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By J. W. Downey, M. V. Nevitt

DURING the course of the present investigation of alloy phases involving transition metals, phases were found in the systems Os-Ta, Os-W, and Ir-Ta. The (Os, W) phase was also recently reported by Raub.1 Pertinent information is given in Table 1. The approximate composition range of sta- bility was determined metallographically on arc-melted buttons that were annealed 72 hr at 1200°C and water quenched. X-ray powder patterns were obtained with a 114.6 mm diam powder camera using filtered copper radiation. The composition for (Os, W) given by Raub (66 atomic pct W) is in agreement with the composition range reported here. However, the lattice constants reported by Raub are: a0= 9.913±0.007, c/a= 0.515. The reason for the discrepancy between the lattice constants reported by Raub and those given here is not known. Acknowledgments The authors wish to thank M. H. Mueller and H. W. Knott for assistance with the X-ray diffraction work, and R. A. Morris for the preparation of the alloys. This paper is based upon work performed at the Argonne National Laboratory under the auspices of the Atomic Energy Commission.

Jan 1, 1958

By Bernt Ellingsaeter, Terkel Rosenqvist

IN the silicothermic reduction of magnesia, burned dolomite is treated with high grade ferrosilicon in an evacuated steel retort at temperatures between 1150° and 1200°C. The following reaction is assumed to occur MgO + CaO + 1/2 Si (Fe) - Mg(g) +- & Ca,SiO, + Fe with the equilibrium constant on the basis of thermodynamic data for the substances involved and assuming unit activity for all solid constituents, Kubaschewski and Evans' calculated the magnesium pressure as a function of temperature logp,, (mmHg) = 15.06-1.61 T- log T- 13,16O/T. Pidgeon and King," who measured the magnesium pressure by means of a flow method, found values about three times the calculated ones. This may be caused by uncertainties in the thermodynamic data, but may also be caused by the formation of other reaction products, such as Ca,SiO,, which is known to be the stable silicate in equilibrium with lime. Whatever the exact reaction may be, it is evident that as long as all other factors are maintained constant the magnesium pressure will vary with the silicon activity, viz: p,, = &,. (p,,) ", where (p,,)" is the magnesium pressure by the reduction with silicon of unit activity. In the present investigation, p,,, was therefore measured for various grades of ferrosilicon and their silicon activities were calculated. The experimental method was similar to that used by Pidgeon and King. Briquettes of burned dolomite and Fe-Si alloys were placed in a 1 in. heat resistant steel tube and were heated to 1200°C. By means of a flow of purified hydrogen, the magnesium vapor was swept into a condenser filled with steel wool. From the amounts of hydrogen used and magnesium condensed the magnesium partial pressure was calculated. First a tube of 28 pct Cr steel, and later a tube of Kanthal D (a ferrous alloy with 22.6 pct Cr, 2 pct Co, and 4.5 pct Al), was used as a heat resistant tube. The latter tube showed the best heat resistance. The dolomite used had the following composition: 43.6 pct MgO, 55.5 pct CaO, 0.2 pct K,O + NalO, 0.2 pct Fe,O,, and 0.3 pct insoluble. The ferrosilicons were prepared from 98 pct Si of technical grade (0.7 pct Al, 0.3 pct Ca, and 1 pct Fe) by melting with various amounts of electrolytic iron of high purity. The alloys thus obtained were analyzed on their iron and silicon contents, which added up to between 99 and 100 pct. The amounts of reactants were chosen so that there would always be an excess of the oxides, and the average decrease in silicon content during the experiments would be about 1 pct. Most of the reaction occurred in the part of the reaction mixture facing the gas flow. The change in the silicon concentration in the part facing the condenser was, therefore, negligible. To facilitate the reaction, about 1 pct fluorspar was added to the briquette mixture. Fluorspar does not enter the reaction, but is known to act as a

Jan 1, 1957

By R. P. Carreker, R. L. Fullman, J. C. Fisher

CREEP tests are usually constant load tests. As deformation occurs, the cross section of the specimen changes so as to maintain approximately constant volume. Until necking starts, A _ l0 A0 - 1 where A is the cross-sectional area, 1 is the specimen length, and the subscript o indicates initial values. Thus, during a tensile creep test under constant load, the stress increases in proportion to the elongation. A A, 1, where S is the stress and F the load applied to the specimen.

Jan 1, 1954

By G. W. Tracy

The material balance equation has been used for many years by engineers to determine reservoir performance. The use of this equation in general has been twofold: first, to determine the oil-in-place in a reservoir; and second, to predict the future performance. The Schilthuis form of the material balance equation, or one equivalent to it, has been used by many of the engineers. The use of the Schilthuis form in predicting future performance has proved to be laborious in that one generally must make several estimates at each step of the trial and error calculation before arriving at a check of the oil-in-place. A method is presented for expediting the calculations. The Schilthuis form of the material balance has been rearranged into a more useable form. In using the material balance to predict the future performance of a reservoir, it has become common practice to estimate the incremental oil production for each step of the calculation which corresponds to a given pressure reduction. Instead of estimating the incremental oil production, the method outlined in this paper better lends itself to estimating the instantaneous gas-oil ratio. A check of oil-in-place is more easily accomplished by estimating gas-oil ratio since it is less sensitive to small inaccuracies. This method incorporates the same self-checking feature inherent in the Schilthius form. DEVELOPMENT OF SIMPLIFlED EQUATION In the development of the simplified equation, the Schilthuis form of the material balance equation will he used. Substituting in Equation 1 for and rearranging terms In Equation 2, the cumulative oil production (n) is multiplied by a factor which is uniquely a function of pressure. Also, the cumulative gas production (G) and net water influx are also multiplied by factors which are a function of pressure alone. These factors are called and are defined as follows: Using these factors, Equation 2 becomes The equation in this form is easier to manipulate mathematically than any of the previous forms which, have been used. Sources of data for the pressure factors are a bottom-hole fluid analysis and the ratio of initial gas cap volume to oil volume in the reservoir. AID IN DETERMlNING THE ORIGINAL OIL-IN-PLACE Each of the curves and +, have a similar shape. Each is infinite at the bubble point pressure. As lhe pressure is reduced below the bubble point, the

Jan 1, 1956

By N. L. Ananthanarayanan, J. F. Libsch

A LITERATURE survey1-' of sintering metal pow-A ders and powder compacts indicates that studies have so far been confined primarily to the latter stages of sintering in relatively coarse powders. Presumably this is due to the difficult techniques associated with studies of the early stages of sintering. Recent experimental and theoretical investigationsL-" on the preparation and the magnetic properties of ultrafine ferromagnetic powders suggest the possi- bility of following the sintering process from a very much earlier stage than has previously been considered. It is now well-known that ferromagnetic powder particles which are below a critical size behave as single domains and exhibit permanent magnet qualities characterized by a very high coercive force. When the same particles are fully sintered, the coercive force decreases to very low values corresponding to those of the solid metal. Thus the coercive force appears as a sensitive parameter which may be measured to study the early stages of sintering. To determine the feasibility of this technique, experi-

Jan 1, 1954

By D. W. Fuerstenau

In 1940 Schuhmann1 showed that the size distribution of a comminuted material can be expressed by the following empirical relationship: y = 100 (|f [i] where y is the cumulative percentage of material finer than size x, k is a size modulus, and a is a distribution modulus which is constant for a given material and machine. During the past few years, considerable emphasis has been given to the investigation of the extent of size reduction resulting from the expenditure of mechanical energy in crushing and grinding. Recently Schuhmann' presented a derivation of the energy-size reduction relationship by postulating that comminution in a device such as a ball mill can be considered to be the summation of many single comminution events, each of which yields a size distribution of particles following the Schuhmann size distribution equation. By grinding

Jan 1, 1961

By N. J. Grant, I. S. Servi, A. Chaudhuri

IN a recent paper by Servi and Grant,' it was illustrated that the slip band spacing and stress based on creep test data were related by the equation: d =1/ where d is the spacing in millimeters and v is the stress in psi, based on a more complete equation proposed by Orowan. It was shown further,' that for a. given grain size, the slip band spacing became larger with decreasing stress (and was independent of temperature), until such time that the slip band spacing becomes greater than about one-half the grain diam- eter. When this occurred, the mechanism of deformation in creep of 2s aluminum at high temperature changed from slip to grain boundary deformation (sliding). Additional metallographic evidence is now available which confirms this in a most interesting fashion.

Jan 1, 1954

By E. S. Greiner

THE hot working of chromium was first reported by Hunter and Jones; who used small pellets of the material obtained by the reduction of chromium chloride with sodium. Later, the working of chromium at 600° to 1100°C was reported by Marden and Rich,2 and at 1250°C by Kroll3 The hot rolled material3 had a Brinell hardness of about 150 (62.5 kg, 2.5 mm ball, 1 min) and was brittle at room temperature. Except for that associated with hardness indentations, no plastic flow in chromium at room temperature has been reported to the author's knowledge. Studies described here have shown slip markings in chromium after deformation at room temperature.

Jan 1, 1951

By C. S. Smith

The partial persistence of grain size and grain shape on melting and resolidifying crystalline substances, as well as the general effects of pre-solidifi-cation and of superheating on nuclea-tion rate, have been attributed to the presence in the liquid of crystalline impurities bearing some structural relation to the principal solid and hence capable of serving as nuclei for its crystallization. That such lattice matching does sometimes occur is well established, but it is surely improbable that a compound possessing both high-temperature stability and the requisite structural similarity should be naturally available in almost every system. It is now suggested that a mechanism for producing appropriate nuclei exists in the crystallization of all but absolutely pure substances. Impurities can he of many kinds. Some will give rise to compounds that are less soluble in the solid crystal than in the liquid. A . crystal forming from a melt or solution containing these will be supersaturated in some degree, and the foreign atoms will commence to segregate during or after solidification. They do not necessarily form pure, unstrained, crystals of the precipitating compound with its normal composition and structure. Generally—at least in the metallurgical examples that have been most studied —the first recognizable nuclei have lattice coherency with the surrounding matrix and have practically the same crystal structure and lattice spacing as the material in which they form, differ- ing only in composition. An extremely thin oxide layer formed under appropriate conditions on or in a solid metal will tend to be coherent with the metal lattice, and the first few atom layers of the oxide in contact with the metal will differ in both composition and structure from massive crystalliue oxide. It will resemble the metal more closely than the oxide. If it did not subsequently change on melting, such an oxide film would constitute an almost perfect "template" or two-dimensional matrix to hold a few atoms of the primary metal in the exact array needed to form a nucleus for solidification. Any precipitating material will adopt the correct spacing over a few atom diameters, and with appropriate substitution of other atoms of the correct sizes a precipitate can match the parent lattice over large areas of cohererlce without excessive strain. In metals, the componentsof a host of oxides, silicides, borides, nitrides, carbides, sulphides, and other compounds are always present in minute amounts. Some of these will be eliminated because of extreme insolubility in the liquid, while others will remain soluble in the solid; occasionally, however, particles will be formed in the solid by coherent precipitation—not of pure substances, but of whatever assortment of atoms best satisfies the joint requirements of availability, affinity, and appropriate average atom size. Of these, many will disappear on melting, but a few will persist unmelted as little rafts of complex composition, maintaining in the liquid a surface of the exact geometry needed to nucleate the solid on subsequent cooling. Their number and size distribution will determine the resulting grain size; the dimensions of the largest will determine the degree of undercooling that can occur before solidification commences. A similar process may operate in the case of phase transformations in solids. The coherent precipitation of supersaturated minor constituents in a low-temperature phase should facilitate the nucleation of this phase on subsequent cooling after transforming into another phase at higher temperatures. At first sight this hypothesis may seem little different from the older ones. It should therefore be emphasized that it does not depend on chance to provide the right compound to form a nucleus, but postulates that every crystal, containing minute amourlts of any of a wide range of impurities, automatically engenders particles having the correct surface structure to serve as nuclei for subsequent solidification. It could operate in any system, metallic, organic, or inorganic. The suggested mechanism is closely analogous to the production of antibodies from antigens in living organisms—indeed, it was a description of the matrix theory of this process that suggested to the writer its crystalline analogue.

Jan 1, 1950

By E. C. Burke

IN view of rather widespread use of calcium as an alloying addition to magnesium alloys, it is rather surprising to find that, although the general features of the Mg-Ca equilibrium diagram are known with a fair degree of certainty,' ," considerable ambiguity concerning the solid solubility of calcium in magnesium exists. By using the disappearing phase technique in a metallographic study, Haughton' found that 0.6 pct Ca was soluble at 300°C and 1.8 pct was soluble at 516°C, the eutectic temperature

Jan 1, 1956

By C. W. Chen

MARTENSITE transformations in ß Cu-Al alloys have been studied by Greninger1 and other investigators. According to Greninger, the parent phase ß1 an ordered body-centered-cubic structure obtained from ß phase by suppressing the eutectoid decomposition, transforms into an ordered hexagonal-close-packed phase in composition containing 12.9 to 14.7 pct Al. The M, temperature decreases with increasing aluminum content; for the alloy containing 14.5 pct Al, for example, the ß1??' transformation occurs below room temperature. More recently, Kurjumow2 studied the transformation in ß Cu-Al alloys with the addition of nickel. His report stimulated new interest in the subject due to the observation of completely reversible transformation without hysteresis in the transformation temperature ranging from 10° to —10°C. In the present paper some characteristics are described of the transformation of Cu-Al-Ni alloys that were partly studied by Kurjumow. Experimental Procedure High purity copper (99.999 pct) and aluminum (99.99 pct) and electrolytic nickel were used in the preparation, by the Bridgman technique, of single crystal specimens which contained aluminum and nickel of 14.5 and 0.5 to 3.0 pct, respectively. Polished surfaces were prepared mechanically. Specimens were then chemically etched to remove distorted material, homogenized at 1000°C for several hours, and quenched drastically to room temperature in a 10 pct NaOH bath to produce the parent phase ß1. The transformation was studied under a microscope and, in some cases, recorded by means of motion pictures. A device similar to that designed by Greninger and Mooradian3 was used to cool and reheat the specimens. Results and Discussion When the specimens were cooled below room temperature, the ß1 to ?' transformation began at 10°C with the appearance of ?' crystals In relief, Fig. la. As the specimen temperature dropped further, the transformation continued, either by the growth of the ?' crystals, with the ß1 — ?' interface moving into the ß1 phase, Fig. 1c and 1d, or by the formation of new ?' crystals, Fig. 1b. As a consequence of the former process, banded structure is observed as a common feature of the low temperature phase. According to the theory of the formation of martensite by Wechsler, Lieberman, and Read,' the bands of ?' phase are probably twin-related, as is the case in the diffusionless phase change of In-T1 alloys,5 but this was not revealed by X-ray tech- niques. New ?' crystals, in needle form, often emerged suddenly across the ?' bands during the transformation. These acicular crystals then grew, both in length and in width, see Fig. 2a through 2d. The transformation on cooling is completed at about -35°C. Upon heating, the reverse transformation started at —10° C, in a manner nearly opposite to the transformation on cooling, and completed at 35°C. There was no noticeable change in the transformation temperature when the nickel content was varied within the limits previously mentioned. Through control of the specimen temperature, the transformation can be started, stopped, or reversed at will. This phenomenon has frequently been observed in the martensite transformation of many nonferrous alloy systems. Other systems are Au-Cd6 and In-Tl.5 ow-- ever, in the latter systems, the transformation is accomplished by single interface motion if the specimen composition is homogeneous and the temperature gradient in the specimen is uniform and sharp, whereas in the Cu-Al-Ni specimens, only multiple interface transformation is observed. The speed of the interface motion appears to be a functionof the rate of temperature change and the temperature gradient across the specimen length. In one case, in which the temperature increased at the rate of 10°C per min and there was no temperature gradient along the specimen axis, the speed of the disappearance of a ?' plate was determined, by the study of the motion pictures made, to be 26 µ per sec. Quench markings were observed on the polished surfaces of specimens. The markings were grouped into one or more sets of different orientations, and were parallel in each set. The ?' plates formed in subsequent transformation were parallel to the markings, indicating that the ?' plates and the quench markings had the same geometric relation-ship to the ß1 matrix. The quench markings on two intersecting surfaces of a specimen were therefore used in the determination of the habit plane of transformation, by the trace method suggested by Barrett.' Results obtained from five sets of markings in three specimens indicate that the habit plane is an irrational plane about 2" from one of the {221} planes. This is very close to the habit plane (3" from 221 planes) of ß Cu-Al alloys containing more than 13.0 pct Al.1 The martensite transformation of Cu-Al-Ni alloys is reproducible. No sluggishness was found between consecutive transformation cycles, although a slight difference in the distribution pattern of the ?' plates was observed, compare Figs. Id and 2d. The transformation can be strain-induced. This characteristic has been tested by a simple method. When a specimen was elastically strained slowly in a vise, ?' plates were gradually produced in the same fashion as during transformation on cooling, This test was done at room temperature, and thus above the M,

Jan 1, 1958

By M. A. Mallinger

A series of laboratory tests was conducted to determine the limits of practicability in regulating the weights of various cement slurries. It was found that slurry weights of 12 to 19 lb per gallon could be obtained by adding bentonite to decrease the weight and barytes ore to increase the weight. It was also found that barytes ore was not usable in all cements. LIGHTWEIGHT CEMENT SLURRIES INTRODUCTION During the drilling and completion of oil wells the magnitude of the hydraulic pressures exerted on certain formations is critical. In many cases considerable care must be exercised to prevent drilling mud weights from becoming too high, and in those wells where loss of circulation is a problem, the use of normal weight cement slurries will generally result in lost returns during casing cementing operations. While mud weights can easily be controlled, it is necessary to exercise care in the selection of weight reducing additives for cement slurries in order that slurry weights may be reduced sufficiently to prevent the loss of a large portion of the cement to the thief formations without seriously affecting the setting properties of the cement. EXPERIMENTAL RESULTS An extensive search revealed that a large number of materials .that might have been otherwise practicable as a weight reducing additive were not acceptable for use with oil we cements because the imposition of pressure on the slurries caused the additive being tested to be compressed or to absorb water from the slurries, resulting in negligible decrease in the slurry weight. This search for lightweight additives disclosed that bentonite, a material very commonly used for reducing the weight of drilling muds and cements, produced the best results without undue harmful effects on the properties of oil well cements. It was found that there was a limit to the amount of benton-

Jan 1, 1950

By L. D. Jaffe, D. C. Buffum

EARLY papers1-' reported that temper brittleness is influenced by microstructure. This conclusion was based on room temperature impact tests, the inadequacy of which has been pointed out. Pellini and Queneau7 measured impact energy absorption at —80O to +25oC for several microstructures. On the basis of the shift, associated with temper brittleness, in the energy vs testing temperature curve they concluded that tempered martensite is somewhat more susceptible to temper brittleness than is tempered pearlite. The range of temperatures was insufficient to give complete curves covering the transition from tough to brittle behavior, so it is difficult to evaluate quantitatively the shift for the different microstructures. Also, the smaller shift of pearlite might be attributed to its already being temper embrittled at its temperature of formation. Accordingly, blanks 2 3/16 in. long were cut from a heat of SAE 3140 hot rolled steel barstock, 5/8 in. diameter, on which other work has been reported? A set of blanks was austenitized 1 hr at 900°c, water-quenched, tempered 16 hr at 675oC, and water-quenched, giving a microstructure of 100 pct

Jan 1, 1954

By Wilbur I. Duvall, Wilson Blake

The microseismic method of detecting instability in underground mines was developed by the U.S. Bureau of Mines (USBM) in the early 1940's. ,3 The method relies on the fact that as rock is stressed, strain energy is stored in the rock. Accompanying the buildup of strain energy are small-scale displacement adjustments that release small amounts of seismic and acoustic energy. These small-scale disturbances, which can be detected with the aid of special geophysical equipment, are called micro-seisims or self-gene rated rock noises. It was further determined that as failure of rock is approached, the rate at which rock noises are generated increases. Thus, by monitoring a rock structure at intervals and plotting rock noise rates vs. time, a semi quantitative estimate of the behavior and stability of the structure can be made. Since sufficient use of the microseismic method is still being made by various mining and construction companies, USBM undertook a comprehensive review of the method and a study of the fundamental properties of rock noises. As all prior work on rock noises has been done with resonant-type geophones, which prevented any analysis of their vibration records, it was necessary to develop the instrumentation and field techniques in order that their properties could be investigated, such as their frequency spectrum and absorption characteristics, and to determine if both P and S-waves are generated by a rock noise. The aim of this program is the design of microseismic instrumentation which can be better utilized as an engineering tool than the presently available microseismic equipment. This new design, based on the basic properties of rock noises, should allow better utilization of these phenomena in the study and location of zones of incipient instability in both underground and open-pit mines. EXPERIMENTAL PROCEDURE To study the waveform of rock noises, it was necessary to develop a microseismic system with a broad bandwidth. To achieve high sensitivity and broad frequency response, commercial ceramic accelerometers were used. The present broad-band microseismic system consists of accelerometers as geophones, low-noise preamplifiers, high-gain amplifiers, and an FM magnetic tape recorder. This seven-channel system has a flat frequency response from 20 to 10,000 Hz, a noise level of less than 2.0 kv, and a dynamic range (including manual set attenuation) of greater than 100 db; it can detect signals with acceleration levels as low as 2 ug. The entire system is solid state and hence battery operated and portable (Fig. 1) Analysis procedures consist of playing back the 30-in-per-sec (ips) magnetic tape recordings at 1 7/8 ips to expand the time scale of a recorded rock noise event and then recording this on a high-speed direct-writing oscillograph. The oscilIographic records are then digitized and run through Fourier integral analysis computer programs to determine the frequency spectrum of a rock noise event. The oscillographic records are also examined visually to determine if both P and S-waves can be recognized in a rock noise waveform. Broad-band microseismic recordings have been made at field sites in a wide variety of rock types and in both underground and open-pit mines. Sites include the Kimbley Pit, Ruth, Nev.; the Galena Mine, Wallace, Idaho; the Colony Development Mine. Grand Valley, Colo.; the Cliff Shaft Mine, Ishpeming, Mich; and the White Pine Mine, White Pine, Mich. DATA AND DISCUSSION Analyses of the recorded data have shown that rock noise frequencies are very broad. Fig. 2 and 3 show typical rock noise events and their frequency spectrums. In addition, it is evident from these figures that the wave form of a rock noise is very complex. The wide frequency variation, 50 to 7500 Hz, is due to many variables; the effect of travel distance is the only one examined in this study. The higher frequency components of the wave are rapidly absorbed with distance or increasing travel time. Fig. 4 shows the change in waveform resulting from an additional travel distance of 195 ft. From these data, it is apparent that a resonant-type microseismic geophone cannot respond to all frequencies generated by a rock noise, and in spite of the fact that the tuned geophone is more sensitive at resonance, a geophone with less sensitivity but broader band width is much more effective in detecting rock noises. In addition, a study of broad-band microseismic records shows that both P and S-wave arrivals are easily detected, as shown in Fig. 5. All records analyzed to date show that most of the energy is in the S portion of the wave; hence, microseismic geophones should be well

Jan 1, 1970

By W. W. Tyler, A. C. Wilson, L. B. Nesbitt

INVESTIGATIONS of thermal conductivity and impact strength of the titanium alloy RC-130-B and 316 stainless steel were undertaken because of interest in strong, nonmagnetic, commercially available alloys of low thermal conductivity for use in low temperature experiments. Measurements of electrical resistivity and thermoelectric power were also made for some of the samples studied. The titanium alloy designated as RC-130-B is manufactured by Rem Cru Titanium Inc. It contains 0.14 pct C, 3.99 pct Al, and 4.7 pct Mn. A general discussion of properties of the two phase Ti-4Mn- 4A1 alloys is given by Finlay and Vordahl.' The alloy is machinable and has a yield strength greater than 130,000 lb per sq in. at 0.2 pct offset. The 316 stainless steel sample used for both conductivity and impact strength measurements was obtained from the Allegheny-Ludlum Steel Corp. and is designated as Allegheny metal 18-8M, Type 316, Grade 316. The sample had received 25 pct minimum final cold reduction and had a Brine11 hardness rating of 255. Several impact tests were made on a sample of 316 stainless which had not received the 25 pct cold reduction. Also several data points are reported giving thermal conductivity and electrical resistivity for a sample of 304 stainless steel taken from stock. Figs. 1 and 2 give thermal conductivity and electrical resistivity data for the titanium alloy and for

Jan 1, 1954

By R. V. Riley

IN the metallographic examination of the alloys of iron and silicon, several investigators1-' have reported on the occurrence of an unusual type of etched structure, particularly in the alloys of higher silicon content. This, the so-called "barley shell" structure, has been observed with iron-silicon alloys over a wide range of silicon content, and under certain circumstances it can be seen upon the micro-sections of pure iron. The barley shell structure may be demonstrated most easily with iron-silicon alloys in the range 8 to 20 pct Si after etching in a hydrofluoric acid base etchant. Two etchants which produce the structure are: Corson's reagent, which is 2 parts hydrofluoric acid, 1 part nitric acid, and 2 parts glycerol; and picric acid reagent, which is 1 part hydrofluoric acid and 1 part saturated solution of picric acid in alcohol. Both when freshly prepared and used for etching commercial silicon-iron alloys containing 14 to 16 pct Si, invariably produce the barley shell structure shown in Fig. la. It is now well known that the barley shell structure is a pseudomorph and the true structure of an alloy of this composition consists of a single phase of silico-ferrite together with graphite as shown in Fig. lb. Lower silicon alloys and even pure electrolytic iron may also be etched in the above reagents to give the barley shell provided the etchant has been either: 1—Stored in contact with glass or silica, or 2—used previously for etching an iron containing silicon. Pure iron etched in perfectly pure hydrofluoric acid base etchants free from silicon contamination gives a normal structure free from the barley shells. Therefore, although the hydrofluoric acid in the reagent primarily is responsible for the barley shells, silicon, or its compounds, also must be present, either in the etching reagent or in the specimen. It was of considerable interest to the author to read the paper by Wachtell,? in which the barley shell etch was deliberately used for the identification of the boundaries of high and low silicon areas in diffusion experiments made upon laminate bars of compacted and sintered pure iron and ferrosili-con powders. This method of utilizing the barley shell etch is novel and in the hands of the investigator gave a useful differentiation between the high and low silicon areas in those specimens. For the reasons already given, however, the technique is not to be regarded as of universal application. Misleading results might be obtained, for example, if two or more specimens were etched in the same etchant. Fresh pure reagents only must be used each time. Provided this is done and the investigators are well aware of the limitations of the method, then the barley shell pseudomorph can be made of limited use in distinguishing between higher and lower silicon areas in a microspecimen of a ferrous material. The greatest of care must be exercised in the interpretation of the results which may be regarded as qualitative only and may, in fact, not be specific to silicon alloys.

Jan 1, 1952

By R. Maddin, W. R. Hibbard

A series of X ray experiments conducted by G. I. Taylor' in 1927 and later substantiated in 1939 by J. A. Collins2 both on axially strained aluminum single crystals, revealed evidence that during single slip crystallite rotation occurs in such a manner that " all parts of the material rotated about the transverse direction in the plane of slip."l The actual method of preparing the specimens for X ray examination is not discussed in detail by Taylor except to say that "this specimen was cut parallel to the plane of slip, as calculated from measurements of marks in the surface of the specimen. It was ground and etched till the effect of the new cuts had disappeared. This was verified by applying the same treatment to an un-distorted specimen. The X ray reflectionsl in this case were perfect ones."' Collins, on the other hand, cut his crystals in a mechanical shaper. These surfaces were polished on No. 1, No. 1/0, No. 2/0 and No. 3/0 papers and on a broadcloth lap using No. 600 alundum as a polishing medium. "Finally, the surface was deeply etched in Tucker's reagent. An unde-formed crystal was prepared in the manner described and X rayed to determine whether or not the machining and polishing operations had produced any strain or distortion in the crystal. The Laue spots all seem to be sharp, free from tails and streaks indicating no detectable strains had been introduced in the crystals." Taylor's X ray technique involved the use of "homogeneous X rays from an iron anti-cathode"; whereas Collins used Ka radiation of copper at 31kv and 20 milliamperes. Glancing angle X ray photograms were taken (1) with the axis of rotation of the spectrometer table in the plane of slip and at right angles to the slip direction, and (2) with the axis of the spectrometer table lying along the slip direction. However, eight minute exposures were used in each case and the angle setting of the spectrometer table was increased by one degree for each exposure. With the discovery of the action of three slip systems3 in the plastic deformation of single crystalline alpha brass where, formerly, only one had

Jan 1, 1950

By O. Schaaber

THE existence of isothermal martensite without the presence of the athermal form thus far has been established only in a 6 pct Mn, 0.6 pct C steel' and a 23 pct Ni, 3.5 pct Mn-Fe alloy.' " Theoretical calculations, moreover, predict this phenomenon to be observable only within narrow composition limits.' In all other steels, it is generally considered that martensite inevitably forms upon cooling below the M, temperature. Even the possibility of isothermal martensite transformation has been questioned for the common steels, although Averbach and Cohen" showed that martensite formation does not stop when the cooling is arrested and that as much as 5 pct retained austenite may transform isothermally to martensite at room temperature. This note presents some observations made on a number of low alloy steels by dilatometric and inductive measurement of isothermal austenite transformation at various temperatures close to the Ms. In the dilatometer studies reported previously, austenitized specimens were immersed in a salt bath maintained at proper temperature and immediately inserted into the dilatometera8' already at thermal equilibrium with the bath. The dilation was read on a dial gage divided into 0.001 mm intervals. Induction measurements were made with a separate excitation source and a test coil, sealed together in a salt-tight case. The increase in the induced voltage caused by the transformation products was recorded at a paper speed of 4 mm per sec. The steels studied are listed in Table I. Specimens prepared from steels 1 and 2 were in the form of hollow cylinders 60 mm long, 10 mm ID, 14 to 16 mm OD, while specimens of steels 3 and 4 were in the form of notched-bar impact test specimens, DVM type. Specimens of steel 5 were in the form of strip, 7x0.3 mm. In the bainitic range, curves representing the amount of transformation vs log time have a single step appearance, as is shown by the curve of isothermal transformation at 320°C in Fig. 1.Y ransformation proceeds in accordance with the Austin-Rickett equationo P -----------= k t" 100-P where P is the percentage of transformed austenite, t is time, and k and n are constants. Near the M, temperature, however, complex curves having two steps are observed. As shown in a previous papera for steel 3 isothermally transformed at 245"C, such complex curves can be separated into two separate transformations or reactions each following the Austin-Rickett equation. The values of n in the equation for a number of such two-step transformations are listed in Table 11 for steel 1. At transformation temperatures of 250" and 235"C, evidence of a second transformation is very

Jan 1, 1956

By D. Turnbull, A. M. Turkalo

It is well known that if copper that has been severely cold-worked by rolling (70-98 pct) is heated to high temperatures a small number of large grains are formed at the expense of the fine grained structure that appears upon primary recrystallization. Dahl and Pawlek,' Cook and Mac-Quarie,2 Ward,3 and Boas and Bowles4 have studied this phenomenon in copper. It has been reported as taking place with measurable velocities in the temperature range 700-1080". Boas and Bowles have reported that the time necessary for the transformation is of the order of days at 700°C. According to Ward3 the number of secondary grains which appear in OFHC copper decrease with increasing perfection of cubical alignment after primary recrystallization; also the perfection of cubical alignment increases with decreasing grain size prior to the final reduction. In this investigation two heats, A and B, of especially high purity copper (99.999 pct) supplied by the American Smelting and Refining Co., were used. The behavior of samples prepared from the two heats was qualitatively very similar providing that the grain sizes established prior to the final reduction were about the same. We observed that in specimens prepared from bars which were relatively coarse grained prior to final reduction secondary recrystallization took place at a rapid rate at temperatures as low as 500°C. This is about 200-300°C lower than the temperature necessary to obtain fairly rapid transformation in OFHC copper. A 0.22 in. thick rectangular bar of lot B was cold-reduced 60 pct by straight rolling and given a penultimate annealing treatment at 250°C. Following this it was cold-reduced 90 pct and heated to various temperatures in the range 450-1040°C. The specimens were about 8 mils thick

Jan 1, 1950

By H. H. Rachford, W. P. Schultz

The use of computing machines to solve physical problems has made it imperative to represent physical data in a form computing machines can use. Although curve-fitting is an old and well-practiced art, there still seems to be some interest in questions regarding what methods can be used and why. Even though there are many good references on this subject, it may be of some value to discuss a particular method which has been found to be useful, and to make available the associated tables for its use in the hope that there can be saved a few of the tedious hours necessary to reduce many of the suggested methods to practice. Although a very brief discussion of the mathematical background of the tables is included immediately below, those interested only in their use can skip directly to the section on Use of the Tables. Direct Fit of a Set of Points A frequently encountered problem is: Given data which can be represented by a smooth curve +(x), to find an easy-to-evaluate function F(x), with only a few coefficients, which is a good approximation of +(x) on the interval 0 5 x 5 x,,. Consider F(x) as a linear combination of m + 1 arbitrary, single-valued, continuous, linearly independent functions, f,(x), Ff.r) = a,f,,(x) + a,f,(x) + . . . -+ aifi(x) + If the value of Q(x) is known or can be read from the curve at the points xj: +(x,), +(x,), . . . +(xj) . . . +(x.), and if n = m, then all the coefficients of F(x) can be determined, and F(x,) — +(x,) = 0 for j =. 0, 1, . . . n. This follows from the solution of the set of linear simultaneous equations. +(x<.) = aofu(x,) + aJI(x0) + . . . + a,,f,,(x,) =a, = f,,(x,) + a,f,(x,) + . . . + a,f,,(x,) +(x,,) = a,,f,(x,,) + a,f,(x,) + ... + a,,f.,(x,,) ...........(2) for the coefficients ai. Although the set a, from the solutions of the set of Equations 2 yields an fix) which gives an exact value of $(x,) for the n + 1 points, there is no restraint on ~(xj in the interval xi < x < xj+,. Indeed, if the points +(x,) are not sufficiently smooth, very serious differences may arise between F(x) in the interval and the smooth curve +(x). Least-Squares Fit It has been suggested&apos; that if n is made to exceed m, and the set a, is found to minimize the function the function F(x) is much less sensitive to small errors in +(xi), and usually provides a much better fit to the smooth function +(x). This is known as the best fit in the sense of the least-squares error. To minimize $, set £ = 0,i = 0,1,... iTi,.....(3) The m + 1 equations from Equation 3 are k—n k=n a.^p /,,(a) f,(xt) + a, X A: = 0 k=O k = n k = n k=0 k=0 +(x.) f,(x,),............(4) one equation being obtained for each i = 0, 1, . . . m. Inasmuch as the arbitrary functions f(x) may be evaluated for x,, k = 0, 1, . . . n, and the +(x,) are known values of the curve to be fitted, the simultaneous Equations 4 may be solved for the set a,. Particular Functions Given the functions fi(x) and the set +(xj), the solutions for require evaluating a number of sums of products as well as the solution of an m + 1 order set

Jan 1, 1956