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By P. H. Lindon, J. C. Billington

Fe-O melts containing 0.045 pct 0 were deoxidized with Mn-Si-A1 alloys. Product compositions were reluted to the melt and alloy compositions and were found to be most sensitive to the aluminum content of the alloy. Low residual oxygen contents could be obtained when aluminum oxide was present in the Products because of the reduction of silica and manganese oxide activities. Flotation of the Products from a quiescent melt was followed both by analysis of the oxygen content and metallographic measurement of inclusion concentration. MnO-SiO2-A12O3 products were found to float most rapidly when their composition was such that their viscosity may be expected to be low. Changes in the particle size distribution indicates that particle coalescence occurred and differences in the degree of coalescence are thought to be responsible for the different flotation rates observed between products 0f differing composition. Measured flotation rates were slower than those Predicted from a model based on Stoke's Law, although alumina flotation might be reasonably accounted for by this model. Interfacial effects between oxide particles and the melt are believed to be responsible for the discrepancy. It has been recognized that deoxidation products constitute a large proportion of the nonmetallic inclusions present in killed steel. The amount of oxide inclusions which originate as deoxidation products depends largely upon three factors. These may be summarized, according to P16ckinger1 as: 1) Amount of primary products remaining in the steel prior to cooling. 2) Residual dissolved oxygen content of the steel after deoxidation. 3) Amount of secondary products, formed during cooling and solidification, which remain entrapped in the solid steel. In a well-deoxidized steel containing residual aluminum and/or silicon, the equilibrium dissolved oxygen content is usually very low and so the maximum amount of oxide which may be produced as secondary deoxidation products is small in comparison with the amount of primary products. It may be seen, therefore, that the amount of indigenous nonmetallic inclusions may be minimized if a low dissolved oxygen content is achieved by deoxidation and if the primary deoxidation products are efficiently removed. Oxides which originate by reaction of the metal stream with the atmosphere during teeming are not considered in the present study. It is known that two or more deoxidizers may result in a lower equilibrium oxygen content when used in conjunction with one another than when any of the individual deoxidizers are used alone. Equilibrium studies by Hilty and crafts2 and by Bell3 have shown that manganese increases the effectiveness of silicon as a deoxidizer, and Walsh and Ramachandran4 relate this to a reduction in the activity of silica in the products as the manganese :silicon ratio in the steel increases. It was also shown by Herty's work on deoxidation of steel by silico manganese alloys,5 that there existed an optimum ratio of manganese to silicon which gave a minimum inclusion content. This ratio was in the range 4:l to 7:l and the (FeO-MnO-SiO2) products formed by such deoxidation practice were found to lie in a composition range having very low liquidus temperatures (1170 to 1250°C approx). The optimum manganese:silicon ratio was then explained by postulating that these fluid products were able to coalesce and that the larger particles formed floated out of the steel very quickly as predicted by Stoke's Law. The present work examines the effectiveness of various Mn-Si-A1 alloys as deoxidizers and their effects on the composition and removal of primary deoxidation products from a quiescent melt. EXPERIMENTAL TECHNIQUE Approximately 250 g of prepared Fe-O alloy, containing 0.045 to 0.055 pct O, were melted in an alumina crucible and deoxidized at 1550°C by plunging a thin steel cartridge containing the deoxidizer below the melt surface. A high frequency induction furnace supplying current at 8.5 kHz was used to heat a graphite susceptor, the interior of which had been machined to give a wall thickness of 0.85 in. to form a receptacle for the alumina crucible. The iron melt was essentially quiescent as the induced current was concentrated at the external surface of the graphite susceptor by the skin effect. A nonoxidizing atmosphere was maintained over the melt by passing a continuous stream of argon through the lid of the susceptor. The melt temperature was measured before deoxidation, and again at the end of an experiment by means

Jan 1, 1970

By C. E. Sims, F. W. Boulger, H. A. Saller

Most of the data on equilibrium constant and the deoxidations potentialities of those elements, considered to be stronger deoxidizers for steel than is silicon, have been calculated from thermodynamic data. The reason for this is, primarily, the obvious difficulty of obtaining direct experimental evidence of equivalent accuracy. This is an excellent use of the principles of thermodynamics and has given valuable data not otherwise available. Such results, of course, can be no more accurate than the physical constants used in the calculations, and one can never be sure that the basic data are either complete or accurate. In fact, as in the case with silicon,1 there are not only discrepancies among the calculated theoretical values of the equilibrium constant for deoxidation of steel but also between the theoretical and experimental values. It is highly desirable, therefore, to obtain experimental values for checks on calculated results whenever possible. If they disagree, both cannot be right, but if there is good agreement, their value is enhanced. The present work was done in an effort to obtain experimental evidence in regard to some of the common alloying additions but more particularly the so-called "strong" deoxidizers for steel. The method used was to determine the minimum concentration of the deoxidizer that would effect a certain definite degree of deoxidation in steel. The criterion of deoxidation was the change from the large globular Type I sulphide to the eutectic Type II as described by Sims and Dahle.2 This change is sharp and definite, and inasmuch as it can be produced with equal facility by aluminum, zirconium, and titanium, it is considered a manifestation of a certain degree of deoxidation and not an alloying effect. Ostensibly such a procedure could give only a comparison of deoxidizing powers and no absolute values. Nevertheless, repeated observations have shown that, when increasing increments of aluminum are added to a steel, the residual aluminum content begins to increase simultaneously with the appearance of Type II inclusions. Thus it seems warranted to postulate that the Type II inclusions appear coincident with the virtual elimination of FeO as an active constituent of the steel. Experimental Procedure The data obtained were primarily from the microexamination of polished and unetched specimens and from chemical analysis. Experimental heats weighing 200 to 250 lb were made in a basic-lined high-frequency induction furnace. The base composition was nominally that of a medium-carbon casting steel to which the appropriate additions were made. Specimens were poured into sand-cast ingots 3 in. in diam as shown in Fig 1. Sand-cast ingots were used to prevent chilling and to allow sufficient time in freezing for normal inclusions to form of a size large enough to be studied readily. In the first few heats, the tapered wall ingot was used, but in the majority, the extra large riser was used to prevent piping in heavily deoxidized steels. Specimens for microexamination were taken from the location shown in Fig 1, and drillings for chemical analysis were taken from a similar location. The procedure was to melt the base composition and deoxidize with the usual manganese and silicon additions and then to pour an ingot. The furnace was then tilted back, and the first increment of strong deoxidizer or special alloy was added and allowed to disseminate through the melt, with enough power on to hold the temperature constant, for 45 sec. Then a second ingot was poured. After this, another increment was added, and after the same holding time another ingot was poured. In this way from 9 to 12 ingots were poured from each heat, each successive ingot having progressively larger total additions of alloy. Eighteen heats were made altogether, and the range of alloys used and additions made are outlined in Table 1. The three principal types of sulphide inclusions found are illustrated in Fig 2. The globular Type I sulphides are characteristic of silicon-killed steels, the eutectic Type II are characteristic of steels deoxidized with a small amount of aluminum, while the larger, angular Type III are usually found in steels with a residual aluminum content above about 0.02 pct. In all specimens studied, the transition from Type I to II either did not occur at all or was very abrupt and clear cut. There never was any doubt as to just which increment produced the change, although the individual additions were small, in the order of 0.01 pct. The change from Type II to Type III was considerably less sharp, and, in some cases, both types were found together. Inasmuch as the formation of Type III sulphides is apparently not a deoxidation phenomenon, they will not be discussed here.

Jan 1, 1950

WALTER N. CRAFTS,* Toronto, Canada (written discussion?).-During the forging of 9.2-in. shells -for the United States Army, it was noticed that better results were obtained in certain instances when test bars had been held sometime before pulling. An investigation, therefore, was made by our metallographer, Mr. F. M. Arnold, to determine the effect of seasoning. The forging consists of a single operation, piercing a solid cast blank. The test sections were cut from the walls by an oxyacetylene flame, one piece from the nose end and one from the base on the opposite side. The test pieces were not heat treated in any way and the tests and seasonings were carried on at normal atmospheric temperatures. The specifica-tions were as follows: Standard 2-in. test bar, 0.505 in. in diameter; elastic limit, over 19 long tons, or 42,500 lb.; ultimate stress, 39.6 to 49.1 long tons, or 87,500 to 110,000 lb. per sq. in.; elongation, over 13 per cent. As a preliminary test two heats were selected; BP555, which was tested and reported failed on elongation on Aug. 20; and B01771, which was tested and reported failed on Aug. 24. On Aug. 29, retests were cut and machined from the same shells and held till Sept. 3 (5 days) when they were pulled. Both sets of results are given below.

Jan 12, 1919

By W. H. Bassett, J. C. Bradley

In their paper on the directional properties in cold-rolled and annealed commercial bronze,' Phillips and Samans suggest that cupronickel, under distinctly different treatments, shows both "45" ears" and "90" ears. Fig. I shows the ears on some cupronickel cups made some 17 years ago for bullet jackets for small arms ammunition. In this case the material heated to 425° C. had "45" ears, while that annealed at 950°C. showed long "90" ears" when drawn with the same tools. The method of cupping, the shape of cupping tools, etc., were found to have very little influence on the earing tendency, but the deeper the cup was drawn, the higher the ears would be. Method of Manufacture Cupronickel cast bars were 1 in. thick. Ordinarily, they were rolled with numerous passes to a thickness of 0.4 to 0.2 in., according to conditions. They were then given a single intermediate anneal, and rolled to finish thickness, frequently 0.032 in. After a last anneal the material was cupped with a "cut and draw" operation. Progress of this is indicated in Fig. 2, illustrating five different stages at which the drawing

Jan 1, 1933

By N. Brown, M. Herman

ORDERING'S effect on the creep strength and other plastic properties of metals is unknown at the present time. Sachs and Weerts' attempted to compare the mechanical properties of the ordered and disordered state by comparing a quenched specimen with one annealed for a long time at a low temperature. This experiment is unsatisfactory because it introduces a possible effect from quenching. Barrett' used a hot impact test, but his method was not sufficiently sensitive to indicate any discontinuity in plastic behavior in the neighborhood of the critical temperature. On the theoretical side, Fisher9 as suggested that short range order would strengthen an alloy, but he gives no conclusions as to the effect of long range order. Cottrell" has discussed the interaction between long range order and dislocations, but does not indicate whether slip in a completely ordered alloy without domain boundaries is appreciably more difficult than slip in the disordered state. Because order exists in so many alloy systems, it is most important to prove experimentally whether long range order weakens or strengthens a metal. This investigation used -brass because: 1) it orders

Jan 1, 1957

THE 127th meeting of the Institute was held in New York, Feb. 19 to 22, 1923. In addition to the usual large volume of technical matters under consideration, the meeting was particularly noteworthy for the amount of attention given to its business session; the convention of local section representatives also was full of interest. The total registration was 1201. The annual business meeting on Feb. 20, President Dwight presiding, was attended by 125 members, who listened with marked attention to the reports and addresses of the several officers. The chairman departed from the stipulated order of business in order to allow more time for the presentation of remarks on the state of Institute affairs. The previously pub-lished reports of the officers were accepted, as printed. On the report of the tellers, the following officers were declared elected: E. P. Mathewson, Director and President-District 0 T. T. Brewster, Director and Vice-president-District 6 Frank M. Smith, Director and Vice-president-District 11 W. H. Aldridge, Director-District 0 G. H. Clevenger, Director-District 1 A. N. Diehl, Director-District 3 Reno H. Sales, Director-District 7 Seeley W. Mudd, Director-District 10

Jan 3, 1923

By A. G. Willard

Quantification of size, shape and composition has been one of the more difficult areas for those concerned with fine particle processing of coal.' Image analysers fed by optical microscopes and by scanning electron microscopes possessing backscatter detectors and energy dispersive facilities now offer techniques to improve the speed and precision of previous methods. This paper discusses the methodology and procedural difficulties associated with the microanalysis of coal. Photographs show display quality on the image analyser monitor and the equipment mentioned. Data illustrating several of the procedures are included. The major portion of data for design and operation of plant for fine particle processing depends on information regarding size, shape and composition of granular material. The lower limits of particle sizes become more important as lower grade deposits are mined. Because of the trends towards treatment of finer materials, the use of image analysis offers advantages in time, effort and accuracy. As energy becomes more critical, the above applies especially to coal processing. The Zeiss Microvideomat 2, a leading member of the second generation instruments, is now available for image analysis. There is a precision television scanning system with monochrome camera, display, control panel and central processor (see Figure 1).

Jan 1, 1980

By Ernest Kirkendall

THE amount of research done in the last few years on the subject of diffusion in solid metals is significant of the importance of this problem. To review the literature dealing with diffusion is unnecessary here. Desch1 in 1912 reviewed the work that had been done on diffusion in solids and gave a bibliography of the literature published before that time. Mehl's paper in 1936 2 is an excellent review of diffusion in metals and contains a large bibliography. Of importance also for its review and bibliography is an article by A. I. Krynitsky.3 While considerable material has appeared in the literature on diffusion in brass, the amount of information is not great compared to that pertain-ing to some of the other alloys. Most of the information published is of a qualitative nature; that which is quantitative varies considerably. Thus the quantitative determination of the rates of diffusion of copper and zinc in alpha brass by a new method appeared worth while. In the present investigation the rate of diffusion of zinc in approxi-mately the same composition alpha brass has been determined at three temperatures.

Jan 1, 1938

By Richard E. McElvain

The mining and other industries have grown and changed with- respect to their requirements for slurry pumps capable of handling high percentages of abrasive materials. Greater solids concentration, higher heads and pressures, and increased flow arc not possible. Today's equipment delivers up to three times the flow-tonnage and 1.3 times the head per stage as compared with pumps of ten years ago. This results in four times the requirement in size and energy. The new centrifugal pumps are capable of handling these requirements at pressures up to 4826 kPa (700 psi), with 6895 kPa (1000 psi) or more being considered for future systems. The latest pumps, functioning at four times the operating requirement on flow-head, weight eight times more than the previous equipment. Efficiency is increased slightly, to about 75 % to 85%. A testing program on equivalent units has confirmed that the added strength and specific design of heavy-duty pumps can meet demanding engineering objectives. Operating life on difficult-to-pump materials is increased from 500 to over 5000 hours of continuous operation; the ten-fold increase in pump operating time is a major design objective.

Jan 12, 1976

At a special inaugural ceremony in Blue Hill, Maine on August 3rd, Governor John H. Reed detonated the first blast to signify the beginning of development work on a new copper-zinc mining venture that seems destined to focus increased interest in the mineral potential of that State. The property which is the first new base metal mine to be discovered in the northern Appalachians in 30 years, is owned by Black Hawk Mining Co., a subsidiary of Denison Mines Ltd. of Toronto. When it goes on-stream in 1966, it will join Ducktown, Tenn., as the only active copper producing region, east of the Mississippi River. According to official reports submitted by the Company to Robert G. Doyle, Maine's State Geologist, Black Hawk has found ore reserves totalling 4.5 million tons. Assays show 2.8 million tons of 2.0'; copper and 0.4 oz. of silver per ton; 1.2 million tons of 16.75% zinc and 0.58% copper; and 0.5 million tons of 6.75% lead with 4.25 oz. of silver per toil and some zinc.

Jan 9, 1964

By G. S. Hume

Three provinces in Canada—New Brunswick, Ontario and Alberta— produce oil and gas in commercial quantities. In addition a small amount of oil is being produced and refined in the Northwest Territories at Norman on the Mackenzie River. The production at Norman is derived from two wells drilled by Northwest (Imperial Oil) Co. in 1920 and 1923. The refined products of the oil are used locally in connection with mineral developments on Great Bear Lake. The production of petroleum by provinces and the consumption of natural gas are shown in Table 3. In addition a small amount of natural gas is produced in the southwestern part of Manitoba from shallow wells for local use. Tables 1 and 2 give detailed information. The greatest drilling activity in 1933 in Canada centered around the southern end of the Turner Valley field, Alberta. In addition to several wells previously commenced in this area, eleven new wells were begun. There were three completions to the Paleozoic producing zone in 1933 in the southern part of Turner Valley and one well was abandoned as a result of being off the favorable structure. Of two wells completed in

Jan 1, 1934

By Reynold Q. Shotts

Chemical methods, based on the relative rates of oxidation of fusain, bright coal, and dull coal by nitric acid, have been devised to determine these coal components.1-4 Results obtained by oxidation methods for fusain have been checked against results obtained from microscopic methods on duplicate samples of the same coals, but to the author's knowledge this has not been done for bright and dull coal components. For this reason it is not certain that the two methods of analysis identify essentially the same chemical or physical units. It would be highly desirable to see results of the application of both methods to duplicate samples, but in the absence of any such data the author has attacked the problem indirectly. From the U. S. Bureau of Mines samples were obtained of three Alabama coals which the USBM had analyzed optically and reported on over the past 30 years. These samples were subjected to analyses by oxidation rate methods. Results of this work, and comparisons with the USBM analyses, have been published. This was the first indirect approach to the problem. The present report attempts a second indirect approach by way of internal validation.

Jun 1, 1955

By F. A. Forward, A. H. Ross, J. Halpern

IN treating carnotite ores by carbonate leaching it is often necessary to subject the ore to a prior roast. Among the advantages that may result from roasting are: 1) improvement in settling and filtering characteristics of the ore; 2) destruction of carbonaceous impurities that would otherwise contaminate the leach solution and consume carbonate reagent; and 3) substantial increase in extraction of vanadium, which is usually low when the un- roasted ore is leached. Recovery of vanadium may be an important factor in processing carnotite ores, and the fact that vanadium is usually recovered in good yield by acid leaching has often been an economic advantage over results obtained with carbonate leaching. It has been found that response of an ore to carbonate leaching, following roasting, depends primarily on its composition and on the conditions of the prior roast treatment, particularly with regard to the roasting temperature, the atmosphere maintained above the charge during roasting and cooling, and the presence of certain reagents. These factors, especially the last, virtually determine the extractions of uranium and vanadium attainable by carbonate leaching, as well as the reagent consumption on leaching, whereas adjustment of the leaching conditions has only a limited influence.

Jan 10, 1957

INSTITUTE MEDALS AND PRIZES ASIDE from the John Fritz Medal, in which the Institute partici¬pates through its representation on the John Fritz Medal Board, the Institute itself has three awards to make annually, as follows the Robert W. Hunt Medal and Prize, the J. E. Johnson, Jr. Award, and the James Douglas Medal. ROBERT W. HUNT MEDAL AND PRIZE The partners of Robert W. Hunt established a fund, which was presented to the Institute at a fitting ceremony on May 27, 1920, to establish an annual medal and a sum of money to be awarded under the following rules: 1. The award shall consist of two prizes, first of a gold medal, second of a sum of money, a certificate to accompany each prize The money prize shall not be awarded to a member over 40 years of age, but under unusual circumstances, both prizes may be allotted to one person provided that he is not over 40 years of age In general it will be understood that the Committee shall award the money prize to the younger men, rather than the medal

Jan 1, 1923

The suggestions of the members of the Institute are very much desired by the Committee on Nominations prior to deciding upon its nominations to fill the places of those officers who retire early in 1917. The Committee must make its final report to the Board of Directors early in October. The members are, therefore, asked to send in promptly their suggestions for Directors as well as for Vice-Presidents and President. The Committee hopes to hear from a large number of the members. The officers to be elected at the annual meeting in February, 1917, are: One officer, known as Director and President. Two officers, known as Director and Vice-President. Five officers, known as Director. The attention of members is called to Articles V and VII of the Constitution, and to By-Law XIII, which reads as follows: "The geographical districts to be considered by the Committee on Nominations shall be as follows, until otherwise ordered by the Board. District No. 1. New England, New York, and New Jersey, excepting New York City and district, which is provided for in the Constitution. (N. B.-New York City and district is designated District 0.) District No. 2: Pennsylvania.

Jan 6, 1916

ASIDE from the John Fritz Medal, in which the Institute participates through its representation on the John Fritz Medal Board, the Institute itself has four awards it may make annually, as fol¬lows: the Robert W. Hunt Medal and Prize, the J. E. Johnson, Jr., Award, the James Douglas Medal, and the William Lawrence Saun¬ders Medal. ROBERT W. HUNT MEDAL AND PRIZE The partners of Robert W. Hunt established a fund which was presented to the Institute at a fitting ceremony on May 27, 1920, to establish an annual medal and a sum of money to be awarded under the following rules 1. The award shall consist of two prizes: first of a gold medal, second of a sum of money; a certificate to accompany each prize. The money prize shall not be awarded to a member over 40 years of age, but under unusual circum¬stances, both prizes may be allotted to one person provided that he is not over 40 years of age. In general it will be understood that the Committee shall award the money- prize to the younger men, rather than the medal.

Jan 1, 1923

By Chu-Phay Yap

This is the second of a series of theoretical papers on the iron-carbon system. The solidus lines obtained as a result of the different methods of investigation fall naturally into three classes; namely, (1) a straight solidus originally suggested by Roozeboom and supported in the main by the work of Carpenter and Keeling, Andrew and Binnie, et al., using the thermal analysis method; (2) a slightly curved solidus obtained by Honda and his associates, using the magnetic and resistance methods: and (3) Gutowsky's solidus obtained by the Heycock and Neville method of quenching at successively higher temperatures. Although the thermodynamic method as shown in the first paper indicates that the straight solidus line is correct, no explanation has ever been advanced to account adequately for the disagreement in the shape and position of the solidus lines obtained. The nature of the solute in austenit.e is theoretically discussed. On the basis of such discussions, the data obtained by Honda and Endo on the change of magnetic susceptibility of steels with respect to temperature were critically subjected to a graphical analysis, which is shown to yield a rational explanation of the curved solidus lines.

Jan 1, 1931

The suggestions of the members of the Institute are very much desired by the Committee on Nominations prior to deciding upon its nominations to fill the places of those officers who retire early in 1917. The Committee must make its final report to the Board of Directors early in October. The members are, therefore, asked to send in promptly their suggestions for Directors as well as for Vice-Presidents and President. The Committee hopes to hear from a large number of the members. The officers to be elected at the annual meeting in February, 1917, are: One officer, known as Director and President. Two officers, known as Director and Vice-President. Five officers, known as Director. The attention of members is called to Articles V and VII of the Constitution, and to By-Law XIII, which reads as follows: "The geographical districts to be considered by the Committee on Nominations shall be as follows, until otherwise ordered by the Board. District No. 1. New England, New York, and-New Jersey, excepting New York City and district, which is provided for in the Constitution. (N. B.-New York City and district is designated District 0.)

Jan 7, 1916

By W. Spencer Hutchinson

THE outstanding engineering accomplishment of the last three decades has been the development and application of more and cheaper power and its use instead of the labor of men and animals. Substitution of power for manual labor has taken effect on every hand in the United States. With the aid of energy mechanically available to his hand, one man does the work that only a few years ago required two, three or even a greater number of laborers. The results in respect to the favorable economic effects are well known; namely, increased production, higher wages and lower costs. On the other hand, the vast social effects, both good and bad, have been none the less important, even if less understood and only casually regarded. The chief sources of energy today are the mineral fuels, coal and petroleum. In the United States they yield more than 90 per cent of the total energy demand. Thirty years ago the proportion of energy supplied by the mineral fuels was likewise above 90 per cent, but the division according to origin was very different. These relations. are shown for the years 1900, 1930 and 1950 in Table 1.

Jan 1, 1933

By J. Lewis, J. Harper, M. F. Ashby

A grain boundary in a metal interacts with second-phase particles, which exert a pinning force (first estimated by Zener) on the boundary opposing its motion. We have computed the shape of boundaries which interact with more or less spherical second-phase particles and have constructed a soap-film model to reproduce the shape of the boundary surface. An important result is that measurement of this shape allows the pressure, or driving force, on the boundary to be measured. We hare applied this technique to grain boundaries in two alloys and hate measured the pinning force exerted by single second-phase jwrticles on the boundaries. It is in good agreement with Zener's estimate. J\. boundary between two grains, or two bulk phases, interacts with small inclusions or particles of a second phase, whether they are gas or solid. This interaction means that the boundary, forced to migrate by a difference in free energy between the material of the two grains or phases which it separates, exerts a force on a particle which it touches, tending to drag it forward. (The movement of inclusions through metals under the influence of this force, has, in fact, been observed. 1-3) Equally, the particle can be thought of as exerting a pinning force on the boundary, tending to hold it back. Zener (in a celebrated private communication4) first realized that this interaction, and the resulting pinning force, existed. His calculation of its magnitude was crude but adequate: a spherical inclusion of radius r blanks off an area nr2 of the boundary on which it sits; since the boundary has an energy of rMM x per unit area, the blanlung-olf decreases the energy of the system by MM: this energy is returned to the system if the boundary is pulled free from the inclusion— a forward movement of the boundary by a distance r will do this—so that the maximum pinning force is Trrym.M- A similar argument can be made for inter-phase boundaries. The nature of the particle itself did not enter this, or two subsequent treatments.5,6 When it is considered, tic leifthe energyoftheb a) The boundary may enter and pass through the particle if the energy of the boundary is lower within the particle than in the matrix. Fig. l(r/). Certain coherent precipitate particles behave like this. h) More usually, the boundary will bend round the particle, enveloping and bypassing it. Fig. l(b). In doing so, it changes the structure and energy of the interface between the particle and its matrix. This means that the boundary does not touch the particle surface at right angles, as early treatments assumed,5'9 but at some angle a which depends on this change in surface energy of the particle, and can be calculated from the equilibrium of surface tensions. Most precipitate particles and inclusions behave like this. Gas bubbles or liquid drops can be regarded as belonging to either group. The progress of bypassing is conveniently measured by the angle shown in Fig. 1. When the nature of the particle is ignored, its maximum pinning force is exerted when - 45 deg. When it is considered, this critical value of is found to depend on a and thus on the nature of the particle. The maximum pinning force lies between nryMM and 2jtjMM (Appendix 1). not very different from Zener's result. In reality, a boundary between crystals has a specific energy and tension which varies with the orientation of the boundary. Furthermore, recent experiments7 indicate that such a boundary is not atom-ically smooth, but has steps on it: migration of the boundary corresponds to the sweeping of these steps across the boundary surface, like the Frank model of crystal growth from the vapor. This means that the interaction of a boundary with particles should really be considered in terms of the way in which particles hinder the movement of these steps. To suppose a grain boundary or interphase boundary to be smooth, and to ignore the variation of its energy with orientation, is to liken it to a soap film. The advantage of this soap film approximation, which we have used throughout this paper, is that interaction energies and boundary shapes can be calculated easily. We have done this by numerical computation and by using a soap film model, and have compared the results with grain boundaries in an aluminum-based and a copper-based alloy. It turns out that the shape of the boundary which bulges between particles allows the pressure an it to be calculated; that is, the local driving force an the boundary can be measured. This has allowed us to check the Zener relationship experimentally.

Jan 1, 1970