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By James W. Wade

THIS discussion of the future supply of lead refers only to the next ten-year period. Beyond that no prediction can be made that would be of sufficient accuracy to serve any purpose. When any commodity is by an unsatisfied demand forced to a higher price level, and the profits of those who are able to produce the commodity are greatly increased, there is awakened a new interest in the commodity on the part of both producer and consumer. The consumer attempts to reduce his costs by developing substitutes or assisting in the development of new sources of supply. Lead is now going through this stage. The lead producer is increasing development expenditure and searching for new mines. The consumer is developing substitutes as illustrated by the increasing use of zinc oxide as a pigment, and the use of dry batteries in radio sets. The search of the Ford interests for lead, by prospecting in Missouri and Idaho, is induced by the effort to develop a new source of supply. Considering the index figures of the Department of' Commerce, it is evident that lead is on a substantially higher price level. For February, 1926, the index figure of lead is 209, while the general commodity price index is only 156, 100 being taken as the base for 1913.

Jan 1, 1926

By AIME AIME

T HE appointment of Herbert Hoover to the portfolio of Commerce in the President's Cabinet is to engineers the fulfillment of a long deferred hope to have an engineer in high political office and is a matter of congratulation to us for three reasons; because he is a mining engineer who represents the highest type of idealistic engineering effort; because he is a past president of the Institute; and because he has probably a broader grasp of world problems than any other living engineer. Frank A. Vanderlip in the preface to his book "What Happened to Europe" tells of the many interviews he had with the most prominent men in Europe which were made possible for him by his eminence as a banker and by the courtesy of the American ambassadors. He cites by name such well known figures as Austin Chamberlain, Sir Auckland Geddes, Monsieur Delacroix, Monsieur Briand, Mr. Padkrewski, Mr. Venizelos, Colonel House, General Pershing, Mr. Baruch, and many others and says :

Jan 1, 1921

By Ovid W. Eshbach

ENGINEERING education has been powerfully affected by the impact of war, just how powerfully can be better understood after considering the postwar problems regarding students, staff, and plant. In time of war no one will question the necessity of expediency of military training. With the cessation of hostilities, expediency gives way to the evolutionary process of strengthening engineering education as need is exemplified by experience. During the war, except for the Navy V-12 program, engineering education was at its lowest ebb of the century. Freshman enrollments were largely limited to those graduating from high school at the age of seventeen; and the upperclass, to those disqualified for active service. In most schools the experienced staff was either in service or government and industrial research. Many may never return to their former occupations. The most immediate problem is that of maintaining and building a staff to meet the enrollment of returning veterans. It is estimated that out of the eleven

Jan 1, 1945

By George S. Rice

ARIAL maps of prospective mineral-bearing territory have become almost indispensable in all the branches of exploration, and have proved particularly useful in the great oil area of the Southwest. About nine years ago aerial photographic mapping in this area was begun. The early product was lacking in scale accuracy and other control features, which limited its effective use. Since then, the evolution of the technique of such mapping has been steady, with several mapping companies collaborating with five of the leading oil companies, and aerial maps have been prepared covering practically the entire area.Improvements in cameras, film, and developing equipment and practice have resulted in more uniform and clearer photographs, but the outstanding development has been the accuracy obtained with respect to scale and all other control features. Maps are no

Jan 1, 1936

By R. B. BRINSJIADE

THE following is an attempt to form a formula by which a mine call be quickly evaluated, after all pertinent physical data have been collected from observations on the ground by a competent mining engineer. ASSUMPTIONS. Let G = price to be paid for the mining property. M = cost of developing the mining property to yield y tons of ore daily. P = cost of suitable plant to treat y tons of ore daily. p = value of said plant when the mine has.been exhausted. C = total fixed capital investment. W = working capital investment

Jan 1, 1908

By William Gilman

IN the past five years, and without much fanfare, Turkey has emerged as a significant figure in the world mining picture. This has been accomplished by a five-year plan now in its last year. A second five-year plan is already under way, ahead of schedule. It will concentrate even more than the first in developing Turkish mines in order to increase present exports of coal, chrome ore, and copper, and to develop new mineral exports as well. To be fully understand the republicic?s mining program should be considered as something more than merely tapping rich resources in the East along the Aegean Sea, in the North among the mountains descending to the Black Sea, and in the West at the foot of the Taurus Mountains. It should also be viewed in the light of a strong nationalist policy with many aspects of state socialism. Turkey declares frankly that all mineral re- sources belong to the nation and all exploitation should be by the state for the twin purpose of modernizing the state and securing foreign exchange for the state by exports. Accordingly, the principal mines are state-operated and a few lesser enterprises, although not state-owned, have at least been put in the hands of Turkish capital.

Jan 1, 1938

By C. W. Robinson

Transportation is the minerals business. Once upon a time the geologist, the engineer and later the metallurgist reigned supreme, but the leading role in mineral development today is the economist-especially the transportation economist. Obviously this trend is more important for large volume, low value mine-to-market movements of such commodities as iron ore, phosphate, potash, coal and petroleum. But, transportation is of sufficient importance to all mining activities to be included in forward planning. Civilization has been influenced by transportation developments to an extent little understood or appreciated. Although industrialists are capable of intelligent historical analysis of this phenomenon, too frequently they have failed to project, or anticipate those changes in transportation techniques which will influence the pattern of industrial growth.

Jan 1, 1971

By Myers, J. F.

The purpose of the mill tests reported herein, was to determine the relative power efficiency of fast and slow rod mill speeds on the ores of the Tennessee Copper Co. The tests were carried out at the lsabella Mill of the Tennessee Copper Co. under normal operating conditions. Every effort was made to keep the ore supply and other conditions constant, but it will be noted that some slight variation did occur. The open circuit 6 by 9 rod mill, and ore, used in these tests have been previously described.' Four motor drive pinions were available and the tests were performed in the following manner: each pinion was used to drive the mill for a period of one week. Constant sampling prevailed during the test run, and a composite sample for each speed test was made. Realizing that some slight liner wear took place during the four-week test-run, and that some slight variation of the ore may have taken place, a second and then a third series of four-week test- runs were made with the four different pinions. The screen analysis of each of the thee-week run samples at the various speeds were composited and the results are shown in Table 1. The authors feel that the 12 weeks of operation consumed during these test-runs would represent fairly the effect of each mill speed. The data of line 37 show that within the error of sampling and plant operation, the tons of minus 65-mesh material generated per horsepower hour was the same at all four speeds.

Jan 1, 1949

By Oliver Bowles

TO keep pace with technical progress is an important function of any industry. All branches of mining may learn important lessons by observing progress made in other branches. The non-metallic mineral industries may learn much from each other as well as from the metal miner and the metallurgist. Recent technical advances which have come to the attention of the Committee on Non-metallic Minerals are presented herewith for consideration and comment. It is planned to present this review for open discussion at the February, 1931, meeting of the Institute. Comments will be welcomed either in the form of written or oral discussion. It is desired that new developments not covered in this paper be brought up at that time. Some notable advances have been made in cement technology. Recognition is now being given to the advantages of closed-circuit grinding of cement raw materials in wet-process plants, with stage removal of the fine materials, It increases mill capacity, reduces the wear of grinding media, and also reduces the power requirement. The method is well known in metallurgical plants, and its acceptance by cement companies is another illustration of the lessons the non-metallic industries may learn from the metal industries. Closed-circuit dry grinding has also proved advantageous for both raw materials and clinker.

Jan 1, 1931

By George W. Powel

IN the nation's effort to raise its magnesium metal supply to meet the ever increasing demand, the Government is relying not only on standard established practice but has extended its support to developments not so well proved-at least, not commercially proved. Within the past few months considerable progress has been made, not only in the definite output of metal but in the exploitation of new processes, the successful adaptation of which should, in a reasonably short time, assure an adequate supply of magnesium. Recent months have also witnessed a reshuffling of the favored methods as well as of the likely raw materials, with the mineral dolomite gaining in interest over its richer but less abundant competitor, magnesite, while the lowly sea water appears to be losing ground to the higher magnesian brines of Michigan and western Texas. Every month sees a new alignment and there are signs that still newer methods or raw materials will be in use before the industry finally stabilizes itself.

Jan 1, 1942

By Clyde E. Williams

MODERN steelmaking has gradually evolved from an inefficient small-scale operation, utilizing tiny units, to a highly efficient one utilizing large units almost completely mechanized. The leading position of the United States in the steel industry is due to the possession of easily assembled high-grade raw materials and large-scale highly developed plants. Modern integrated steel operation is largely one of material handling. Mining and transportation of iron ore, coal, and fluxes, coking the coal in by-product ovens, smelting the ore with coke and limestone in blast furnaces, converting the resulting pig iron into steel in the Bessemer, or in the open hearth when supplemented with scrap, and fabricating the resulting steel ingots in the shapes of commerce all are done on a huge scale, mostly by machinery, most of the labor being employed either in operating the machine or keeping it in repair. At the same time the quality and uniformity of the product have been greatly increased by the development of scientific knowledge and operating skills. Thus, the steel industry in this country is highly developed both mechanically and technically.

Jan 1, 1942

By Emery R. Hayhurst

SILICOSIS has been described in a report of the American Public Health Association as a disease due to breathing air containing silica, characterized anatomically by generalized fibrotic changes and the development of miliary nodulations in both lungs, and clinically by shortness of breath, decreased chest expansion, lessened capacity for work, absence of fever, increased susceptibility to tuberculosis (some or all of which symptoms may be present), and by characteristic X-ray findings. ... The disease is divided arbitrarily into first, second, and third stages for convenience of description and possible compensation purposes. At least two distinct types of silicosis are recognized, acute and chronic. The acute form was reported as early as 1713, when a British patent for grinding flint by wet methods was granted because the dry powdered material "proved very destructive to mankind, so much that any person, ever so healthful, working in that business cannot possibly survive over two years."

Jan 1, 1936

DR. PeRsifor Frazer, Philadelphia, Pa. (communication to the Secretary):* Mr. Campbell's very interesting contribution, after complimentary mention, finally decides against the acceptance of the classification proposed by me in a paper bearing the same title and read at the Wilkes-Barre meeting, May, 1877.2 That paper was written primarily for the Second Geological

Jan 1, 1906

By Henry R. Linden

The demand for natural gas continues to increase at higher than anticipated rates, partly because of its widening price advantage over most other fossil fuels when the cost of air-pollution control is included. However, there are clear indications that the natural gas supply from the conliguous 48 states and continental shelves will not keep up with this rapid growth in demand indefinitely. Projections are presented which define the extent of potential deficiencies from the 1970's to the year 2000. Among the sources of supplemental gas - imported pipeline natural gas from Canada and Mexico, tanker import of liquefied natural gas, and synthetic pipeline gas from coal and oil shale -by far the most abundant at potentially competitive costs is pipeline gas from coal. The state of development and relative economics of the various coal gasification processes are reviewed. It is shown that synthetic pipeline gas could become a very substantial market for bituminous coal and lignite at current mine-mouth prices - 60-70 million tons of coal for each trillion cubic feet of synthetic pipeline gas produced. This corresponds to only slightly more than the current annual increase in gas demand. Although annual discoveries (gross additions to proved reserves) of natural gas in the United States are still on a general upward trend from the current level of 22 trillion cu ft annually, most forecasters do not expect this to increase substantially in the foreseeable future. For example, the updated (to include 1966 and 1967 data) mathematical model of natural gas discovery and production in the U.S. developed by the Institute of Gas Technology (IGT)' projects that discoveries will level out at about 25 trillion cu ft annually in the late 1970's and during the 1980's and then decline to about 21 trillion cu ft by the year 2000 (Fig. 1). This adds up to a new supply for the period 1968-2000 of about 790 trillion cu ft. Experts who usually reflect the producers' viewpoint, such as Radford L. Schantz of Foster Associates,* are relatively more pessimistic. In contrast, a forecast just made by the U.S. Dept. of the Interior is much more optimistic.3 It assumes an increase in gas discoveries of 2.2% per year over the period 1965-80, reaching about 30 trillion cu ft in 1980. If this rate of increase were extended to the year 2000, annual discoveries would reach 46 trillion cu ft at that time, for a total over the period 1968-2000 of about 1100 trillion cu ft. To these forecasts of new gas discoveries must be added proved reserves of roughly 290 trillion cu ft,4 bringing total U.S. supplies for the rest of the century to nearly 1100 trillion cu ft (IGT) and possibly as high as 1400 trillion cu ft (U.S. Dept. of the Interior). This is approximately the same range as that of two estimates of total remaining recoverable natural gas supply: Potential Gas Committee, 980 trillion cu ft5 and IGT, 1450 trillion cu ft.6 Only the 1965 estimate by the U.S. Geological Survey7 suggests that economically recoverable natural gas supplies will not be exhausted around the end of the century. These forecasts are, naturally, based on the assumption that changes in technological, economic, and regulatory environment as they affect the gas industry will be of an evolutionary, not revolutionary, nature. The various forecasts of potential natural gas supply must now be compared to forecasts of natural gas demand (Table I). The general consensus is that the recent Future Requirements Committee projection to 1990' (extended to the year 2000 by the most recent U.S. Bureau of Mines (USBM) projection9) represents the minimum gas requirements (Table 11). They add up to a total of 1030 trillion cu ft for the period 1968-2000. Even this minimum anticipated gas demand exceeds the total remaining supply estimate by the Potential Gas Committee and would nearly exhaust the proved reserves plus new discoveries projected by IGT. The supply situation would appear much tighter if the demand projections of the Texas Eastern Transmission Gorp.10 and the American Gas Assn.(A.GA.)'' were used (Table I). Yet, these higher forecasts probably do not include the effects of such new markets as gas fuel cells, use of liquefied natural gas as a transport fuel, etc. They also may not fully reflect the impact of air quality control on the fuel market. Obviously, the probable discrepancy between projected supply and demand can only be accommodated in four ways. 1) Rapid increase in exploration and drilling activity to provide new supplies in the amount projected by the optimistic U.S. Dept. of the Interior forecast, coupled with an increase in net pipeline imports from Canada and Mexico from the present 0.5 trillion cu ft per year

Jan 1, 1970

By J. G. Patchett, R. W. Rausch

Fresh waters and the presence of clay in many Rocky Mountain and West Coast sands require special methods of log analysis. Archie's saturation equation requires addition of a shale correction term, and the SP equation must also be modified to account for clays. Suitable equations were developed several years ago, but have not been widely used due to the algebraic complexity. A computer-oriented method has now been developed to overcome this problem. The basic shaly sand equations are rearranged in four different ways to permit solution for various sets of available input data. Essential to application of the method is the correction of observed SP values to those that would be observed if the resistivity of the formation waters were exactly interchangeable with the activity. A graphic method for doing this is given. Where conditions require consideration of the effect of clay in the sands, the method presented has been found to improve the accuracy of water-saturation determinations. INTRODUCTION Log interpretation in many Rocky Mountain and West Coast basins is complicated by rapid vertical and lateral changes in water resistivity. Calculation of formation water resistivity from the SP curve becomes difficult in zones that contain clay, since changes in SP deflection may be due to changes in either clay content or water salinity. In hydrocarbon-producing reservoirs, the problem is further complicated because hydrocarbon saturation also reduces the SP.1 A log interpretation system using computers has been developed to provide a solution to this problem, based on equations proposed by de Witte.2 Four different simultaneous solutions of de Witte's equations have been made. Each solution method uses a different set of input data as independent variables. Thus, a choice of solution method is possible, depending upon the logs run and the availability of other data. Two of the solutions do not require a knowledge of water resistivity. This system is intended to be used primarily in multiple sandstone-shale sequences of low and moderate resistivities where the principal contaminant in the sandstones is clay. However, where sufficient regional data are available, interpretation in single-zone sandstone reservoirs can also be improved by using the method. THEORY AND HISTORY OF SHALY SAND ANALYSIS The log interpretation formula originally proposed by Archie3 in 1941 is applicable only to rock-fluid systems wherein the rock has negligible electrical conductivity. In 1949, Patnode and Wyllie4 showed that if the rock itself can be considered conductive due to the presence of clay, a different calculation approach is necessary. During the following years, this problem was investigated at great length, as was the related problem of the effect of rock conductivity on the SP.5-11 These investigations established functional relationships between SP, resistivity, water saturation and water resistivity for such a formation. Refs. 2 and 12 provide summaries of these studies. Unfortunately, practical use of these relationships required that water resistivity be known independently from the SP. Although log interpretation methods for rock systems containing clay were proposed at that time,' they were not generally accepted for routine use. There are three principal reasons for this. First, in many field situations involving high-salinity water, rock conductivity may be neglected (even if present) without introducing appreciable error. This may be seen by considering the following expression for waier-saturated rock.' 1/R2=1/R1+1/FRn....(1) where 1/R, is conductivity due to clay. As Rw becomes small, I/FRw becomes much greater than 1/R, which may be neglected. Where 1/R, may be neglected, the sandstone is called clean. If the term may not be neglected, the sandstone is termed dirty or shaly. For resistivity purposes, the classification between clean and shaly sands then depends not only upon the conductivity due to shale in the sand, but also upon the resistivity of the associated water (shale is used here to mean surface condition due to disseminated clay). A sand of given conductivity might safely be treated as clean in association with high-salinity water, but would require shaly sand methods if associated with fresher waters. Shaly sand methods are not required in many areas having saline waters; but in Rocky Mountain and West Coast sands having relatively fresh waters (often more than 0.3 ohm-m resistivity at formation conditions), the shaly sand methods are needed. Errors Rw calculations from the SP due to the presence of shale are likewise related to water salinity. In saline water formations drilled with fresh mud, the ratio of mud filtrate resistivity to water resistivity is high, the SP is large and the presence of shale can introduce large errors in water resistivity calculated by the conventional method. When the resistivity ratio is low, the errors are smaller. At zero SP, no error would result from shale. Thus, from the SP viewpoint, a given rock could be shaly if associated with a saline water, and clean in association with a fresh water, which is the opposite of the resistivity-oriented definition above.

By Leonard H. Goldman, Harold E. Marr

The PGT uranium assay probe is a borehole tool developed by Princeton Gamma-Tech over the last several years. It has the ability to do an in-situ assay of uranium in the presence of any amount of disequilibrium. It has some advantages over coring including cost, speed of analysis, and accuracy. In this paper we would like to give a brief description of the measurement and then show some sample logs from South Texas. Uranium exploration and development is carried out primarily by gamma logging since uranium daughters are prolific emitters of gamma rays. The conventional gross gamma tool for uranium logging is limited in value because of the inability of this tool to distinguish uranium from its daughters and other naturally occurring radioisotopes, such as potassium and thorium. This problem becomes severe in cases of disequilibrium. Disequilibrium, in a geological context, is defined as the condition when the gamma radiations from the daughter products are being emitted in a location different from that of the parent uranium. In the decay chain of uranium almost all the gamma radiation emitted in the entire chain comes from the daughter product, bismuth-214. Bismuth-214 is separated from uranium by several long-lived isotopes that are chemically active and have different physical properties, often resulting in shifts in the location of bismuth- 214 relative to the parent uranium. In the United States orebodies exhibiting disequilibrium are a common occurrence and the use of a gross gamma log to delineate uranium orebodies can lead to errors. At present the solution to the disequilibrium problem is extensive coring followed by chemical analyses of the cores. There are several drawbacks in using this technique. First is the high cost of coring, the second is the fact that no results are available for days, or typically, weeks after the drilling is done. Thus for development work, coring and drilling must be done on a grid basis and many additional holes are cored to ensure that the entire orebody is mapped. Another disadvantage to cores is the fact that a small volume is sampled, the volume of the core itself. This leads to problems in the mapping out of the orebody when the ore de- posit is not very homogeneous. The PGT probe described in this paper is a new solution to the disequilibrium problem. Basically, the probe measures radiations that come almost directly from uranium itself. The first daughter of uranium, which is protactinium-234 (Pa-234), is only separated from uranium by a 24-day half-life and no disequilibrium problems build up in such a short time. The PGT probe measures the intensity of a one MeV gamma line emitted by Pa-234 and, using this information, calculates the concentration of uranium. The PGT probe is 24" in diameter and 12 feet long. The probe contains a microprocessor which passes the information to a larger minicomputer in the truck. All data is analyzed on site, and the results from a high speed printer are presented to the geologist. Data is also available on 9- track IBM compatible tape for further processing. The PGT probe output is linear with uranium concentration. The only correction factor is for borehole size, and that only becomes important in boreholes bigger than seven inches in diameter. Dead time is compensated in the probe itself and no problems have been encountered in ore zones up to several percent UjO8. In addition to the uranium assay, a conventional gross gamma log is plotted alongside. Grade thicknesses for zones above cutoff are calculated as well as disequilibrium factors. COMPARISONS During its commercial operation PGT logged a series of 18 holes that had been cored and assayed. All of the holes in this series were logged in normal operation by regular field operators. The time to log each hole was generally under an hour, and in typical operation a PGT logging truck will do between 7 and 8 holes a day. The results of the comparison of the PGT and the core assays are presented in a series of figures showing plots of the PGT assay, core analysis and gross gamma measurements. The first three figures show individual holes with the gross gamma plotted along with the core and the PGT assays. All three logs were from holes on the reduced side of a rollfront deposit in South Texas. In Figure 1 we see the two wings of the roll- front at 143 ft and 150 ft separated by a barren zone. The wings are well defined both by the PGT assay and the core. There is approximately a one foot shift which can be attributed to drilling errors. The gross gamma is showing a rather severe discrepancy, being considerably lower and not showing the barren zone. The grade thickness calcula-

Jan 1, 1980

By M. S. Azun

I do not at all agree with the basic points of the author's conclusion. The use of lognormal or normal model to respond to the attribute distribution function should be carefully questioned. If fitting a distribution function of regionalized variables is the main purpose, one may employ one of certain well-known families of distributions, such as Tukey's lambda functions. For instance, the distribution function of gold assay values studied by Krige (Krige, 1978) may fit the lognormal model well, but one should not exclude that the basic idea of using the distribution function of observed data is to have insight of the physical mechanism that gives rise to the regionalized variables. In Applied Geostatistics, there are many examples considering only lognormal or normal model for the distribution function of geostatistical data even if the observed distribution function has more than one mode. Of course, using lognormal or normal model always brings easy computation for the statistical properties of attribute under investigation. Still, I object to adopting any of those models without having any "statistical inference." As seen from the author's paper, lognormal and normal model produce the same average grade (0.746% copper) and almost the same sample variance. Therefore, which model explains the probabilistic behavior of ore deposit is always an important question that should be replied by the geostatistician using not the common sense but the statistical and probabilistic methods. For kriging procedures, such as linear kriging, one should describe either second order stationary properties or bivariate properties of regionalized variables. Second order properties, such as correlogram function or semivariogram function, are the inputs of the so-called kriging equations. Selecting one of any useable models for the observed second order properties, such as spherical model, is not easy since the models are not based on the correlations structure of the regionalized variables. How those models being used in Applied Geostatistics can be distinguished is another important problem. One may develop many fitting models to respond to the observed second order properties of regionalized variables. However, I suggest that the model should be based on the probabilistic behavior of geologic process. The author used spherical model for copper, wolfram, and silver grades from isotropic sector (Fig. 2, 4, 3b) and exponential model for silver grades obtained along raises in isotropic sector (Fig. 3a). It seems that those semivariograms given in Fig. 3b for isotropic sector and Fig. 4 may be described by the random model implying that regionalized variables do belong to renewal process (Azun, 1983). If I knew the total number of data points used in estimation, may prove that my conclusion is correct. Recalling the test for the first order sample correlogram value, the test procedure is introduced such that the independence is rejected if [Ir(1) I > Za/2 N1/2] where Za/2 is the a/2 percentile of standard normal random variable and N is the total number of samples used in estimation (Azun, 1983). For the other observed semivariogram functions I suggest the author might try to use the so-called "Markovian model" describing not only the correlation structure of regionalized variables, but also the physical mechanism that produces the regionalized variables. The Markovian model for correlogram function is, [p (h) = T 1ih , h>1 ,] The Markovian model for the other second order properties of ReV are also derived. [T veß], in the above equation, show, for example, structural change and mineralizational variation in a considered deposit, respectively (Azun, 1983). In selecting any model, it is not easy to search for the "best" response to the observed second order properties of ReV's. The Markovian model, based on a theoretical understanding of underlying mechanism, gives more information about the occurrence of regionalized variables and respond to all properties. Random model and the so-called hole effect structure can be easily defined as a special form of the Markovian model (Azun, 1983). An estimation of any second order properties of regionalized variables may be computed through (N-1) lag. However, the dependency between the regionalized variables may be deemed to have "died out" after the so-called stationarity width (range). In practice, the estimation is carried out through 25% of the total number samples available. Therefore, the large fluctuations around the zero level and variance for correlogram or covariogram function and semivariogram function, respectively, cannot be observed. Since the number of pairs involved in the estimation of higher second order properties is small, the estimation variance at those lags is large. There is no need to show higher order estimated second order properties. After using one of any kriging procedure for block estimation, the distribution function of average grades has the same mean as the drilling sample grades but

Jan 1, 1986

By E. Lifshin, R. E. Hanneman

QUANTITATIVE applications of the electron micro-beam probe frequently involve the evaluation of complex mathematical expressions and/or the analysis of large amounts of experimental data. The purpose of this communication is to describe briefly a versatile and useful computer program system that is applicable to analyze rapidly a wide variety of practical microprobe problems. This system consists of a group of ten FORTRAN programs that can be stored on tape, cards, or in the memory disc of the computer. These programs, or links, can be run individually or in any prespecified sequence without interrupting the operation of the computer or without destroying information which is being transfered from one link to another. For the program system described here a GE-235 computer with disc storage was used, so that the DCHAIN method of program linking was employed. Included in the library are programs to: 1) initiate analysis of a new set of data and transfer control between all other programs in any predetermined manner; 2) generate theoretical calibration curves of composition vs relative intensity; 3) generate empirical deviation parameters from least-square fits of experimental calibration data from standards of known composition; 4) convert raw X-ray data to corrected composition; 5) determine inter diffusion coefficients by Matano analysis of con centrat ion -distance data on a uniaxial diffusion couple; 6) determine activation energies and frequency factors of temperature-activated processes such as diffusion; and 7) generate calibration curves for determination of the thickness of thin films using microanalysis. A detailed description of these computer programs and their underlying principles is available on request from the authors."' The first program to generate theoretical calibration curves of corrected relative intensities vs composition uses the Poole and Thomas atomic number correction' and the Philibert absorption factor' with a voltage-dependent mass absorption coefficient for electrons in the alloy. A modified Castaing fluores- cence correction is also used which includes the effects of both Ka and KO radiation and over voltage.' Once the theoretical curves have been calculated in 1 wt pct intervals, these results are least-squares fit to obtain Ziebold deviation parameters' which are stored in COMMON in the computer memory. The net discrepancies between the original theoretical calibration curve and the regenerated curve using the Ziebold parameter are computed. Although this link is explicitly written for K-K fluorescent interactions, it can be applied to K-L, L-K, and L-L interactions as previously disc~ssed."~ Similar programs have also been written to utilize the Wittry fluorescence correction, Birks combined corrections, and various other corrections.' These modified programs have proved to be quite useful for quantitative comparisons of the results of the various theories. The program for conversion of raw X-ray data to corrected composition includes corrections for drift, backround, and instrumental dead time. The corrected intensities are converted to composition by use of the Ziebold equation"2 and parameter obtained from the program system. The results can be obtained for either atom or weight fractions. In addition to accurately computing interdiffusion coefficients the Matano analysis program calculates least-square smoothed values of concentration, concentration gradient, and curvature for each point on the raw input concentration profile. In order to obtain high accuracies a unique method of performing a least-square polynomial fit to incrementally advancing profile segments which overlap is used.' This program has been successfully modified for use in ternary diffusion problems3 and can readily be modified to handle analysis of diffusion profiles which include phase boundary discontinuities. This link is generally applicable to analysis of interdiffusion data obtained by other techniques as well as by the microprobe. The primary function of the next program is to least-squares fit experimental diffusion data to the normal Arrhenius function: D = Doexp(-Q/RT), to obtain values of Do and Q. In addition the probable error and one, two, and three u statistical confidence limits of DO, Q, and log D are evaluated. This program is also directly useful for analysis of any other simple temperature-activated processes including conductivity, and certain deformation and chemical processes. The program to generate calibration curves for film-thickness determination using the microprobe is based on a numerical integration of the equation derived by Cockett and ~avis.' Values of film thickness obtained by this program for copper on various substrates are in good agreement with measurements made by other techniques. Versions of the above program system have been prepared for use with or without a remote teletype connection to the computer for processing on either a real-time or time-share basis. The instrumentation coupling a microprobe to a teletype for automatic data collection and analysis by the presently described program system has been reported elsewhere by the authors.' If teletype equipment is not used to communicate with the computer, standard methods of card reading and tape reading can be used. In either

Jan 1, 1967

By H. W. Knott, M. H. Mueller

The crystal structures of Ti2Cu, Ti2Ni, Ti4Ni2O, and Ti4Cu20 have been determined using powder specimens examined by X-ray and neutron diffraction. Lattice constants have been determined for all four phases using X-ray powder diffraction films. Atom positional parameters of all four phases have been determined from observed neutron intensities. X-ray diffraction calculated intensity data have been presented also for the phase Ti2Cu to point out the particular suitability of neutron diffraction in this case. Interatomic distances have been determined using the positional parameters obtained from neutron diffraction. ALTHOUGH some investigations of the crystal structures have been made of these four compounds previously,'-13 it was the purpose of the present investigation to expand the previous work in order to locate the various atoms, determine their coordinates, and to confirm or to correct some of the previous work. It was convenient to group these four compounds together since they are related chemicallv and/or structurally. The compound Ti2Cu is tetragonil; and Ti2Ni, Ti4Ni2O, and Ti4CU2O are all large fees of the same space group. Ti2Cu has been previously reported as a fee phase by Laves and Wallbaum;1 and Rostoker2 which was possibly the oxide phase, Ti4Cu20. Joukainen, Grant, and Floe;3 and Trzebiatowski, Berak, and Ramotow-ski4 have also reported a phase of this composition. karlsson5 has reported a small fct phase of the composition Ti3Cu which may be the presently discussed Ti2Cu phase. More recently Ence and Margolin6 have reported a small fct phase for Ti2Cu and the present authors7 together with Nevitt8 have briefly reported it to be a bet related to the fct with a co three times the length of the co of the fct and have also reported that this phase has a very limited composition. Further refinements will be reported which have varied some of the parameters of this bct structure slightly. Ti2Ni has been reported as a fee phase by Laves and wallbaum;1 Duwez and taylor;9 Rostoker;2 Poole and Hume-Rothery;10 and Yurko, Barton, and parr.11 In a later paper Yurko, Barton, and parr12 have given the complete structure of this phase based on an X-ray diffraction study which was independently confirmed with neutron diffraction by Mueller and knott.7 Additional crystal structure information will be given. Ti4Ti2O, Ti4Cu2O, and a number of other compounds including Ti4Fe2O have been reported as fcc phases by Rostoker,2 and more recently Nevitt13 has confirmed the Ti4Ti2O phase. Rostoker,2 however has reported diffraction lines for Ti4Fe2O which do not have all odd or all even indices. These lines, therefore, cannot be observed if this compound has a fee structure. This same error has crept into the diffraction results reported for TiNi2O and Ti4Cu20 in the ASTM powder data which has been credited from Rostoker's data. Complete crystal structures of these two phases will be presented. Although all four of these structures have large unit cells and hence do not lend themselves for completely resolved neutron powder patterns, a sufficient number of individual reflections was observed for solving the structure. They also serve as good examples of some of the advantages to be gained by using both neutron and X-ray diffraction techniques. EXPERIMENTAL PROCEDURE All of the alloys were prepared by arc melting. The starting metals had the following purity: Cu 99.999 pct, Ni 99.83 pct, and Ti 99.92 pct. Oxygen was introduced into the two oxide phases as chemically pure TiO2, with the remainder of the titanium coming from the above mentioned metal. All of the sample buttons were annealed in evacuated Vycor tubes, the two binary phases for 5 days at 700°C and the two oxide phases for 3 days at 900°C. Oxygen analyses were performed on all four phases by two independent laboratories with the following amounts of oxygen present in atomic percent; Ti2Cu-0.06, Ti2Ni-1.03, Ti4Ni2O-13.95, and Ti4Cu20-13.87. The stoichiometric amount for the oxide phases is 14.29 at. pct. Since all of the samples were very brittle they were easily reduced to a powder for diffraction measurements. The lattice constants given in Table I were determined for the four compounds from X-ray diffraction patterns of powder samples exposed to filtered copper radiation using a 114.59 mm diam Debye-Scherrer type camera using the Straumanis loading. None of the patterns showed a detectable amount of a second phase. The lattice constants were obtained from an IBM 704 computer program employing a least squares treatment with systematic correction terms as previously reported.14

Jan 1, 1963

By Jei Y. Choi, Paul G. Shewmon

The surface self-diffusion coefficient of copper (D,) has been measured between 847° and 1069 "C for six different orientations. These were the(111), (110, (100, and three higher index surfaces. The activation energy for Ds (designated Q s) was found to be about 49 kcal per mol for all six surfaces, and Do about 2 x 104 sq cm per sec. At any temperature Ds varied by no more than a factor of three over these orientations. It is shown that, if the free energy of a surface atom is uniquely determined by its number of nearest neighbors, it follows from the Principle of microscopic reversibility that Qs should have the same value for all surface orientations, and Ds should vary little with orientation. This model also suggests that for clean fee metals Qs ~ 2/3 AH, (heat of vaporization). This is true for copper. ALTHOUGH it has been appreciated for several decades that atoms can diffuse more rapidly on a surface than through the bulk of a crystal, it has only been in the last few years that reliable values of the surface self-diffusion coefficient (Ds) have become available. Tracer studies of Ds had been attempted prior to this period, but when a tracer is placed on a surface, an ever increasing fraction of it is drained off into the lattice. The correction for this loss involves a very difficult, and as yet unperformed calculation. Those who have worked with tracers have not corrected for this loss.1, 2 Thus their results indicate that Ds is greater than the self-diffusion coefficient in the lattice (Dl), but it has not been established that they give quantitative data on Ds. A procedure which avoids the problem of tracer loss is to study the rate of mass-transfer under the effect of surface tension. If the surface asperity being studied is very small, the mass transfer occurs entirely by surface diffusion. The kinetics at which a grain boundary groove forms on an initially plane surface is a well-studied case of this type. The smoothing of a slight scratch in an otherwise flat surface is another procedure that has been studied. If these grooves are up to 20 to 30 µ in width, the dominant mechanism for mass transfer is surface diffusion (at least in the case of metals with low vapor pressures), and the widths can easily be measured with an interference microscope. Of these two, mass-transfer techniques only in the case of grain boundary grooving has a rigorous mathematical treatment been given. This was done by Mullins.3,4 His analysis predicted that in the case of copper in an atmosphere of an inert gas, surface diffusion should be the dominant transport mechanism. This analysis gave an equation for the groove profile and predicted that the width of the groove would increase as (time)1/4. Mullins and Shewmon showed that both of these predictions agreed with experiments.5 Thus the validity of the values of Ds given by this procedure seems to be well established. Gjostein has used copper bicrystals and the grain boundary grooving technique to determine Ds and the activation energy for surface selfdiffusion (9,) in the [001] direction on surfaces ranging between the (100) and (110) planes.= He reported that Qs = 41 kcal per mole and Do = 6.5 x 102 sq cm per sec for all orientations studied. Since the results did not change with the dew-point of the dry hydrogen atmosphere or the type of refractory tube used, he concluded that the surfaces were clean, or at least that the results were not influenced by any impurities chemisorbed from the atmosphere. The work reported here reproduces and extends Gjostein's study in that D s and Q s were determined for copper over a wider range of orientations. To study the effects of impurities, two purities of copper were used as well as cathodic etching to remove any possible electropolishing film. Gjostein postulated that the diffusing atoms on a surface near a low index plane are the few atoms which are adsorbed on the smooth region between ledges or steps in the surface. A more rigorous derivation of the equation relating Ds to the concentration and jump frequency of these adsorbed atoms is given here. Using this treatment, our empirical observation that Q s and D s are essentially the same for all surface orientations can be shown to follow from the assumption that the free energy of a surface atom is uniquely determined by its number of nearest neighbors. The studies of D s using the scratch technique have been carried out by Blakely and Mukura on nickel,' and by Geguzin and Oveharenko on copper. The latter study using copper gives values of D s roughly

Jan 1, 1962