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By W. K. Godfrey

The highest compressive strength cement has the highest bond strength in tests in which the cement is subjected to a confining pressure. After perforating, the bond strength is reduced to nearly zero when the pipe is supported by weak cement. Perforating does not affect the bond strength, however, when the pipe is supported by strong cement. Pipe supported by weak cement is damaged by perforating with expendable capsule jets, but is not damaged by perforating with the hollow carrier gun. High strength cements are recommended for oil wells that are to be perforated. Introduction The purpose of this work is to determine the effect of jet perforating on the bonding strength of oilwell cement at simulated down-hole conditions. Bond strength is a good criterion for determining the effectiveness of cement in performing its main function, i.e., that of isolating zones. According to the literature on the subject, the optimum cement strength for perforating is low and should not exceed 2,000 psi compressive strength. This conclusion was based on the appearance of bullet and jet perforations in neat and gel cements largely done in the absence of a confining pressure more than 15 years ago. Discussion Literature A relatively weak cement has been recommended in the literature as having optimum properties for perforating. In 1947, Oliphant and Farris tested bullet perforating of neat cements at various curing times.' Some of the tests were made at down-hole conditions. They reported that the optimum cement strength for perforating was about 2,000 psi compressive strength. Enlarged holes occurred when strength was too low, and the cement shattered and cracked when the strength was too high. In 1951, Morgan and Dumbauld tested bullet and jet perforating of neat and gel cements at surface conditions.' They reported that optimum cement has a compressive strength less than 2,000 psi. In their tests at atmospheric pressure, high strength cement shattered and cracked when perforated. Thus, the optimum cement strength was based on the appearance of neat and gel cement after perforating. In 1953, Clark showed a relation between cement strength and fluid shutoff.' He concluded that a 500 psi compressive strength is required for good fluid shutoff and that maximum bonding ability is developed at approximately 1,000 psi compressive strength. In 1964, Bell and Shore invalidated most of the conclu sions by the previous authors when they demonstrated that atmospheric pressure tests cannot be used to determine casing deformation and damage that will result from perforating under down-hole conditions.' They showed that the higher the hydrostatic pressure, the more restricted will be the expansion of gases generated by the charge. Less casing deformation and damage occurs under down-hole conditions than at atmospheric pressure. In recent work, Bearden et al. reported that jet perforating at surface pressure with the hollow carrier gun caused the cement sheath to shatter and crack.' The perforating, however, did not seriously affect the pressure required to leak past the casing cement bond. Only three cementing mixtures were tested, and presumably they had strengths in excess of 2.000 psi. Bearden et al. also reported that the hydraulic bonding strength increased as the compressive strength increased. Their hydraulic test showed that approximately 1,000 psi pressure is sufficient to break the casing cement bond for a well aged neat Portland cement sheath. Unfortunately, the tests were not run with a confining pressure, so Bearden et al. were merely measuring the strength of their outer 8%-in. casing. In our investigation, we measured the hydraulic bond strength of cement to pipe under a confining pressure and found that the bond strength was not limited to 1,000 psi. Cement Bond The bond strength is a good criterion for measuring the effectiveness of cement in performing its main function, that of preventing interzonal communication of fluids behind the casing. Measuring bond strength after perforating should be a good quantitative method of determining optimum cement properties, and should be a better method than that used by previous investigators,11 ' who simply observed the appearance of the cement after perforating.

Jan 1, 1969

By E. S. Wheeler

THE rapid increase in the use of monel metal and malleable nickel in the form of sheet, rod and tube has resulted in a similar increase in the demand for these metals in the form of castings. These castings range in size from small valves and pipe fittings weighing a few ounces to large centrifugal pumps, gate valves and marine propellers, some of the latter weighing as much as 24,000 lb. A group of such castings is shown in Fig. 1. A large nickel agitator is shown in Fig. 2. FIG. 1.-A GROUP OF MONEL METAL AND NICKEL CASTINGS. Monel metal castings are widely used in accessories for steam power plants and in a variety of chemical plant. equipment where the corrosion resistance, high strength and toughness characteristic of this metal render it particularly valuable. Nickel castings find extensive use in the construction of corrosion resistant apparatus, and are often used in conjunction with wrought nickel sheet and tube in the fabrication of equipment for handling a variety of chemical and food products, particularly dairy products. In response to this demand for castings, numerous foundries have undertaken the production of castings of these metals and have met with varying degrees of success.

Jan 1, 1930

By J. R. Spencer

When supplies of high pressure mercury or other liquids are required in analytical work, it is convenient to have the source of supply at a relatively constant pressure and available in sufficient volume to satisfy the requirements of the apparatus in use. It is also desirable that the pressuring device be as simple and as inexpensive as possible and convenient to operate. This pump combined with a small storage reservoir containing gas under pressure has the attributes of (1) positive control of the maximum output pressure through the use of a regulator in the low pressure air supply; (2) an increasing capacity as the rate of withdrawal of mercury from the pressured system is increased; and (3) simplicity, requiring only the use of a lathe, drill press, and welding unit in its construction. DESCRIPTION Essential parts of the pump are shown in Fig. 1. In appearance the unlt is similar to the usual steam pump in common use in industrial applications although considerably smaller in size. The main differences lie in the area ratio of the air and mercury pistons and in the design of the air valve mechanism. Approximate diameters of these pistons are 4.25 in. to 0.375 in. respectively, giving an area ratio of about 130 to 1. The air piston (2) is attached to the end of shaft (4), with the mercury piston being merely a reduced extension of the shaft. Mercury intake and discharge to the pump are controlled by high pressure check valves that screw into the ports indicated at (6). Air supply is controlled by the valve assembly mounted on top of the

Jan 1, 1950

By W. D. France, H. l. Burghoff

FABRICATORS of copper and copper alloys have contended with the problems of reconversion during the past year in endeavoring to return to the full-scale production that is demanded of them. The problems have not been easy, for the industry, like so many others, has had to deal with strikes of long duration, and material shortages, particularly in the raw materials, copper, zinc, lead, and tin. Despite all these obstacles, it was possible to gear production to new peacetime records during the latter part of the year. This was made possible not only by the use of multiple shifts of personnel, but also by the improved production equipment, the development of which had been stimulated by wartime necessity. The work of installing new and better equipment is still continuing, and virtually every company is engaged in improving or planning to improve its processes.

Jan 1, 1947

By R. A. Meussner, R. T. DeHoff, F. N. Rhines

ZINC diffuses through copper more rapidly than does tin. Accordingly, when a ternary diffusion couple is made, by bringing an 0 copper-zinc brass into contact with an a copper-tin bronze at fixed high temperature, it is to be expected that zinc will diffuse into the bronze faster than tin diffuses into the brass. Adjacent to the brass side of the couple the total alloy content (zinc plus tin) should diminish, therefore, while next to the bronze side the alloy content should increase. Since the path of compo- sition change must be continuous, in a single-phased alloy, it should follow a curved and, in general, an S-shaped course. The realization of this prediction is demonstrated in Fig. 1, where the composition paths of two ternary diffusion couples are plotted on the appropriate isotherm of the copper-tin-zinc phase diagram. The diffusion couples were both made from a binary copper-tin alloy analyzing 5.0 pct tin placed against binary copper-zinc alloys analyzing 18.9 and 29.3 pct Zn, respectively. These alloys were produced from electrolytic grades of copper and zinc and a pure grade of straits tin, melted under borax in clay-graphite crucibles and cast in a vertical iron mold. Cylindrical pieces 1 in. in diam and 1 % in. long were machined from the casting and were faced by metallographic polishing to good matching end surfaces. Pairs of the cylindrical pieces were held

Jan 1, 1959

By Thomas Leonard Watson

I. HISTORICAL. BARITE has been mined for many years in various parts of Virginia, probably the earliest mining-operations being in Prince William county, within 600 ft. of the Fauquier county line, about 4 miles south of east from Catlett, a station on the Southern Railway. It is claimed that the mineral was mined here as early as 1845. Mining-operations in Campbell and Pittsylvania counties in the Piedmont region, and near Marion in Smyth county, in the southwest Virginia Valley region, were begun about 30 years ago. The mining and milling of barite on a commercial scale in Tazewell and Russell counties are more recent, and commenced about 15 years ago. II. GEOGRAPHICAL AND GEOLOGICAL DISTRIBUTION. Barite occurs in many counties in the State, as shown in Fig. 1, but the industry has been confined to only a few of them. Its occurrence is noted in two of the three major divisions of the State-namely, the Piedmont region east of the Blue Ridge, and the Paleozoic area west of the Blue Ridge. In the Piedmont region the mineral has been mined in the following counties:, Bedford, Campbell, Louisa, Prince William, and Pittsylvania. In the region west of the Blue Ridge, composed of Paleozoic sediments, barite has been mined in Montgomery, Russell, Smyth, and Tazewell counties. Of the counties mentioned, Bedford, Campbell, and Pittsylvania of the Piedmont region, and Russell, Smyth, and Tazewell of the Valley region, have been the principal producers. In 1906, operations were confined to five counties-Bedford, Louisa, Pittsylvania, Russell, and Tazewell-but in the first two counties named there was no production, the work being solely development.

Jan 9, 1907

By William M. Courtis

While assaying some copper carbonate ore from the Frazer claims, Similakameen, B. C., I noticed that on parting the gold button a deep orange solution was formed. The button gave off pink bands in the nitric acid, which became deep orange at a short distance from it; and as it traveled over the surface of the porcelain dish, it left a deep orange track behind. As the button brightened in the cupel, it appeared to have a bronze color; but I have since found that when amarillium is in large excess of the gold, the button is a very dark gray. The button parted easily. To the orange solution I added a salt (NaCl) solution, shook in a silver testbottle, and filtered. With H2S I obtained a precipitate, which I supposed due to platinum. However, on further tests, it did

Jan 1, 1903

By P. Pietrokowsky

RECENTLY a comprehensive investigation of the various sigma binary alloys was published by Duwez and Baen.1 It was shown that the following conditions are necessary for the formation of the sigma phase: (1) the difference in atomic diameters of the two alloying metals must not be more than about 8 pct; (2) of the two elements which form sigma, one must exhibit a body-centered cubic structure while the second metal must be face-centered cubic, at least in one of its allotropic forms. In addition, a tetragonal unit cell was proposed and powder patterns of six sigma phases were indexed for d spacings greater than 1.640 kx. Since the indexing, based on tetragonal symmetry, led to only fair agreement, the possibility of sigma being orthorhombic was investigated. Various methods for indexing orthorhombic powder patterns are de- scribed in the literature.' The method used in this investigation was a graphical examination of the differences in values of sin' 9 for the adjacent lines of the powder diffraction pattern. This method led to a complete indexing of the Cr-Co (60-40) pattern. Because of the strong similarity between the various sigma alloys, it was then possible to assign indexes to the patterns of Fe-Cr (50-50), Fe-Cr-Mo (30-30-40), Fe-V (50-50), Co-V (50-50), and Ni-V (50-50). The values of sin' 9 and indexes of the six sigma alloys, together with visually estimated intensities, are presented in table 1. In general, the similitude between the six patterns is quite good. For spacings greater than 1.75 kx a few differences are noticeable. In the Ni-V pattern, no (320) exists and the two strong lines (030) and (031) are separated by only two lines of lower intensity, unlike any of the other sigma patterns. However, very little is known about the Ni-V phase diagram and it is possible that the equal atomic percentage composition in this system lies in a two-phase region. At lower spacings there is a close analogy between the patterns. The planes

Jan 1, 1951

Jan 1, 1949

By J. S. Vanick

AN extremely hard, tough, and strong, white or chilled cast iron has been applied for the past several years to industrial and mining services in which its unusual properties have been confirmed by its ability to deliver in many instances much better performance than plain chilled iron, or other wear-resistant materials. It is being produced regularly by alloying a good base composition of chilled or white cast iron with essentially 4 to 6 per cent of nickel and 1 to 2.5 per cent of chromium. Such a material can attain a hardness exceeding 600 to 750 Brinell as against 380 to 530 for corresponding grades of plain chilled iron. The strength is approximately doubled and the toughness significantly increased. These properties make it especially useful for many applica-tions requiring a high hardness for resistance to wear, abrasion, attrition, deformation; to some extent to high compressive loading and to a lesser but important degree to corrosive action. A wide variety of commercial castings is being successfully produced from this iron, ranging in size from the small-grain grinding plates or burrs through medium-sized castings such as sand pumps up to large, heavy castings such as rolls for metal rolling or cement grinding. The composition of this white cast iron may be roughly bracketed within the range shown in Table 1.

Jan 1, 1933

By W. C. Ashby, C. A. Kolar

Extensive reclamation experience in the midwest dates from the 1930s with trees, from the 1950s with pastures, and from the 1970s with row crops. Superior growth and productivity of mined land over unmined land can be shown for forest and pasture, related to type of rooting medium after mining and kinds of plants gown. Superior reclamation to crops is actively being studied. Recent regulations have greatly altered the potential for superior growth of trees, pastures, and crops.

Jan 1, 1984

By J. S. Vanick

An extremely hard, tough, and strong, white or chilled cast iron has been applied for the past several years to industrial and mining services in which its unusual properties have been confirmed by its ability to deliver in many instances much better performance than plain chilled iron, or other wear-resistant materials. It is being produced regularly by alloying a good base composition of chilled or white cast iron with essentially 4 to 6 per cent of nickel and 1 to 2.5 per cent of chromium. Such a material can attain a hardness exceeding 600 to 750 Brinell as against 380 to 530 for corresponding grades of plain chilled iron. The strength is approximately doubled and the toughness significantly increased. These properties make it especially useful for many applications requiring a high hardness for resistance to wear, abrasion, attrition, deformation; to some extent to high compressive loading and to a lesser but important degree to corrosive action. A wide variety of commercial castings is being successfully produced from this iron, ranging in size from the small grain-grinding plates or burrs through medium-sized castings such as sand pumps up to large, heavy castings such as rolls for metal rolling or cement grinding. The composition of this white cast iron may be roughly bracketed within the range shown in Table 1.

Jan 1, 1933

By Henry D. Hibbard

I. INTRODUCTION. THESE impurities are perhaps the most important things in steel-especially steel made by the oxidation processes-the effect of which has not been at least approximately determined. By oxidation processes I mean the Bessemer and Siemens-Martin, during which the metalloids in the charge are removed by oxidation. It has been truly said that it is a clear advantage to have a new name for a new thing. To secure this and to economize space, let us adopt the name sonim (plural sonims) to designate the solid non-metallic impurities existing in steel or other metal. I would define a sonim as a solid non-metallic portion of matter existing as an impurity in metal. A piece of sand, brick, clay, or such material, imbedded in metal, would be considered as a foreign body, not as an impurity, and therefore not a sonim. The studies of sonims of which the results have been published hitherto, have been made chiefly or wholly on finished or at least on cold steel, without much, if any, regard to the specific methods by which the steel was made. While many of the results so obtained are valuable, they give little help in determining the cause, effect, or cure of the disease. It is not enough, in such a study, to know merely the commercial name of the process; for within the field of each process lies a great number of possible variations, each of which will yield a result differing in some respect from all others; and the control of sonims is particularly dependent. on the metallurgical treatment of the metal, because of the inability of analytical chemistry to throw much light on their presence, condition, and effect, as they usually occur in commercial steels. The microscope aids more, perhaps, than chemistry in their study.

Apr 1, 1911

By A. E. Martin, Gerhard Derge

IF the molecular constitution of molten slags were better known, the nature of chemical reactions in slags and between slags and metals could be better understood and as a consequence might be better controlled. Constitutional information can be obtained by studies on either the molten or the solidified slags. Valuable as the studies on solidified slags admittedly are for many purposes, especially as control methods in steelmaking, they are always of questionable value in giving information on the molecular constitution of liquid slags. However, the characteristics of molten slags such as viscosity, rates of diffusion, and electrical conductivity can be determined experimentally and interpreted along with other knowledge on slag-metal and slag-gas reactions so as to provide direct information on liquid slags. Metallurgists are accustomed to regard reactions in molten slags as involving only neutral molecules, whereas it is quite possible that ionic constituents are actually involved. For example, the dissociation of calcium silicate usually is represented as Ca2SiO4 = 2CaO + SiO2 although a reasonable alternative would be to write Ca2SiO4 = 2Ca+2 + Si04-4 Such ionic dissociation has been suggested frequently without adequate experimental proof. This paper deals especially with electrical conductivity measurements on slags of the blast-furnace type. These measurements were made to determine whether or not slags are ionized and, if so, to provide a qualitative estimate of the extent of ionization. Electrolysis experiments that indicate the identity of the ions present are also reported. Since the presence of ions has not been considered carefully in modern slag studies, the relevant literature will be reviewed. REVIEW of LITERATURE In 1906 Aiken1 obtained a patent for a continuous process of producing iron electrolytically by passing a direct current through a bath of FeO-SiO2 to which iron oxide was added periodically to maintain a uniform concentration. The patent also included the addition of CaO and MgO to the bath to lower its melting point. The silicate melts involved were thus in the same system as basic open-hearth slags but with higher FeO and lower CaO contents. Electrical conductivity measurements were made on some molten silicates by Doelter2 in 1907. Natural silicates, such as

Jan 1, 1943

By E. Ryba, D. J. Michel

SAMPLES of REZn2 (RE = rare earth) intermetallic compounds prepared by a variety of techniques have been shown to exhibit an extensively twinned micro-structure.1-4 We have recently conducted compression tests at room temperature on specimens of HoZn2 prepared by a powder metallurgy technique.' The microstructures of specimens before and after testing are shown in Fig. 1. The "before" specimen, Fig. l(a), shows the basic twin structure of this material. Fig. l(b) shows the microstructure of the "after" specimen just below the fracture surface and reveals considerable cross-twinning as well as additional

Jan 1, 1970

New equipment for seabed sampling, presently at the prototype stage, operates on the principle of diamond core drilling with wire line core barrels and is designed to drill cores from the seabed at depths down to 200 m with a continuous recovery of cores from an attendant vessel. The machine operates on the seabed by remote control from a console on the vessel. Neither installation nor operation requires the use of divers. Principal Applications Principal areas of application for the drill which is dubbed Maricor include investigation drilling in the continental shelf, mapping geological conditions before large drilling platforms are installed and exploring proposed undersea tunnel routes.

Jan 11, 1973

By Fred C. Bond, Walter Maxson

Since the last publication of tabulated results of grindability tests by the authors1 the total number of ball-mill tests made has more than doubled, and rod-mill tests have become increasingly important. Nearly all of the standard closed-circuit ball-mill and rod-mill tests made to date are included in the present tabulation, together with additional information not previously published. Standard Ball-mill Grindability Tests The method of conducting these closed-circuit tests has not been altered. A sample of the ore or other material is stage-crushed in rolls set at 1/16-in. opening with a 6-mesh screen until all of it has passed the screen. The combined minus 6-mesh screen undersize is mixed, sampled and screen-analyzed, and its apparent specific gravity is determined by packing and shaking in a standard container, and weighing. The apparent specific gravity ordinarily is about 60 per cent of the true specific gravity. The unit volume present in the mill .in all tests is 700 C.C. of the packed minus 6-mesh roll product, and the number of grams occupying 700 C.C. is the unit test weight. This weight is placed in the mill dry, ground for the number of revolutions estimated to be necessary, discharged, and screened mechanically in three testing sieves of the mesh size at which the test is to be conducted. The oversize, or circulating load, is weighed, sufficient fresh minus 6-mesh feed is added to bring the total weight up to that of 700 c.c., and the charge is returned to the mill for a second grinding period. All standard ball-mill tests are conducted at 250 per cent circulating load, and the number of revolutions in the mill necessary to obtain this circulating load at any grinding period is estimated from the results of the previous period. The number of net grams of screen undersize produced per revolution of the mill approaches its final equilibrium value after several grinding periods, and this is recorded as the grindability, or relative ease of grinding, of the sample. A cylindrical ball mill, 12 by 12 in. inside, with a smooth lining and rounded corners, is used with a revolution counter Under standard grinding conditions it runs at 70 r.p.m., and contains a charge of 285 iron balls weighing 20,125 grams, ranging from I½ to ¾ in. in diameter. Tests are conducted at the mesh size to which the ore is to be ground in practice, and the capacity- to be expected from a given mill is calculated by comparing the grindability with that of a similar standard ore whose performance characteristics arc known. No satisfactory general formula for convertillg standard grindabilities into corn; rnercial power-consumption values has been

Jan 1, 1943

By Walter Maxson, Fred C. Bond

Since the last publication of tabulated results of grindability tests by the authors1 the total number of ball-mill tests made has more than doubled, and rod-mill tests have become increasingly important. Nearly all of the standard closed-circuit ball-mill and rod-mill tests made to date are included in the present tabulation, together with additional information not previously published. Standard Ball-mill Grindability Tests The method of conducting these closed-circuit tests has not been altered. A sample of the ore or other material is stage-crushed in rolls set at 1/16-in. opening with a 6-mesh screen until all of it has passed the screen. The combined minus 6-mesh screen undersize is mixed, sampled and screen-analyzed, and its apparent specific gravity is determined by packing and shaking in a standard container, and weighing. The apparent specific gravity ordinarily is about 60 per cent of the true specific gravity. The unit volume present in the mill .in all tests is 700 C.C. of the packed minus 6-mesh roll product, and the number of grams occupying 700 C.C. is the unit test weight. This weight is placed in the mill dry, ground for the number of revolutions estimated to be necessary, discharged, and screened mechanically in three testing sieves of the mesh size at which the test is to be conducted. The oversize, or circulating load, is weighed, sufficient fresh minus 6-mesh feed is added to bring the total weight up to that of 700 c.c., and the charge is returned to the mill for a second grinding period. All standard ball-mill tests are conducted at 250 per cent circulating load, and the number of revolutions in the mill necessary to obtain this circulating load at any grinding period is estimated from the results of the previous period. The number of net grams of screen undersize produced per revolution of the mill approaches its final equilibrium value after several grinding periods, and this is recorded as the grindability, or relative ease of grinding, of the sample. A cylindrical ball mill, 12 by 12 in. inside, with a smooth lining and rounded corners, is used with a revolution counter Under standard grinding conditions it runs at 70 r.p.m., and contains a charge of 285 iron balls weighing 20,125 grams, ranging from I½ to ¾ in. in diameter. Tests are conducted at the mesh size to which the ore is to be ground in practice, and the capacity- to be expected from a given mill is calculated by comparing the grindability with that of a similar standard ore whose performance characteristics arc known. No satisfactory general formula for convertillg standard grindabilities into corn; rnercial power-consumption values has been

Jan 1, 1943

By C. P. Proctor

WESTERN Pennsylvania, eastern Ohio, and Illinois are carrying out experiments wherein much more slate and other impurities are loaded with the coal in the mine and hauled to the surface preparation plant for removal. In general everything is sent to the cleaning plant although there may be some gobbing in the mine. No conclusions have been announced as to the effect of such a mining system on clean coal costs. Such factors as ability of the surface plant to handle the impurities, land and facilities for disposing of the impurities, and the transportation facilities underground should be considered.

Jan 1, 1942

By D. de Fontaine

A convolution procedure is described for obtaining an analytical expression for the composition profiles of solute concentration:; in binary solid solutions. The free energy of solutions containing such compositional inhomogeneities can then be evaluated and the stability of spherically symmetric clusters (G.P. zones, for short) us a function of their radii and central compositions can be studied accordingly. Two characteristic zone radii are defined: the minimum radius (RM) corresponding to the smallest zone for which growth is energetically favored over dissolution, and the critical radius RK) corresponding to zones associated with the minimum work of formation. The values of RM and RK coincide at the two classical limits of nucleation and growth and spinodal decomposition. As the spinodal is approached, however, RM and RK diverge increasingly and it is proposed that the initial] decomposition morphology is governed more closely by the minimum, rather than by the critical radius since the former possesses no singularity within the m eta stable phase boundary. Reversion is briefly discussed in the light of the foregoing and it is shown that a set of reversion temperatures located between the coherent miscibility gap and the coherent spinodal must correspond to a given distribution of low temperature zones. SINCE the early works of Guinier1 and preston,2 the kinetics and morphology of GP zones have been studied extensively, see Ref. 3, for example, for a recent review. Nevertheless, a completely satisfying theoretical treatment of the decomposition of meta-stable or unstable binary solid solutions is still lacking due to the almost unsurmountable mathematical difficulties that one encounters in attempting to solve the pertinent diffusion equation which, in principle, describes the whole process. This equation, first derived by Cahn for the initial stages of spinodal decomposition,4 is a nonlinear partial differential equation of the fourth order in anisotropic space, a general analytical solution of which is completely out of the question. From this equation, some prediction can be made, however, concerning the later stages of spinodal decomposition5 and a recent numerical solution6 of the equation in the case of one- and two-dimensional composition modulations of a solid solution inside the spinodal has led to the following considerations: the sinusoidal morphology7 is to be expected only for solutions of average composition c, located near the center of the coherent miscibility gap.8 For solutions with co closer to the spinodal decomposition, depleted shell zones9 should constitute the first recognizable decomposition product, later evolving to iso- lated, enriched preprecipitates in a uniformly depleted matrix as this must, in all cases, constitute the final metastable morphology, barring, of course, loss of coherency and change in crystal structure. In agreement with the qualitative description of Bonfiglioli and Guinier,l0 it thus appears that the various models discussed by previous authors are, in fact, idealized successive stages of the general decomposition process. Unfortunately, corresponding calculations for a solid solution outside the spinodal are not yet available because of two additional difficulties: it is essential that the diffusion equation be solved in three-dimensional space, and furthermore, one must include in the equation an appropriate "source term" describing the statistics of the creation of composition fluctuations required to trigger the nucleation events. At present, a general treatment of this problem does not appear to be tractable. Nevertheless, by using a modelistic approach, i.e., by selecting a priori certain composition variation profiles and by evaluating their associated free energies, one can draw certain conclusions relative to the stability of these isolated composition modulations or "zones", both outside and inside the spinodal. This is the object of the present investigation. THEORY We shall now describe a standard four-parameter spherically symmetric GP zone, evaluate its free energy according to the Cahn and Hilliard11 formula (Eq. [5], below), and plot the corresponding energy surfaces as a function of zone amplitude and radius as

Jan 1, 1970