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By J. R. Kyte, L. A. Rapoport

The material balance equation for partiai or complete 1:trter-drivc reser1,oir.s been re-arranged to include a pressure irrferferencr ternr. This pressure interfernce term was ohtained from the theory established hy Morinda. A .successful progranl deissed to solve the resrclritlg c,qrration in a few hours on a nleelitr .sizeti, digital compuier. No prior knowdelge of the properties of the eqrrifer is required in the solution. 7' ri~rl calculations areatle using various assumed con!binuiions of value of the constant expretsing the qquifer properties correspoinds to the best fit ohtained between observed and calculated field history. Details of the method of calculaion are illus trated by an example. INTKCDUCTICN A method 01' calculating the material balance equation for a partial water-drive reservoir completed in an aquifer has been described in the literature." Pressure interference i'rc,m other pools iocated in the same nquiucr is not taken into account in this solution. When present, the pres- sure interference effect must be included in order to make a complete performance analysis. A correction for this effect has been developed using the theory cstahlished by Mor-tada.' Manual calculation of the material balance for water-drive reservoirs is a formidable task. Such manual ca1culation when interference eflects are includcd would be impossible to completc in any reasonable time period. However, a medium-sized stored program, digltal conlputer can he used satisfactorily. The method is described in the following sections. THECKETICAL CONSIDEKATIOhS The material balance equation for a reservoir producing by partial or total water drive, as proposed by Van Everdingen, This relationship is linear for Z/a from which thc slopc, Z, and the intercept, N, can be obtained by the least-squares method from the data points. It is not necessary lo know the aquifer properties to uktain oplimum values tor 2nd IV. Various assumptions are made tor At,,: where 11 is production time, seconds (oilfield between the equal successive time intervals into which the history is divided. t,, h It, times the number of equal time periods from i.e.. the total dimen-sionless time interval from It is noted that the dinlensionless time interval, At,,, involves all the relevant aquifer properties. Accordingly, any assunlption of is an assumption of the combined aquifer properties which pertain to the solution of the equation. Deviations of the data points from a straight line arc calculated for each assumption of and the value of A, correspond ing to the minimunl deviation is chosen as the optimum solution. This method is described in Ref. 1 and 2. Thc material balance solution is usually made with an initial assumption that the reservoir being studied is located in an infinite aquifer from which there are no other withdrawals. Deviation of the points by amounts greater than can be attributed to inaccuracies in field data may be the result of: (1) boundary effects of a limited aquifer, (2) pressure interference from othcr pools completed in the .sarne aquifer, and (3) a combination of these effects. Differentiation of these effects can be made only on the basis of geologic data. Pressure interference from other fields will result in a pressure drop at the original oil-water boundary having an interference component, The measured instantaneous pressure drops at the oil-water

By Lysle E. Shaffer

INCREASING attention has been given in the last decade to the possibilities of mine leasing in the West. The practice as described in this article does not refer to the leasing of entire properties for corporate operation. It is intended to deal rather with the advantages and problems incident to leasing portions of properties to individuals who themselves, individually or in groups, do the actual mining and transportation of the ore. These individuals are sometimes called "leasers" and sometimes called "tributors." The contracts under which they work set up an independent relationship of lessor and leaser, between themselves and the mineowner or operator. This relationship has many advantages to both sides over those created by the ordinary relationship of employer and employe. From the standpoint of the owners there is no liability on independent contractors for industrial injuries, social security taxes, unemployment taxes, or the manifold restrictions of the Federal Labor Relations and Wage Hour Acts and similar state acts where they exist. As the leaser's income depends on the quantity and quality of ore produced, there is a distinct incentive for maximum production of a good grade of ore. This in turn promotes careful mining of the areas under lease. Ordinarily in mining, labor cost is a high percentage of the total cost of operation. Under a leasing system, even if the leasers be allowed to retain half of the gross values that they produce, and the owner or operator gets half, in the case of marginal ore bodies this is ordinarily more than the lessor would realize if the property were worked by day labor. In some instances mineral deposits under a leasing system may become ore, whereas under a day-labor system they would

Jan 1, 1948

By K. E. Nelson

The effect of thorium and zinc variations on the strength and 100-hr creep characteristics of Mg-Th-Zn-Zr alloys was investigated. Optimum resistance to creep at 650° and 700°F are attainable within a certain range of thorium and zinc contents. This range does not conform to that which develops maximum tensile properties. RAPID advances have been made during the last few years in the development of magnesium alloys for elevated temperature applications demanding high resistance to creep. The beneficial effect of rare-earth metals on the creep resistance of magnesium alloys has been emphasized by a number of publications1-13 and such alloys are now in commercial production. The use of thorium as an alloying ingredient in magnesium was mentioned by McDonald and also in two Alien Property Custodian patent applications.10,17 The initial observation of Sauerwald that thorium contributes still higher creep resistance to magnesium than is attainable with rare-earth metals has recently been substantiated.'" " In fact, it has been demonstrated that the useful temperature range of magnesium alloys is appreciably extended by the use of thorium. In all cases, it was observed that zirconium must be included in the alloys in order to render them fine grained and more readily castable. Several recent publications:2-27 indicate that a still further improvement in creep resistance and a further extension of the useful temperature range can be realized by the addition of zinc to alloys. The primary purpose of this paper is to present the results of a comprehensive study of the effect of zinc on the strength and creep characteristics of Mg-Th-Zr alloys. Compositions covering the range of thorium content from M to 6 pct and zinc content from 0 to 5 pct have been investigated. The creep characteristics at 650" and 700°F reported in this paper are based on results of tests of 100-hr duration. It is appreciated that creep tests of 100-hr duration might not yield adequate data for design purposes for parts with much longer expected life. However, for the purposes of the present discussion, it is felt that the combination of stresses and temperatures used in the 100-hr creep tests have yielded a clear representation of the compositional variation of creep resistance at the temperatures investigated. Creep tests of 1000-hr duration are now in progress on a few of the most promising alloys. Preparation and Testing of Alloys The alloys studied in this intensive investigation were prepared in 25 lb capacity mild steel crucibles. The thorium, zinc, and zirconium were alloyed and poured as described in earlier publications The thorium was introduced into the melt in the form of a Mg-Th hardener," the zinc added in the metallic form, and the zirconium alloyed in the form of the commercial hardener containing magnesium and 30 to 50 pct Zr.10, 26 Fluxing practices for melting and refining were the same as for magnesium-rare-earth metal-zirconium alloys. The melts were sampled for analytical determinations and poured into separately cast 1/2 in. diameter standard tensile bars. The test bars were given a precipitation treatment of 16 hr at 600°F in laboratory furnaces. It has been shown by other tests that a high temperature solution treatment followed by an aging treatment is unnecessary for the development of optimum properties in Mg-Th-Zn-Zr alloys. The selection of 600°F as the aging temperature was based on an attempt to achieve metallurgical stability without coalescence of the undissolved phases and the attendant loss in strength. The thorium, zinc, and zirconium contents of each melt were determined chemically. The zirconium contents are reported in two parts, "soluble" and "insoluble," referring, respectively, to the portions present in the alloy which are soluble and insoluble in dilute HCl acid. Distinction is being made between these two components of the zirconium content in the alloys because it has been found that only that portion of the zirconium content which is soluble in dilute inorganic acids affects the structure and properties of the alloys. The usual impurities consisting of copper, iron, manganese, and nickel were determined spectroscopically. The analysis for each melt is listed in Table I. A description of the methods of tension and creep testing has been detailed in earlier papers. The tests were performed with the cast skin re-

Jan 1, 1954

By H. l. Burghoff, A. I. Blank

J. J. Kanter.*—The authors of this paper have demonstrated that at 500°F their alloy will elongate, under appropriately adjusted stress, one or two per cent over a period of 6000 hr. Then they show that after the alloy has so elongated, it will still elongate anothcr 40 per cent if it is tested at ordinary temperature. I should like to ask the authors how much more than 2 per cent over a period of 6000 hr. their alloy will elongate at 500°F. H. L. BuRghofE.—We do not know, because we have not carried out stress-rupture tests on this material. I believe your point concerning the desirability of stress-rupture testing is very well taken. In the material that we have subsequently tested we have not seen any signs of deterioration. We do not know how much further it is possible to go beyond the 2 per cent before finding grain-boundary separation. We have not encountered any under the conditions of the test. W. E. Kingston.†—IS this particular type of copper susceptible to strain-aging, and if so at those comparatively low temperatures, is that going to affect the shape of the curve? By strain-aging I mean the phenomena that certain ferrous alloys show in which the resistance to deformation increases suddenly during the low-temperature creep cycle, apparently due to some precipitation type of reaction, perhaps analogous to hydrogen embrittlement. H. L. BUrghoff.—I believe that this material is not subject to strain-aging of this type. It is very high in copper content, of course, nearly loo per cent. There are some very minor impurities and it carries a small amount of phosphorus, which, unless it is present as an oxide, should be in solid solution well within the solubility limits. I believe it does not precipitate

Jan 1, 1945

By Charles E. Locke

DEPRESSION in all lines of the mineral industry except gold, which began in 1930 and continued, even worse, through 1931, had its effect on ore concentration. Construction was limited to the completion of plants already begun. Every possible economy was adopted. Changes and improvements involving expense were postponed. Research was largely abandoned. Operations became highly efficient and costs were cut down, although this did not necessarily mean a lower cost per ton because of the greatly reduced capacity at which mills were run. Lower metal prices caused the operators to seek the optimum ratio of concentration and grade of concentrates looking toward maximum economic recovery; that is, net profit. In the crushing field no marked changes occurred. The Symons cone crusher for intermediate work is in use almost everywhere. Its manufacturers claim that 900 machines have been installed in 21 countries, replacing two previous steps of crushing and yielding a product sufficiently fine to form a satisfactory feed for rod mills and ball mills. A new Telsmith crusher has appeared which has curved jaws something like the Symons cone and consequently the same advantage as the latter.

Jan 1, 1932

By Charles R. Simcoe

The stress-strain curves in the microyield region for various Fe-C solid solutions shown by Davies and Ku are typical examples of parabolic curves defined by the expression a = kEn 111 These data, when replotted on log-log coordinates, as shown in Fig. 9, exhibit three essentially parallel straight lines. It is apparent that carbon increases the flow stresses, but does not affect the exponent n. In other words, the only factor in Eq. [1] affected by in in carbon content is the constant k. As Eq. [1] is written k is the stress at a strain of 1.0. This is unsatisfactory for examining data in the microyield region. Therefore, the equation can be altered to the form: to permit the use of the authors' microyield stress at a strain of 10-6 as k. Extrapolating the curves in Fig. 9 to a strain of 10-6 gives stress values of 2000, 3200, and 5400 psi for 0.008, 0.014, and 0.02 pct C, respectively. These values do not agree exactly with the authors' measured values, but this will not affect the following discussion. The effect of carbon content on the slopes of the stress-strain curves shown in Fig. 2 of the paper by Davies and Ku can be analyzed by differentiating Eq. [2] with respect to strain. Thus: where n is always less than 1.0. Since n is essen- tially constant as a function of carbon content for the data under discussion, the slopes of the stress-strain curves depend only on k and E. If the slopes are examined at various selected Plastic strains. i.e., 10-6, 10-5, and so forth, it follows from Eq. [3] that the dif-ferent slopes for the different carbon contents depend only on the different values of ke=10-6. Thus, the larger ke=10-6, the steeper the linear stress-strain curve will rise with increasing plastic strain. This

Jan 1, 1969

By ROBERT H. BOOTH

THE happy intra-plant relationships of the Bridgeport Brass Co. are largely attributable to the interest of the management in this important business factor. In furtherance of this development Carl F. Dietz, President of the Company and a member of the Institute, has contributed the novel plan for the objective presentation of business economics, described herein. All of the officers of the corporation are active in its management and they together with many other workers filling both executive and subordinate positions have a substantial financial interest in the enterprise. The viewpoint of this organization is fairly reflected by the following quotation from Roosevelt's "The Foes of Our Own Household."

Jan 1, 1924

By R. A. Young

Zinc metal production in the operating plants in the United States during 1948 was approximately equal to that of the year 1947, although new developments during the year assure higher output in 1949, if economic conditions are favorable. In the Western plants, the man-power shortage was almost completely overcome and new capacity has been or is in the process of being added to three plants; thus by December of 1948 daily zinc metal production had risen to the highest point since May of 1944 despite strikes in one large primary smelter and in one secondary plant.

Jan 1, 1949

By A. A. Steel

(Spokane Meeting, September, 1909.) DURING. the summer of 1905 I was employed by the U. S. Geological Survey to investigate the geology, Mining, and preparation of barite in most. of the fields of the United States. The Eastern districts have been more or less completely described ; the Virginia field in detail by Thomas L. Watson, in his paper, Geology of the Virginia Barite-Deposits,' and other fields in abstract., including statistics of production and references to current literature, by various authors .2 There have also been published a few details of the occurrence of barite in the lead-mines of Washington county, Mo.3 The other accounts of this district are erroneous and meager, and since this field is the most important one in the United States at the present time, a detailed description of the local geology seems doubly desirable. Barite-deposits are scattered over nearly the whole of Washington and adjoining counties, but. the product, is all mined from the areas indicated upon the sketch-map, Fig. 1, and is shipped from the stations of the St. Louis, Iron Mountain &. Southern railway, between Blackwell and Potosi, from 45 to 60 miles SW. of St.. Louis. The topography is for the most part gently rolling, with slightly graded streams, usually less than 200 ft. below the higher hill-tops. Along Mineral fork and Indian creek are :some steep bluffs and cliffs, affording good exposures of the

Feb 1, 1910

By J. K. Edgar

For a number of years the production and use of super-purity aluminum (better than 99.99 pct) has been steadily increasing. High-grade lots of. such aluminum show certain outstanding characteristics not found in lower grades containing principally silicon, iron and copper as impurities. One such characteristic is the so-called "self annealing," that is, the re-crystallization of the heavily cold worked metal at room temperature.' Interest therefore is aroused as to the effects of the impurities. It is well known that the amounts of silicon and copper which occur in aluminum of better than 99.95 pct are completely soluble, at least at elevated temperatures (above 200°C). Iron, on the other hand, is known to be fairly insoluble in solid aluminum. Thus, a knowledge of the limits of this solubility would he of considerable use in studying the characteristics of the high purity metal. All investigators have agreed that iron has very low solubility in solid aluminum. Rosenhain, Archbutt and Hanson2 reported traces of an aluminum-iron phase in the "purest samples of aluminum obtainable." Gwyer and Phillips3 reported that an iron constituent was visible under the microscope in metal containing ".0088 per cent iron." Roth4 found that in the solid state the solubility of iron in high purity aluminum was 0.01, 0.01, 0.017 and 0.022 pct at 225, 320, 500 and 600°C respectively. Dix5 working with alloys containing less than 0.03 pct impurities, concluded from microscopic and chemical analyses of eutectic areas that the eutectic composition was close to 1.7 pct iron. Dix placed the eutectic temperature at 65s°C. Archer and Fink,6 using high purity aluminum-iron alloys, found that the hypoeutectic liquidus intersects the eutec-tic horizontal at 1.7 pct. This is in fair agreement with the investigation of the aluminum-iron system by Gwyer and Phillips who placed the eutectic at 1.89 pct iron with a freezing point of 653'C. Preparation and Chemical Analysis oP Alloys Electrolytically refined aluminum (99.991 pct aluminum) and a high purity alumi-num-iron alloy (11.45 Pet iron) were used in the preparation of the alloys for this investigation. To aid in controlling the iron content of the experimental alloys, an alloy of lower iron content was prepared first from these materials. The high purity aluminum was melted and heated to about 700°C in a plumbago crucible coated with alundum cement and the aluminum-iron alloy was then added. The alloy was thoroughly stirred, fluxed and skimmed and then chill-cast into notch bars. The aIlalyses of the three materials are given in Table I. The alloys for the determination of the solid solubility of iron in aluminum were prepared by melting 600 g total of the aluminum plus the required quantity of the aluminum-iron alloy (No. 92531). These

Jan 1, 1949

By T. H. Alden, H. W. Schadler

The strain rate dependence of the flow stress of the eutectoid Zn-Al alloy has been determined as a function of mechanical processing, microstructure, and temperature. The best superplastic properties result from the ultrafine, equiaxed structure produced by solution treatment and isothermal transformation at 0°C. Lamellar structures produced by isothermal transformation and coarse equiaxed structures produced by annealing also exhibit strain rate sensitivity in excess of 0.5, but at higher stresses and lower strain rates than the finest structure. Solution treatment and isothermal transformation eliminate the effect of prior processing history. Small composition variations in the binary alloy do not influence the mechanical properties. Below the eutectoid transformation temperature (.275C) increasing temperature lowers the flow stress at all strain rates. The data do not favor any of the present proposals for the mechanism of superplastic flow. ALLOYS of zinc and aluminum, near the eutectoid composition, have been investigated for: 1) the flow stress-strain rate and elongation behavior,1, 2) the transformation kinetics,3 and 3) structure,3"5 but the structure sensitivity of the mechanical properties is poorly understood. Using a near eutectoid alloy water-quenched from 380°C, Backofen et aL2 estab- high and increases with increasing strain rate. They found a correlation between strain rate sensitivity and tensile elongation as expected from the increased resistance to necking that a high strain rate sensitivity provides.296 The large elongation at high strain rates is attractive for metal forming. Since most other superplastic alloys7-l3 do not show high strain rate sensitivity at such a high strain rate (for the exception see Ref. 12) there is the possibility of a unique deformation mechanism for this alloy. The sensitivity of the mechanical properties of the eutectoid alloy to thermal history1 suggests a structure sensitivity that has not been demonstrated. Gar-wood and Hopkins3 identified a lamellar product for material transformed between 200" and 260°C. The size of the lamellae decreased with decreasing temperature. They also demonstrated that an unresolved transformation product formed below 200°C. A granular two-phase material was resolved for specimens quenched to below 150°C by Mitbauer and sauerwald4 who observed coarsening of the structure after annealing. The role of grain boundaries in superplastic deformation is suggested by the strong effect of grain refinement in encouraging this phenomenon at high strain rateS7-11, 13 and is emphasized in several proposals about rnechanism7, 8, 12 and in a theory14 of high-temperature deformation. Alden8 showed metallographic evidence that grain boundary sliding is occurring extensively at strain rates where m is large but less at high strain rates where normal plasticity is observed. Holt and Backofen10 have shown that sliding also oc-

Jan 1, 1969

By Shosei Serata

Conventional roof bolting may be giving ground to a new technique that utilizes only the ground itself to stabilize mine openings. This newly developed stress control technique (SCT) has initially been used in sedimentary ore bodies that are both overlain and underlain by weak strata. The technique is also suited to the design of production panels and main entry systems, and is readily adaptable to room and pillar as well as total- extraction mining, including both shortwall and longwall coal mining. In applications where the technique has been used, the requirements for roof bolting and floor renewal were virtually eliminated. The SCT comprises three basic methods and covers a wide range of problems associated with failing roofs and heaving floors in underground mines (see Table 1).

Jan 5, 1976

By Charles T. Holland

In connection with the problems of bumps in coal mines, much has been written concerning the manner in which roof action and methods of mining enter into the pressure effects observed but little has been written upon the relationship between the physical properties of coal and associated rocks and the cause of bumps. The question of the strength of bituminous coal, of its elasticity, and the energy it can absorb and store has been neglected to a considerable extent in connection with this problem. It is generally agreed that one of the necessary conditions for bumps is a strong coal.' Therefore, since the strength of coal is an important factor, a study of this property should be made. several investigators have conducted laboratory experiments upon the strength of coal, using small cubical or rectangular test pieces. An attempt will not be made to go into all of these investigations, but they are briefly summarized in Table I. Experiments of the U. S. Bureau of Mines and of Lawall and Holland (pp. 27 and 34 of ref. 9), however, indicate that regardless of whether the coal is a soft and weak semihituminous (Pocahontas No 3) or a hard and strong bituminous (Stockton) coal, the maximum ultimate unit stress developed in laboratory tests is higher in small cubes than in larger cubes of the Same coal.

Jan 1, 1942

By Charles T. Holland

In connection with the problems of bumps in coal mines, much has been written concerning the manner in which roof action and methods of mining enter into the pressure effects observed but little has been written upon the relationship between the physical properties of coal and associated rocks and the cause of bumps. The question of the strength of bituminous coal, of its elasticity, and the energy it can absorb and store has been neglected to a considerable extent in connection with this problem. It is generally agreed that one of the necessary conditions for bumps is a strong coal.' Therefore, since the strength of coal is an important factor, a study of this property should be made. several investigators have conducted laboratory experiments upon the strength of coal, using small cubical or rectangular test pieces. An attempt will not be made to go into all of these investigations, but they are briefly summarized in Table I. Experiments of the U. S. Bureau of Mines and of Lawall and Holland (pp. 27 and 34 of ref. 9), however, indicate that regardless of whether the coal is a soft and weak semihituminous (Pocahontas No 3) or a hard and strong bituminous (Stockton) coal, the maximum ultimate unit stress developed in laboratory tests is higher in small cubes than in larger cubes of the Same coal.

Jan 1, 1942

By Herman Van Fleet, Frederick W. Neil, O&apos

The object of this paper is to describe the present status and possil~ilities of liquid oxygen as an explosive based upon the investigations, research and practical work of the Ingersoll-Rand Co., and of the Air Reduction Co., from early in 1922 to date. The following work was done. 1. A study of the history and physical theory of L. 0. X. as an explosive. (No attempt will be made in this paper to give the history or theory, as this has already been covered by the literature on the subject.) 2. An investigation of the use and the practice with L. 0. X. in the iron mines of Lorraine where L. 0. X. has its largest application in Europe. Although L. 0. X. is extensively employed in the iron mines of Lorraine, many of the mines using it exclusively, and blasting with it a total of approximately three million tons of iron ore per year, the fact that the mining practice in Lorraine1 is to drill comparatively shallow holes and blast only a few holes at a time, renders the data obtained there of very little value in estimating the possibility of replacing dynamite with L. 0. X. in American mining methods. In fact, in the iron mines in Lorraine, L. 0. X. replaced black powder, or its equivalent. 3. Laboratory research work on properties of absorbent materials. 4. Work in the Bureau of Mines explosive laboratory at Pittsburgh, Pa., on the properties of L. 0. 3. cartridges. 5. Practical work underground with L. 0. X. cartridges in the Kitherbee-Sherman iron mines at Mineville, N. Y. 6. Practical work in the quarries of the Calcite Quarry Co., Myers-town, Pa. 7. Practical blasting in several quarries and open-pit mines.

Jan 1, 1927

By C. E. Sims, C. A. Zapffe

MANY hundreds of publications have appeared during the past 78 years that treat the subject of hydrogen in iron and steel,105 but conclusions regarding the functions of hydrogen in causing some important defects in steel are still unsatisfactory to many; and other hydrogen-caused phenomena yet remain to be identified with this gas. The most widely discussed of these defects is hydrogen embrittlement, but the conception, perhaps the popular one, that embrittlement is due to hydride formation does not conform to the known facts.104 The true identity of hydrogen embrittlement seems instead to lie in a mosaic nature of metal crystals, which is a concept not yet accepted by most metallurgists. A study of hydrogen embrittlement therefore provides new viewpoints in regard to the crystalline substructure of steel. A second widely discussed hydrogen-caused defect is the "flake" or "shatter crack." Although it is generally agreed that the presence of hydrogen is a prerequisite for their appearance, it is also realized that internal stress plays a decisive part. The relationship of hydrogen to internal stress has not been explained very clearly; nor is it always clear what the relationship is between a "flake" and a "snowflake," or between a "fish eye" and a "shatter crack." More importantly, the relationships among hydrogen embrittlement, hydrogen-caused fissures such as "flakes" and the ultramicroscopic structure of steel have scarcely been recognized. The present investigation attempts to provide an explanation for the embrittlement of steel by hydrogen by showing cause for accepting the "block" concept of metal crystals, and then to show how the numerous hydrogen-caused defects are interrelated in the light of this concept. EVIDENCE OF SUBSTRUCTURE IN METAL CRYSTALS It appears that the concept of a crystal as an aggregate of smaller multi-atom units must be accepted in some form if the behavior of metals is to be understood. The abundant literature on the evidence of an ultramicroscopic "mosaic" structure in metals and other crystalline substances suggests that the physicist has provided the metallurgist with an invaluable new insight. The exact picturization that any one physicist provides may be open to question, but the fact that there is some such fundamental substructure seems undeniable. The present work makes no pretense of comprehensively treating the imperfection structure theories. Nor will conclusions be drawn here regarding the exact nature of the substructure of crystals. However, the acceptance of some imperfection theory of fundamental attributes seems so necessary to an understanding of the behavior of hydrogen in steel that the following brief

Jan 1, 1941

By L. L. Seigle

Free energies, heats, and entropies of mixing of solid Fe-Au alloys have been measured by the galvanic cell method between 800° and 900°C. A positive deviation from Raoult's law and a large excess entropy of mixing were observed, both attributable to lattice distortion caused by the disparity in component atom sizes. Since the terminal solid solutortiontions are not regular, thermodynamic properties computed from the location of the mis-cibility gap do not agree well with measured quantities. The electromotive force data suggest some changes in the existing Fe-Au phase diagram. ALTHOUGH a considerable amount of information has been accumulated about the thermodynamic properties of metal solid solutions which exhibit negative deviation from Raoult's law, particularly those in which ordering occurs, relatively few experimental measurements have been made on solutions with positive deviation. This is due to the infrequency of broad homogeneous regions suitable for experimental measurement in solutions of this type, since any marked positive deviations from ideality lead to restricted solubility and the formation of miscibility gaps. Thermodynamic data reported in the literature for such systems have usually been calculated from the location of the miscibility gap boundaries under the assumption that the entropies of mixing are ideal, i.e., the terminal solutions are regular.' One of the few binary systems with both positive deviation and a wide homogeneous range in the solid is the Ni-Au system. A recent investigation of solid Ni-Au alloys' revealed that the entropies of mixing were much larger than ideal and consequently thermal data computed from the phase boundaries assuming regular solutions were seriously in error. Theoretical considerations put forward by Zener indicated that high entropy values should generally be associated with systems possessing a miscibility gap in the solid, when this is due to differences in the size of component atoms. These facts suggest that the regular solution assumption is a poor approximation for many solid solutions with positive deviation and that reliable thermodynamic data generally cannot be obtained by conventional methods from the location of miscibility gap boundaries. The Fe-Au system, Fig. 1, resembles the Ni-Au system in certain respects. The presence of a miscibility gap in the solid indicates a large positive deviation from ideality, but there is nevertheless an extensive single phase region suitable for experimental measurement. The following investigation of solid Fe-Au alloys was carried out in order to obtain additional data on the thermodynamic properties of metal solid solutions with positive deviation from Raoult's law and to further compare thermodynamic data computed from miscibility gap boundaries with those measured experimentally. Experimental Method The thermodynamic properties were derived from measurements of the potential developed between pure solid iron and Fe-Au alloys in a high temperature galvanic cell. The experimental apparatus and technique were the same as those used for the Ni-Au alloys and described in a previous report.' Cell electrodes were 1/16 in. diam rods swaged from chill-cast ingots and annealed for one week at 850°C. The alloys were prepared by melting fine gold granules under argon with pure iron obtained from the National Research Co. The cell electrolyte was

Jan 1, 1957

By Hugh Neill, O&apos

In previous papers,' the author has reported the results of experiments on the straining in tension of a single-crystal test piece, about 0.6 in. long, of vacuum-melted electrolytic iron containing 1.8 per cent. of silicon. The crystal was originally in the "as cast" condition, and was stressed slowly along a tetragonal axis so that slipping along conjugate gliding planes finally transformed the original cylindrical portion into a pair of fracture wedges. One of these fracture wedges was sectioned along the stress axis in a plane at right angles to the edge of the wedge. A metallographic study of this plane of section led to the conclusion that slip had taken place in the (111) direction along (112) planes making a V shape with the stress axis. The present paper describes the results of scratch-hardness tests conducted on the same section, in order to determine the distribution of strain hardness therein, followed by annealing, and considers the resulting variations in hardness. These observations supplement those made by Krivobok2 on similar material reduced 25 per cent. by hammering (i. e., by impact) in the cold. In order to investigate ageing effects, two small crystals of the same alloy were also tested. The Specimens Employed The principal specimen, A, was prepared for the metallographic examination leading to the determination of the slip planes of the crystal. Therefore the work described in this paper was conducted on metal which had been repeatedly etched and had been allowed to rest for about 30 months after straining. It consisted of a section of the fracture wedge and contiguous unstrained head of the test piece taken along a tetragonal axis parallel to the direction of stressing, the plane of section originally being not far removed from the (011). Several subsequent grindings

Jan 1, 1985

By Paul H. Lu, Fred D. Wright

Numerous laboratory tests and field measurements conducted by different persons have indicated that most mine rocks behave viscoelastically rather than elastically. Hence, for an accurate and realistic design of underground structure, the time factor should be taken into account, and the theory of viscoelasticity can be used. By considering the time factor, the time-safe-strength may be used for economical design instead of liberal safety factors with design based on the elasticity theory. The deflection and moment distributions on an elastic roof slab resting on elastic pillars have already been studied.l In this chapter, the stress- strain analysis for a viscoelastic mine roof resting on pillars of the same material or on supports of different material is first considered theoretically. Viscoelastic solutions for deflections, moments, and shears are de- rived from the elastic plate theory on the basis of the elastic-viscoelastic correspondence principle. The Laplace transformation technique is employed as the operational method in the mathematical treatment. The roof slab materials are represented by four different rheological models and four different loading histories are considered. The method of finite difference equations is employed for solving the partial differential equations, using FORTRAN programs to calculate roof deflections, moments, and shears. Numerical examples are given for one of the four models under two of the four loading histories with regular and staggered pillar patterns. The results are discussed in terms of the variance with time of deflections, moments, and shears as well as their variation in space due to the dimensions and configuration of the structure system. A viscoelastic slab resting on viscoelastic pillars or on elastic supports

Jan 1, 1972