aging cycles; the tensile properties were determined, therefore, up to aging times of 25-hr duration. The alloys, used in this investigation were prepared in the laboratory by remelting commercial ingots of the appropriate composition according to the procedures described in a previous paper" as the "crucible method." All melts were given the standard superheating treatment in order to insure the maintenance of a uniform grain size of 0.003 to 0.004 in. Standard test bars, 61/2 in. long with a 2½ in. long reduced section having a diameter of Y2 in., were cast from these melts in green-sand molds using a four-bar pattern. The alloys were heat treated according to the following schedules: AZ92A alloy: 500" to 780°F in 2 hr + 780°F (24 hr) AZ63Aalloy: 500" to740°Fin2 hr + 740°F (16hr) In commercial practice," AZ92A alloy is heat treated at 770°F for 18 hr and AZ63A alloy is heat treated at 730°F for 10 hr. The slightly higher temperatures and longer periods of heat treatment were used in order to obtain as homogeneous a solid solution as possible and thus to minimize inconsistencies in the

Jan 1, 1952

By J. H. Westbrook, R. W. Guard

The influence of a number of alloying additions on the structure and hardness of Ni3Al (?') has been studied. Three general effects have been observed.. solid-solution hardening, strain aging, and defect hardening arising from deviations from stoichiometry. The solid-solution hardening phenomena are complicated relative to binary terminal solid solutions due to the possibility of virtually independent substitution for the component elements and to the concomitant effects of strain aging. In many superior nickel-base high-temperature alloys the elevated temperature strength is attributable to the presence of a dispersion of Ni3A1 (?') in a solid-solution matrix. Examples of such alloys are Inconel X-550, Inco 713, Waspalloy, and Nimonic 80. It is, therefore, appropriate to seek a further understanding of the properties and alloying behavior of this compound. Ni3Al, the compound most rich in nickel in the nickel-aluminum binary system, was first detected by litakal but not established with certainty until the much later studies of Bradley and Taylor' and Alexander and Vaughan.3 More recently the mechanism of formation was clarified by Floyd4 who showed that Ni3Al is the product of a peritectic reaction at 1395°C between the melt and the compound NiAl in agreement with the original suggestion of Alexander and Vaughan.3 Ni3Al has the ordered face-centered-cubic or Cu3Au structure in which the nickel atoms occupy the face centers and the aluminum atoms the cube corners, a0 = 3.570A. Despite earlier reports to the contrary. the compound apparently remains ordered at least to 1000oC.5 It exists over a narrow range of compositions (-3 pct wide) whose limits and temperature dependencies thereof have been reviewed recently by Taylor and Floyd.' Most previous workers have found Ni3Al to be both hard and brittle7,8 although Maxwell and Grala8 obtained 2.5 to 6 pct tensile elongation at room temperature and Alexander and vaughan3 described the material as "hard and tough" on the basis of observations made while preparing metallographic specimens. In a recent study one of the present authors found that although considerable intergranu-lar brittleness was evident: individual grains of a coarse-grained inert atmosphere arc-melted specimen were readily deformable.l0 The same study also showed Ni3Al to have an anomalous temperature dependence of hardness in that such a curve exhibits a number of peaks between room temperature and 800°C which could not be associated with any microscopically observable precipitation reactions or polymorphic transformations. It was, therefore, proposed in the present study to elucidate the anomalous high-temperature strength behavior and to examine the solid-solution alloying of this compound and the effects of such alloying on hardness. Sample Preparation and Experimental Procedure-Samples, both of pure Ni,Al and of various alloyed solid solutions based on Ni3Al, were prepared by arc melting 100-g buttons in an inert atmosphere arc furnace. All buttons were heat treated for 4 hr at 1275oC and examined metallographically for homogeneity. Microstructures were typically homogeneous and single phase with ASTM grain size about 1 and unusually clean grain boundaries. Chemical analyses showed good correspondence (within a few tenths of a percent) with intended compositions. Microindentation hardness data were obtained from room temperature to 800°C in vacuo using a balanced-beam type loading system in an instrument to be described in detail elsewhere." In general a 100-g load, a loading rate of 1 mm per min and an indentation time of 15 sec were used. Various indenter materials were used according to the materials bein tested because of specimen-indenter interaction. Fl Measurements of the Vickers-type indentations were made at room temperature. Hardness-temperature curves were run at least twice on each sample to ensure that surface work-hardening effects had been eliminated." Precision lattice-parameter measurements were made on powder samples using a back-reflection

Jan 1, 1960

By C. S. Smith, E. W. Palmer

IN 1934, when Gregg and Daniloffl wrote their excellent monograph on the alloys of iron and copper, the most recent literature on the constitution of the alloys indicated a narrow single-liquid area for 20" above the liquidus with a closed liquid mis-cibility gap above this. Since that time, however, a number of investigators have confirmed the much earlier studies of Mushet2 and Stead3 who, among others in the nineteenth century, had described the true state of affairs. Liquid copper and iron are completely miscible in the absence of carbon, but small amounts of carbon cause liquid segregation. In 1934, one of the writers' mentioned evidence for the absence of liquid separation in carbon-free alloys at temperatures up to 1700°C. Two years later, Mad-docks and Claussen5 unequivocally established the absence of liquid segregation and published a revised diagram, reproduced in fig. 1. They also studied the limits of the two-liquid area in ternary alloys of iron, copper, and carbon as a function of carbon and iron content. In the same year Simpson and Bannister" and Schumacher and Souden7 described in some detail the properties of alloys containing 50 to 75 pct Cu. More recently Hodges et al.16 have developed the copper-rich alloys for use as high-strength conductors. In 1937, Iwase, Okamoto, and Ameniya8 published data on the miscibility gap in ternary alloys of iron, copper, and carbon that supported the conclusions of Maddocks and Claussen, and definitely located the two-liquid area at temperatures of 1450" and 1540°C. They also reported that additions of 1 pct Al, Ni, Pb, Sn, or Zn caused no segregation in 50 pct Cu alloys at 1540°C. The use of copper in amounts approximating 1 pct has found industrial employment to an increasing degree in both wrought and cast steels, for such steels are capable of being precipitation-hardened following normalizing, and have high yield strengths. This is summarized by Gregg and Daniloff,1 Sallitt,9 and Lorig and Adams,10 while Alexander" gives additional information on the heat treatment of copper-steel castings. Lippert12 has described Digby's two-phase steels containing copper and chromium. The work described in the present paper was done in the years 1932 to 1934, at which time much of the information was new. The excellent work subsequently done in other laboratories but more promptly published makes the present paper in part only a confirmation of what is now well known. There has not, however, been published any unified study of

Jan 1, 1951

By R. I. Jaffee, H. R. Ogden, D. J. Maykuth

IN THE past year, Jaffee and Campbell&apos; and Finlay and Snyder2 reported on the mechanical properties of titanium-base alloys, some of which were in the same ranges of composition as are covered in this paper. In this paper, evidence confirming that given by Finlay and Snyder on the effects of carbon, oxygen, and nitrogen on titanium will be presented; and, in addition, new data will be given on the effects of these elements on the flow properties and phase transformation of titanium. Materials and Preparation of Alloys The preparation and general properties of iodide titanium have been adequately described elsewhere.&apos; , As-deposited iodide titanium rod, prepared at Battelle, of Vickers hardness less than 90 was employed as the base metal in the present work. This was the same material as that used by Finlay and Snyder.2 The probable analysis reported by them for standard quality metal holds here also: N 0.005 pct, 0 0.01 pct, C 0.03 pct, Fe <0.04 pct, A1 <0.05 pct, Si <0.03 pct, and Ti 99.85 pct. Carbon was added in the form of flake graphite supplied by the Joseph Dixon Crucible Co. Oxygen was added in the form of c.p. grade TiO, powder, produced by J. T. Baker Chemical Co. Nitrogen was added in Ti3N4 powder, supplied by the Remington Arms Co. Individual ingots weighed 7 or 8 g. Carbon, oxygen, or nitrogen was added by placing the corresponding powder in a capsule made from as-deposited iodide titanium rods and melting the capsule with the balance of the charge. The charge was are-melted with a tungsten electrode on a water-cooled copper hearth under a partial vacuum of very pure argon (99.92 pct minimum). Melting was practically contamination free. Vick-ers hardness increases of less than 10 points were normal for unalloyed iodide titanium control melts. Nitrogen analyses of are-melted iodide titanium showed a nitrogen content of 0.005 pct, about the same as is present in the as-deposited rod. No tungsten pickup was found in a melt of iodide titanium analyzed for tungsten. Weight losses in melting nitrogen-free alloys were very small and varied consistently from nil to 0.015 g (0 to 0.2 pct). This permitted the use of nominal composition for these alloys. Chemical analyses made for carbon, which can be analyzed conveniently by combustion methods, justified this procedure. Where nitrogen was added, considerable splattering took place. Here it was necessary to analyze for nitrogen by the Kjeldahl method. The ingots were hot rolled at 850°C to about 0.045 in. thick. After hot rolling, the strips were descaled by mechanical grinding, and then given a cold reduction of 5 to 10 pct to insure a uniform thickness throughout the length of the specimen. The edge strips and the tensile strips were annealed in a vacuum of 1x10-4 mm Hg pressure for 3 1/2 hr at 850°C and furnace cooled. Methods of Investigation Hardness Measurements: At least five Vickers hardness measurements were taken using a 10-kg load on each sample in the following conditions: (1) top and bottom of each ingot, (2) top and bottom surface of as-rolled and annealed sheet, and (3) on cross-section of annealed sheet and all quenched specimens. Tensile Tests: Tensile tests were conducted on Baldwin-Southwark testing machines having load ranges of 600 or 2000 lb. Tests were made on 1-in. gauge-length specimens, 3 1/4-in. overall length, 1/2 in. wide, 0.040 in. thick, with a reduced section 1 1/4 in. long and 0.250 in. wide. Two SR-4, A-7 strain gauges, one mounted on each side of the specimen, were used to measure the strain over a limited range to determine the modulus of elasticity. After the modulus of elasticity readings had been taken, load vs. strain readings were taken, using only one strain gauge, at increments of 0.0001 in. until the yield points were passed and then at 0.001-in. increments to the limit of the strain-gauge indicator (0.02 in.). Strain readings above 0.02 in. per in. were taken every 0.01 in., using dividers to measure the strain between the 1-in. gauge marks until the maximum load had been reached. Crosshead speed, when using the SR-4 gauges, was 0.005 in. per min, and, when using dividers, 0.01 in. per min. Flow Curves: Flow curves were determined using the true stress-true strain data obtained during the tension test. The usefulness of this type of information has been dealt with very adequately elsewhere by L. R. Jackson,&apos; J. H. Hollomon,6 and many others. Flow curves of true stress vs. true strain could be converted to the more conventional cold-work curve of 0.2 pct offset yield strength vs. percentage of cold reduction by means of the transformation, 1/1 = 1/1-R, where R is the fraction reduction in cold working. Thus, the true strains corresponding to percentage reduction can be calculated, and the 0.2 pct offset yield strengths scaled off the — 6 curve by taking the true stresses corresponding to the values of 6 + 0.002 strain. Heat Treatment: For the transformation studies, the alloys were heat treated in a horizontal-tube furnace using a dried 99.92 pct argon atmosphere, and quenched into water. Essentially no contamination was found after several hours of heat treatment at temperatures up to 1050°C. Metallography: Specimens were prepared in the

Jan 1, 1951

By J. A. Rowland, C. W. Funk

THIS investigation is a part of the United States Bureau of Mines work in conserving the Nation&apos;s resources. The isothermal sections presented were developed as a guide to a comprehensive investigation of the properties and fabricating characteristics of copper-base alloys containing manganese and tin. These alloys are being investigated as possible replacements for the commercial bronzes containing substantial quantities of tin. Development of the isothermal sections has, therefore, been limited to the area between 0 to 20 pct Mn and 0 to 25 pct Sn. Since Heusler1 reported the ferromagnetic properties of the Cu-Mn-Sn alloys in 1903, the system has been the subject of several investigations. These studies were largely concerned with correlation of magnetic properties and crystal structure.2-6 Vero,&apos; however, established the solidus surface of the system, between 20 pct Mn and 40 pct Sn, by thermal and microscopic methods. The a, ß, and y solid solutions were also observed by Vero and reported to extend into the interior of the ternary system. For the present study, the annotated diagram of the Cu-Sn system prepared by Raynor&apos; and the Cu-Mn diagram by Dean and coworkers9 were used as the binary borders of the ternary system. Procedure The metals used in this investigation were electrolytic manganese, washed cathode copper, and three-star tin. The manganese, produced at the Boulder City pilot plant of the Bureau of Mines, had a purity of 99.9 pct; the copper contained less than 0.004 pct Bi and 0.001 pct S; the tin contained 0.070 pct Pb, 0.070 pct Sb, 0.050 pct Fe, and 0.065 pct Si. Heats of 1 lb were melted in alundum crucibles with a 3-kw induction furnace. The heats were chill-cast in iron or copper molds to form 6-in. ingots 3/4 in. in diameter. Molds were washed with graphite or zirconia, depending on the manganese content, and preheated to 150°C. The maximum impurity content of any alloy was 0.03 pct Fe, 0.02 pct Si, and 0.02 pct Al; in most cases, they contained less than half this quantity of any of these impurities. Composition of the alloys and their treatment prior to homogenizing are shown in Fig. 1. Designations adjacent to each composition refer to the heat numbers. With a few exceptions, ingots containing 20 pct Sn or less were hot-swaged. These ingots were swaged, after a 24-hr preheat at 650°C, to obtain a total reduction of 70 pct in cross section. Intermittent reheating was necessary, and reductions were limited to either 0.025 or 0.050 in. in diameter per pass. Selection of a 200-hr homogenizing treatment was based on extensive experiments which indicated that virtual equilibrium was reached after 150 hr. Structures were retained by quenching in water. Grain sizes in the specimens homogenized at 350" and 450°C were generally small. These homogenizing treatments were preceded by a 50-hr anneal at 650°C to facilitate phase identification by increasing the grain size in these specimens. The specimens were furnace-cooled from this temperature to the homogenizing temperature, and the heat treatment was continued for the standard 200-hr period. The homogenized samples were bisected to provide an internal section for metallographic examination. Optimum definition of the microstructure was obtained by successive polishing and etching. Quarter-strength ASTM copper reagent No. 13 gave the most satisfactory results.10 Filings from interior sections of the samples were used for diffraction studies. These filings were annealed in evacuated glass tubes at homogenizing temperatures for periods exceeding 50 hr and quenched in water. During this treatment the manganese content was reduced by significant amounts, probably by vaporization. This change in composition was considered in applying the diffraction data, which were used only as a means of identifying phases where the data were consistent with the metallographic evidence. Phase Identification The a solid solution is readily distinguished by the copper-colored, twinned, polyhedral grains, as shown in Fig. 2, and a face-centered cubic X-ray pattern. Tukon indentations, using a 25-g load, indicate a Knoop hardness of 155 for a quenched from 650°C. Using white light developed by a Wratten 78 A filter, the ß grains in etched specimens have a dark brown tint in contrast to the lighter copper-colored grains of the a phase. Knoop hardness values of 284 were obtained for the ß structure in specimens quenched from 650°C. The ß structure was also distinguished from the a phase by its body-centered cubic lattice. The acicular structure appearing in Fig. 3 was evident in several alloys of higher tin content after quenching from either 750&apos; or 650°C. Since a trans-

Jan 1, 1954

By Nicholas J. Grant, Michio Yamazaki

Cast copper alloys containing 10, 20, and 30 pct Ni and 0.75 to 0.80 pct Al were machine-milled into chips, then comminuted in a rod mill to fine flake powder utilizing a number of processing variables. The powders here internally oxidized, mostly at 800°C, in a low-pressure oxygen atmosphere. The consolidated powders were hot-extruded into bar stock. Room-tenmperature tension tests, stress-rupture tests mostly at 650°C, but also at 450° and 850°C, and hardness measurements after various annealing temperature treatments to study alloy stability were perfomted. Excellent room-temperature strength, high rupture strength at 650°C, and resistance to recrystallization at 1050°C were obtained. Problems in optimizing conditions for internal oxidation of Cu-Ni base alloys are discussed. THE interesting high-temperature properties of SAP&apos; have stimulated considerable effort in the study of more refractory alloy systems where the potential for high-strength alloys at high temperature is great.2-13 A number of methods have been utilized to produce the desired fine, hard particle dispersions, of which internal oxidation2,9,7 of dilute solid-solution systems offers considerable promise by virtue of the potential for producing ultrafine, well-dispersed oxides. While most of the published works are concerned with pure metal matrices, a number of investigators have studied the effects of solid-solution strengthening.10,19 Use of more complex alloy matrices (for example, aging systems) has been unsuccessful because overaging still occurs at high temperatures in the oxide-containing alloys.14.15 Solid-solution strengthening is, however, effective at very high temperatures9,10 and might be expected to contribute importantly to the strength of oxide-dispersion strengthened alloys. For this study, internal oxidation of solid-solution alloys of copper and nickel, containing small amounts of aluminum, was chosen as the method of alloy preparation. PREPARATION OF ALLOYS Three copper alloys containing about 10, 20, and 30 pct Ni and each containing 0.75 to 0.80 pct A1 (enough to yield about 3.5 vol pct alumina) were prepared as air-cast ingots measuring 2.5 in. diameter by 6 in. high (see Table I for the analyses). Processing steps for all the alloys were as follows (also see Table 11): 1) Homogenization of the ingot at 982°C (1800°F) for 45 hr in an argon atmosphere. 2) Machine milling of ingots into fine chips. Average thickness was about 0.1 to 0.2 mm. 3) Hydrogen reduction of chips at 593°C (1100° F) for 1 hr to reduce copper and nickel oxides. 4) Rod milling of chips to finer powders. 5) Hydrogen treatment of powders as in step 3. 6) Internal oxidation of the powders. 7) Hydrogen treatment of oxidized powders as in step 3. 8) Hydrostatic compression of evacuated powders. 9) Sintering of compacts in hydrogen. 10) Hot extrusion. Variations in processing among the alloys were made in steps 4, 5, and 10 (see Table 11). In the past, two methods were utilized to internally oxidize alloy powders. Preston and Grant3 surface-oxidized dilute Cu-Al powders to obtain the necessary amount of oxygen to oxidize the solute metal (aluminum and silicon), and then permitted the formed copper oxide to diffuse and react with the solute in an argon atmosphere. Bonis and Grant4 exposed Ni-A1 and other nickel alloys to an oxygen pressure derived from the decomposition of nickel oxide at a preselected temperature, in an argon atmosphere. Both methods are applicable and can be modified to generate a range of oxygen pressures for oxidation of the solute but not the solvent metals. Procedure I: Surface Oxidation of Alloy A3, Cu-10Ni-0.76A1. Powders of -20 to +28 mesh were surface-oxidized at 500°C (932°F) to obtain the desired amount of oxygen for oxidation of the aluminum to alumina; the powder was then sealed in Vycor and heated at 900°C (1652°F) for various times up to

Jan 1, 1965

By Colman Goldberg

IT is customary to plot crystallographic planes or axes on a Wulff stereographic net which is ruled with parallels of latitude and meridians of longitude. If a single crystal is placed at the center of a sphere, the coordinates of a crystallographic plane or axis are the coordinates of the point where the axis intersects the sphere. The standard (HKL) projection is the projection for which the sphere is rotated so that the (HKL) pole is at the center of the projection. Schiebold and Sachs&apos; and many others have published standard projections for the more important planes of a cubic crystal. With Tables I and 11, it is possible to plot any plane (HKL) of a cubic crystal on a standard (001) projection if the absolute values of the individual H, K, and L are nine or less, which is almost always the case. Using the methods outlined by Barrett,&apos; the standard (001) projection can be rotated so that any arbitrary plane is at the center of the projection. The tables are believed to be important for two reasons: 1—The heretofore published standard projections usually are not of the proper size to fit the stereographic nets available. With these tables a standard projection can be made which will be of exactly the proper size for the available stereographic net. 2—With the tables, planes that do not appear on the previously published standard projections can be easily plotted. For these reasons, the tables are especially useful in the study of optical reflections from etched surfaces and can also be used to make a standard projection for the axis which is normal to the macroscopic surface. (This axis can be found by X-ray or optical methods.) Then if the crystal is etched, the effect of the etchant can readily be determined by comparing the latitude and longitude of the reflecting planes (as determined with an optical goniometer) with the standard projection that has been prepared. Use of the Tables Fig. 1 shows the meridians and parallel which have been designated as zero longitude and latitude. The tables themselves are self-explanatory. The

Jan 1, 1953

By R. W. Guard

ALTHOUGH etching techniques have been developed for revealing dislocation sites in several metals and ionic crystals,h t is valuable to extend the technique to new metals. An etch pit method for nickel has been developed on the basis some suggestions of Dr. John R. Cuthill of the National Bureau of Standards who had observed etch pits in creep specimens of nickel. The etchant used was proposed first by wensch2 for revealing grain size in nickel. The present paper describes the evidence that the technique can be used to reveal dislocations and gives the conditions under which etching can be carried out. The specimens examined were vacuum melted high-purity Ni (99.985 pct Ni) and commercial "A" nickel (99.8 pct Ni). Both materials contained greater than 0.008 pet C and had been annealed in nitrogen or dry hydrogen at 1100o to 1200°C. This gave a grain size of 1.5 mm in the high-purity nickel and 0.050 mm in "A" nickel. Tensile specimens (0.254 in. diam) were deformed from 0.25 to 10 pct at room temperature and then heated for 1/2 hr at different temperatures from 400" to 900°C. The specimens were sectioned longitudinally then polished electrolytically in 60 pct H2SO4 and etched in 35 pct H3PO4 solution at 0.2 to 0.4 v for 30 sec to 3 min. The best method for setting the proper voltage for etching is to increase the voltage until gas bubbles are evolved vigorously from the specimen and then cut it back by 10 pct. It is necessary to heat the specimen above 500°C after deformation in order that etch pits will be formed. This "decoration" treatment permits carbon to segregate to the dislocation rendering them sensitive to etching. It was demonstrated that carbon was the decorating impurity by decarburizing some specimens in wet H2 at 1200°C. The susceptibility to etch pitting was lost following this treatment but could be restored by carburizing in contact with graphite. Some rearrangement of the dislocations in the as-deformed structure occurs on heating at 500oC and above so that the technique can not be used to study the nature of dislocation patterns in deformed specimens. Extended etching does not change the number of pits although the background becomes rough and the pits quite large. The polycrystalline specimens with various strains were examined after annealing at different temperatures. Typical patterns are shown in Figs. 1 and 2. In the unstrained specimen, Fig. 1, the density of pits is 2.5 X 10&apos; per sq cm. All grains show pits regardless of their orientation although there is a

Jan 1, 1961

By E. N. Mazza, H. S. Kalish

The effect of sintering types 302, 3028, and 430 stainless steel powder compacts in hydrogen and dissociated ammonia was investigated. It was found that sintering in dissociated ammonia resulted in as much as 0.5 wt pct increase in the nitrogen content of stainless steel even though the dissociation of the gas was complete. Sintering in hydrogen, on the other hand, reduced the nitrogen content of the stainless steel to less than 0.01 wt pct. In the case of the 302-type stainless steel, the low nitrogen content resulted in a material that was largely ferritic, whereas the high nitrogen content rendered the material fully austenitic. Sintering in dissociated ammonia resulted in lower density, generally lower tensile strength, less ductility, and higher hardness than sintering under equivalent conditions in hydrogen. The reduction of oxides on both stainless steel and iron particles was found to be effected by hydrogen partial pressure in the sintering atmosphere. Compacting pressure was found also to effect oxide reduction during sintering. DISSOCIATED ammonia often is used as a substitute&apos;.&apos; for hydrogen in sintering and in annealing, since economic advantages sometimes can be obtained by such a substitution. In addition, anhydrous ammonia contains very little impurity. Thus, dissociated ammonia gas is very dry whereas tank hydrogen often must be freed of oxygen and water vapor prior to use in many applications. The sintering of stainless steel powder compacts as well as bright annealing is well recognized as requiring a hydrogen atmosphere and for the foregoing reasons dissociated ammonia is frequently substituted. It has generally been overlooked, however, that the nitrogen in dissociated ammonia might have an important effect on the sintering process and on the properties of stainless steel compacts. Considered an inert gas in many applications, nitrogen, on the other hand, is very reactive with cer- tain metals. Dissociated ammonia could not be used for hydriding zirconium or titanium. Nitrogen reacts with columbium, tantalum, chromium, uranium, thorium, and many other active metals. Iron and iron-base alloys are, for the most part, inert in nitrogen but there are many borderline cases. It has been reported that stainless steel stabilized with columbium or titanium should not be sintered in dissociated ammonia.3 olybdenum has been reported as reacting with dissociated ammonia to a minor extent.&apos; Although most of the reactions with iron-base alloys are attributed to the action of un-dissociated ammonia and the action of nascent nitrogen, Uhlig4 showed how readily pure molecular nitrogen reacts with and diffuses into 18-8 stainless steel at 1150°C. He also pointed out how readily nitrogen diffuses out of 18-8 stainless steel when heated in pure dry hydrogen, and these thorough investigations on the subject show that commercial stainless steels are nitrogen-bearing, since they are melted in air. The effects of nitrogen in stainless steel, particularly the 18-8 Cr-Ni type, previously have received considerable attention." In 1926, it was pointed out

Jan 1, 1956

By J. E. Hilliard, J. W. Cahn

calculation has been made of the standard deviations to be expected in the measurement of volume fractions by areal analysis, lineal analysis and four point-counting Procedures. The effect of experimetztal errors is not included. Our conclusion is that a point count using a two-dimensional grid will be the most efficient method of volume fraction analvsis providing the grid spacing IS coarse enough. The predicted standard deviation for such an analysis is shown to he in good agreement with that determined experimentally. A metallurgist wishing to estimate a structural property by means of quantitative metallography is often faced with a choice between several different procedures. In such a case, he will naturally wish to know: a) Which procedure is the most efficient in the sense of requiring the least effort for a given precision? b) For a given procedure, what are the conditions for maximum efficiency? c) Under these conditions, how many measurements are required to attain a given precision? It is our aim in this paper to provide at least partial answers to these queries as they relate to the estimation of volume fractions from measurements on a random two-dimensional section of an opaque specimen. The commonly used techniques1,2 for volume-fraction analyses are based on one or more of the following principles: i) For an areal or Delesse3 analysis: That the areal fraction of a three-dimensional feature intercepted by a random plane provides an unbiased estimate of the volume fraction of that feature. ii) For a lineal or Rosiwal4 analysis: That the fractional intercept on a line passing at random through a two-or three-dimensional feature provides an unbiased estimate of, respectively, the areal or volume fraction of that feature. iii) For a point-count analysis: That the fractional number of randomly or regularly dispersed points falling within the boundaries of a two-dimensional feature on a plane, or within the boundaries of a three-dimensional feature in a volume, provides an unbiased estimate of, respectively, the areal or volume fraction of that feature. The absence of bias referred to in these principles does not, of course, imply that the results of an analysis will be free of error, but only that the expected result is equal to the true one. Application of the foregoing principles provide the following six possible experimental procedures: a) An Areal Analysis—This involves the measurement with a planimeter (or other means) of the area of a constitutent intercepted by the plane of polish b) A Two-Dimensional Random Point Count—Apos-sible experimental procedure for this analysis is to superimpose a sheet of transparent graph paper on a micrograph, and then use a table of random numbers to select coordinates for the points. c) A Two-Dimensiotuzl Systematic Point Count-Similar to b) except that the points are distributed in a prescribed manner, usually at the corners of a lattice superimposed on a micrograph or the screen of a projection microscope. d)A Lineal Analysis—A measurement of the fractional line length intercepted. It is usually performed by traversing the specimen under the cross hairs of a microscope and recording the distance travelled in each constituent. e) 4 One-Dimensional Random-Point Count— This could be performed by traversing the specimen with stops at random intervals to identify the constituent then present under the cross hairs. f) A One-Dimensionul Systematic Point Count— Similar to e) except that the traverse is stopped at prescribed (usually equal) intervals. It will be noted that the point-counting procedures b) and c) can be regarded as methods of estimating the areal fraction. Similarly, e) and f) are indirect methods of making a lineal analysis. All of the six procedures described above involve at least one stage of sampling. Thus, quite apart from any experimental errors, there will always be a statistical uncertainty associated with the final results. It is with the calculation of this uncertainty that we will be concerned. To avoid unnecessary repetition, the statistical relationships that will be used in the calculations are collected together in the appendix. For a fuller discussion reference should be made to one of the many textbooks5,6 on statistics. For symbols relating to the specimen structure we will follow as far as possible the terminology used by Smith and Guttman.7

Jan 1, 1962

By H. M. Otte, A. L. Esquivel

A new leasl-squares method is Presented for determining lattice parameters of hexagonal or tetragonul structures. The method is adapted for use on electronic computers and involves a reiterative procedure. The correction factor employed raries linearly with the lattice parameter, a (determined from the Brag, angle). In contrast, Cohen&apos;s method and recent modifications of it use a correction factor that varies incersely as the squure of the lattice paramneter, a. While the recent modifications attempt to improve the precision of the extrapolated lattice parameter, a, (or-cu). by stressing the importance of the weighting factor. the present approach emphasizes the need for choosing the correct extrapolation function. A comparison between the present method (the Linear method) and Cohen&apos;s method indicates that the Linear method may be more appropriale in certain cases. through a priori no critertion appears to he available for making a chorce between the methods. The size of hexagonal and tetragonal crystal lattices is determined by two parameters, a, and c,. Although in principle the two lattice parameters can be determined independently from reflections for which h - k = 0 and 1 = 0, respectively, in practice this may be inconvenient (because of the angular positions at which these reflections may occur) or not easily possible (because of low intensity). Furthermore, if a high precision or accuracy is required, the limited number of reflections of this type available, particularly in the high-angle region, is not sufficient for the necessary corrections (mainly due to absorption) to be determined with accuracy. Several methods1-7,11-13 have been proposed employing all reflections, to obtain the optimum values, a. and co, either by a trial and error procedure or a least-squares fit. Of the latter method, cohen&apos;s5 is the best known one since it provides explicit expressions for the optimum a. and c,. However, Cohen&apos;s method is only strictly valid if an extrapolation function is used that varies linearly with l/a2 or lie2 (see Section 3), a requirement that does not appear to be generally appreciated. On the other hand, all the better known and more widely used A recent trial and error method was proposed by Massalski and King8,7 who computed extensive auxiliary tables of axial ratios vs the functions A = [(4/3)(h2 + hk +k2) + l2+(a/c)2] and C = A(c/a)2 used in computing a and c values from the observed Bragg angles. These values of a and c were then plotted against a function which permitted linear extrapolation. As a criteria; for the "optimum" values, Massalski and King rely upon a visual fitting of the line through points representing reflections of low 1-index points to compute the extrapolated value of ao and high 1-index reflections to obtain CO. The successive computations and graphical plotting required to reach the "optimum" value are quite lengthy and tedious even on a desk calculator and no quantitative assurance is obtained of having in fact selected the optimum value.* If the method of Massalski and King is used on an electronic computer, then their published tables become redundant and a least-squares fit becomes a natural selection for the choice of optimum values. Such an approach will be called the Linear method. For work now in progress on the effect of certain physical variables on the lattice parameters of hexagonal crystals, it has become essential to determine the confidence limits of small changes in the lattice parameters. Since extrapolation functions that varied linearly with a and c actually also appeared to vary linearly with l/a2 or l/c2 when tested against published as well as our data, a comparison of Cohen&apos;s method and the Linear method was considered desirable (Sections 3 and 4). For the latter method an electronic computer was required since a reiterative procedure to obtain the optimum ao and co values had to be employed. The purpose of this paper is to describe the principles of the Linear method, illustrate its application, and compare it with Cohen&apos;s method. 1) THE LINEAR METHOD The standard practice in obtaining the lattice parameters in the Debye-Scherrer method is to

Jan 1, 1965