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By Walter Weeks

CONSIDERABLE difference of opinion seems to exist as to whether the rate of air flow when a fan is placed on a given duct should be determined by the use of static pressure or total pressure characteristics. A little study will show that both methods are correct. Assume that a fan is connected to a duct by an expansion piece as shown in Fig. 1, and that steady flow is established. Considering the atmospheric pressure as zero pressure, let the static head at the outlet of the fan be h and the velocity at this point be v1. The total head at the outlet is then h + v1/2g? The total head at this point must be equal to the total head at the end of the duct plus the losses that have occurred between the two points. Let f be the friction loss in the straight duct, s the shock loss in the dif- fuser, and V2 the velocity at the end of the duct. Then h+ v12/2g=v22/2g + f + s FIG. 1.-FAN ON DUCT. A curve showing the value of the left-hand side of the equation for different rates of flow is the total pressure characteristic of the fan, while a curve showing the value of the right-hand side is the total pressure characteristic of the duct. If these two curves are plotted on the same chart, the intersection indicates the rate of flow when steady flow is established.

Jan 1, 1930

By J. A. Hren, C. M. Wayman

RECENT investigators have noted anomalous behavior in the electrical resistivity of vanadium below room temperature. Rostoker and Yamamoto1 in studying the vanadium-oxygen system hypothesized that the body-centered-tetragonal phase existing from 15 to 34 at. pet O at approximately 800°K was really a low-temperature allotrope of vanadium that was stabilized by oxygen. In measuring the electrical resistance of cold-swaged vanadium rod over a range of temperatures, a small discontinuity was observed at approximately 240°K, supporting their notion of allotropy. However, the magnitude of the observed discontinuity was extremely small. Loomis and Carlson2 in studying the ductile-brittle transition in vanadium also made resistance measurements and reported a discontinuity near 200°K. More recently, White and Woods3 showed that the electrical resistivity from room temperature to approximately 100 °K was not linear and at variance with the Bloch-Griineisen law. Instead of finding a discontinuity, they observed a deviation from linearity below 200°K. In discussing their results they pointed

Jan 1, 1961

By P. H. G. Durville

ANY metal which contains even a small percentage of aluminum possesses certain peculiarities of appearance and properties which are exhibited both when the metal is melted and after it solidifies. Pure aluminum, or an alloy containing a small proportion of aluminum, can be melted without flux-except for a layer of charcoal-because a film of aluminum oxide and metal forms at the surface of melted aluminum. Although very thin, this film is air-proof, and it prevents the metal underneath from oxidizing. This oxidized film does not move easily on account of its toughness and high surface tension. One very important point in connection with this process of still casting has not been strongly enough stressed, namely, that the same kind of surface film with the same peculiarities forms over the surface of all melted alloys that contain even a small proportion of aluminum. Experienced foundrymen know how desirable it is to cast aluminum under its "skin" or under the surface of the film which tends to remain still. In the case of red copper, when in fusion, the surface shows pure copper only. This is due to the fact that liquid copper constantly absorbs the copper oxide which forms on the surface. By closely examining melting copper the oxide can be seen dissolving in the bath, and going into solution just as pulverized sugar dissolves in water. When copper is cast in the open, either in wire bars or cakes, the surface of metal exposed to the air is covered by a film of black, oxide that cannot be absorbed by the metal.

Jan 1, 1927

By Alan Morris

IN a previous paper1 the results of cutting tests on free-cutting brass rod were reported. Investigation was made of the effects of variation in lead content, microstructure and cold drawing. The author's reply to the discussion of that paper includes a study of the directional cutting properties of drawn and annealed rod. The present paper records the results of tests made on series of samples in which the tin, iron and copper contents have been varied. The apparatus, used and method of testing are described in detail in the previous paper. The machine is of the pendulum-operated milling type used and described by Airey and Oxford.2 Angular readings of the height to which the pendulum rises after falling from a fixed position, both when a cut is made and when the pendulum swings freely, give the basis for calculation of the energy consumed in making a cut. Careful weighing of the sample before and after cutting gives a measure of the amount of metal removed. The results are expressed in foot-pounds per cubic inch of metal removed, and have been called "unit cutting energy." In the course of the discussion of the author's earlier paper, W. B. Price reported large-scale tests involving some 50,000 lb. of material. These tests indicated that the addition of as much as 0.6 per cent of iron and 0.25 per cent of tin had apparently no adverse effect on the high-speed cutting characteristics of the rod. The rod also contained a small amount of nickel. The test results reported here tend to confirm his observations.

Jan 1, 1933

By Lester Woolsey

THE State Department can be of assistance to Americans in the petroleum business directly and indirectly. During the past few months, at the Arms Conference, it had a large hand in dealing with affairs indirectly affecting the oil problem. The conference has somewhat relieved the emphasis on naval strategy in relation to oil supply by limiting the number of naval vessels or the fleets of the Great Powers and in maintaining the "open door" in the Far East in respect of the development of the natural resources of that region by defining that policy in a nine-power treaty. The largest competitors of the. United States in the petroleum field are parties to that treaty. The Department of State also has stood steadfastly for the principle of equal opportunity in the Dutch East Indies, Mesopotamia, and Persia. The Department of State has been of indirect assistance in connection with oil problems by insisting on the recognition of treaty rights and other guar-antees, such as most-favored-nation clauses, and mandate provisions. I am not speaking as a representative of the Depart-ment of State, as L now have no connection with that institution, but my experience of several years as a member of the department and my practice since my resignation have given me opportunity to see the department from both the inside and the outside, and to measure its limitations as well as its resources.

Jan 7, 1922

By Robert Maddin

crystal prior to, polishing in order to eliminate coring. This treatment may be accomplished by wrapping the single crystal tightly in very thin, dead soft, brass foil and annealing in the presence of air for 20 hr at 800°C. Since the wrapping encircles the sptcimen three to four times, only a very slight amount of oxidation occurs on the specimen surface. On unwrapping one of these cylindrical single crystals. in. in diam by ro in. long (72.75 pct cu, 27.23 pct Zn, 0.01 pct P11, 0.01 pct re), mall light-gray depnrrits in the form of circular arcs werenoted on the part nf the foil which had been in contact with the single crystal, Fig r. (By superim- approximatetl). These deposits, which, from their color, suggest the appearance of sublimated zinc, were found to coincide roughly with a set of octahedral planes nearly perpendicular to the rod axis. The pattern shorn in the figure held no relation to the profle of the sample since the markin~s on the crystal More annealing werc attributed to traces of cube planes. It seems very likely that the deposits were formed by sutllimation of zinc diffusing from octahrdral planes since diffusian would Eogically take place along planes of maximum atomic spacing. However, it is difficult to understand why a continuous sublimation of zinc should occur from a single crystat in contact with a wrapping roil OF the same composition, and why diffusion would take place along specific octahedral planes and in a regular pattern.

Jan 1, 1949

By Van Manning

IN SUBSTANCE, the international aspects of the petroleum industry, as these relate to the United States, are as follows: The domestic production is not keeping pace with the domestic demands; our best engineering talent warns us of the imminence of a decreased production by our oil wells, although more oil is needed; and the only practical source whence this increasing demand can be supplied for some time to come will be the foreign fields. Other nations have given thought to the future and, in recent years, have shown a tendency to adopt strong nationalistic policies regarding their petroleum resources, policies that hinder or prevent the exploitation of these resources by other nationals. In consequence, we find that, facing a probable shortage of the domestic supply, our nationals are excluded from foreign fields; and this in spite of the fact that foreign nationals have been permitted to enter into and exploit, our own oil resources on an equality with American citizens and without hindrance or restrictions. This country: has supplied the larger part of the petroleum consumed by the world and yet, with a failing supply imminent, it finds that those countries that have been drawing upon our resources to supply their needs are showing a tendency to exclude us from their resources. In this way we shall be transferred from a position of dominence to one of dependence; and only by sufferance of those countries that are now seeking financial or political control of petroleum supplies, shall we be able to obtain the oil we will need.

Jan 2, 1920

By R. Fahn

Bentonites are best suited for the preparation of acid activated clays with efficient adsorption properties. They are weathering products of acid volcanic ashes and natural deposits are spread worldwide. The main constituent of bentonite is aluminum hydrosilicate montmorillonite with a high ability to swell. Physical and Chemical Properties of Montmorillonite The clay mineral montmorillonite is named after its place of discovery, near Montmorillon in southern France. The structure of this clay is shown in [Fig. 1]. The montmorillonite crystal consists of about 15-20 silicate plates. Each silicate plate is composed of three layers. The central one is formed by aluminum or by ferric hydrate octahedrons, the two outer ones consist of silicon dioxide tetrahedrons. In the presence of water, the montmorillonite crystal swells and water molecules become deposited between individual silicate layers. Two types of natural bentonites are known: the Western type, which is a natural sodium bentonite (high swelling grade), and the Southern type, an alkaline earth or calcium bentonite (low swelling grade). Southern bentonites have efficient adsorption properties of their own. They are called natural active earths or fullers earths. Acid Treatment of Bentonite Under the influence of a mineral acid, the exchangeable alkaline earth ions of bentonite are substituted by hydrogen ions. Moreover, depending on the acid concentration, temperature, pressure, and reaction time, a more or less pronounced leaching process takes place. Thereby Al-, Fe-, and Mg-ions are extracted from the octahedron layers. This results in a change in the crystalline structure of montmorillonite and in an increase of its specific surface area and porosity, as shown in [Fig. 2].

Jan 1, 1983

By Thomas Fraser

"AIR-SAND" is the term which has been given to a process of separating refuse material from coal by means of a body of dry sand artificially fluidized and maintained in that condition by a continuous stream of air bubbles flowing through the sand body. By proper regulation of the rate of air flow, this fluid air-sand body may be maintained at such a density that coal will float near the surface and the refuse, which is heavier, will sink through the sand to the bottom of the container. This separation is a float-and-sink operation similar to the separation of wood chips and stones in water; the one floats and the other sinks, irrespective of size of pieces. This was the objective sought in the development of this method of cleaning coal-a dry process which requires no preliminary sizing of the coal. METHOD OF PRODUCING THE AIR-SAND MEDIUM Figure 1 shows the cast-iron cell used for testing at the Central District Experiment Station of the Bureau of Mines, Urbana, Ill. This consisted of two castings: a. rectangular box 12 in. square in cross section and 18 in. tall, open at both ends and flanged on the bottom; and a cubical box also 12 in. square inside, with a closed bottom and flanged top. A porous diaphragm is bolted between the flanged ends of the two castings. The upper part of the cell above the diaphragm is filled with river sand screened through 20 mesh without removing the dust. Air under suitable pressure is admitted to the lower part of the cell below the diaphragm. The air passes through the diaphragm and bubbles up through the sand, distending the mass and throwing the sand particles into motion.

Jan 2, 1926

By T. H. Aldrich

This paper is intended only to give a preliminary account of experiments made, and conclusions reached, concerning the treatment of certain refractory low-grade gold-ores, the profitable reduction of which may furnish a useful guide to the solution of similar mining and metallurgical problems, not only in the gold-bearing belt of the Southern United States, but perhaps in other regions also. It must be regarded as simply a " report of progress," preceding a more elaborate and conclusive report of regular practice. The mines of the Hillabee Gold Mining Co. are located upon what is generally known locally as Hog Mountain, on the northern edge of Tallapoosa county, Ala., about 15 miles from Goodwater and 14 miles from Alexander City, stations on the Central of Georgia railway. Gold has been known since 1839 to exist on this property, where it was discovered in that year by a man named Johnston. The property was worked for placer-gold by the old miners, and there are now the remains of four attempts to operate it by stamp-mill and plate-amalgamation. The present owners purchasid it in 1896, and since that time they have experimented at frequent intervals, in order to devise a process that would satisfactorily recover the gold. In 1903 regular operations were begun. Geologically, the mountain consists of an intrusion of what has been pronounced true granite in altered sedimentary slates. The cooling of the granite produced shrinkage-cracks, which have become veins. There is considerable question as to the period of the slate formation; but it is undoubtedly, in my opinion, of Carboniferous age. The veins, about 50 in number, strike N. 60° to 80° E.; dip approximately 65' from the horizontal; vary from a few inches to 25 ft. (being in gen-

Jan 1, 1909

By H. l. Burghoff

THE presence of tellurium in copper and, by inference, in copper alloys, has been considered seriously detrimental and has been avoided. In particular, very small amounts of tellurium have been found to produce red-shortness, although the effects on cold-working and ordinary physical and mechanical properties have not been known so definitely. References in the literature are few, but as long ago as 1881, Egleston1 reported that 0.083 per cent tellurium in fire-refined copper rendered the copper red-short and therefore worthless for hot-rolling. In hot-rolling copper cakes containing this amount of tellurium, he found that fine cracks appeared in the cakes on the first pass through the rolls, the cracks opening further in successive passes. When cold, the metal was said to be tough and malleable. A few years ago, during the course of an investigation in our laboratory on copper-base alloys, it was found that tellurium-bearing alloys could be machined much more freely than similar alloys not containing tellurium. The study was pursued further in this direction, and considerable data were obtained, which indicated that certain tellurium-bearing alloys might have properties of commercial interest. The work eventually led to patent protection,2 a wide range of tellurium-bearing copper-base alloys being covered. This article presents results obtained on the effect of tellurium on the. mechanical properties of three copper-base alloys: commercial bronze (90 Cu, 10 Zn), 1.5 per cent tin bronze (98.5 Cu, 1.5 Sn), and silicon bronze (96 Cu, 3Si, 1 Zn).

Jan 1, 1937

By W. Rostoker, H. Nichols

The embrittlement by mercury of aluminum alloys in various states of anneal, cold work, and aging has been studied. It is shown that single phase and non-precipitation hardened structures irrespective of de,pee of prior cold work demonstrate some small measure of yielding before fracture occurs. Sub-yield-stress failure is confined to the aged state, and embrittlement is accentuated by small plastic prestrains. With large plastic pyestrains, embrittle~nent is progressively reduced. In previous work' it was shown that the propensity of commercial aluminum alloys for embrittlement when wetted with mercury seems to be related primarily to the intrinsic strength in the normal un-wetted condition. The data from a large number of commercial alloys in various states of anneal, cold work, and/or aging gave a generalized relationship. At low strength levels, the wetted fracture strength increases proportionately to the increase in tensile strength; but above 65,000 psi normal ultimate strength, the trend is abruptly reversed, and the wetted fracture stress decreases proportionately to the increase in tensile strength. This paper will demonstrate that the simple character of this relationship between normal tensile strength and wetted fracture strength is fortuitous. It will be shown that structure and thermal-mechanical history are clearly relevant factors. The term brittle fracture has been used to connote the geometry of the fracture surface (transverse vs shear plane) or the negligible extent of preceding plastic strain. At its maximum effectiveness, liquid metal embrittlement can satisfy both criteria—fracture transverse to the axis of tension and without observable plastic strain. In this paper, brittle fracture will signify failure at stresses below the engi-

Jan 1, 1962

By R. W. Brauchli

During the last few years the compila-tion of formation logs from rotary well cuttings has become common practice among petroleum geologists. This meth-od has undoubtedly furnished a great amount of information valuable for both scientific and commercial purposes. How-ever, in spite of its great usefulness it has certain drawbacks, principally in the contamination of cuttings by cavings. In extreme cases this contamination can reach such proportions that it is next to impossible to draw conclusions with any degree of certainty as to the nature of the formations penetrated by the drill. This difficulty was frequently encoun-tered during the development of the Okla-homa City Field. In many cases where Wilcox sand-the most prolific sand of this field-was drilled, the samples con-sisted almost entirely of shale cavings with only traces of sand. In order to obtain more reliable knowl-edge of the formations encountered while drilling it is therefore necessary to resort to more coring, and above all to improve our present methods of coring. With this in mind a study has been made of the results of coring in the Oklahoma City Field, and the present article is mainly confined to a statistical analysis of the relation between recovery, diameter of cores and drill pipe, length of cores and a few other factors. Most of the coring in the Oklahoma City Field was done during the early part of, the development. A total of around 18,000 feet or 0.3 per cent of the total footage drilled before February, 1932, has been cored, and about 80 per bent of the cores were taken in the Simpson formation at a depth below 6,000 feet.

Jan 1, 1933

By Frederick G. Bulkley

That portion of the geological structure of the Leadville district which rests upon the Archæan is made up of sedimentary beds of Silurian and Carboniferous formation, consisting of many conformable strata of limestones, quartzites, and shales, which have a total present thickness of about five thousand feet. Interbedded with these strata are found, under somewhat fixed lams of regularity, sheets of intrusive igneous rock,' varying in thickness from a foot or two to several hundred feet. These consist for the most part of various types of felsite rocks, classed, by the sanction of common and long-continued usage, under the general term of porphyries. Mr. S. F. Emmons, in the abstract of his " Report upon the Geology and Mining Industry of Leadville," says in this connection : In their mode of occurrence the type-feature is that of intrusive masses, which are developed on a scale of unprecedented magnitude, and follow certain horizons with remarkable regularity.... It is probable that this mode of occurrence of eruptive rocks, viz., as intrusive masses which originally did not reach the surface but were forced up to a certain horizon and then spread out bettween the beds, is far more common than has hitherto been suspected by geologists. It is difficult to conceive of the conditions under which a fused mass could pry open strata to a width of one thousand feet or more, overcoming the weight often thousand feet of superincumbent rocks, and spread itself out in a continuous sheet between the beds to a distance of ten miles beyond the point or line of eruption. That they did exist, however, can be clearly demonstrated in this region.... In one single section over fifteen sheets, many several hundred feet thick, were counted between the Blue Limestone and the top of the Carboniferous. The region here under discussion is made up of a series of great

Jan 1, 1885

By F. Weinberg

INTEREST is currently being directed toward grain boundary morphologies in zinc in terms of grain boundary facetingl and grain boundary energies.' Some years ago the present author attempted to measure grain boundary energies in 99.999 pct purity Zn as a function of boundary angle, using the standard procedure of measuring equilibrium angles of the boundary traces at triple points. This followed an investigation he carried out on preferential melting of |H (112) Fig. 1—Electron transmission micrograph of a stacking fault, grain boundary intersection in copper. GRAIN BOUNDARY STACKING FAULT Fig. 2—Schematic representation of the intersection of Fig. 1, indicating inclination angles 0 and trace angles $. specimens were prepared by the Bollman technique in an electrolyte of 70 pct methanol, 30 pct HNO3 main-tained at -30°C. The interfacial free energy of the high angle grain boundary and of the stacking fault is assumed to be thermodynamically equivalent to the corresponding in-terfacial tensions. In terms of the true dihedral angles & between the intersecting interfaces, the equilibrium of interfacial tensions in the direction parallel to the stacking fault yields: ysF = -ygb(cos F1+ cos ±cosF2) Here, ysF is the stacking fault free energy and ygb is the grain boundary free energy, assumed equal on both sides of the intersection. Forces acting normal to the grain boundary, of the form ??gb/?F,l are assumed negligible as the grain boundary remains straight for a considerable distance on either side of the intersection. The micrograph of Fig. 1 may actually consist of several closely spaced stacking faults on the same slip plane. The actual point of intersection between the grain boundary and the first stacking fault, and the equilibrium configuration of the intersection, should not be affected by the presence of the other faults, as

Jan 1, 1970

By W. G. Pfann

WHEN a molten zone traverses a long, solid ingot in a level, open boat the ingot becomes tapered. While the taper may be slight after one zone pass, it can be appreciable after repeated zone passes, even to the extent of causing an overflow of matter at the end of the boat. It will be shown here that such matter transport by a molten zone arises from the volume change on melting and that it corresponds in magnitude and direction to the magnitude and sign of the volume change. It will be shown also that the mechanism of matter transport is basically similar to that of solute transport by a molten zone, which has been discussed elsewhere,1,2 and that the two processes can be described by similar equations. Finally it will be shown that matter transport can be prevented by inclining the ingot at a critical angle. Contraction on melting results in forward transport, that is, transport in the direction of zone travel; expansion on melting results in reverse transport. The way in which forward transport arises from the contraction on melting may be seen as follows: At the starting end of a solid horizontal ingot of uniform rectangular cross section of height h., form a molten zone of length 1, as shown in Fig. 1. The height h of the liquid will be h. where a is the ratio of density of solid to that of liquid. Advance the molten zone, at constant length, a distance dx. The volume of solid melted will be hdx; the volume of solid frozen will be Izdx, because the height of the freezing solid will tend to be equal to that of the liquid. The resultant change, dv, in liquid volume will be the difference in these quantities multiplied by the density ratio. Hence the following equation may be used for a zone at any distance x from the origin: which is valid in all but the last zone length in the

Jan 1, 1954

By F. K. Pence

THE reduction of the firing of clay wares to a science has been one of the most difficult problems of modern ceramic engineering. The number of factors involved in the treatment of these wares has been such a complicated composite of the chemical and the physical properties that, according to the old practice, results depended rather on the art of the operator than on any scientific data available. The combined influence of the chemical and physical properties of clay minerals renders it difficult to apply the data obtained in one operation to the forecasting of details to be applied in another. In maturing clay-ware bodies by the application of heat, the chemical reactions involved are, in general, incomplete. The object frequently is to secure a certain physical quality, as density, color, or strength, rather than any particular chemical composition or development: This is more generally true of the so-called crude clay products. In the case of certain more high-grade wares, as the porcelains, it is necessary to reach the temperature required to bring about a certain molecular development or crystalline structure; but even here, time and temperature are at work and must be considered jointly. The conditions attending the firing of clay wares has led to the use of certain devices in the measurement of the progress of the firing process whereby the influence of the various burning factors on the clay composition under fire is indicated. In the simplest application of this practice, samples of the ware itself are so placed as to be drawn for observation at various intervals during the burn. Although the appearance is affected by the quick cooling treatment, by experience, this practice is successfully used, particularly in the brick industry. The settle of the setting of brick, as measured from the top of the kiln may also serve as a guide in the firing operation. Another example is found in the stoneware industry, where the practice of arranging test pieces made of the same composition

Jan 9, 1919

By F. E. Lucas

This paper is offered with considerable diflidence, since some of the statements made may not agree with the opinions of other members of the Institute. What I give is the result of some years of experience in the operation and construction of coke-ovens, and observation of plants in America and Europe. Although my title is " The Manufacture of Coke," I have found it impossible to do justice to the subject without touching on a number of points which, while not strictly involved in the making of coke, yet are of paramount importance from an economic standpoint. There are, indeed, many points of interest, on each of which a separate paper of considerable length might be written, but the scope of my paper will permit me only to touch lightly some of them, in the hope that what I say will promote a full discussion on the whole question. Those of us who are interested in the manufacture of coke are under an obligation to the American Institute of Mining Engineers, which has opened its meetings to the discussion of this subject. I do not believe that there is any question to-day more worthy or more in need of discussion. When geologists and mining-men tell us that, at the present rate of consumption, our coal-fields will be exhausted in a few generations, me should welcome any means that will conserve these deposits as far as possible, and give us the greatest amount of heat or power from every ton mined. I shall try to show that much can be done in this direction through the by-product coke-oven, and that it should stand second to none as an economic factor in the industrial world. I shall here deal exclusively with the by-product oven, except for the comparative statement I hare prepared, showing the saving to be effected by coking in by-product instead of beehive orens. It should be borne in mind that this comparison

Jan 1, 1913

By Lester Tarnopol, Ralph Hultgren

A considerable interest in the subject of superlattices has been manifested by many papers and reviews that have recently appeared, both in physical and metallurgical publications. This interest is due largely to the apparent simplicity of the ordering process, which permits the explanation of many phenomena on the basis of elementary theory. Moreover, ordering may cause important changes in the physical properties of alloys. In this paper, we shall discuss the causes of superlattices in terms of simple properties of the elements that give rise to them, together with a series of experiments performed to test our conclusions. Evidence is presented that in some cases the process of ordering is more complex than might be supposed. While the different species of atoms are usually found in random positions in alloy lattices, in some cases unlike atoms tend to be nearest neighbors. Bethe's1 "order of neighbors" is a statistical measure of thib tendency. At suitable compositions it is possible for atoms in large regions to be regularly arranged, which causes superlattice lines to appear. in X-ray diffraction patterns. Bragg and Williams2 haw dealt with this "long-distance order" in their fundamental work 011 superlattices. Excellent discussions of superlattices are to be found in current reviews TheRmodynamic Considerations Thcrmal vibration tends to destroy order. The magnitude of the effect can be determined from the entropy of mixing, which is calculate from first principles. Since the ordered state has the lower entropy, it must also have a lower internal energy to be stable at any temperature. The difference in internal energy determines the critical temperature at which long-distance order disappears. According to the, theory of Bragg and Williams,~

Jan 1, 1939

By Lester Tarnopol, Ralph Hultgren

A considerable interest in the subject of superlattices has been manifested by many papers and reviews that have recently appeared, both in physical and metallurgical publications. This interest is due largely to the apparent simplicity of the ordering process, which permits the explanation of many phenomena on the basis of elementary theory. Moreover, ordering may cause important changes in the physical properties of alloys. In this paper, we shall discuss the causes of superlattices in terms of simple properties of the elements that give rise to them, together with a series of experiments performed to test our conclusions. Evidence is presented that in some cases the process of ordering is more complex than might be supposed. While the different species of atoms are usually found in random positions in alloy lattices, in some cases unlike atoms tend to be nearest neighbors. Bethe's1 "order of neighbors" is a statistical measure of thib tendency. At suitable compositions it is possible for atoms in large regions to be regularly arranged, which causes superlattice lines to appear. in X-ray diffraction patterns. Bragg and Williams2 haw dealt with this "long-distance order" in their fundamental work 011 superlattices. Excellent discussions of superlattices are to be found in current reviews TheRmodynamic Considerations Thcrmal vibration tends to destroy order. The magnitude of the effect can be determined from the entropy of mixing, which is calculate from first principles. Since the ordered state has the lower entropy, it must also have a lower internal energy to be stable at any temperature. The difference in internal energy determines the critical temperature at which long-distance order disappears. According to the, theory of Bragg and Williams,~

Jan 1, 1939