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By Richard G. Warren, Michael M. Minor, Gayle J. Thomas

INTRODUCTION Los Alamos Scientific Laboratory (LASL) initiated its effort in the Hydrogeochemical and Stream Sediment Reconnaissance (HSSR), a part of the Department of Energy (DOE) National Uranium Resource Evaluation (NURE) program, in late 1975. Since that time, LASL has completed sampling of the Rocky Mountain states of New Mexico, Colorado, Wyoming, and Montana at a density of about one water or waterborne sediment sample per 10 km2 and has sampled about 85% of Alaska at a density of at least one per 25 km2. Analytical results for these samples are reported by National Topographic Map Series (NTMS) quadrangle. All collection and analytical procedures have been standardized from the outset (Sharp, 1977; Sharp and Aamodt, 1978). Until early 1979, only uranium results were reported for these samples; thereafter, results include analyses for at least 42 additional elements in the sediment samples. Each LASL HSSR report also includes a discussion of the relationship of these analytical data to known or possible uranium resources; more recently, these data have been re- examined for their relationship to resources for other metals (Beyth et al., 1980; 1980a). Analytical results for LASL HSSR sediment samples are both comprehensive, including 43 elements, and precise, allowing close inter-comparison of data between quadrangles. A recent HSSR study shows that elemental concentrations in sediment samples from the Dixon Entrance quadrangle in Alaska are insensitive to the choice of sieve size fraction and do not vary significantly between stream locations a few meters apart, except for extremely high elemental concentrations (Warren, et al., 1980). Elements that are particularly reproducible include thorium, hafnium, and the .ram earth elements. Fortunately, sensitivities for these elements, which are often associated with uranium, are excellent by the nondestructive analytical technique of neutron activation analysis that LASL employs. Wet chemical techniques may not always give reliable results for these elements in sediment samples due to the difficulty of dissolving the resistate mineral phases that normally contain these elements. LASL has recently open-filed results for a large number of NTK3 quadrangles; to date analyses have been reported for about 605 of the quadrangles within the states of the Rocky Mountain region. As a result, uranium analyses am now complete for all sediment samples collected from the state of Wyoming. We have chosen to sumnarize the analytical results for Wyoming and portions of adjoining states hereafter termed "the ~ Wyoming regionn (Fig. 1 ) ; nearly 24 000 uranium analyses and nearly 17 000 analyses for 42 additional elements are available for sediment samples collected from this area. The DOE open-file report numbers are shown in Fig. 1 for reports open filed before September 1, 1980. The Wyoming region provides an ideal area for an examination of regional geochemical patterns ex- hibited by sediment samples. It is endowed with a variety of exposed geologic units and with widely distributed uranium districts associated with host units of several ages. However, discussion will focus on rock units of Eocene and Precambrian ages because they are widely exposed and host the majority of the uranium resources within the region (Fig. 2). Miocene units are also widespread and host mineralization in the Brown's Park Formation (Fig. 2). Epigenetic uranium mineralization occurs in sand- stones of lower Eocene age such as the Wasatch, Battle Springs, and Wind River Formations whereas vein type mineralization occurs in Precambrian crystalline rocks. Precambrian rocks within the region consist of a variety of granitic and meta- morphic rocks with l .4-2.8 billion year ages, except within the Uinta Arch, where they consist of a sequence of very low grade metamorphosed or unmetamorphosed 1.0 billion year old sedimentary rocks. Precambrian rocks have served as sources for much of the clastic material comprising the lower Eocene units, and may also have provided the source for the uranium in mineralized Eocene or Miocene sandstones (Stuckless, 1979). The remainder of this paper describes the relationship of elemental concentrations in HSSR sediment samples to exposures of Eocene and Precambrian rocks. The results are used primarily to determine where these Precambrian rocks might provide the most suitable uranium source areas and to infer the direction of transport toward adjacent depositional basins during the Eocene.

Jan 1, 1980

By J. E. Spruiell, F. H. Patterson, B. F. Shuler

The microstructures and textures developed by the working of high-purzly thermochemically deposited tungstem sheet have been inuesligated. Greater than 60 pct reduction was required to deslroy the columnar grain structure which existed in the as-deposited sheet. With increasing reductions the texture gradu-ally charged from the initial as-deposited orientation with (100) parallel to the sheet normal to a (100}(011) ideal ovienlation with some spread about the rolling direction. This texture was retained after recrystalli-zation a1 2000°C. THE processes for depositing tungsten by hydrogen reduction of tungsten hexafluoride have been under development for the past several years.1,2 The nature of the deposition process is such that the as-deposited material contains a highly oriented columnar grain structure perpendicular to the deposition substrate. This well-defined columnar structure may be useful in certain applications293 but a wrought or equiaxed structure may be desired for some components such as tubing. Knowledge of the effects of working ther-mochemically deposited (TCD) tungsten is therefore necessary in order to establish the feasibility of obtaining worked and recrystallized microstructures and textures. The details of a recently developed technique for thermochemically depositing flat, uniformly thick tungsten sheet are presented with emphasis on the effects of deformation by rolling on the microstructure and texture. Although no work has been previously reported on the rolling and the annealing textures of TCD tungsten, there have been some determinations of textures for cold-rolled tungsten foil prepared from powder-metal -lurgy billets.4-8 The general description is that of a predominantly lurgy{100}(011) texture, with some spread about the rolling direction as an axis. pugh5 reports data both for cold-rolled and for annealed foil having about 96 pct initial cold work. He observed no change in texture, except for a decrease in the spread, for annealing treatments of 30 min at temperatures up to 1800°C. On annealing at 1900°C, both the low-temperature components plus new components which were described alternately as {001}(320) plus {001)(230) or as {100}(011) ± 12 deg about the sheet normal were observed. Above 1900°C, the new orientation existed alone, and it was stable up to 2500°C, the highest temperature that Pugh investigated. THERMOCHEMICAL DEPOSITION OF TUNGSTEN SHEET High-purity tungsten sheet was reproducibly deposited on the inner walls of a molybdenum mandrel by the thermochemical reaction WFs(g) + 3H2(g) - W(s) + 6HF(g). The mandrel was heated by a five-zone tube furnace which afforded a controllable fixed-temperature profile. Sheets measuring 1+ by 12 in. have been deposited with uniform thicknesses of up to 0.145 m. As shown schematically in Fig. 1, the purified reaction gases were metered into a mixing chamber at a Hz-to-WF6 ratio of 15 and preheated to 350°C. The flow rate of the WF6 was 300 cu cm per min at stp. These gases were directed through a conical injector into the deposition chamber. Inside this chamber hydrogen reduction of the WF6 to pure tungsten metal occurred on the hot walls of the molybdenum mandrel at a total pressure of 5 Torr. Typical temperatures for the five zones in the chamber were, respectively, 565", 540", 550°, 570°, and 590°C. The hydrogen fluorlde generated from the reaction, the excess hydrogen, and some un-reacted WF6 were pumped on through the scavenger

Jan 1, 1968

By N. Nemeth, L. L. Sirois

The role of the filter medium in continuous-vacuum filtration and the special circumstances which influence the resistance to flow through the porous cake and filter cloth are discussed. Due to negative pressure differential, gas bubbles evolve in the slurry, constrict passages in the filter cake and medium, and further restrict flow through the tortuous channels. Filtration is a liquid-solid separation process taking place at a porous medium under a pressure differential. The liquid passes through the medium; the solids are retained on the medium as a partially dewatered cake. Filtration is far from a simple process and has been described in terms ranging from "complex" to "subtle." Because of the many variables involved, no unified filtration theory has been developed, and the filtration process is still considered very much an art. In industrial filter design, basic relationships, whether derived for idealized conditions or developed empirically, are usually adapted to suit local conditions. In the mining industry where continuous-vacuum filtration is the main dewatering process, the physical state of the concentrates and the relatively low pressure differentials permit the assumption that the cakes are noncompressible, an assumption which leads to the use of theoretically sound rate equations. Notwithstanding this simplification, there are other problems, unique in the application of vacuum to dewatering, and until now completely ignored, which demand special attention. The basics of filtration involve the capture of solids on, while permitting the flow of liquid through, a porous layer of cake and cloth. Flow is determined by the structure of the solids which make up the cake and the particles permanently attached to the cloth. The problem of this structure, essentially one of solid geometry, has been considered insoluble by Hatscheckl as early as 1907 and by Freshwater as recently as 1967. Since cake structure is determined by the slurry parameters, that problem is far too large for inclusion in this study. For theoretical considerations, uniform buildup of the filter cake must be assumed; and for efficient practical operation, the resistance of the medium must be kept constant over long periods. The latter can be achieved by careful selection of the filter cloth, since the greatest part of the total filtration resistance will develop at the cake-cloth contact. This paper discusses the role of the filter medium in continuous vacuum filtration and the special circumstances which influence the resistance to flow through the porous cake and the filter cloth.

Jan 1, 1971

By H. l. Burghoff

During the course of preparation of crystals of alpha brass for an investigation of their creep characteristics, a number of critically oriented crystals were produced. In each of these specimens, Po, the specimen axis, lay near some important crystallographic direction or on or near the border of two possible slip systems. Because of the unusual nature of their orientations, it was considered of interest to deform these specimcns in simple tension and to study orientation changes and any unusual occurrences, different from what would be expected for specimens ill which only one slip system had distinctly the highest maximum resolved shear stress. Choice of actual operating slip system in a crystal offering an immediate possibility of two slip systems would be expected to be due to chance., defeet, or some inhomogeneity. Even in an ideally perfect crystal so oriented, the natural oscillations of the atoms about their lattice positions would give rise to a condition wherein one slip system would be farored over the other at the critical shear stress. In the large, nonperfeet crystals of the present investigation, slip on both systems, but in different portions of the specimen, might occasionally be expected. Determination of Orientation and Operating Slip System Orientations of specimens before and after deformation were determined by Greninger&apos;s back-reflection Laue method.&apos; Elam2 has shown that deformation of alpha brass crystals proeceds as with crystals of aluminum and of copper; that is, the slip plane is a {111) plane and the slip direction is a <110> direction. There are, however, four possible slip planes of {111) form and each plane has three possible slip directions, so that there is a, total of 12 possible slip systems in a face-centered cubic lattjce. It is evident that the system for which the tangential component of shear is maximum will function

Jan 1, 1940

By H. l. Burghoff

During the course of preparation of crystals of alpha brass for an investigation of their creep characteristics, a number of critically oriented crystals were produced. In each of these specimens, Po, the specimen axis, lay near some important crystallographic direction or on or near the border of two possible slip systems. Because of the unusual nature of their orientations, it was considered of interest to deform these specimcns in simple tension and to study orientation changes and any unusual occurrences, different from what would be expected for specimens ill which only one slip system had distinctly the highest maximum resolved shear stress. Choice of actual operating slip system in a crystal offering an immediate possibility of two slip systems would be expected to be due to chance., defeet, or some inhomogeneity. Even in an ideally perfect crystal so oriented, the natural oscillations of the atoms about their lattice positions would give rise to a condition wherein one slip system would be farored over the other at the critical shear stress. In the large, nonperfeet crystals of the present investigation, slip on both systems, but in different portions of the specimen, might occasionally be expected. Determination of Orientation and Operating Slip System Orientations of specimens before and after deformation were determined by Greninger&apos;s back-reflection Laue method.&apos; Elam2 has shown that deformation of alpha brass crystals proeceds as with crystals of aluminum and of copper; that is, the slip plane is a {111) plane and the slip direction is a <110> direction. There are, however, four possible slip planes of {111) form and each plane has three possible slip directions, so that there is a, total of 12 possible slip systems in a face-centered cubic lattjce. It is evident that the system for which the tangential component of shear is maximum will function

Jan 1, 1940

By C. S. Smith, L. Guttman

It is shown, from a study of geometric probabilities, that the average number of intercepts per unit length of a random line drawn through a three-dimensional structure is exactly half the true ratio of surface to volume. Since the surfaces can be internal or external, the area of grain boundary or of the interface between any two constituents in a micro-structure can be measured. Other metric relations are tabulated that may be of use in studies of the microstructure of polycrystalline, cellular, or particulate matter generally. IN many fields of scientific investigation the structure of cellular aggregates or random arrays of discrete particles imbedded in some matrix is observed on a two-dimensional section and inferences are drawn therefrom as to the real structure in three dimensions. The biologist&apos;s microtome slice, the petrologist&apos;s thin section, and the metallurgist&apos;s plane polished and etched sections are common examples, although the problem is a general one. Scientists have commonly limited their thinking to the same dimensionality as their structures, and the few attempts that have been strictly three-dimensional in character have been laborious and noteworthy. From a metallurgical standpoint it is often of considerable importance to know, in addition to the volume fraction of two or more components in an alloy, the amount of two-dimensional interface between crystals. Such grain boundaries (which may separate either two identical crystals differing only in orientation or two crystals differing in structure, and possibly also in orientation) have a determining factor upon the mechanical behavior. It is at these boundaries that melting commences, that stress-induced corrosion occurs, and that various precipitates (harmful or otherwise) first appear. The boundary is doubtless of equal importance in nonmetallic crystalline aggregates such as rocks, ceramics, and concrete, and the biologist is deeply concerned with the area of cellular membranes. Many synthetic cellular foams involve similar structural problems. The very term structure usually implies the presence of interfaces and a complete understanding of structure involves nothing but an analysis of the geometrical, metrical, and topological relations between the various interfaces (zero, one and two-dimensional) that exist in a three-dimensional structure. Even systems lacking sharp physical interfaces often have interrelated gradients of composition or velocity (as cored crystals or turbulence cells) in which a neutral surface can be treated as a two-dimensional interface. In an earlier paper by one of the authors&apos; the question of cell shape was considered in terms of simple topological principles without regard to physical dimensions. The determination of the actual size of grains in two dimensions is carried out in a routine fashion in innumerable metallurgical laboratories (see, for example, the ASTM standard methods of grain size determination2), though this is done merely to check the uniformity of a product and has no relation to the actual three-dimensional shape or size of the grains. Some authors have discussed the three-dimensional problem but only on the basis of assumptions as to idealized grain shapes.:&apos;-&apos; Quantitative measurements of microstruc-tures to obtain the volumetric relations of various phases have been carried out by petrographers for many years and are of increasing popularity among metallurgists." The present paper will show how, on the basis of no assumptions other than randomness of sectioning (usually realizable in experiment), it is possible to learn a great deal about the three-dimensional structure. The relations to be derived will generally be used on random arrays of cells or other particles, although they are equally applicable to ordered arrays and even to isolated objects of complex shape provided that suitable random sections can be made. Total Area of Interfaces in a Sample Consider a typical microstructure of a single-phase polyerystalline metal, such as that shown pres- in Fig. 1. The plane cross section shown contains a network of lines which subdivides the area into two-dimensional cells. The lines, of course, represent merely the intersection of the two-dimensional plane of sectioning with the two-dimensional interfaces between adjacent three-dimensional cells. The structure also contains points at which two or more lines intersect: in three dimensions the points are, of course, lines. In the more general case there may be in three dimensions isolated particles surrounded by a single interface without contact with others, and both two and one-dimensional features which do not necessarily connect with others. On the two-dimensional section these will appear as areas delineated by a closed line (as at a and b, Fig. 2), as isolated lines

Jan 1, 1954

By H. E. Cline, D. F. Stein

A fine lamellar structure with interlamellar spacings ranging from 0.I to 3.7 was Woduced by high-speed directional solidification and used to study the interaction of dislocations with an array of bimetallic bound-am.es. The tensile flow properties were measured at elevated temperatures and the results interpreted in terms of an image force model. As the width of the plates decreases the strength increases according to a Hall-Petch relation, suggesting pile -ups. Considerable strengthening was also observed at elevated temperatures. In recent years composites containing a strong but brittle phase and a ductile but weak phase have been studied extensively in the search for a high-strength material with adequate ductility.&apos; However, the strength of these composites has been limited to a volumetric average of the strengths of the component phases. In this paper we will show that a composite made by directional solidification of a Cu-Ag eutectic has strength properties that substantially exceed the strength of either of the metals in the composite, and an explanation for this increased strength will be presented. The Cu-Ag eutectic is a near ideal material to study for several reasons. The eutectic structure is made up of alternate plates of silver-rich and copper-rich phases with the same crystal structure.2&apos;3 In addition, the mechanical and elastic properties of silver4 and copper5 are known over a wide range of temperatures and the eutectic microstructure is stable to nearly the melting point.6&apos;7 Therefore, the properties of the eu-tectic are readily comparable to various theories involving the mechanical properties of copper and silver. The experiments consisted of producing directionally solidified Ag-Cu eutectic material, determining the structure and performing tensile tests at different temperatures and strain rates. EXPERIMENTAL A) Solidification and structure. A cylindrical ingot 2.2 cm in diam and 15 cm long was prepared from 99.999 pct pure materials and cast in argon. The ingot was placed in an alumina crucible and was direc-tionally solidified at 7 x 10"4 cm per sec in a Bridg-man apparatus in argon. Metallographic examination at both ends and along the length of the ingot showed a uniform structure that consisted of fine alternate plates of silver- and copper-rich phases. The plates were aligned parallel to the growth direction, as shown in the longitudinal section, Fig. 1, and were in small randomly oriented domains of parallel plates as viewed in a transverse section, Fig. 2. Four smaller ingots 0.175 in. in diam were solidified at speeds of 2Xlo-&apos;, 4.4 xlo-&apos;, 4.4 x 10-3, and4.4x10-4 cm per sec to produce a range of lamellar spacings. Replica electron micrographs were taken to resolve the individual plates as shown in Fig. 3. The copper-and silver-rich plates in the larger ingot were about

Jan 1, 1970

By Edward A. Loria

Vanadium is one of the materials being considered for use in fast-breeder nuclear reactors. It is a good heat conductor and nearly transparent to radiation, properties regarded as ideal for nuclear fuel containers. The problem has been the metal lacks ductility needed for forming. In our program at Reno Laboratory the effects of the U.S. Bureau of Mines (previous affiliation) the effects of oxygen, nitrogen, and carbon have been reported21,22 nd most recently the effects of boron and boron with carbon.23 The continuing study by the Ames Laboratory of the effects of hydrogen, the most subtle and fugitive element in its relationship to structure and properties, is commendable. The solubility of oxygen, nitrogen, and hydrogen in vanadium (and other bcc metals as well) is related to material purity. With the available limit on metal purity and the interaction (clustering) of hydrogen with the other interstitial and substitutional elements present in their base metal, would the authors comment on the tolerance of hydrogen in relation to oxy- gen that will avoid intergranular fracture and above what content or how seriously harmful in oxygen at various carbon levels? Understanding the true effects of hydrogen (and other interstitial impurities) in vanadium depends on knowledge of the amount present under various conditions and its distribution between various possible positions. Significant amounts of hydrogen may be in "thermo-dynamic" solution, but not as individual atoms in interstitial positions. It may be in grain boundaries, in subgrain boundaries, in vacancies, or in dislocations. Some of the hydrogen may be paired or in complexes with impurities in substitutional solid solution in vanadium. This makes the analysis of the effect of hydrogen vastly more difficult. It should not be expected that hydrogen in grain boundaries will affect slip in the same manner as hydrogen in interstitial positions, nor will the complexes react to heat treatment the same way as hydrogen in dislocations. It is gratifying that the authors have quoted results from two of our inestiations,&apos; but neglected one2&apos; which applied the Petch theory to electrorefined vanadium of high purity and analyzed the effects of oxygen, nitrogen, and carbon on the ai and ky values obtained by the extrapolation and grain size methods. Details can be found in the paper. Briefly, we obtained a ui value of 10,300 psi (t = 5150 psi) at 273°K. The metal also exhibited profuse twinning with high ductility at 123" and 77°K. Nitrogen was more effective than oxygen in increasing ui, the increase being about twice as much for the same impurity level. Carbon additions resulted in only minimal changes in Ui. The corresponding ky increased as oxygen and nitrogen increased, with nitrogen being more effective. Carbon additions resulted in little change. Although the difference in yield strength of vanadium was explained on the basis of the Cottrell-Bilby model of the tearing away of dislocations from the impurity atoms,

Jan 1, 1970

By H. Kazemi

An ideal theoretical model of a naturally fractured reservoir with a uniform fracture distribution, motivated by an earlier model by Warren and Root, has been developed. This model consists of a finite circular reservoir with a centrally located well and two distinct porous regions, referred to as matrix and fracture, respectively. The matrix has high storage, but low flow capacity; the fracture has low storage, but high flow capacity. The flow in the entire reservoir is unsteady state. The results of this study are compared with the results of the earlier models, and it has been concluded that major conclusions of Warren and Root are quite substantial. Furthermore, an attempt has been made to study critically other analytical methods reported in the literature. In general, it may be concluded that the analysis of a naturally fractured reservoir from pressure transient data relies considerably on the degree and the type of heterogeneity of the system; the testing procedure and test facilities are sometimes as important. Nevertheless, under favorable conditions, one should be able to calculate in-situ characteristics of the matrix-fracture system, such as pore-volume ratio, over-all capacity of the formation, total storage capacity of the porous matrix, and some measure of matrix permeability. INTRODUCTION The analysis of flow and buildup tests for obtaining in-situ characteristics of oil and gas reservoirs has received considerable attention in the past decade. Most of the available techniques result in reliable conclusions in macroscopically homogeneous reservoirs or in the homogeneous reservoirs with only certain types of induced and/or inherent heterogeneity (such as wellbore damage, etc.). In general, the greater the degree of heterogeneity, the less the reliability of the information deduced from the pressure transient data. A commonly encountered heterogeneous system is a naturally fractured reservoir where two types of distinct porosities occur in the same formation. The region containing finer pores may have high storage and low flow capacities. This is called the matrix. The remaining region may have high flow capacity with low storage. The latter region is generally the set of interconnecting fractures and fissures of the rock, and for this reason it is called the fracture. Ordinarily, we wish to obtain the permeability and porosity of each region and perhaps the frequency of the fracture distribution in a reservoir. Such information is necessary for reservoir engineering. Other information, such as wellbore damage, will be useful in evaluating possible remedial work for such fields. Few authors have suggested theories to aid in calculating the in-situ characteristics of a naturally fractured reservoir similar to what we have described above. Pollardl suggested that a naturally fractured reservoir contained three distinct regions: a damaged or an improved region surrounding the wellbore, and the two remaining regions the same as described earlier. He suggested that the flow was taking place from the tight matrix into the highly conductive fractures, then into the we wllbore region and finally into the well column. He concluded that the average pressure buildup in each of these distinct regions can be expressed approximately in terms of an exponential decay function of time. He also hypothesized that the decay coefficients for each of these functions were significantly different from each other; consequently, each of these functions became dominant in turn, in the process of pressure buildup. Thus, by a proper graphic plot of the logarithm of wellbore pressure differences vs buildup time, each of these functions could be determined (see Fig. 1). Pollard suggested methods of determining the wellbore damage and fracture volume. Later Pirson and Pirson2 extended

Jan 1, 1970

LIST OF MEMBERS AND ASSOCIATES ARRANGED ACCORDING TO STATES AND TOWNS ALABAMA Aldrich, Aldrich, W F Anniston, Noble, A E, Smith, N B Aibacoche, Bradley, D II Bessemer, Fergusson, V Birmingham, Aldrich, T H, Aldrich, T H, Jr, Bowron, J, Bowron, C E, Davis, F H, Dimmick, F D, Hillman, McCarthy, M E , McCormack, McCrery, Ramsay, E, Shook, A M Bridge¬port, Wheeler, S K Ensley, McDonald, S, Shook, J W Fanbanks, Hamil¬ton, A L Helena, Squire, J Huntsville, Moss Lehigh, Toulmin Oxmoor, Green¬amyer, A G Plasma, Gage Rock Run, Garvin Sheffileld, Miller, D I Tuscaloesa, Lodge, J University, McCalley Woodward, Bukofzer, Woodward, A H ALASKA Dawson, Buck Douglas Island, Corbus, J P , Macdonald, J Hames, Le Wald, E A Jualin, Hoggatt, W B Juneau, Denby, Gaifield, Garside, Hamp¬ton, W H Rodman Bay, Phillpots Snettisham, Tisdale Sumdum, Thane Tel¬ler, Hirshberg, M R Treadwell City, Batcheller, J H , Kinzie Valdez, Esterly, G M Yukon, Dawson, Elmer, J M ARIZONA Bisbee, Clark, G C, Coombs, H L , Douglas, W, Hoatson, Parnall, S A, Pelton, R T, Ricketts, L D, Sherman, G F G, Smith, F W, Smith, H A Black Diamond, Bagge Blanchard, Cummins, Murray, J J Casa Grande, Rich¬mond, A B Clifton, Colquhoun, Grabill, Murray, H T , Plater, Smith, J D A, Veitch, Watson, W S Congress, Goodloe Crown King, Alexander, G E Douglas, Cornell, Kraemer, E L, Lee, G B, Rutherford, F Globe, Berray, Hoar, Snell Harrisburg, Smith, F C Jerome, Clark, W A, Thomas, C A Kingman, Treadwell, Wallace, J P Kirkland, Bretherton, G K Kofa, Lamp¬shire, J O , Pomeroy, H G Mayer, Haggott, E A Metca j, Blumenkranz, M , Forbes, D L H Morenca, Clark, C D, Fleming, J B, Honey man, Mills, C E, Wallace, L R Morristown, Stevens, H W Nogales, Glove, H G, Sandoval, A , Sandoval, P Octave, Rose, G W Phoenix, Armstrong, T , Butler, C E, Defty, Lindsay, L Prescott, Blauvelt, H , Bunker, C E, Claypool, W M , Drescher, F M , Fairbank, Nissen Tombstone, Gage, Poindexter, C L , Staunton, Walker, E W Troy, Cutting Tucson, Blake, W P, Burgess, De Lashmutt, I, McCleary, Mann, Prout, J W , Jr ARKANSAS Fayetteville, Purdue Fort Smith, Bache, F , Denman, H Little Rock, Fordyce, Scholz CALIFORNIA Alameda, Arents, King, L Arnador City, Downs, Tregloan Angeles Camp, Dig¬gles, R N , Kenney, C E Antioch, Belshaw Auburn, Coe, I J Ballarat, Thorns Berkeley, Abadie,, Christy, Dozier, Hall, F F , Hersam, Landfield, Lind¬say, L , Mansfield, N T, Morley, W S , Sharwood, W J Bag Oak Flat, Dron Bodae, Hamilton, W R, Hoover, T, Hoover, T J, Jackson, B L , Nutter , E, H Bullion, Power, H T Callahan, Scott, E H Campo Seco, Baird Cartero,

Jan 1, 1910

By J. C. McKinnell

The appraisal of an oil lease may often be mad,? through production decline analysis, which requires description of the functional relationship between the oil production rate and either cumulative production or time. Heretofore, attempts to define the function appropriate to a given set of production data have depended to some extent on subjective procedures. The purpose here is to introduce an objective solution, obtained by combining the principle of least squares with the theory of equations. MATHEMATICAL ANALYSIS The fundamental differential equation appropriate to a general class of decline curves may be written. Solution of Eq. 1 for general boundary conditions may be written in terms of either the cumulative oil production or time: These equations constitute the mathematical expression of the so-called hyperbolic decline. Their complete description for a given set of production data requires the numerical evaluation of the three parameters1.&apos;, n, D, and (go),. For the special case of n = 0, Eq. 2 becomes q. = (q.), - DiN with the corresponding expression in terms of time being q. = (qa),e...........(5) Similarly, for the special case of n = 1, Eq. 3 becomes with the corresponding expression in terms of cumula- tive oil production being q. = (q.),e " &apos;.......(7) Eqs. 4 and 5 constitute the mathematical description of the so-called exponential decline; Eqs. 6 and 7 are the mathematical description of the harmonic decline.&apos;,&apos; Returning to the hyperbolic expressions, Eqs. 2 and 3 may also be written, q: = sNp + b........ (8) and where a = 1 - n; s = (n— 1)D,(q0);"; b = (go):-"; a&apos;=-n;s/= nD,(qo);"; and b&apos; = (go);-. Note that both Eqs. 8 and 9 are linear in either time or cumulative production with respect to an exponential function of the production rate. In other words, a straight line relationship results for both variables when associated with the appropriate power of q,. This fact is of prime importance in the application of statistical analysis. . STATISTICAL ANALYSIS For a given oil lease, the time, production rate and cumulative production are recorded records. To establish predictive formulas from Eqs. 2 and 3, it remains to determine numerical values for the three parameters [n, D, and (q,) .] through an investigation of the past history. Upon interpreting a, s and b as parameters, Eq. 8 may be expressed for every time interval of interest, i, over the past history as follows. (q,): = s(Np), + b........(10) In general, Eq. 10 will not be satisfied exactly, because of the assumptions in the expression of Eq. 1, and the errors and anomalies universally associated with production data. It will instead define the residual, s(Np), + b- CO=d......(11) Squaring both sides and summing over all the data points, m, under consideration yields

By W. J. Romanow

RECENT papers by Williams, Sherwood, and Boothby,1 Seybolt et al.2 Heikes; and Roberts4 attest to the increasing importance of the hexagonal ferromagnetic compound MnBi. Since the magnetic properties of MnBi crystals are highly anisotropic, it is useful and necessary to have appropriate aids for determining their orientations—a (00.1) standard stereographic projection and a corresponding table of crystallographic angles for this structure. The tables of crystallographic angles for the hexagonal system available in the literature5 are computed for c/a ratios greater than that of MnBi and cannot satisfactorily be used to find the crystallographic angles of MnBi. A table of angles between the crystallographic planes (HK.L) and (hk.1) was calculated for MnBi from the formula0 F=are cos Hh+Kk+ 1/2(Hk+hK) + 3/4 (a/c)2Ll/v(H2 + K2 + HK + 3/4 (a/c)2L2) (h2+ k2+hk + 3/4 (a/c)2l2) on an IBM Type 650 Magnetic Drum Data Processing machine. The lattice constants used are listed in Table I and are those determined by Willis and Rooksby7 at 20°C. More recently published values obtained by both X-ray and neutron diffraction"&apos; show no difference from these significant to the calculation. From the crystallographic angles between the basal plane (00.1) and the general plane (hk.1) in Table I, an (00.1) standard stereographic projection was made for MnBi which is shown in Fig. 1. Acknowledgments The author wishes to thank R. G. Treuting and J. N. Hobstetter for their technical assistance, and Miss D. P. Booth for programing the IBM machine for the calculations. He appreciates the opportunity to read the paper of B. W. Roberts of General Electric Co. prior to its publication. References 1H. J. Williams, R. C. Sherwood, and 0. L. Boothby: Bulletin Amer. Physical Soc., 1956 vol. 1, p. 132. 2 A. U. Seybolt, H. Hangen, B. W. Roberts, and P. Yurcisin: AIME Trans., 1956, vol. 206, p. 605: Journal oF Metals, May 1956. 3R. R. Heikes: Physical Review, 1955, vol. 99, p. 446. .B. W. Roberts: A Neutron Diffraction Study of the Structures of Manganese B.W.Roberts:ANeutronDiffractionBismuthide, Physical. Review, 1956, vol. 104, p. 607. 5 A. Taylor and S. Leber: AIME Trans., 1954, vol. 200, p. 190; JouRNal of Metals February 1954. « C. S. Barrett: Structure of Metals, 2nd Ed., p. 635. McGraw-Hill Book Co. New York and London, 1952. 7B. T. M. Willis and H. P. Rooksby: Proceedings Physical Soc., London, 1954, vol. 67B, p. 290.

Jan 1, 1958

By Raymond Mancha

A TEST of any fan requires the determination of such data as fan pressure, air volume handled by the fan, and power input to the fan shaft. When testing operating mine fans of the centrifugal type, test methods have been employed, for the sake of convenience, that permit great latitude in detail of procedure resulting in wide variance in results by different investigators. Some controversial aspects of field fan testing are the result of past failure to define dearly the various forms of fan pressure and to a lack of understanding of the accurate procedure for the measurement thereof. Also, the anemometer for air-volume measurement, although convenient, if carelessly used and maintained is subject to a wide error range with variation in method of application and in instrument accuracy. The appearance of the axial-flow type of mine fan offers the possibility of refinements in field testing that were impractical with the centrifugal fan. First of all, the fan inlet and outlet are more sharply defined, giving loser agreement as to just where the fan begins and ends; thus there is less disagreement as to the proper location for measurements of fan pressure. The area of passage into the inlet of an axial-flow mine fan usually constricts, causing high air velocities with accompanying steadiness of flow. Thus the fan inlet offers an ideal location for accurate air-volume measurements with the Pitot tube, the proper use of which is well established by code. Thereby the controversial aspects of such measurements are eliminated. Use of the Pitot tube also facilitates a more accurate measure of fan pressure, since the individual pressures measured can be properly weighted, as will be explained later. Determination of power input to the axial-flow mine fan operating in the field is subject to the same inaccuracies as with the centrifugal fan if the axial-flow fan is also belt driven. However, because of the higher rates of rotation usual with axial-flow fans, direct-driven units are more numerous and it is unnecessary to assume a drive efficiency, thus eliminating one possible source of error. It is the purpose of this paper to define and explain the various types of pressure measurements involved in a field test of an axial-flow mine fan, and to further explain the proper use of the Pitot tube when measuring pressures and volumes. DEFINITION OF FAN PRESSURES The two fan pressures most commonly discussed are fan total and fan static pressure, each of which has the same meaning regardless of whether the fan is blowing, exhausting, or blowing and exhausting, as in the case of a fan with ducts connected to both outlet and inlet. Fan total pressure is the amount by which the total pressure of the air delivered by the fan exceeds the total pressure of the air received by the fan. This pressure is a measure of the maximum amount of the work done on the air by the fan that is available for external use.

Jan 1, 1942

By P. S. Rudman

The allotropic volume changes of the ,metallic elements are reviezoed with the conclusion that in general atomic volume is conserved to better than 1 pct in such transformations. A table of the atomic volumes of the metallic elements is given and its use in considering the size factor in alloys is discussed. The importance of the concept of atomic-size factor, due to Hume-Rothery and coworkers,&apos; is firmly established. Most attempts at quantitative formulations of this concept have employed the atomic radius (half some interatomic distance) as the measure of size and innumerable tables of such radii exist. This is probably, however, an unfortunate choice of parameter. Firstly, discussion in terms of interatomic distances requires a knowledge of the crystal structure. While this is known, except for a few cases, for the elemental structures, there are still many undetermined alloy structures. Secondly, except for the simpler structures, face-centered cubic (Al),* body-centered cubic (A2),* and hexagonal-close-packed (A3).* with ideal axial ratio, there is no unique in- teratomic distance, an m y decision must be made as to which distance, or which average of the distances, should be used. However, the most important point is that for metals the dominant bonding parameter can generally be expected to be atomic volume and not interatomic distance. This is perhaps most explicitly stated in the Wigner-Seitz cellular method.&apos; In this approximation, cellular polyhedra of atomic volume v are replaced by spheres of radius Y,: 4/3 ?rs3 = v. That is, there is no reference to the interatomic distances. If atomic volume is in fact the dominant parameter, then in allotropic transformations we might expect to find atomic volume approximately conserved. For example, in the A1 ? A2 transformation we would thus have

Jan 1, 1965

By Billy L. Crowder, John M. Fairfield

The implantation of B+ , P+, and As&apos; into silicon has been studied with the purpose of making shallow p-n junctions. The influence of such parameters as 1) ion energy, 2) target orientation and temperature, 3) total dose, and 4) annealing schedule was investigated. An energy range of 70 to 300 kev was used for boron and phosphorus implants and up to 500 kev for arsenic. It is found that the experimental projected range agrees well with theory and that shallow junction depths can be made reproducibly. ION implantation has received much attention recently as a technique for doping semiconductors. Specifically, it has the potential of supplementing or replacing the diffusion process as a method for making p-n junctions. In a few specific cases it has been used successfully to make semiconductor junction devices. Potential advantages of ion implantation doping over diffusion techniques are: 1) It affords greater control of shallow junction depths (< 0.2 µ) while maintaining high peak concentrations. This is particularly important for high-speed switching devices, since lower junction capacitances and resistances can be achieved. 2) More precise registration of small planar structures can be realized if proper masking procedures are employed. This advantage is especially useful in the design of high-density integrated circuits. It has been used to advantage in FET fabrication since the edge of the source or drain can be aligned precisely at the edge of the gate electrode.&apos; 3) Ion implanatation permits lower temperatures than diffusion techniques. This factor alleviates the problem of compatibility of diffusivities often encountered when designing multiple-junction structures. Also, the lower temperatures create fewer thermal defects and dislocations, which may account for the high efficiency of some ion-implanted solar cells.2 4) Impurity profiles can be more easily tailored to resemble ideal distributions. Successful exploitation of the potential advantages of ion implantation techniques will depend on increased knowledge and understanding of the subject. The factors likely to be influential in determining impurity distribution profiles in ion-implanted single-crystal targets have been reviewed by J. F. Gibbons.3 In addition to the mass and energy of the implanted ion, the total dose, target orientation, and target temperature are important parameters. The annealing temperature required for removing lattice damage and incorporating the implanted species on an electrically active site is very important. This paper describes an investigation of some of these factors. Implants of boron, phosphorus, and arsenic into silicon have been studied. Energy ranges of 50 to 300 kev were used for boron and phosphorus and up to 500 kev for arsenic. In addition to the implantation energy, the effects of total dose, target temperature, and post implant anneal have been investigated. EXPERIMENTAL PROCEDURE The implantation targets were silicon wafers cut from Czochralski-grown crystals, lapped, and chemically polished. The orientations were (111), (110). and (100) with misorientations of up to 7 deg from the principal axis. For this study, accurate target alignment (i.e., within 0.1 deg) was not available and quoted misorientation values should be regarded as approximate . The implantation equipment consisted of an ion source, a 300-kev linear accelerator tube, an electromagnetic separator, and the associated target supporting and beam focusing assemblies. The ion source was a simple oscillating electron type source,4 which has been described elsewhere.5 The gaseous compounds BF3, PF5, and AsH3 were used as ion sources for B+, P+, As+, and AS+&apos;. Analyzed current levels of up to 20 pamp could be obtained; however, for this investigation target current levels of 1-3 µ amp were usually employed. The analyzed ion beam was collimated through a double slit (1.4 x 0.4 cm) and swept perpendicularly to the long axis of the slit such that an area of about 2 sq cm on each target was covered. Dosages of around 1015 cm-2 were normally employed, but smaller amounts were also used for comparison. A uniform flux density over the bombarded area was assured by the continuous use of profile monitors similar to those described by Wegner and Feigenbaum.6 Post-implant annealing was accomplished in an argon atmosphere in a temperature range of 600" to 950°C. It was not part of the purpose of this investigation to study the annealing kinetics; however, some isochronal and isothermal anneal experiments were conducted to determine the time and temperature necessary to render a reasonably high portion of the implanted ions electrically active (i.e., higher than 50 pct). Post-implant anneal temperatures of around 900° and 600°C were required for boron, and arsenic and phosphorus implants, respectively. Arsenic and phosphorus implants increased in conductivity rather abruptly at the proper anneal temperature of the isochronal curve, but boron increased more gradually over a wider range. Isothermal anneal curves were reasonably flat after 10 min, so an anneal time of 1/2 hr was used for the experimental results described below. The profiling techniques were: 1) neutron activation analysis, 2) differential sheet resistance,7 and 3) junction staining.8 The differential sheet resistance technique is commonly employed in this type of study. Its principal disadvantage is the uncertainty of the ef-

Jan 1, 1970

By C. Wachmann

The theory presented ill this paper makes possible examination of the phenomenological aspect of secondary oil recovery by alcohol flooding. Limitutions of the theory are contingent on three primary assumptions: (1) chemical equilibrium, (2) no fingering, and (5) no dispersion. The second assumption implies one-dimensional flow. In a geometric sense the theory extends the Buckley-Leverett construction to systems of two slightly miscible fluids and to systems of three components. This is made possible by considering single-phase fluids to be made up two phases, namely of an excess of one phase and a negative amount of the other phase. The procedure is discussed in the paper. The theory also permits direct determination of the relationship between the aqueous phase saturation and the concentration of water in the aqueous phase in a zone of variable composition. The velocity of planes of constant water concentration and of constant saturation can be computted likewise and the existence of saturation discontinuities inferred. Consequently the behavior of such a Zone, which may exist at some time between a displaced and a displacing fluid, May be determined. mathematical details are given in Appendices. Problems of experimental verification are pointed out on the basis of a supporting experiment. Implications of the theory and effects of violations of primary assumptions are discussed briefly. The major conclusion is that, if the primary assumptions are met, with pure alcohol and alcohol-rich .slugs piston-like displacement of oil and water is possible. INTRODUCTION The recovery of oil from porous media by alcohol displacement has been studied for several years. Extensive experimental investigations into alcohol flooding have been carried out in the laboratory although little has been done in the field. A large amount of practical information is available, the extent being indicated by the first three papers cited 1-3 and their respecrive bibliographies. This has permitted the Formulation of inferential theories. A more analytical approach in which theories are developed primarily by reasoning from known physical principles and relationships has, however, lagged behind. In fact, an analytically derived theory of alcohol displacement has not been available. The theory presented in this paper on oil and water displacement by alcohol from a porous medium is a result of the analytical approach. The theory is idealized, as certain assumptions had to be made to make the mathematics tractable and reduce complexity of argument. In particular, major assuptions concerning conditions of equilibrium, interfacial stability, longitudinal mixing, etc., led to the exclusion of fingering, for example, from all considerations. In many laboratory experiments reported in the literature fingering could not be avoided. There is, therefore, disagreement between theories based on experimental evidence available and the analytically derived theory presented here. This theory presented is based on known physical data and makes use of the Buckley-Leverett construction and its suggested extension. The mathematical derivation of the theory is given in Appendices. Three examples relevant to alcohol displacement are discussed to explain the use of this theory: (1) system of two immiscible fluids (the Buckley-Leverett case); (2) system of two slightly miscible fluids involving an extension of the Buckley-Leverett construction; and (3) system of three components, including injection of pure alcohol or alcohol-rich fluid as a special case, which involves a more general extension of the Buckley-Leverett construction. In these discussions strict assumptions were made to impose equilibrium conditions and exclude mixing and fingering. Effects of relaxing these assumptions and consequent extensions of the theory are indicated. The complexity of the alcohol displacement process makes experimental verification of the theory essential. Some relevant evidence is offered in this paper.

Jan 1, 1965

By E. W. Davis

The mixing of fine ores with fuel and burning under induced draft is called sintering in iron-ore practice and either sintering or roasting in copper and lead metallurgy. The first development of sintering was the Huntington-Heberlein process, in which fine sulfide ores mixed with fuel were charged into a pot and burned under the action of an upcast current of air introduced at the bottom of the pot. Modern development has resulted in two types of machine; the continuous Dwight-Lloyd machine, which consists of heat-resisting grates and a moving beltlike type of hearth constructed of metal, in which air is drawn downward through the bed, and the stationary Greenawalt batch process, which operates in the same manner as the Dwight-Lloyd except that the hearth is stationary. The recent rapid increase in the use of sintering has been the result of two great advances in metallurgical process—flotation and the treatment of flue dust. The Dwight-Lloyd machine is used in many plants for agglomerating flotation concentrates and at the same time reducing the sulfur content to furnace requirements and it has become standard practice to treat iron blast-furnace flue dust by either the Greenawalt or Dwight-Lloyd machine, so that it can be recharged into the furnace. The mining of low-grade magnetite iron deposits and their beneficiat-ing by grinding and magnetic separation resulted in a fine concentrate extremely detrimental to blast-furnace practice. These concentrates are sintered and made into ideal material for blast-furnace use. Incidentally, coke savings of about 400 lb. per ton of pig are reported. Sintering at Evergreen Plant The application to limonitic iron ores is the most recent development of the sintering process. The first plant in the Lake Superior region was erected by the Minnesota Sintering Co., a subsidiary of the Evergreen Mining Co., at Ironton, Minn., in 1924. This plant was designed to treat Cuyuna Range iron and manganiferous ores containing low silica, high moisture and a structure objectionable because of a large proportion

Jan 1, 1930

By Alexander L. Field

The rate of elimination of carbon largely controls the time required to make a heat of steel by the basic open-hearth process and to an important degree determines the cost of refining. Practical experience has led to the generally accepted belief that the use of slags relatively high in iron oxide, such as are required to bring about rapid refining, leads to a certain sacrifice of quality in the product. As a consequence, a compromise must be made between the exceedingly slow rate of carbon drop which would correspond to the ideal case and the rapid rate which would best satisfy the condition of minimum cost. An increase in rate of refining necessarily implies an increase in the concentration of iron oxide dissolved in the metal. However, even for the infinitely slow rate that corresponds to slag-metal equilibrium, the metal would contain a certain definite concentration of dissolved iron oxide. It is a matter of great practical importance, therefore, to determine the quantitative relation between the minimum or equilibrium concentration of iron oxide in the metal and the higher concentrations which must actually obtain in practice. The present paper is devoted to the development of certain equations, derived from the established laws of physical chemistry, which will enable this relation between rate of refining and the degree of oxidation of the metal bath to be computed from operating data. So attempt is made to exhaust the possibilities of this general method of treatment. In considering rate of refining, attention is mainly confined to rate of carbon elimination. However, the equations are of a more general nature and their application may readily be extended. The results of the preliminary calculations given herein indicate that increased rate of refining may have a decided effect in increasing the concentration of iron oxide dissolved in the metal. The uncertainty which attaches to the calculated value for this relationship arises in part from probable errors in experimental data on which the calculations are based, and in part from the lack of complete or favorably disposed information on basic open-hearth practice. When the relation between rate of refining and degree of oxidation of the metal has been more accurately established than has been done in the present paper, it will then become possible to consider what comprises

By d&apos, John C. Entremont

Pure iron was inductively melted in small refractory crucibles and optical pyrometer and immersion thermocouple readings were simultmzeously taken. The resulting emissivities of the liquid iron surface obtained were found to be greatly affected by both the gaseous atmosphere and geometrical changes in the physical setup. Quantitative values for these effects are indicated. FOR many applications in both the laboratory and plant, optical pyrometry is still the best means of measuring temperatures in the incandescent range. A prerequisite in evaluating the correct temperature is a good value of the emissivity of the surface. To obtain the emissivity from the tabulated values of the literature can be very confusing and often far from correct. There are many reasons for these difficulties, and it is not within the scope of this paper either to enumerate or to discuss them all. Its purpose is to show quantitatively how several factors affect the apparent emissivities obtained from experimental measurements on liquid iron surfaces. The black body is the reference state for the quantitative values of emissivities and is defined1 as a body which absorbs all radiation incident on it, reflecting none; such a surface emits more radiation per unit area per unit time than any surface which reflects any radiation, and is given a value of unit emissivity. All bodies having reflective power thus have emissivities less than unity and are considered nonblack or grey bodies. The ratio of the radiant energy emitted by the flat, nonblack surface to that of a perfectly black surface of equal area and temperature is the emissivity of the surface. The above definitions are applied to flat, polished, opaque surfaces, very seldom encountered in actual measurements, and for this reason many authors have suggested that the word "emittance" be used for real bodies rather than emissivity. The emittance has reference to the material and its configuration rather than to its properties in the idealized state. Recent observations of molten iron in a small refractory crucible indicate that not only the configuration of its surface but the geometrical arrangement of its surrounding and the nature of the surrounding atmosphere have a pronounced effect on the emittance. Neglect of changes in such conditions may lead to errors as large as 40°C at 1600°C. Thus it is suggested that the term "apparent emissivity" be used and that it be recognized that its value pertains to a particular experimental arrangement only. As a result of not recognizing these differences in emissivities, which are obtainable from changes in the physical setup of an observation, many investigators have incorrectly quoted their values as those of the emissivities of particular materials rather than as an apparent emissivity for their particular arrangements. As a consequence, values of the emissivity of liquid iron ranging from 0.3 up to 0.55 are found in the literature. In an effort to establish an accurate optical temperature scale for liquid iron solutions in which de-oxidation studies were to be carried out, it was observed that the temperature relationship, obtained by simultaneously taking immersion thermocouple

Jan 1, 1963

By John G. Simmons

A tutorial account of the tunnel effect between metal electrodes separated by a thin insulating film is presented. Energy diagrams of metal-insulator -metal sandwiches are briefly discussed, and the isothermal and thermal J-V characteristics for symmetric and asymmetric tunnel junctions are derived from a generalized expression. Experimental data from tunnel junctions are presented, and it is shown how, correlation between theory and experiment permits a determination of some of the oxide properties. Finally, the barrier heights in AT-Al2O3-A1 junctions determined by various inr3estigators are discussed. The object of this paper is to give a tutorial account of the electric-tunnel effect between metal electrodes separated by a thin insulating film and to illustrate its utility in the study of metal-oxide interfaces. This paper will emphasize the theoretical aspects of the electric-tunnel effect: however, a brief account of the more recent experimental work will be presented. A more comprehensive experimental study of the tunnel effect will be presented in the following paper by Drs. Pollack and Morris, see p. 497. We will open with a discussion of the energy diagrams for metal-insulator-metal junctions and what we mean by the electric-tunnel effect. Following this is an account of the theoretical studies of Sommerfeld and Bethe, and Holm, and the recently reported calculations on symmetric and asymmetric junctions using the generalized formula. The theoretical presentation is concluded with calculations on the temperature dependence of the tunnel J-V characteristic. In the experimental section, it is shown how barrier heights and thicknesses are determined by comparing the experimental data with the theory. Finally, the results of various investigators on the determination of the barrier heights in Al-Al2O,-A1 systems are discussed. I) POTENTIAL BARRIERS BETWEEN CLOSELY SPACED ELECTRODES Since it is necessary to supply energy to a metal in order to observe electron emission from its surface, it is evident that the potential energy of an electron within a metal is lower than that of an electron at rest outside the metal. It follows, then, that the electron must undergo a change in potential as it crosses the metal-vacuum interface. In the Sommerfeld1 free-electron theory of metals it is assumed that the free electrons, the electrons responsible for the electrical characteristics of metals, move in a constant potential environment in the metal, and are contained within the metal by a potential barrier at the metal-vacuum interface. It will be evident that the idea of a constant potential environment is a very idealized model, since the potential energy of an electron is influenced by all of the atoms and the other electrons within the metal; however, its use is justified by the many excellent results it gives.2 Fig. l (a) is the energy diagram of the model envisaged by Sommerfeld; the metal is represented by a potential-energy well of depth V,; the vacuum level represents the energy of an electron at rest outside the metal. At 0°K the electrons, which exist in pairs in discrete energy levels, fill up the well to an energy ?, the Fermi level. The distance, Vo - ?, from the Fermi level to the vacuum level is known as the work function of the metal, and represents the minimum energy required to free electrons from the interior of the metal at 0°K.

Jan 1, 1965