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By David C. Peters, Robert S. Crosson

A method of error analysis has been applied to the location technique of non-linear least squares iterative inversion in order to evaluate the resolving power of several seismic array configurations with various assumed earth models and errors and inaccuracies in arrival times. The results obtained demonstrate that lateral accuracies of location are improved significantly when the depth of the miner is known. Lateral location to within 100 feet appears achievable in many instances. If it is possible to refine earth models significantly beyond what has normally been assumed in this work by the use of on-site data, or if the mine is shallow (300 feet or less), accuracies of-about 30 feet or so may be attainable. Inaccuracies in earth models of about 5% are found to contribute much more heavily to these location inaccuracies than errors of a few milliseconds in picking arrival times; however, arrival time errors of 15-20 ms or above will dominate these model inaccuracies. The expected accuracy of location is found to fall off very rapidly as the miner moves outside the array. The strength of this effect depends markedly upon the geometry of the array configuration and can be reduced by careful design. Also, as the size of the array is increased, expected location errors within the array are not altered much, but continue to match the error associated with the smaller array over a larger area (assuming that all stations can still pick up the miner's signals). Better location accuracy, especially with respect to depth control is achievable in an earth where the velocity is depth-dependent (increasing with depth) than in one which is homogeneous. This is an advantage since the

Jan 1, 1974

By Roy Greenfield

Estimates are given for the distance from a seismometer at which a miner can probably be detected. The procedure in making these estimates was to first establish the natural noise levels at the output of a surface seismometer for the 25 to 100 Hz frequency passband. The noise levels give the range of values which may be expected in areas with no man-made noise. For each noise level, we give the detection threshold which, when exceeded, indicates that a signal has been received. Based on the signals recorded by Westinghouse, curves are given which show the peak signal amplitude as a function of source- to-receiver distance (slant range). Curves are given for the Westinghouse seismic thumper, a 50-pound timber, and a sledge. For a given type of source, the receive signal strength depends more strongly on slant range than on any other factor. However, there is approximately a five-to-one scatter in the amplitudes. Thus, further study of factors affecting the signal amplitude might allow better estimates to be made for any particular geological setting. Combining the signal amplitude with the detection thresholds for the different noise conditions gives the distances at which a miner should be detected. These are given in Table l* below. [ ] The text also gives the increase in detection ranges which should occur if steps are taken to increase S/N by 10 dB. We feel that 10 dB is a conservative estimate of the improvement possible. During an actual rescue operation, the seismic crew and system should be capable of making on-site estimates of their detection capability, based on measurements of the site noise, and upon the best available estimates of the

Jan 1, 1974

By W. W. Gerberich

SINCE the original formulation of fracture mechanics concepts,&apos;y2 relatively little work has related the fracture mechanics description of metal behavior on a gross, structural component scale to the behavior of its microstructural constituents. The purpose of this note is to suggest the utilization of fracture mechanics to describe material behavior on a microscopic scale. A Fracture Concept for Two-Phase Structures. A critical displacement concept considering the tough unidirectional phase in a relatively brittle matrix is first examined. It is assumed that a flaw exists at position 1 as depicted in Fig. 1. As the crack moves from position 1 to 2 the plastic zone could be of the shape described with the size approximated by the Dugdale3 model: where c is the half-crack length, OO is the applied stress, and oyS is the yield strength. Hahn and Rosen-field4 have presented a simple fracture criterion for homogeneous materials based upon the displacement at the crack tip. They also have shown the equivalence of the critical displacement, v*, to fracture toughness by Kc = (2v*oysE)1/2 [2] The displacement at the crack tip is given by and the displacement at any distance in front of the crack tip may be determined knowing the plastic zone size and utilizing the development of Goodier and Field.5 Recalling Fig. 1, the value of v* for fracture in material M1 may be calculated from Eq. [2] providing the critical stress intensity factor is known. As the material is loaded, when vc > vM1 the crack moves from position 1 to position 2 where it encounters the tough second phase. If vc2 < vm2, then the crack will be arrested providing the width of the M2 phase is sufficiently large. This condition is necessary since the displacement at position 2 has increased due to the longer crack length. Thus, the displacement at the distance X (representing the dimension of the second phase) in front of the crack may be larger than the critical displacement for failure in the brittle material. If v, > vm, then failure will proceed in the brittle material. The value of v, may be calculated as indicated above. This latter consideration is the same as predicting fracture of a brittle second phase at some distance in front of a crack located in a ductile matrix. Experimental Evidence. On a macrostructural scale, tungsten wires in a ductile Be-Cu matrix are seen to fracture well ahead of the main crack front in Fig. 2. Utilizing a Kc value of 14.2 ksi-in.1/2 obtained by Schroder et al.6 for as-received tungsten, the critical displacement 2v*, for fracture is calculated from Eq. [2] to be about 6.5 X 10-5 in. The crack tip displacement, 2vc, is calculated from Eq. [3] to be 0.0028 in. indicating that fracture would occur at a considerable distance in front of the crack tip. From the ratio of v*/vc and the plastic zone estimate of Eq. [I], the distance in front of the crack tip at which a tungsten wire should fracture is calculated to be about 0.195 in. As shown in Fig. 2, a fractured wire occurs at a distance of 0.140 in. (fractured in three places), not at 0.250

Jan 1, 1968

By J. M. Seeman, R. A. Dodd

If some solution-quenched supersaturated aluminum solid solutions, e.g.., Al(Cu), are plastically deformed at room temperature and then aged at 200oC, the hardness may first decrease before increasing in the usual manner &apos; A similar transient softening is observed, even in the absence of plastic deformation, when a thin foil or small-diameter wire Al(Cu) specimen is rapidly quenched from the solution-treatment temperature and then aged.&apos; Also, some solution-quenched and neutron-irradiated alloys undergo an initial hardness decrease during subsequent aging.3 The usual explanation of the transient softening in the above examples involves the effect of vacancies introduced by plastic deformation, rapid quenching, and neutron irradiation, respectively However, the mechanism of softening is not unequivo-cably established. In the first-noted case, Gane and parkins&apos; observed that the softening was approximately proportional to the difference in the atomic diameters of solute and solvent, and it was argued that, if a large relative difference in atomic diameter promoted vacancy-assisted room-temperature solute diffusion to dislocations, dislocation climb occurring during subsequent aging at 200°C could cause transient softening. Some substantiation of this theory was offered by the additional observation that discontinuous yielding of solution-quenched polycrystalline Al(Cu) tensile specimens was suppressed by interrupting the test for a short aging treatment at 200°C. Of course, reversion (resolution of GPI) at 200°C would also cause softening, and Sil-cock4 expressed the opinion that the softening in the case of Al(Cu) must be partly associated with reversion. Also, Hirsch5 commented on the possibility that, if jogs cause hardening, an anneal at 200°C should straighten the jogged dislocations and result in softening. However, parkins&apos; has re-expressed his belief that these mechanisms are not entirely consistent with the observed serrated stress-strain curves. Experimental. New data has now been obtained for Al(Cu), Al(Ge), Al(Mg), and Al(Zn) primary solid-solution alloys. These alloys were prepared from metals exceeding 99.99 pct purity, and specimens 4 by 4 in. diam were solution-treated, quenched, deformed 10 pct in compression at room temperature, and aged at 200&apos;C in a cottonseed oil bath for various times. Generally, these operations could not be carried out in rapid succession, so the alloys were stored in a freezer between treatments to minimize aging. The variation in hardness with aging time, Figs. 1 to 4, was determined by microhardness testing with a 3.0-kg load. At least five readings were averaged to obtain each data point, and all measurements were taken about the center circumference of each cylinder (region of maximum deformation). Each specimen was used to obtain only one data point, i.e., specimens were not replaced in the aging bath after measurements were made. In

Jan 1, 1968

By H. R. Ogden, E. S. Bartlett, A. G. Imgram

Unmodified disilicide coatirigs were applied to sheet-tensile specimens ofCb-Dg3 and Mo-TZM veJractovy- metal alloys. Coating thickness, degree of coating-substrate interdiffusion, and specimen geonzetry (notched and plain were included in the variables studied. Tensile tests were made to determine the ductile-lo-brittle transition temperature. The disilicide coating modestly increased the transition temperatlre of TZM, but had no effect on 043. Neither material condition (recrystallized or stress-velieved) nor specimen geometry (notched or unnotched) significantly altered the effects of coatings on the transilion temperatures of. the alloys. Cracks in the brittle coatings did not propagate into the substrate, and fracture modes appeared to be the same for both un-coated and coated specimens. MOST potential structural applications for refractory metals and alloys involve exposures to oxidizing environments at elevated temperatures. The general lack of oxidation resistance of these metals will require protective coatings to allow fulfillment of their potential. Currently preferred coatings for the oxidation protection of refractory metals are brittle intermetallic aluminides or silicides. These are typically formed on the surface of the refractory-metal substrate by a diffusion reaction between the substrate and a gaseous or liquid medium that is rich in aluminum or silicon. Because of the brittleness of these coatings, they will sustain no plastic deformation at low temperatures. They are frequently cracked by cooling from the coating temperature because of the thermal-expansion mismatch with the substrate alloy. Even if they survive cooling intact, they crack rather than sustain deformation under load at low temperatures. Thus, when a coated refractory metal is strained beyond the elastic limit of the coating at low temperatures, the mechanical environment of the substrate would include both static and dynamic cracks. These might be expected to influence the flow and fracture behavior of the substrate. This could be manifested in an altered fracture mode and/or an increase in the normal ductile-to-brittle transition temperature of the refractory-metal substrate. This paper presents the results of a research program that was conducted to determine the influence of the presence of a brittle surface coating on the low-strain-rate tensile behavior of typical refractory metals at low temperatures. EXPERIMENTAL PROCEDURES Material Preparation. Thirty-mil-thick sheets of molybdenum TZM alloy (Mo-0.5Ti-O.1Zr) and colum-bium D43 alloy (Cb-IOW-1Zr-O.1C) were obtained commercially. These alloys were selected as substrate materials representing two classes of materials important in current refractory-metal technology. The TZM was in the stress-relieved condition, and exhibited a heavily fibered grain structure. The D43 had been processed by the duPont "optimum" fabrication schedule,&apos; and exhibited slightly elongated grains typical of this process. Tensile specimens of two geometries were prepared from these materials: 1) plain specimens with 0.2-in.-wide 1.0-in.-long gage sections; 2) specimens similar to above, but with a 0.06-in.-diam hole drilled in the center of the gage section, providing a stress concentration factor, Kt, of 2.5. The "notch" geometry was selected to represent a typical condition of a rivet hole or other geometric discontinuities as might be encountered in various applications. Machined specimens were degreased, with a final rinse in acetone, prior to the application of coatings. Specimens of each substrate and configuration were pack-siliconizedin a particulate mixture of 80 pct A1203, 17 pct Si, and 3 pct NaF. Specimens were embedded in this mix (contained in graphite retorts) and coated in an electrically heated argon-atmosphere furnace under time-temperature conditions to effect nominal 1- and 3-mil-thick silicide coatings: Coating Thickness, mils Thermal Treatment 0.6 to 1.4 24 hr at 982°C 2.4 to 3.2 48 hr at 1093°C Coating kinetics were similar for both the TZM and D43 substrates. These treatments had little or no visible effect on the substrate microstructure as determined by optical metallography. The coatings on TZM were essentially single-phase unmodified disilicides, while those on D43 showed substantial evidence of modification by proportionate reaction with the respective substrate elements or phases, as shown in Fig. 1. It was recognized that these coatings might not be particularly desirable regarding protective capability. However, it was desired to circumvent possible inter -ferring chemical interaction with the substrate by pack additives such as chromium, titanium, boron, aluminum, and other elements that typify the better protective coatings for these materials.&apos; Thus, the results presented apply specifically to the simple silicide coatings investigated. They may not be rep-

Jan 1, 1967

By O. R. Bergmann

Two approaches were taken to obtain direct experimental evidence jar the existence oj a jet in the explosion-cladding pvocess: 1) direct observation of the claddirg jwocess by rtzeans ojf kig-h-speed photography using a fvartziiy catnera and 2) use of a plated-surface experiment in contribution with clzetrzical analysis. The framing-camera records showed clearly the presence of a jet it1 the form of what appears to be a line spray. The jet velocity is considerably highev than the detonation velocity arid in vacuum it is almost twice as high as the detonatiou velocily. The results jrorrz the plated-surface experiment also corzfivtned the preseizce of- a jet. The artzoutlt o,f etzergy dissipated in the jetting process was foundd lo be consislent with the basic theovetical model o/ the cladding mechanism.. MaNY reports on metal working with explosives have appeared in the literature during the last few yearsThis paper describes experiments concern- ing the mechanism of the explosive metal-cladding process. It has become increasingly important as a unique method for bonding metals and a typical cladding arrangement is shown in Fig. 1. A theoretical analysis of the mechanism of explosive bonding and a description of the nature and types of bond zones obtained was given by Cowan and oltzman." A further discussion of the basic principles of the process, a detailed description of the different bond-zone types, and extensive information on the properties and the applications of explosively bonded metals was recently published by Holtzman and cowan. " The process is now in commercial use by E. I. du Pont de Nemours & Co. The concept of the existence of a jet during metal bonding with explosives forms a central part in the theoretical analysis of the cladding mechanism described by Cowan and Holtzman When a layer of explosive is detonated on a metal plate that is separated from a second metal plate by a small distance the metal plate in contact with the detonating explosive is accelerated by the detonation pressure. An angle is established between the undeflected and deflected portions of the plate. Subsequently the deflected portion of the first plate collides with the second metal plate.

Jan 1, 1967

By T. F. Bower, M. C. Flemings, H. D. Brody

A series of experiments are reported which show thai reasonable assumptions for analysis of solute redistribution in solidification of castings and ingols illclr(de: negligible undercooling before nuclcation of solid phases, negligible increase of solute in advance of the tips of growing dendrites, complete diffusion within the Liquid oer distances the order, of dentrite arm spacings, platelike dentrite t/o?$holog?.. Qzmli/ali,e and periment is obtained JOY Al-Cu alloys front measurements of amount of nonequilibrium second phase, minimum solute content at the centers dentrites arms (after solidification), and 3) change in minimum solute content in dentrite arms during solidification. In a previous paper&apos; analyses were given describing solute redistribution in dendritic solidification. The analyses were undertaken primarily to permit prediction of "severity of microsegregation" in a casting or ingot after solidification and cooling to room temperature, but can also be used to predict "local fraction solid&apos; as a function of temperature in the solidifying alloy. Numerical results were given for Al-Cu alloys. The aims of this paper are to examine the validity of some of the assumptions of that analysis, and to compare predictions of the theory with experiments. All experiments reported are on Al-Cu alloys, the bulk on Al-4.5 pct Cu alloy. EXPERIMENTS Experiments conducted were on small ingots, 41/2 in. in diam by about 10 in. high. solidified in a controlled thermal environment (i.e., in a resistance-heated, re-circulating air furnace, whose temperature could be controlled to 1°C). In one series of experiments, the ingots were solidified very slowly (solidification time was varied from 8 to 1000 hr) and at constant rate of heat extraction. In a second series of experiments the ingots were solidified ( &apos;unidirectionally". Fig. 1 is a sketch of the method of making the two different types of ingots. The unidirectionally solidified ingots were fully columnar, and the slowly solidified ingots had equiaxed structures, Fig. 2. In making the slowly solidified ingots, the mold employed was carbon steel, coated with inert refractory. Typically the mold and its environment were heated to 700°C. The molten alloy was then poured into the mold and the temperature of the system equilibrated above the liquidus. The environment of the mold was next cooled with a controller responding to a differential thermocouple that measured the difference between the temperature of the melt and the temperature of the mold environment. The differential thermocouple consisted of one chromel-alumel junction in the melt connected in opposition with a second junction in the furnace. The potential across the differential thermocouple was input to the controller which acted to keep this potential at a set. constant value; hence the temperature difference between the two junctions was maintained nearly constant. Major resistance to heat flow in the above apparatus was between the metal surface and the furnace atmosphere, not in the metal itself. By maintaining a constant temperature difference between the metal and the furnace atmosphere, the controller maintained an essentially constant rate of heat extraction during solidification, regardless of amount of heat released by the metal per unit temperature change. When the metal temperature dropped just below the eutectic temperature. the ingot was removed from the furnace and water-quenched. The unidirectionally solidified ingots were cast in a similar mold to the foregoing except that provision was made to extract heat through the bottom face of the mold by passing air or water through the mold base, Fig. 1. For these experiments, metal and mold temperature were again equilibrated above the liquidus. Temperature of the mold environment was then held

Jan 1, 1967

By Richard L. Ashbrook, John F. Wallace

Several high-temperature eutectics of cobalt and nickel alloys were modified by small additions of selected elements. Thes-e alloys were compared to unmodified melts for microstructural variations. A few modified compositions were selected on the basis of structure and their tensile and stress-rupture behavior determined. The results of stress-rupture tests in air at 1800 F and room-temperature tensile tests of four high-temperature eutectics showed modification capable of producing substantial improvements in properties. The microstructures were altered and mechanical properties improved by: a.) dispersing a subordinate phase more uniformly throughout the matrix; b) replacing large continuous -network or platelike constituents with small equiaxed discontinuous phases; and c) by forming new, finely divided phases. tHE term "modification" is most commonly used to describe the refinement in microstructure of the Al-Si eutectic that occurs as a result of rapid cooling from the melt or on slow cooling after treatment with small amounts of sodium.1 "Modification" has also been used to describe the change from flake to spheroidal graphite in the austenite-graphite eutectic of cast iron.2 This change of graphite shape is accomplished by small additions of cerium or magnesium.3 Other systems have also been shown to be capable of modification, for example: Pb-Sn by copper;4 Al-Cu by sodium;5 Al-Mn by sodium;5 and Pb-Sb by aluminum.5 Although modification of Al-Si alloys and cast irons is usually accompanied by improved mechanical properties, a general definition of modification has been suggested to include the effect of small quantities of impurity elements on the microstructures of all eutectic alloys, regardless of the effect on the mechanical properties.6 In this paper, the term "modification" is employed in a broad sense to include the formation of third phases or even the supplanting of one of the binary eutectic phases by a third phase. The mechanism of modification, as for any solidification phenomenon, must be considered primarily in terms of nucleation and growth. Although both nuclea-tion and growth mechanisms are required to explain all the phenomena observed in connection with the solidification of modified eutectics, various investigators have usually favored one or the other.7"16 It has been shown that modification of a binary eutectic can be effected by addition of a solute element that has greatly different distribution coefficients or k values in the two phases of the eutectic. Under these conditions, differences in the temperatures at the solid-liquid interfaces of the two phases retard the growth of one phase with respect to the other.4 It has also been shown that increased undercooling favors a transition from a rodlike eutectic to a globular eutectic.17 A mechanism proposed for the transition from lamellar to rodlike eutectics depends on the concept of constitutional super cooling.18 The modification of eutectic alloys may be of interest for high-temperature service as well as at room temperature. Although "high-temperature eutectic alloys" may appear to be a contradiction in terms, many eutectic systems, including those studied in this work, have melting points in excess of 2400°F. One of the mechanisms by which high-temperature alloys are strengthened is dispersion of a relatively brittle phase such as an oxide, carbide, or an inter-metallic compound throughout a ductile matrix. For a given volume fraction of dispersed phase, strength is increased by decreasing the size and spacing of the dispersed particles.19&apos;20 Furthermore, room-temperature ductility may also be increased by changing the shape of a brittle dispersed phase from platelike to equiaxed or spheroidal.8 Overaging and redissolving of the secondary phase limit the maximum temperature to which precipitation-hardened alloys can be used. However, in a binary eutectic system, both phases coexist up to the melting point. Although all eutectic structures are not completely stable,21 a dispersion-hardened cast high-temperature alloy might result if a fine distribution of one of the eutectic phases could be obtained during solidification. An additional reason for interest in eutectic alloys is their excellent castability.22 Since eutectic alloys, like pure metals, freeze at a single temperature rather than over a range of temperatures, their castability is superior to solid-solution alloys with long liquidus to solidus ranges. The purpose of this research was to study the effects of small solute additions on the microstructure and mechanical properties of a number of high-melting-point eutectic compositions.

Jan 1, 1967

By D. A. Woodford

In a constant-load creep test, if the density of nlobile dislocations is assumed constant for strains exceeding that corvesponding to the minimum creep rate, it is shown that the creep rate may be approximated by the equation where E is the nominal strain, o0. is the initial stress, and a&apos; the stress fov unit dislocation velocity. The constant C contains the mean density of mobile dislocations and n is a measure of the stress sensitivity of dislocation celocity. This equation is shoum to be applicable to published data on an alloy steel and on nickel. The degree of plastic instability and hence the creep ductility is dependent on the calue of n for these materials. When instability becomes gross and local macroscopic necking occurs, the assumptions are no longer valid. On the basis of this equation, and the strain-time relation derived from it, a method of predicting the creep behavior at different stresses is suggested. MOst analyses of creep data have been concerned with time-dependent transient creep or time-independ- ent secondary creep in constant-stress tests. The far more widely used constant-load test has been neglected in terms of a mechanistic approach. In general, since the strains involved are usually small, the same laws for transient creep may be applied to both types of tests. However, there is no steady-state creep in a constant-load test since the stress increases continuously. Any apparent steady state observed on a strain-time plot is either fortuitous or illusory, and is generally revealed as a continuously varying creep rate on a carefully constructed strain rate vs time plot.* Transient creep may be understood in terms of a simple differential equation representing the change in mobile dislocation density with time:&apos; where p is the density of mobile dislocations. The first term on the right is related to first-order kinetics of dislocation multiDlication and the second to second-order kinetics of exhaustion. On the basis of this equation, several authors2-4 have found good agreement with experimental transient creep curves for a number of materials. When k1p = k2p2, a steady-state creep

Jan 1, 1968

By S. G. Epstein

Using the capillary-reservoir technique, electromi-gvation rates of cadmium and indium in liquid bismuth were measured at several temperatures. The electric mobility of cadmium Jrom 305° to 535°C and indium from 310° to 595°C can be expressed as a function of temperature by the equations UIn = 1.52 x 10-3 exp sq caz per v-sec Migraion of both solutes was cathode-divected at a rate rnore than four tiMes tHAt previously found for siluer in liquid bisnmth. The electric mobilities of cadmium and indiulrz in liquid bismuth at 500° C are nearly identical with their respective mobilities in mercury at room temperature. AS part of a systematic study of the variables which are considered to control electromigration in liquid metals, the electromigration rates of cadmium and indium in liquid bismuth have been measured. Mass transport properties of silver in liquid bismuth have been reported previously,&apos; and measurements of tin and antimony in liquid bismuth are forthcoming. Comparisons will be made with literature values for these same solutes in mercury.2&apos;3 This series of solutes was selected to determine the effect of the solute valence on its electromigration. Silver, cadmium, indium, tin, and antimony have nearly equal atomic masses but have chemical valences ranging from +1 to +5. They are all fairly soluble in bismuth above 300°C and all have radioactive isotopes, which are an aid in making analyses. EXPERIMENTAL TECHNIQUE Electromigration of cadmium and indium in liquid bismuth was measured by the modified capillary-reservoir technique previously described.&apos; In this method irradiated cadmium or indium is added to bismuth to form alloys containing about 1 wt pct solute (<2 at. pct solute). Several quartz or Pyrex capillaries: 1 mm ID and 5 cm long, vertically oriented, are simultaneously filled in the reservoir of the liquid alloy. A direct current is passed through two of the capillaries, which contain tungsten electrodes sealed in the upper end. The other capillaries sample the reservoir during the experiment. After a measured time interval the capillaries are removed from the reservoir and rapidly cooled. The glass is then broken away from the solidi- fied alloy, which is then weighed, dissolved in acid, and analyzed for solute content by chemical and radiochem-ical techniques. An electric mobility (velocity per unit field) can be calculated from the amount of solute entering or leaving each capillary by the simplified expression1 in which Ui is the electric mobility of the solute, ?mi the solute weight change, Ci the solute concentration of the reservoir, I the current, p the alloy resistivity, and l the duration of the experiment. This expression is valid as long as the experiment is terminated before a concentration gradient develops across the capillary orifice. Earlier experiments showed that the concentration gradient formed initially at the electrode changes with time and eventually reaches the orifice, due to back-diffusion. This condition produces a solute exchange between capillary and reservoir by diffusion or convection, opposing the electromigration, which results in a lower measured value for the electric mobility. To determine if the concentration gradient had reached the orifice, the capillaries used in some of the experiments were sectioned at 1-cm intervals and the solute content of the alloy from each section was radiochemically determined. A typical concentration profile for an experiment with indium in bismuth is shown in Fig. 1; cadmium in bismuth showed similar behavior. As illustrated in the graph, very little back-diffusion has occurred in the capillary containing the cathode, since the concentration gradient is confined to the upper 1 cm of the capillary. In the capillary containing the anode, however, the concentration gradient is much broader, extending nearly to the orifice, even though the net change in solute concentration is nearlv the same in both capillaries. Since cadmium and indium probably lower the density of bismuth when alloyed, depletion of the solute from the alloy adjacent to the anode would increase the density of the liquid in the uppermost region of the capillary. This would give rise to convective mixing within the capillary, causing the broadened concentration gradient. Conversely, the alloy adjacent to the cathode should have a reduced density as the solute concentration is increased by migration, explaining the "normal" concentration profiles found in these capillaries. This disparity was not found for electromigration of silver in bismuth. Both metals have similar densities at the operating temperatures, and nearly symmetrical concentration profiles were found in the two capillaries of each exueriment. This density effect was also apparently encountered when an attempt was made to measure diffusion coefficients for indium in liquid bismuth by the same technique which was successfully used to measure diffusion of silver in bismuth.&apos; Capillaries 1 mm ID and 2 cm

Jan 1, 1968

By R. L. Stegman, M. R. Achter

Nickel, fatigued in vacuum, shows intragranular crack initiation and growth at low temperatures. An increase in temperature initially prolongs fatigue life due to a more homogeneous distribution of slip. With a further temperature increase, the mode of failure undergoes a transitiotz to intergranular crack initiation with concurrent recrystallization which results in a shorter life. The transition temperature varies with bending strain and specimen purity. UNTIL recently, very little work has been done on the effect of temperature on the mechanism of fatigue and the resultant variation in fatigue life. Except for mild steel, where strain aging raises the strength at moderate temperature, fatigue lives had been shown to decrease with an increase in temperature. In their review article, Allen and Forrest&apos; summarized the work of McCammon and Rosenberg and of Forrest and Mann on the fatigue of copper from -269" to 325°C. The fatigue life vs stress curves remained roughly parallel over this temperature range, the fatigue strength decreasing progressively with increasing temperature. When testing was done in vacuum, the present authors&apos; found the results for nickel were different from those quoted above. Initially, the fatigue lives increased with temperature and then decreased as a grain boundary mode of failure was observed. The initial increase was attributed to a more homogeneous distribution of slip, a condition which was not as conducive to crack initiation as the bunching of slip lines observed at 20°C. Ronay, Reimann, and wood3 observed a similar change of slip line distribution in brass, tested in air, with rising temperature. Our previous observations were based on preliminary work with relatively few specimens, fatigued at comparatively low strains. To learn more about the mechanisms, the present investigation was undertaken for the purpose of studying systematically this effect over a wider range of strains and as a function of purity of the nickel. EXPERIMENTAL PROCEDURES The testing equipment, procedures, and specimen geometry have been described elsewhere.&apos; An optical technique to measure bending strains was used as de-

Jan 1, 1968

By William C. Sleppy

The nmgnetic susceptibility of heat-treatable aluminuin alloys is sensitive to chanyes such as solution or dissolution of solute and the precipitation of mew phases. By measuring the change in the magnetic susceptibility of aluminum alloys caused by various heat treatments, an empirical relation was found from which atomic arrangements in dilute binary alloys of copper, zinc, and magnesiutn in aluminum have been delineated. The relation predicts the ultimate formation of C1LA12 when copper is precipitated from solid solution in aluminum. Euidexce joy silovt- range order is found for copper in solid solution in aluminum in the sense that copper atoms avoid being nearest neighbors to an extent greater than would result from a purely random arrangertzeizt. Hume-Rothery has predicted such short-range order joy solid solution of copper in aluminum The Al-Zn system agrees with evidence obtained from X-ray scattering at small angles and predicts a tendency for zinc atoms to cluster in solid solution in aluminum. In the Al-mg system, the empirical relation indicates an approach to randor distribution of magnesium in solid solution in aluminum with a tendency for magnesium segvegation which increases with incveasing temperature. ThE magnetic properties of metals are complicated by the fact that contributions are made to them both by electrons of a "metallic" type which belong to the crystal as a whole, and by electrons in states localized on particular atoms. An expression1&apos;2 for the bulk magnetic susceptibility of aluminum may be written as the sum of three contributions: where XA1 is the bulk susceptibility of aluminum per gram of material (in the cgs system, the units are those of reciprocal density); Xa1+3 is the diamagnetic contribution of the electrons localized in ion cores; Xa1 is. the paramagnetic spin contribution of conduction electrons often called Pauli paramag-netism: Xa1 is the diamagnetic contribution of the conduction electrons often called Landau diamag-netism. Ion core diamagnetism arises from the precession of the electron orbits which occurs when a magnetic field is applied to a system of electrons moving about a nucleus. Its contribution to the magnetic suscepti- bility is small, temperature-independent, and unaffected by alloying. The conduction electron diamagnetism is also temperature-independent and arises from the translatory motion of the electrons. For perfectly free electrons this contribution should be exactly one-third of the Pauli spin paramagnetism, but this relation is seldom even approximately true. Blythe2 determined the conduction electron diamagnetism in pure aluminum and found it to be extremely small. Any change in the conduction electron diamagnetism caused by alloying is neglected in this work. The Pauli paramagnetic contribution3 to the magnetic susceptibility of aluminum depends upon the number of electrons that occupy excited states and whose spins can be turned parallel to an applied magnetic field. The number of electrons free to turn in the field is proportional to the temperature and each spin contribution to the susceptibility is inversely proportional to the temperature. A slight temperature dependence of Pauli paramagnetism occurs when the number of electrons occupying excited states cannot increase sufficiently to balance the inverse dependence on temperature of each spin contribution. The decrease of the magnetic susceptibility of aluminum with increasing temperature is attributed to a temperature dependence of the Pauli paramagnetism. Estimates of the Pauli paramagnetism of aluminum have been made by several workers.2,4,5 All of the values are in reasonably good agreement with each other. In this work Xal at 17°C is taken as 0.761 X 10-8 cu cm per g. An expression similar to [I] can be written for the magnetic susceptibility of an aluminum base alloy containing a fractional weight percent x of solute:&apos; Xa = (1 -x)XAl+3 +xXsoluteion * XaPauli +Xadia) [2] where X, is the magnetic susceptibility per gram of alloy, Xal&apos;3and Xsolute ion are the ion core diamag-netic contributions, and xpauli and xdia are the Pauli and diamagnetic contributions of conduction electrons in the alloy. If the components of a mixture are not alloyed but simply mixed together in their pure states without producing a new phase, then the magnetic susceptibility of the mixture is given by the Wiedemann additivity law: Xm =x1X1 +x2x2 + ..xnxp [3] where X, is the susceptibility per gram of mixture and xnXp are the weight fractions and susceptibilities, respectively,-. for the pure components. The additivity law is not applicable to alloys because the outer electronic structures of the components are changed by alloying.&apos; Both the Pauli paramagnetism and Landau diamagnetism are affected; hence the magnetic susceptibilitv of an alloy is usually different from that calculated using the additivity law. In this work the difference, X, -X,, is taken as a measure of the change caused by alloying.

Jan 1, 1968

By R. H. Richman, F. Borik

A 0.3 pct C-12 pct Cr-6 pct Ni steel was rolled to 93 pct reduclion in area as austenite at 510°C, and then partially transformed as desired to ~rlartensite by qnenching to - 196°C. Pole figures for the austenitic matrix and for the martensitic product were separately determined by an X-ray transmission method. The deforitration texture of&apos; the warm-worked austenite is characlerized by (110)(225) components, and is thus closely similar to those produced in a brasses. The pole jigure of the martensite in partially transformed material agrees well with that which can be constructed by transfortnation of the {110)(225) orientations according to either the Kuvdjuniov- Sacks or the Nishi-yatuu relatiotship. Howeuer, an important result of this construction is that me-third of the predicted orientations are missing. A graphical analysis can then be used to show that in deformed austenite certain crystallographic variants of martensite (related to the most probable austenite slip systems) are suppressed, resulting in this preferred transformation. The evidence for preferred transformation is corroborated by the measured elastic anisotropy of warm-rolled and fully transformed H-11 steel. EXTENSIVE plastic deformation of a polycrystal-line aggregate in a manner that causes flow predominantly in one direction results in a preferred orientation of the constituent crystallites. The particular orientations that are produced depend upon the crystal structure and composition of the material, as well as upon the temperature, mode, and degree of deformation; in any case, the preferred crystallo-graphic orientations, or textures, are reflected in directionality of mechanical properties. Although such anisotropy may be exploited in certain specialized applications, it is more commonly diminished or eliminated by heat treatment lest it interfere undesirably in subsequent forming operations or in structural design. In the recently developed thermomechanical treatments that significantly enhance the strength of some steels,1,2 considerable deformation of the metastable austenite prior to the martensite transformation is essential to the strengthening process. If the austenite is textured by the deformation, and if the transformation to martensite proceeds according to one of the relationships established for transformation in annealed austenite, then it must be expected that the martensite will also possess a preferred orientation even though the multiplicity of martensite orientations possible in a given austen- ite crystal will tend to restore some degree of randomness. The existence of a residual anisotropy, both mechanical 3-6 and crystallographic,&apos; has been substantiated. In the latter crystallographic investigation, preferred orientations were determined for the martensitic structure of an SAE 4340 steel rolled 72 pct as austenite at 833°C and then quenched. However, the choice of a composition that transformed almost completely to martensite during the quench to room temperature did not permit direct measurement of the prior austenitic texture. In fact, when the "ideal orientations&apos;&apos; associated with well-known fcc rolling textures were converted, alone or in combination, to martensite according to the Kur-djumov-Sachs (K-s)&apos; or Nishiyama8 relations, the agreement obtained with the observed martensite texture was only fair at best. Recently a pertinent aspect of the austenite to martensite transformation was reported by Bokros and parker,10 who found that certain habit-plane variants of martensite were suppressed by tensile deformation of Fe-31.7 Ni single crystals prior to the necessary subzero cooling. It might be anticipated that the consequences of such preferred transformation are sustained during the formation of martensite in warm-worked austenite that has a well-developed deformation texture. The present investigation was undertaken first to establish more firmly the relation between preferred orientations in plastically deformed austenite and in the resulting martensite, and second to examine the textures for evidence of deformation-induced preferred transformation. EXPERIMENTAL PROCEDURES An alloy containing 0.3 pct C, 12 pct Cr, 6 pct Ni, and the balance iron, was selected because the mar-tensite-start temperature (M,) of about -100°C allowed convenient experimental manipulation of either austenite or martensite at room temperature. Furthermore, this composition can be readily deformed as metastable austenite at moderately elevated temperatures without intervention of appreciable isothermal or athermal decomposition products. The alloy was austenitized at 1150°C, aircooled to 510°C, rolled unidirectionally at this temperature to 93 pct reduction of cross-sectional area, and finally oil-quenched to room temperature. Partial transformation to martensite was accomplished by quenching to -196°C as needed. The rolled stock was reduced in thickness from 0.067 to 0.010 in. by etching in a solution of 5 pct HC1, 45 pct HNO3, and 50 pct water, and further thinned by careful mechanical polishing to maintain the two sides of the sheet parallel within 0.0003 in. After mechanical polishing to 0.005 in., electropolishing in 1:9 perchloric-acetic acid solution produced a final thickness of 0.002 in. The preferred orientations were determined from

Jan 1, 1968

By John W. Cahn

Tile avevage value of the mean curvature of surfaces in a specimen can be precisely delermined by sitrlple measurements performed on random sections or on 1 vojectiotzs of these surfaces. For surjaces enclosing particles, the quanlity is sllown to be velated to the probable tlurrrhev ot particles intevcepted by a random platne and, under certain conditions, to the perimeter of their Projected image and to the increuse in surjace area when the particles grow. Many of the velalionsl~ips are valid for any shape or size of the particles. THE recent growth of the field of stereology or quantitative microscopy is largely the result of the discovery of a limited number of rigorously defined geometrical parameters that can be precisely measured on random sections or projections of a structure without assumption about particle shape.&apos; Such parameters have been the volume fraction and surface area and line length in a unit volume. The present paper introduces the average of the mean curvature of surfaces in a volume, and shows that it can be rigorously measured by counting methods alone. AVERAGE CURVATURE ON A PLANE Consider a curve y = v (x) on the xy plane. The curvature Kp in the plane at any point is given by Kp = (dZy/dx2)/[1 + (dy/dx)2]3/2. The average curvature along the curve may be defined as Kp = (1/L) fKpdl |1] where dl = [(dx)&apos; + {dy)2]1/2 is the length of an element of the curve and .(dl = L is the total length of the curve. The integral on the right-hand side of Eq. [l] will be called the total curvature, It is dimensionless and readily evaluated by substituting d = arctan (dy/dx) to give ah which is the change in direction of the tangents to the ends of the curve, Fig. 1. Hence, Kp = (1/L)(?h) [2] It can also be seen that Eq. [2] is applicable in the limit of sharp corners. Even though the curvature is infinite at a corner, f Kpdl remains integrable and equal to the change of angle. The signs of the quantities Kp and dl are arbitrary and, if the areas adjoining the curve are equivalent, there seems to be no compelling reason to fix the signs. For a closed curve, however, it becomes worthwhile to use the signs to distinguish among different types of areas or phases enclosed. For such a closed curve AO = t2r and As a convention, we shall take the direction of the integration along the curve in such a way that the area or phase under consideration (henceforth called a) is kept to the left side of the curve, Fig. 1. Then Kp is positive where the curve is concave and negative where the curve is convex. For a closed curve Ad - +2n if the curve encloses a, and Ad = —2n if the curve is surrounded by a. PLANAR SECTIONS OF THREE-DIMENSIONAL STRUCTURE OF ISOLATED a PARTICLES Consider next a planar section of a microstructure containing particles of a in a matrix. We place no restriction on shape of connectedness of these particles, and begin by considering the curvature of only the boundary between a particles and matrix&apos; Clumps of contiguous a particles are then treated as a single a particle. The two-dimensional section will show in a unit area na simple closed curves enclosing a particles and nh closed curves of holes, in-

Jan 1, 1968

By John Chipman, Raymond L. Orr

Recently reported high -temperatlnre thermal data have been incorporated in a reuieu&apos; of the therinody-r~ar,zic propesties of iron. The recent data permit mot corlsisterlt and reliuble choices to be made for many of the pvoperties, resnlling in bettev eslablished tabrtlations of the thermodynamic functions. Values of Cp, h°t- - H°298. s°t - S2sa, and (G°T -H298/T are tabulated for -the solid and liquid phases of iron in both stable and melastable regions. Consistency of the tabulations has been maintained to the precision necessr~vg to yield the Gibbs energy change belween the bcc (a, 8) and fcc (y) phases of iron at temperatures pertinenl to alloy studies. THE importance of the metal iron has stimulated many investigations of its thermodynamic properties at elevated temperatures. Reviews and summaries of the data have appeared from time to time. Among these the 1951 paper of Darken and smith&apos; deserves highest recognition for the quality of its criticism and for the precision and thermodynamic consistency of its tabulations. These and the more recent table of Kaufman, Clougherty, and weiss2 reproduce the Gibbs energy of the (a, 6)--Y transformation with sufficient sensitivity for alloy studies. Other recent compilations of equal validity3-&apos; make no attempt to do this. Since this Gibbs energy change is not greater than 22 cal per g-atom over the temperature range 1100° to 1800°K, it is obviously desirable to tabulate values of (G°t - H298)/T to four places of decimals even though the absolute accuracy would not warrant such precision. The necessity for reconsideration of the problem is emphasized by the recent publication of several important researches on the enthalpy and heat capacity of iron. The older work is well-covered in the reviews cited and will be mentioned here only when actually employed in the tabulations. GAMMA IRON Transition temperatures are taken from the selec -tions of Elliott and Gleiser,5 based on the work of Boulanger7 and earlier workers. For the a-y (A3) transition at 1184°K we retain the value 215 cal per g-atom adopted by Darken and smith.&apos; It has received confirmation in the recent work of Dench and Kubaschewski,&apos; and of Braun8 using adiabatic calori-metry, and of Wallace, Sidles, and Danielson10 using a pulse heating technique. The enthalpy data of Olette and ferrier" and of Anderson and Hultgren12 at higher and lower temperatures may be extended to 1184°K to give the following values which are adjusted to the required value of ? 1184 Ha,1184 Ha 298 = 8030 cal per g-atom [11 hr,1184-ha298 = 8245 cal per g-atom [2]

Jan 1, 1968

By S. R. Goodman, Hsun Hu

The formation of secondary - recrystallization tex-tlires in cube-textured 18-8 stain less steel (Type 304) Ilas been studied at three temperatures. Prolonged annealing at 100°&apos;C protluces a PredoninanGly (520) [OOZJ-type texture, which is related to the cube te.ture of the primary lnatrix by a rotation of approxivzately 22 deg around the [001] axis in the rolling direction. Annealing at 1200 or 1300°C facers the formation of the (123)[272/-type texture, which is related to the matrix texture by a [111] rotation of app.voxiniately 40 deg. These observations suggest that in the secondary recrystallization of cube-texlut-ed stainless steel an apparent actilation energy for growth is higher for grains related to the tncrtuix Og [111] rotations thun those reloted by [100] rotations. THE formation of secondary-recrystallization textures in cube-textured primary matrices of fcc metals has been studied widely by various investigators. For Fe-40 pct Ni alloys, Pawlek&apos; and wassermann2 reported that the orientations of secondary grains were related to the cube texture by rotations of 30 and 38 deg around [001] in the rolling direction. However, Rathenau and custers3 found that, while in one Fe-48 pct Ni alloy, most of the secondary grains were oriented with respect to the cube-textured matrix by rotations around [001] of 26.5 deg, in another alloy of a different origin, the orientations of secondary grains were related to the cube texture by rotations of approximately 35 deg around a [lll] axis. Similar orientation relationships were also observed between the secondary grains and the cube-textured primary matrices of copper.4"a No attempt was made to differentiate these two types of orientation relationships; reorientation by either a [111] or a [100] rotation was considered to be equally favored. The present investigation consisted of a study of the secondary recrystallization textures in cube-textured stainless steel. It was noted that the secondary grains formed in stainless steel were considerably smaller than those of Fe-Ni alloys or copper. This offered the advantage that the secondary recrystallization texture could be determined by the texture-goniometer technique, and a more detailed study of the textural development during the course of secondary recrystallization could be made. The effect of annealing temperature on the formation of secondary-recrystallization textures was also investigated. MATERLAL AND METHOD It was shown earlier"-" that a strong cube texture can be obtained in 18-8 stainless steels by rolling at 800°C to produce the copper-type deformation texture, followed by annealing at 800" to 1000°C for recrystallization. To improve the cube texture for the present study, a commercial-grade 18-8 stainless steel (Type 304) was rolled at 800°C first to 5 mm (0.2 in.) thick plates. Three of these plates were then stacked and welded together along the edges into a sandwich assembly. After annealing at 900°C for 20 min: the assembly was finally rolled at 800&apos;C to 90 pct reduction in thickness with reheats and end-for-end reversals after each pass. Only the central strip, which was reduced from 5.0 to 0.50 mm (0.7 in. to 0.020 in.) thick, was used. The chemical composition of the steel in weight percent was as follows: C, 0.06; Mn, 0.38: Cr, 18.71; Ni, 9.56: P, 0.011; S, 0.009; and Si, 0.39. The purpose of rolling the strip in a sandwich assembly was to prevent direct contact between the central strip and the rolls. It was observed earlier" that, when the strip was rolled at 800°C without being enclosed in a sandwich assembly, the cube texture obtained by subsequent annealing at 900" or 1000° C for recrystallization was largely confined to the central section of the strip, while most of the recrystallized grains formed in the surface section of the strip were not cube-textured. This was obviously due to the fact that the actual temperature at the strip surface during rolling, as a result of direct contact between the strip and the cold and massive rolls, was considerably lower than 800°C. By using a sandwich assembly for hot rolling, the cube texture obtained upon subsequent annealing for recrystallization was found to extend through the entire thickness of the strip. After rolling, the central strip was taken from the sandwich assembly. and cut into specimens. Prior to annealing. the specimens were etched to 0.25 mm (0.010 in.) thick. A tube furnace provided with a purified, dry argon atmosphere was used for annealing. Textures were determined by the reflection technique. using a Siemens automatic texture-goniometer and ZrOz-filtered MoKa radiation. With a time constant of 4 sec. the preferred orientation of the secondary grains could be measured satisfactorily by the integrated intensities. Both (111) and (200) reflections were measured, and corresponding pole figures were constructed according to the techniques described previously.10 The agreement between results deduced from these two reflections was excellent. RESULTS AND DISCUSSION Secondary-Recrystallization Texture due to Prolonged Annealing at 1000°C. Fig. 1 shows the primary-recrystallization texture of a specimen annealed at 1000°C for 30 min. A substantial improvement in both sharpness and intensity of the cube texture, owing to the present processing method, can be noted readily by comparing Fig. 1 with similar pole figures shown earlier in Refs. 9 and 11. Secondary recrystallization

Jan 1, 1967

By Merton C. Flemings, Harold D. Brody

Analyses that include diffusion of solute in the solid phase are formulated to describe solute redistribution in dendritic solidification of metallic alloys. The analyses are based on conditions that include negligible undercooling before nucleation of solid phases, negligible increase of solute in advance of the tips of growing dendrites, complete diffusion within the liquid over distances the order of dendrite spacings, and a plate-like dendrite morphology. The classical nonequilibrium freezing equation, Cs = kCo(I - fS)k-l accurately describes solute redistribution between dendrite arms for the solidification processes considered, provided diffusion in the solid is negligible. To account for the effect of diffusion in the solid, an analytic expression is given which is similar inform to the classical expression. 172 addition, a numerical-analysis procedure is etnployed to examine in more detail the effect of diffusion both during and after solidification. The analyses are intended for application to solidification of castings and ingots to describe a) final solute distribution after solidification and cooling to room temperature (microsegregation) and b) local fraction solid as a function of ternperatcre within the solidifying casting or ingol. SOLUTE redistribution in cellular and dendritic solidification has been discussed quantitatively in recent papers&apos;-3 and in a series of earlier work.4-6 However, none of the analyses developed have permitted close correlation of theory with final solute distribution (microsegregation) observed in castings and ingots. In this paper, discussion is given of approximations which may reasonably be made in mathematical treatment of microsegregation, and analyses are presented based on these approximations. Numerical results are given for Al-Cu alloys. In a second paper the analyses will be compared with exeriment.7 CLASSICAL ANALYSIS The classical quantitative treatment of solute redistribution within a closed "volume element" has been derived repeatedly, for example by Gulliver,4 Scheil,&apos; and Pfann.&apos; This "classical nonequilibrium solidification equation" is written for constant partition ratio: where Cs = interface composition of the solid when the weight-fraction solid within the "volume element" is fs (weight fraction, wt pct); k = equilibrium partition ratio; Co = initial alloy composition within the volume element (weight fraction, wt pct). Assumptions of Eq. [11 are: 1) There is negligible undercooling before nuclea-tion, or from curvature or kinetic effects. 2) There is no mass flow in or out of the volume

Jan 1, 1967

By C. E. Coleman, D. Hardie, A. E. Wraith

A photoguaplric method of measuring crack velocities has been applied to an examilzation of- the effect of hydrogen on the impact properties of zirconium. Results indicate that the crack in hydrided zirconit travels at about 26 m per sec whereas that in the uacuum -annealed is dependent on the speed of the hammer. RECENT work on the effect of hydrogen on zirconium reveals that when hydrided zirconium is tested in slow bending the crack producing failure can be unstable. The mode of fracture seems to involve the crack linking up broken hydrides by a ductile mechanism in the zirconium matrix.2" In order to compare the fracture of zirconium with that of other metals which show unstable crack propagation, notably steel, the rate of the crack spread must be known. As the methods previously used for measuring crack growth are either unsuitable for the present work5-&apos;&apos; or very costly," a simple technique has been devised in which the maximum crack velocity is derived from a series of crack position-time measurements. EXPERIMENTAL PROCEDURE The experimental arrangement is shown schematically in Fig. 1. The flash unit12 was triggered when the Charpy hammer touched the specimen and the 6-psec flash of the lamp delayed by a preselected time interval in the range 100psec to 10 msec. The camera was left on open shutter during the test. From direct measurement on a calibrated photographic print, Fig. 2, the position of the crack and the specimen was found at a known time after impact and, from a series of such tests using an appropriate range of flash-delay times, the crack velocity was estimated. Preliminary experiments were carried out on mild steel above and below its transition temperature. Vacuum-annealed zirconium, and zirconium hydrided to 100 ppm H were then tested at 20" and 150°C. For comparison, Zr-2.6 pct Nb alloy (in the 0 + transformed /3 condition), vacuum-annealed or hydrided to 100 ppm H, was tested at 20 C. The chemical analyses of these materials are given in Table I. For the high-temperature tests a fine chromel-alumel thermocouple was spot-welded onto each specimen close to the notch. The test piece was heated up to 200°C to allow enough time for preparing the apparatus while the specimen cooled to the testing tem- perature. It was assumed that the specimen cooled uniformly. The accuracy of the flash-delay time was better than i2 pct i 5 psec. The crack length was taken as its maximum distance traveled normal to the length axis of the specimen. Errors in these measurements arise as a result of the uncertainty in the location of the crack tip and the difficulty in defining the exact position of the crack starting point. The latter was due to the bonding and large amounts of deformation at the hammer contact point, especially in the vacuum-annealed specimens tested at 150°C. The maximum error in the measurements was however estimated to be about 5 pct. DISCUSSION OF RESULTS From the trial experiments using mild steel above its transition temperature it can be seen from the plot of crack length against time after impact, Fig. 3. that a reasonable estimate of the maximum crack velocity at the surface of the specimen may be made. Other features of note are the initiation time before the crack is first seen and the slowing down period

Jan 1, 1967

By C. B. Alcock, M. G. Hocking

The kinetics of the growth of sulfate layers on blocks of Cu20 has been studied between 688" and 800°C. At 788c the over-all weight increases followed the parabolic rate law, with k = 216 30 sq mg per cm4 min, using a 1:1 entering gas mixture of SO2:02. At 757 after an initial linear period the parabolic rate law was followed, with k = 57.8 10 sq mg per cm4 min. The gas mixture required a platinum catalyst to produce the maximum SOs pressure. The sulfation rate at 757&apos; and 788c was high until all the CUZO had changed into a core of CuO, when it became very much lower. At 757°C marker experiments showed that the sulfates (CuO. CuS04 and CuSO4) grow outwards from the oxide surface, but CuO. CuS04 mixed with CuO was found beneath the markers. At 688 markers were found at the CuO. CuS04/CuS04 interface. Visual observations at 757 showed a liquid eutectic moving beneath the sulfate surface. causing very rapid sulfation and extruding to solidify as thick &apos;needles" up to 8 mm long. Marker experiments have shown conclusi.cely that CuO grows on Cu20 in air by the outward migration of copper. ThermODYNAMIC measurements on the sulfate and basic sulfate of copper, reported recently,&apos; are followed here by measurements of the rates of formation of these sulfates on cuprous oxide, in order to provide a background for the understanding of roasting processes. peretti2 and McCabe and Morgan3 have shown that the phase Cu20 lies next to Cu2S when the sulfide is roasted under conditions where sulfates will be formed. Since this would present too complex a system for kinetic study, the present work4 has been based on the kinetics of sulfation of the oxide phase. The results of a study of the kinetics and mechanism of the sulfation of cobaltous oxide have recently been reported.4,5 Results on the sulfation of cuprous oxide have also appeared,6 but are at variance with those to be reported here. This seems to be because the previous workers6 did not obtain constant SO3 pressures from the SO2/O2 sulfating gas mixtures used, as will be discussed later. Wadsworth, Leiter, Porter, and Lewis found that the sulfates produced when SO2/O2 mixtures are passed over Cu20 at red heats are CuS04 and the basic sulfate CuO.CuSO4. When the decomposition of CuS04 was followed&apos; by differential thermal analysis, a stage corresponding to CuO .CuS04 was reached before decomposition into the oxide occurred. APPARATUS The vertical furnace used for quantitative studies was a conventional resistance-heated and propor- tionately controlled furnace with an even zone (1 deg) which was 4 cm long. The gas mixtures of SO2 and 02 were made by mixing measured flows from capillary flowmeters and drying over phosphorous pentoxide before passing them into the Pyrex top-piece of the furnace assembly. A mullite tube of bore 2% cm was used as reaction vessel and at the bottom of this tube was a trap for SO3, which condensed as a colorless liquid. The residual gas was led into a fume cupboard for ventilation to the atmosphere. The furnace used for visual observations of needle growth and other phenomena consisted of a transparent silica reaction tube of bore 3 cm, having an optically flat silica window sealed into its wall. The reaction tube was clamped vertically, inside a mullite tube of bore 4 cm and length 42 cm which was heated by Kanthal windings. The window in the silica reaction tube was arranged opposite a hole 3 cm wide and 2 cm tall which had been cut in the wall of the mullite winding tube 19 cm from its top end. A binocular microscope was used to look through the window, illumination being provided by a focusing microscope-lamp offset sideways and downwards. The oxide block to be sulfated was suspended from the removable Pyrex top-piece to the reaction tube, by means of which it was inserted at the start of the experiment, and through which entered the S02/02 gas mixture. The variation of the temperature inside the reaction tube with horizontal and vertical displacement from the window was investigated, and, while it can be said that the temperature was constant 1 deg, its value at a given position was known only to 12 deg. In both furnaces, the oxide block to be sulfated was suspended from a small silica hook immediately downstream from a platinum thimble used as catalyst, which was held on a long silica rod from a Pyrex spring attached to the removable Pyrex top-piece of the furnace. The spring was only included in the quantitative sulfating furnace; its sensitivity was 1.4 cm per g and it was found to be free from creep in a 16-hr test when carrying the working load. The extensions were followed by a cathetometer which could be read to 0.001 cm, corresponding to i0.7 mg. Extensions of the spring were measured on adding weights between 5 and 500 mg to the working load (thimble + oxide block), and Hooke&apos;s law was closely obeyed. SAMPLES Cuprous oxide blocks were prepared by oxidizing Johnson Matthey "Specpure" copper sheet of 1 mm thickness (impurities: iron at 3 ppm, silver at 2 ppm, lead, nickel, sodium, and silicon each at 1 ppm, calcium, chromium, magnesium, and manganese each at less than 1 ppm) for 6 days in air at 1000°C in a re-crystallized alumina boat. It has been reported7 that when Cu20 is prepared by heating copper sheet for 1 day the central plane of the blocks produced consists

Jan 1, 1967

By D. W. G. White

The surface tension of zinc has been determined by the sessile-drop method in a progvam emphaszzing detailed experimental care. The surface tension oj. the pure metal was measured over a range of ternperature from the melting point (419.6"C) to 540°C. At the melting point, the suvface tension of zinc was found to be: 1) 99.99+ pct Zn - 757.0 5 dynes per cm 2) 99.999+ pct Zn - 761.0 5 dynes per CI 3) 99.9999 pct Zn - 76&apos;7.5 5 dynes pev cna From experiments carried out in a closed, isothermal cell, the temperatuve coejyicient of the surface tension (6y/6T)p, , of zinc xas found not to be negative but to be postiue. A positive tenzperatre coefficient indicates a greater depee of order in the surface than in the body of the lquid. Houlezer, by delibevately inducing continuous zaporization, a temperature coefficient of su)face tension with a negative slope can be produced. The work reported herein was undertaken as part of a larger program of fundamental research on the properties of molten zinc and zinc alloys. This program grew out of a continuing interest at the Mines Branch in the behavior of liquid metals in the foundry and of a desire on the part of the zinc industry for reliable basic data. The work was originally begun in cooperation with the Consolidated Mining and Smelting Co. Ltd., Trail, B.C., and was subsequently continued from 1960 to date in association with the Canadian Zinc and Lead Research Committee and the International Lead and Zinc Research Organization. Although the surface tension of liquid zinc has of course, been measured before, as Table I and Fig. 1 demonstrate, there is not good agreement among the existing values. Such disparities arise because sources of experimental error are insufficiently controlled. This situation places the reader in doubt. One result may be correct within narrow limits—even fortuitously—yet, because there is not agreement between several values, none can be accepted with conviction and all become suspect. It seemed, therefore, in the circumstances, that there was room for further work embodying considerable emphasis on experimental care in order that, within a small margin of error, an accurate value might be obtained. It was in this spirit that the work was undertaken. METHOD The sessile-drop method -as adopted for this work. In this method, when applied to liquid metals at elevated temperatures, the outline of the meridional section through a drop resting freely on a horizontal surface is recorded photographically. Certain parameters

Jan 1, 1967