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By H. Rush Spedden, A. M. Gaudin

IN the belief that a critical study of its operating problems might be a sound investment, the Cuban American Manganese Corporation initiated an ore-treatment research in cooperation with the Massachusetts Institute of Technology One of the early objectives of this research naturally became the relationship of the microscopy of the Cuban ores of the Corporation to their flotation treatment The operations in Cuba have already been described by F S Norcross, Jr 7 and the laboratory study of manganese oxide flotation goes back a number of years 4 Broadly speaking, the difficulties encountered in the flotation of manganese ores are that the consumption of reagents is extremely high, the concentrate contains more silica than is desirable and the tailing losses are relatively high An appreciable betterment on any of these scores would achieve a definite betterment in costs, quantity of minable ores, and quality of product The microscope study discussed in this paper was made on samples from the Quinto mine, from the Ponupo mine, and from mill products at various stages of passage of the ore through the mill The writers have had access to Company records and in particular to the petrographic studies made on thin sections of ore by the late Professors R J Colony and Philip Krieger, of Columbia University They acknowledge their debt to both of these men for the help derived from the reports Manganese oxides are black, friable, smudging It is therefore, very difficult to judge operations by inspection The mineralogy of manganese compounds seems to be confused, and the authors believe that many more minerals have been described than actually exist Much of this difficulty is due to the prevalence of the structural conditions that will be discussed further in this paper, namely, the porosity and the friability of the ores, and the extremely intimate association of minute manganifeous mineral crystals with impurities of various sorts By all odds the most important manganese mineral in Cuba is the one that in this paper is called "psilomelane " The name "psilomelane" has been used in so many different ways that the choice of it for this ore may not be approved by all However, it seems to be the best under the circumstances This mineral accounts for about 97 per cent of the manganese in the ores of the Quinto and Ponupo mines and in the mill feed The remaining odd 3 per cent consists mostly of pyrolusite together with minor amounts of other manganese oxide minerals DESCRIPTION OF PSILOMELANE Aggregate Structure In grains or lumps, psilomelane has a characteristic fibrous appearance and seems

Jan 1, 1942

By James R. Stuart

AS the available remaining properties of iron ore reserves on the Mesabi Range are opened up for mining, the various properties located under lake beds are brought nearer an active status. The actual physical problems involved in stripping these properties do not act as a deterrent so much as the legal and political problems that are encountered. When it is proposed to destroy a natural lake that has been used by the public for many years, much local as well as state opposition may be encountered regarding its destruction. Public hearings must be held and some adverse publicity is likely to result. The ownership of the ore under the lake and the rights of the abutting property owners must be settled, and protection from damage caused by a disturbance in surface and subsurface drainage is likely to be demanded by property owners some distance from the proposed mine area. The Embarrass Mine, located near Biwabik, Minn., falls into this classification. A portion of the orebody lies under what was formerly Syracuse Lake, this body of water having been removed in the process of stripping the mine. An additional problem in the case of a meandered body of water is the establishment of a meander line that can be projected downward as mining progresses to form the basis for a satisfactory division between lake bed and upland ore shipments for royalty purposes. Fig. 1 illustrates the complications encountered in maintaining these divisions. A balance point was agreed upon in the center of the lake to make an equable division of lake bed ore to the abutting properties. The entire lake bed has since been adjudged the property of Minnesota. Lake Characteristics Lake bed stripping problems with which this paper is concerned necessarily are limited to a specific type of lake, namely the glacial lakes of the Lake Superior region. One characteristic common to these bodies of water is a deposit of fine black mud or silt on the bottom, frequently underlain by a layer of impervious blue clay. This is also true of the muskeg areas of the region, which present almost identical problems as lakes in stripping. The actual removal of the water and the lake bed material is a routine matter more or less standardized as to equipment, and the period of time required can be estimated easily on the basis of volume and capacity. More important than the foregoing is the execution of preliminary work, and above all, the timing involved. An account could be prepared based entirely on statistical and cost data which would give a very fair picture of the time required and cash outlay needed to effect the removal of a body of water preliminary to stripping the orebody. However, the real interest from the standpoint of the operator and the engineer who carry responsibility for completion of the job lies in the unexpected emergencies and the action of various materials involved in the stripping when the balance has been upset through diversion of water courses and the reduction of the lake level. Runoff and Drainage Lakes are located in natural basins that catch all the rain water and runoff water for a considerable area. Where a lake is involved having an inlet and outlet or a sizeable water course running through it, the drainage area may include a watershed covering many square miles. All available data then must be collected to supply a history extending over as many years for which information can be gathered on the flow of streams, annual rain and snowfall, and most important, the peak flows to be expected. Where the diversion of a stream around the stripping area is a part of the problem, this last factor is of great importance since it controls the cross-section to be selected for the diversion channel and the volume to be removed in its excavation, as well as affecting the hydraulic considerations to be met in the design of the completed channel. Characteristic material in the overburden found at the Embarrass Mine is illustrated in Fig. 2. Well Pumping Pumping from the well holes was started well in advance of the draining of the lake. Fig. 3 shows a gradual lowering of the water table with no noticeable fluctuations during the period in which the lake was being dewatered. Unfortunately, because of tight ground, a maximum flow to the wells was not maintained. This retarded the rate at which the water table was reduced so that in the course of stripping the excavation soon extended below the water table, and the great bulk of the pumping was handled from a system of sumps in the pit itself. Any dewatering program projected by prepumping from wells, a glorified well point system, would have to be started well in advance of the stripping to be of any great advantage. Preliminary drainage of the surface over the mine area is entirely apart from the actual elimination of the lake bed itself. Since the lake is what is called a perched water table because of the impervious character of the lake bottom, the adjoining surface may be dewatered below the surface of the existing lake and the flow will not be affected by the proximity of that body of water. This condition actually has been demonstrated through the establishment of a number of observation holes where a small churn drill was used to put down the holes and a 3-in. pipe was installed for taking water level

Jan 1, 1952

By AIME AIME

THE portrait of Herbert Hoover, President of the United States, recently painted by Philip A. de Laszlo at the request of the four Founder engineering societies, was unveiled at a special meeting in the Engineering Societies Building on Feb. 15. The portrait was delivered by Gano Dunn, chairman of the Hoover Medal Board of Award, who said, in part:,

Jan 1, 1932

By Kent R. Van Horn, W. P. Sykes

Since Honda and Murakamil in 1918 proposed their constitutional diagram of the carbon-free iron-tungsten system, considerable effort has been expended by several investigators in attempts to define more positively the structural features of the alloys. The existence of an intermediate phase corresponding to the formula Fe3W2 (68.7 per cent W) was proposed from evidence of a purely metallographic nature by one of the present authors2 in 1926. Since that time the identity of this phase has been confirmed by Arnfelt3 and by Takeda,4 both of whom employed X-ray methods as well as the microscope and the chemical analysis of isolated microconstituents. According to Arnfelt, Fe3W2, as crystallized from the iron-rich melts at a temperature above 1450° C., contains by analysis 68.7 per cent W. The lattice of this phase is characterized by trigonal symmetry. Arnfelt, moreover, proposed a second intermediate phase formed at some temperature between 1450" and 1000" C. by a peritectoid reaction involving Fe3W2 and the iron-rich solid solution. A melt containing 25 per cent W was cooled to 1000" C. and heated for 100 hr. The precipitated tungsten-rich constituent was separated and found by analysis to contain 62.6 per cent W. This composition agrees closely with that represented by the formula Fe2W (62.2 per cent W). Diffraction patterns from the concentrated precipitate showed a hexagonal unit cell. Takeda confirmed the data of Arnfelt regarding Fe3W2 but was unable to detect Arnfelt's second intermediate phase. While Takeda failed to describe in detail the treatments employed, he stated that in alloys containing 40 per cent W which were quenched after heating at various temperatures between 1200" and 1450" C. no evidence of the second phase (Fe2W) was observed 'either in the microstructure or in the diffraction patterns of isolated residues. He therefore considered the existence of this low-temperature hexagonal compound as disproved.

Jan 1, 1933

By Halbert Powers Gillette

In every chemical reaction heat is either developed or absorbed, and this plus or minus heat of formation is as definite in quantity as the weights of the reacting elements. In this paper I shall show that each chemical element and each chemical radical has its own definite heat-valency,—a fact which, so far as I know, has hitherto escaped the attention of investigators, but, I feel sure, will be admitted after the demonstration here given, and may lead to some practical conclusions of value. When Berthelotys " law of maximum work " was found to have so many inexplicable exceptions, the pendulum of a scientific theory swung away from a recognition of the truth underlying that proposition; and this reaction went so far that not only has thermal chemistry been relatively neglected by recent investigators, but it is not uncommon now to find textbooks on physical chemistry which practically ignore all that Thomsen, Berthelot and others have done. To this temporary tendency of thought I attribute the failure to recognize the principles herein announced and explained. Not long ago, while studying tables of the formation-heat of various salts, I noticed that in this respect all potassium salts in solution differ from the corresponding sodium salts by 9.3 cal.1 I found also that similar differences exist between other salts, not only when the basic radical is varied, while the acid radical remains constant, but also when the acid radical is the variable. Thus chlorine salts in solution differ from bromine salts in this respect by 10.9 cal. Upon further study, I found that Thomsen had noted similar constant differences, but, so far as I can ascertain, he appears to have attached no great significance thereto.

Jan 1, 1904

By A. E. Lee

THE Blackwell Zinc Co., Inc., a subsidiary of the American Metal Co., Ltd., operates a horizontal retort zinc smelter at Blackwell, Okla. The plant has 14 furnace blocks of 800 retorts each, fired with natural gas on a 48 hr cycle. Over 13,000 tons of zinc-bearing material, chiefly sulphide flotation concentrates, are treated monthly to produce slab zinc and high lead-cadmium fume. In 1942 a program of rebuilding and modernizing the smelter was started. By 1947 furnace smelting capacity had been increased to a point where roasting and sintering facilities were inadequate, and it was necessary to purchase oxidized materials to supplement sinter production. The seven 210 ft Ropp roasters and three 42 in. x 44 ft Dwight-Lloyd machines then in use had been in service at least 20 years and were in need of major rebuilding. Thus it was entirely practical to consider all new equipment and a change of method rather than rebuilding and repairing obsolete units. A study of the problem indicated that roasting as such could be eliminated and roasting and sintering accomplished in one step by a modification of the Robson process,' which had been used since the early 1930's by the National Smelting Co., Ltd., at their plants at Avonmouth, England, and Swansea Vale, South Wales. Francis P. Sinn, General Manager, Zinc Smelting Operations, The American Metal Co., Ltd., who was familiar with the practice in England, suggested the use of one large machine for the entire operation from concentrate to sinter. One step sintering appeared to best meet Blackwell's plant requirements and indicated substantial savings in labor, gas, coal, and repair costs. Choice of Machine Size The sinter machine size was set at 12x168 ft for a rated capacity of 540 tons per day. This tonnage, produced on a five day week, would meet the seven day requirements of the 14 furnace blocks. The one large machine was quoted at a lower cost than two or more 6 ft wide machines of similar total capacity. Further, the larger machine could be housed in a smaller structure and only one set of equipment for charge preparation and delivery and for disposal of sinter cake was needed. One machine on a five day week made possible a concentration of the skilled operating personnel and required less men than a plant including two or more machines and related equipment circuits. Fewer units of equipment meant less maintenance, and the two down days weekly allowed ample time to repair and, if necessary, to make up lost production. Experience had indicated better sintering quality and rates with larger masses of material, not only on wider machines, but also in deeper beds. The ratio of windbox perimeter to area for the 12x168 ft machine is 0.179, compared to 0.353 for a 6x102 ft machine and 0.617 for a 42 in. x 44 ft machine. This meant less air leakage with resulting fan power savings and less spoilage of charge along the pallet sides. Performance Initial operation of the new sinter plant was made in November 1951 and regular production attained late in December. The average product sinter output during 1952 and the first half of 1953 has been 18.2 tons per hr. The average for one month has been as high as 22.4 tons per hr. Considerable experimenting with varied operating conditions accounts in part for the below capacity — 24 tons per hr — average output, and work to further improve production rate continues. A typical sinter analyses is 66.0 pct Zn, 0.3 pct Pb, 0.1 pct Cd, 0.3 pct S, 8.0 pct Fe, 2.0 pct SiO,, 0.8 pct CaO, and 0.2 pct MgO. Use of this material has made possible increases in furnace burden and improved furnace operation over the former practice using sinter made from Ropp roasted concentrates. Better lead and cadmium elimination in sintering has permitted the furnace production of slab zinc lower in lead and cadmium. Anticipated economies of operation have largely been gained. The sinter plant is operated by seven men per 8 hr shift — one head operator, three equipment operators and three sweepers — plus one oiler on day shift only. While it has been necessary at times to operate seven days a week to produce the required sinter tonnage, the five day work week usually has been adequate. Consumption of natural gas for sinter bed ignition is 200,000 to 300,000 cu ft per day. Green Ore Sintering Practice The 30 to 31 pct sulphur content of the —200 mesh zinc concentrates is the fuel used to sinter the charge, no coal addition being required. In the feed to the machine, sufficient concentrates are added to crushed return sinter fines containing 0.3 to 0.5 pct sulphur to produce a charge averaging 5.0 to 6.5 pct sulphur. Since the return sinter used in Blackwell's practice is varied from — 1/2 to — 1/8 in., the actual sintering mixture of fine sinter and concentrates is somewhat higher in sulphur. The coarser sinter particles are too large to resinter and merely aid porosity in the sinter bed. The ratio of concentrates to return sinter in the charge ranges from about 1:4 to 1:5.5. Variations are based on the appearance of pried up bed sections, bed exit gas temperature trends, windbox suctions, and return sinter size. Sufficient sulphur must be used to obtain fritting of the charge into a soft sinter cake and to aid in the elimination of lead and cadmium. Excessive feed sulphur will result in partial slagging of the cake impairing porosity and prolonging sintering time.

Jan 1, 1954

By J. R. Cahoon, H. W. Paxton

The possibility of using unidirectionally solidified, two-phase alloys as an approximation to fiber composite materials is investigated. The short-term me.chanical properties and failure modes of unidirectionully solidified A1 (rich)-Cu alloys containing ap -Proximately 0, 17.5, and 27.7 vol pct of 0 phase 'fibers" are determined at temperatures from 25" to 500" and compared with those obtained for conventionul SAP alloys. In a previous publication,' hereafter referred to as I, the possibility of understanding some of the room-temperature mechanical properties of unidirectionally solidified castings was explored. For Al(rich)-Cu and Al(rich)-Mg two-phase alloys over a substantial range of compositions, the yield and ultimate strengths and common ductility measures were very adequately predicted from the principles of fiber strengthening4 and the analysis of ductility outlined by Gurland and Plateau." The results obtained in I suggest the possibility of using unidirectionally solidified, two-phase alloys to simulate fiber composite materials where the inter-dendritic second phase or constituent acts as the reinforcing material. Recent attempts concerning the fabrication of fiber conlposites have concentrated on producing composites with a good bond between fiber and matrix and with very long fibers so that their maximum contribution to the strength of the composite may be realized. However, these objectives are difficult to attain in practice and present fabrication processes are either extremely laborious or costly.13 The slow, unidirectional solidification of eutectics has received considerable attention as a method for producing composite materials. 5,6 This method can fulfill both of the above objectives but it is currently laborious, expensive, and has the additional disadvantage that the volume fraction of reinforcing phase cannot be easily varied. On the other hand, unidirectionally solidified, two-phase alloys, also with a good bond between the phases, are relatively easy to make and the volume fraction of reinforcing "fibers" can be easily varied by changing the average composition of the alloy. The disadvantage of the cast alloys is that the mechanical effectiveness of the "elongated interdendritic reinforcements" (EIR)* may be reduced due to their rela- tively short lengths, the w factor in Eq. [2] of I. However, if the EIR have a high strength their contribution can be considerable. For composite materials containing discontinuous cylindrical fibers of various lengths the ultimate strength is given by1 where it is assumed that the composite fractures when the fibers fail. In Eq. [I], a, is the stress in the matrix just prior to failure of the composite, Vf is the total volume fraction of fiber reinforcing constituent, Vf(l+) is the volume fraction of fibers whose lengths exceed the critical length, I,, which is defined as the shortest length of fiber in which the stress can build up sufficiently to break the fiber. af is the fracture strength of the fiber material, w is a factor accounting for the discontinuity of those fibers whose lengths exceed I,, 1-/d is the average aspect ratio of those fibers whose lengths are shorter than I,, and t is the shear stress in the matrix at the fiber-matrix interface. The factor w is dependent on the length of the fibers and also on whether deformation of the matrix occurs plastically or elastically. However, for a given length of fiber, w is smaller when elastic deformation of the matrix is assumed.' It is of interest to consider the properties of simple unidirectionally solidified, two-phase alloys at elevated temperatures in view of the possibility of using suitable modifications for high temperature service. Knowledge of the creep behavior of these materials is still rudimentary (although under active investigation) and the present paper concerns itself with short time tensile properties of some alloys similar to those investigated in I (i.e., unidirectionally solidified Al(rich)-Cu alloys). Unidirectionally solidified alloys containing 5.6, 17, and 23 wt pct Cu were tested parallel to the direction of solidification at temperatures from 25" to 500°C. In the present investigation, the alloys were homogenized for 2 days at 535°C giving a matrix of homogeneous a phase (5.2 wt pct Cu) and an interdendritic constituent (EIR) which was completely Q phase (53 wt pct Cu). EXPERIMENTAL Alloys of nominal composition 5.6, 17, and 23 wt pct Cu (containing approximately 0, 17.5, and 27.7 vol pct 8 phase, respectively, after homogenization at 535°C) were prepared by melting 1200 g of A1 (99.99 pct) in a high purity graphite crucible and adding the appropriate amount of freshly cleaned copper chips (99.9 pct). The molten alloy (at 700°C) was poured into a preheated graphite mold (also at 700°C) and the ingot unidirectionally solidified by impinging water on the steel baseplate of the mold. The alloy was degassed immediately

Jan 1, 1970

By Robert H. Richards

The extent to which sizing by sieves should be carried, as a preliminary to the separation, by jigging, of minerals of different specific gravities, has been a matter of controversy for many years. The subject has been investigated by several authorities, yet the ground does not seem to have been completely covered, nor are the questions involved entirely settled. For my present purpose I shall refer to but three investigators—Rittinger, Munroe, and Hoppe. In seeking additional light, I have gone over part of the old ground which has been considered satisfactorily settled; and since these preliminary tests have thrown light on some points, they have been included in this paper. In the investigations here described, I have confined myself, for several reasons, wholly to small sizes—grains of 0.1 inch in diameter and less. Rittinger's work was mainly done upon larger sizes, and there is much need among millmen of information concerning the smaller sizes. Moreover, these sizes brought the investigation within the means at my disposal. The laws that have been claimed as the laws of jigging by the several authorities are: 1. The law of equal-settling particles. 2. The lam of interstitial currents. 3. The law of acceleration. 4. The law of suction. The first of these has been considered by investigators, generally, to be the most important of all, and the larger part of the work of jigging is thought to be governed by it. But that it does not cover the whole of jigging is clear to all; and to account for the increased efficiency which we may call the extra jigging-catch, the other three laws have been advanced. The investigation described in this paper was undertaken to determine, as far as possible, to what extent each of the four laws con-

Jan 1, 1895

By S. Gstalder, J. Raynal

Consideration was given to simple tests which could be performed on rocks to give a measure of rock drillability. Various methods of breaking rocks were considered and the hardness test developed by Schreiner was selected for this study. The test involves application of an increasing load on the rock face through a flat-faced cylindrical punch until rupture occurs. Test results show that hardness is a good measure of the breaking strength of rocks. Useful relationships are shown to exist between hardness and other physical quantities such as specific disintegration, Young's modulus and sonic velocity. Specific disintegration (volume of rock broken per unit of work input) provides a possible means of comparing the effectiveness of other methods of rock breakage. The relationship between hardness and sonic velocity may be very significant for it may be possible to deduce rock drillability from sonic log data. provided that a mineralogical factor is taken into account. TO test further the results of the work, laboratory drilling tests were performed which closely simulated down-hole pressure conditions. Correlations of drilling results with rock hardness measurements were quite good. It was concluded that rock hardness, as measured in the laboratory or as deduced from sonic logs, could be used in relations for predicting rock drilling performance. INTRODUCTION Drillability of rocks cannot be defined in an absolute manner by a single quantity or measured by a single test. Resistance of rock to drilling depends to a large extent upon the means used for rock destruction. This complicates drillability classification of rocks for there may be as many classifications as there are methods of rock breakage without known functional relations between them. The objective of this work was to develop. in terms of rock destruction behavior, means of selecting the best drilling method for a given rock or the conditions for optimum output from a given drilling method. ANALYSIS OF ROCK DESTRUCTION TESTS Gauthier and Baron' have reviewed the many test methods which have been developed for determining the resistance of rocks to breakage. These include drilling tests, punch tests, scratch tests, resistance to shock, wear tests, etc. A standard drilling test might be to determine the time required to drill a standard depth (1/16 in.) in a rock using a bi-cone microbit (1 1/4-in. diameter) when a standard load (417 Ib) is applied at a standard speed of bit rotation (110 rpm). From the standpoint of similarity, the results of microbit drilling tests would seem to be most representative of the several methods suggested above. However, evaluation of drilling performance by this method is only qualitative and cannot be applied directly to actual drilling conditions. Punch tests basically measure rock hardness. Punches of various shapes and sizes, including small cones for Vickers' and Knoop's tests, the wedge for Epstein's test and the right circular cylinder for Schreiner's test, have been used. Results of these tests lead to a quantitative hardness classification which would seem to be related to the resistance of rock to bit-tooth penetration. Scratch tests are related to the resistance of rocks to abrasion such as would be encountered in drilling with diamonds. Either the width of the scratch obtained at a fixed load or the load required to give a scratch of a fixed width may be used to evaluate surface hardness of the rock. This should be related to the resistance of the rock to wear. The above tests, and probably many others. give relative measurements of the breakage or destruction characteristics of rocks. There is no direct relation between results of these tests and the drillability of rocks. Also, the tests each measure different quantities which have different dimensions and they do not permit direct comparison of numerical values. As one step in rectifying the above difficulties. it is proposed that the results of all test methods be expressed in terms of volume of rock destroyed per unit of work required; this is referred to as "specific disintegration". Test results may then be reported in a form which shows both a classification of rocks in regard to each method and a comparison of methods with regard to each rock. The disadvantage in using specific disintegration is the difficulty of measuring this quantity with accuracy. The volume of rock damage is difficult to measure. as is the true value of work input. Rock heterogeneity adds to the

Jan 1, 1967

By C. S. Matthews, M. Prats, R. I. Jewett, J. D. Baker

By mathematical analysis it was found that injectivity history of a uniform five-spot pattern can be calculated by rather simple formulas. These calculated injectivities were found to agree rather well with injec-tivities measured in a potentiometric analog. With this as a basis, a simple method was finally developed which allows prediction not only of rate of injection but also of rate and kind of production at the production well, for a uniform five-spot. Using this method formulas for the eflective injectivity and production behavior of a waterflooded reservoir having a wide range in permeability can be calculated by considering that the reservoir consists of several layers, each having a uniform but different permeability. Rather good agreement is shown by a comparison of the observed production history of a field in the Illinois basin and that calculated by the methods just described. INTRODUCTION The importance of being able to predict the injection rates for a water flood is well known, for upon injection rate depends the life of the flood, the size of pumping and treating facilities, and the rate of oil recovery. One method of determining rates of injection is through a pilot flood. However, it appears that even if a pilot flood is resorted to, a theoretical method for calculating injection rate will be valuable in extending field results to times after inter- ference and to locations of other five-spots. It is also important to be able to predict the production history of a flood. Such prediction must generally be done by theoretical means, since in general a small pilot flood will not furnish much quantitative information in this regard because of the distortion after oil-bank interference. Methods for predicting the behavior of five-spot water floods have been proposed by Yuster and Cal-houn' and by Hurst.? However, these methods do not consider the effect of the mobility of the different fluids in the reservoir. Other investigators3,4,5,6 have determined the effect of the water-to-oil mobility ratio on the production history by means of different experimental techniques. Most of the published work applies to homogeneous sand bodies, does not provide information for determining the injection requirements of a flood, and seldom considers the rate of build-up of the oil bank as it fills up the partially depleted reservoir.* The present work was undertaken because of the lack of predictive method which takes into account mobility ratio and the rate of buildup of oil bank resulting from the void space in a partially depleted reservoir. As water is injected into the reservoir, which contains oil, water, and gas in macroscopically homogeneous saturation, it forms several banks ahead of the injection well. In each bank or region there is assumed to be only one mobile phase—water in the water bank, oil in the oil bank and gas in the gas region. The saturation in each region and a plan view of the banks are shown in Figs. 1 and 4, respectively. FACTORS AFFECTING INJECTION AND PRODUCTION RATES Results in this report are determined as functions of the three parameters, F, M, and M, , and of a fourth parameter, r,/L** which relates the size of the well to the flood spacing. The parameter F is the displacement factor defined by Hurst in Ref. 2. It determines the rate of build-up of oil bank as it fills up the partially depleted reservoir. When gravity effects are neglected, the four parameters just given are sufficient to describe the waterflood behavior for horizontal and homogeneous reservoirs having incompressible liquids. Definition of InjectIvity The dinlensionless injectivity (or injection rate) used in this report is defined by

By P. L. De Bruyn, R. J. Charles

THE transfer of kinetic energy of translation into other forms of energy by impact is a fundamental process in most crushing and grinding operations. During and after the impact process the original source energy may be accounted for in any of the following possible forms: 1) Kinetic energy of translation of both the impacted and impacting objects. 2) Kinetic energy of vibration of the components of the impact system. 3) Potential energy as strain energy of the components of the system or in the form of residual stresses. 4) Heat generated by internal friction during plastic deformation or during damping of elastic waves. 5) New surface energy of fractured materials. At any instant during the impact process only the strain energy of the components of the system can contribute directly to the brittle fracture process. If fracture is the desired result, as in comminution, it would seem advantageous to choose or arrange the conditions of impact so that a maximum amount of the original kinetic energy could be converted to strain energy at some moment during a single impact. The present work deals with determination of these desirable conditions for a simple case of impact and application of the principles involved to general cases of impact. Experimental Method: Longitudinal impact of a rod with a fixed end was chosen as the impact system for investigation. The rod was mounted horizontally and the fixed end was formed by butting one end of the rod against a rigidly mounted steel anvil. The rod, of pyrex glass, was 10 in. long by 1 in. diam with both ends rounded to a 6 in. radius. The rounded ends permitted reproducible impacts on the free end of the rod and assured a symmetrical fixed end. Pyrex was selected as the rod material because of the marked elastic properties of such glass and the similarity of fracture between pyrex and many materials encountered in crushing and grinding operations. The frequency of natural longitudinal oscillation of the rod was 10 kc, and thus simple electronic equipment could be used for observation of strain changes occurring in the rod at this frequency. As shown in Fig. 1, impacts on the free end of the rod were obtained either by a pendulum device or by a spring-loaded gun. Relatively heavy hammers (100 to 600 g) of mild steel were used in the pendu- lum impacts, while fairly light projectiles (20 to 80 g) were fired from the spring-loaded gun. One of the main objects of the experimental work was to obtain the strain-time history of the rod as a function of the mass and kinetic energy of the impacting hammers. For this purpose a technique involving wire resistance strain gages and a recording oscilloscope was employed. Five gages were applied at equidistant sections along the rod, and by means of a switching arrangement the strain-time history at any section, and for any impact, could be obtained in the form of an oscillograph with a time base. The equation relating strain and voltage change across a strain gage through which a constant current is flowing is as follows: e = ?v/iRF [1] ? = strain, ?v = voltage change, i = gage current, R = gage resistance, and F = gage factor (from manufacturer's data — SRA type, Baldwin Lima Corp.). With the above equation an oscillograph depicting voltage change vs time on a single trace can be converted directly to a strain-time diagram if a calibration of the vertical response on the oscilloscope screen for specific voltage inputs is available. In the present case the calibration was obtained by photographing precisely known audio frequency voltages on the same oscillograph as that on which a voltage-time trace from a strain gage had been made. Synchronization of the beginning of the single trace with the beginning of the impact was accomplished by permitting contact of the impacting objects to close an electrical circuit from which a voltage pulse, sufficient to initiate the trace, was obtained. The struck end of the rod was lightly silvered for purposes of electrical conduction so that it would form one of the electrical contacts. Markers every 100 micro-seconds on the traces served for a time base calibration. Determinations of the kinetic energies of translation prior to impact were made in the case of the pendulum hammers by measuring the height of fall of the hammer and in the case of the projectiles by measuring the exit velocity from the gun barrel by means of an electrical circuit employing light sources, slits, and phototubes.' During the experimental work it became evident that the time of contact between the impacting object and the rod was an important variable in the impact process. Measurements of the times of contact were made, therefore, for every impact for which a strain-time record was obtained. The time of contact was determined by permitting the impacting components, when in contact, to act as a closed switch and discharge a condenser at relatively constant voltage. The discharge was observed and photographed with a time base on the oscilloscope screen.

Jan 1, 1957

By D. Turnbull, J. C. Fisher

ACCORDING to the "reaction-path" modell,2 of martensite nucleation, the shear angle of the embryonic martensite plate must be treated as a variable, and included in any calculation of nucleus critical size. Also, as can be deduced from this model, the interfacial free energy between austenite and martensite does not reach its final value until the shear is completed. It is zero for zero shear angle. However, in order to account for the kinetics of the martensite transformation, some sort of interfacial energy barrier appears to be necessary even with the reaction-path model, for otherwise the volume and the energy of formation of the critical size nucleus both collapse to zero.3 Cohen independently suggested that surface energy could be incorporated into the reaction-path model, with the overall free energy of a martensite embryo being a function of its volume and shear angle.' It is possible to estimate the energy associated with the formation of a critical-size martensite nucleus starting with the reaction-path model and including a surface free-energy barrier. As the dependence of interfacial free energy upon shear angle is unknown, a simple type of dependence will be assumed, with the belief that the true dependence would not lead to appreciably different results. Consider the work required to form a lenticular martensite plate with radius r, thickness t, and shear angle 8. There are three contributions; one being the interfacial free energy, one being the free energy change in the martensite plate, and one being the free energy increase in the surrounding austenite. The interfacial free energy u is assumed to depend upon the shear angle 0 according to the relationship s=s0(?/?0)n [1] where 8, is the equilibrium shear angle and n is an exponent that may lie in the range 0 n 2. The work required to form the interfaces of a martensite plate then is W. = 2pr² s0(?/?0)n [2] The free energy change per unit volume of martensite is composed of two parts, one the ordinary volume free energy ?f1. which is negative, and the other the elastic strain energy G?m²/2, where G is the shear modulus and 7, the shear strain relative to the martensite structure. This expression for the strain energy is valid only when the shear strain ym, is sufficiently small that the martensite is within its linear elastic range. There is no doubt that ym, lies beyond the linear elastic range for embryos that are considerably subcritical. However, for critical nuclei it will be shown that ym, is 1.5 pct or less, within the linear elastic range of martensite. For embryos of nearly critical size, then, the strain energy of the martensite is correctly given by G?m²/2. The shear strain in the martensite is ym, = 8, — 8, and the work required to form the strained martensite is Wm --= (pr²t/2) [?fv + G(?O - ?)²/2] [3] The free energy change in the austenite is entirely that due to elastic distortion. The elastic strain is not uniformly distributed in the austenite, being large near the martensite plate and small elsewhere. Approximately, however, the energy corresponds to a uniform shear strain ya= (?t/2)/r [4] throughout the volume 4pr³/3 surrounding the plate. The work required to strain the surrounding austenite then is Wa = (4pr³/3) (G?a²/2) = (G?²/6) prt² [51 For simplicity, the same shear modulus G is assumed for each structure. The total free energy for forming a plate then is W = W3 + Wm + Wa. = 2pr² s0 (?/p?0)n + (pr²t/2) [?fr+G(?0-?)²/2] + (G?²6) prt2 [6] This expression is correct for nuclei and for embryos of nearly critical size, where, as will be shown, the strain energy in the martensite is correctly given by the expression G (? — ?)². Having W as a function of r, t, and 8, as in Eq. 6, there is a saddle-point where W has a stationary value, W subsequently decreasing indefinitely as the nucleus volume increases along the reaction path. The stationary value of W is the energy of the critical nucleus. The critical nucleus has radius, thickness, and shear angle such that ?W/?r - awlat: = ?W/?p? = 0. Performing these differentiations and calculating the critical nucleus energy, W* = [8192p(G?/6)²;s/27 ?fv4] [7] where a= (?/?0)3n+1[l +G(8"-8)'/2af.]' [7a] and where 8 is to be determined from the equation (1 + 3n/4) + G8(6O - (9)/[Af. +G(6>o-6>)72] = 0 [8] For ?f, near —200 cal per mol or —10" ergs per cc, and 8, near 1/6, as for iron-base alloys, Eq. 8 gives ?0 - ? ~ - (4 + 3n) ?f1./4G0O [9] as the difference between the equilibrium shear angle and the actual shear angle for a critical nu-

Jan 1, 1954

By T. A. Wilson, S. L. Hoyt

The plastic deformation of slender single crystals of zinc has been described in some detail in the paper by Mark, Polanyi and Schmid,' which has become a classic, and also by one of the present authors in a somewhat shorter account. 2 The study of single-crystal zinc is termed classical because zinc single crystals offer, perhaps, the best material yet available for the study of atomic behavior during deformation and the effect known as "strengthening" in metals. A considerable amount of additional work has also been done on single-crystal zinc, but as it is not closely related to the present paper it will not be considered. Throughout all the former work, the mechanism of plastic deformation first described by Mark, Polanyi and Schmid has been assumed to hold. This may be said to offer the strongest confirmation of its correctness. Even so, the picture of the process has never been as completely portrayed as is desirable. The first object of the present paper is to describe work that has been done in this field, and which is even yet being carried on, in the hope that a more complete picture may be obtained. Mathewson and Phillips3 have recently described a new mechanism of the deformation of zinc based on their study of large rectangular crystals. One of their conclusions was that deformation produced twinning with a rotation of some of the basal planes into positions 94" removed from their original position; a position almost the same as that of the prismatic planes before twinning. A second conclusion was that fracture occurred along these basal planes in their new position, and, therefore that fractures previously regarded as prismatic were in reality basal. Such findings are of great significance and they raise a question as to the generality of such behavior. Professor Mathewson's opinion is that even the slender cylindrical single crystals behave in the same manner as his large rectangular crystals when strained by simple tension.

By Winston A. Wong, John J. Jonas

Commercial purity aluminum was deformed by extrusion over the temperature range 320° to 616°C and the strain rate range 0.1 to 10 per sec. Flow stresses and strain rates were calculated from the experimenLa1 ram pressures and speeds. The stress-strain rate-lemperature relationship in extrusion was found to be similar to that in creep. Extrusion, torsion, compression, and creep data extending over ten orders of magnitude of strain rate and over two orders of magnitude of stress were correlated by a single creep equation. It was concluded that hot-working is a thermally activated process, in which the rate-controlling mechanism is either the climb of edge dislocations or [he motion of jogged screw dislocations. The microstructural changes observed during extrusion were consistent with the proposed deformation mechanisms. ALTHOUGH great progress has been made in understanding the technology of extrusion, very little is known about the actual deformation mechanisms operating during flow. Previous accounts describing extrusion have indicated that the relationship between ram speed (V), pressure (P), and temperature (T) can be given as follows:1 V = apb and P = A' exp(-AT). In these equations, a and b are constants which depend on temperature, A' is a constant which depends on ram speed, and A is a "coefficient" with a different value for each metal. Although these equations have fairly wide application, they do not contribute much to a fundamental understanding of the deformation. Furthermore, extrusion has not hitherto been considered as a thermally activated rate process. This lacuna is surprising because hot-working is similar to high-temperature creep in several respects. There is, in fact, a fair body of experimental evidence suggesting that the material response under hot-working conditions is similar to that occurring under creep conditions, in spite of the many orders of magnitude difference in strain rate.2"4 Since creep has been extensively analyzed in terms of dislocation mechanisms, the comparison of hot-working to creep is useful, for it can suggest the possible deformation mechanisms operating during hot-working. In this paper, the hot extrusion of aluminum will be examined from the point of view of thermally activated deformation mechanisms, such as operate during creep. EXPERIMENTAL PROCEDURE The experimental procedure consisted of extruding commercial purity aluminum* over a range of ram velocities and temperatures at constant die reduction by the direct method. Details of the experimental equipment have been published elsewhere.5 Extrusion was carried out at each of the following billet temperatures: 320°, 376°, 445°, 490°, 555°, and 616°C at the following constant ram speeds: 0.002, 0.008, 0.02, 0.1, and 0.2 in. per sec.* All results were obtained using a square-shouldered die with an extrusion ratio of 40:1, giving a reduction in area of 97.5 pct. The ram force was the dependent variable, and was measured by means of strain gages on the ram and was plotted as a function of ram travel. The sequence of events before making an extrusion was duplicated before each run so as to minimize as much as possible variations in experimental conditions. For example, after the equipment had been assembled, the billet was allowed to heat up to temperature inside the insulated container. Once the container attained the desired temperature, a period of 1/2 hr was allowed to elapse before the extrusion was made. This time was found to be required to allow the billet to reach a steady-state temperature, as determined from previous tests. When all was ready, extrusion was carried out without interruption; that is, the billet was upset and extruded in one operation. EXPERIMENTAL RESULTS AND DISCUSSION The two usual experimental approaches for investigating high-temperature deformation exhibit an important common feature. In the first approach, which corresponds to creep, a constant stress (or load) is applied to the material at constant temperature and the resultant strain is recorded against time. After an initial transient stage, a state of constant strain rate exists (secondary creep), in which a steady-state condition is established which is sensitive to variation in either applied stress or temperature. In the second approach, a constant strain rate is applied and the resultant flow stress is recorded. This corresponds to the situation in hot torsion or hot compression, where it is observed that, for a constant test temperature, there is an initial rise in stress to a steady value which is maintained up to very high strains. In tests of this type, a steady-state region is also established in which the stress is sensitive to variation in either the strain rate or the temperature.3,4,6-16 In both types of tests, therefore, a steady-state region is established after an initial transient. In the case of hot-working this region may be called steady-state hot-working, and it is analogous to steady-state creep with which it has many common features. Stress Dependence of the strain Rate in Extrusion. In order to assess the stress dependence of the strain rate under extrusion conditions, and to compare it to that of creep, as well as of hot torsion and hot compression, the extrusion data were analyzed according to power, exponential and hyperbolic sine creep equations.

Jan 1, 1969

By M. Deighton, R. N. Parkins

The metals Cd, ,Wg-, Sn, TI, Zn, and Zr reach a peak hardness after a criticfir1 deformation by rolling- and then soften with fwther rolling-, thereby exhibiting wovk softening. Optical metallography on Cd, Mg, and Zn shows that work softening is accompanied by a change in grain size occurring during deformation. The creep of zinc from -1l° to +60°C at stresses in the range of 7.9 to 17.3 kg per sq mm is given by € = e0 -t- Bt + Kt +at6. The third and second rate constcints are related by the equation a = K~ K6 and their stress and temperature dependence can be represented by the equations K = A, . exp - (u, - Bu)/kT. A model based upon the stress activated glide of sub-boundaries is proposed which qualitatively accounts for the metallog-raphic observations. Expressions, which are in reasonable quantitative agreement with the ex-pe~inzental observations, are derived for the creep of zinc. THE term "work softening" has been used previously by Polakowski1 and by Cottrell and stokes2 to describe phenomena where further strain of a deformed material leads to a decrease in flow stress. In both cases, however, the conditions were changed for the second straining. Here, the term "work softening" is intended to refer to a decrease in flow stress after continued straining in the same direction at the same temperature: work softening is the antithesis of "work hardening". Work softening of zinc was reported by chadwick3 and in discussion of that paper Jenkins4 indicated that cadmium also work softens. More recently work softening has been reported5 in two magnesium alloys, -99.5 pct Mg. Chadwick found that the hardness, 0.2 pct Proof Stress and the UTS of electrolytic zinc all increased with progressive cold reductions up to 30 pct and then progressively decreased with further rolling. Gay and Kelly6 used a back-reflection X-ray technique to study the effect of cold rolling zinc and found that although deformations greater than 2 to 5 pct reduction in thickness produced some recrystallized grains, deformations greater than 40 pct caused com-plete spontaneous recrystallization. At deformations greater than 60 pct the material was found to consist solely of recrystallized grains, -20 pm diam, the size of which decreased with increasing reduction and was much less than the initial grain size of the annealed material (-300 pm diam). Similar results were also reported for cadmium, tin, and lead.6 Gay, Hirsch, and Kelly' suggest that these experiments indicate recrys-tallization takes place when the dislocation density exceeds a certain value. However, no measurements of MATERIALS AND EXPERIMENTAL PROCEDURE The purity of the metals used in this work is indicated by the following figures: Zn (99.99); Cd (99.94); Mg (99.95); T1 (99.99). The zirconium was iodide crys tal bar with a probable purity of about 98 pct. The metals were obtained in the form of 0.25 in. thick strip or 0.425 in. diam rod by various fabrication methods and then annealed to ensure complete re-crystallization. Hardness-deformation curves were obtained at room temperature by rolling 4 in. thick strip under conditions which left a surface adequate for diamond pyramid hardness tests immediately after rolling. The hardness was taken as the niean of five impressions made using a 5 kg load and the time elapsing between rolling and making the last impression never exceeded 5 min. The zinc specimens for creep testing were from 3 by 3 by 4 in. cast slabs which were rolled to 0.10 in. thickness starting at 350°C and finishing cold. The resulting strip was cut into pieces 1 in. wide and annealed in batches. With suitable choices of annealing temperature between 100" arid 400°C five different grain sizes varying from 4.54 x 10' to 3.03 x l05 grains per sq cm (530 to 20 um diam) were obtained. Creep tests were done in compression using a sub-press, based on a design after Ford,8 in which the strip is compressed between dies 0.100 in. wide under conditions of plane strain. Since there is no lateral spread of the material, the area of contact between the dies and strip remains constant throughout the test and the application of a constant load, using the load maintaining device of a hydraulic testing machine, resulted in a constant stress. Covering the dies with strips of P.T.F.E. reduced frictional effects to a minimum. The creep strain was obtained by measuring the travel of the crosshead of the testing machine to a sensitivity of 0.1 pct reduction in thickness. The complete subpress assembly was contained in a steel box and for tests above the ambient this was filled with liquid paraffin and heated electrically. Temperatures below the ambient were obtained with a cooling mixture of acetone and solid carbon dioxide in the box. The liquids were stirred and the temperature of the specimen, which was controlled to ±0.5"C dur-ing a test, was measured by a thermocouple placed near the dies. Compression testing of cylindrical specimens was also carried out in the subpress using hardened flat discs separated from the test material by P.T.F.E. sheets which obviated barrelling of the specimens. Various initial strain rates were supplied by the hydraulic testing machine, and the deformation was measured by a clock dial gage resting on the cross-

Jan 1, 1970

By M. G. Corson

Until recently, the characteristics of cast copper have seldom been studied and such study as has been made has been inadequate. The prevailing idea seems to be that since pure copper is infrequently used in the cast stlate, there is no reason for trying to establish precise data regarding the properties of the metal in that condition. On the other hand, wrought copper either in the shape of sheets or wire rarely fails in service, except as a result of the action of reducing gases at the annealing temperatures, so there is little incentive to study the properties of the cast shapes —cakes, bars, ingots and billets—for the sake of tracing the causes of failures of the wrought metal to the cast stock. However, about a decade ago, wirebars of American origin often cracked badly while being hot-rolled in mills in Germany. This Icd to four investigations: by E. Seidl and E. Schieboldll by P. Siebe12 by 0. Bauer and G. Sachs,3 and by G. Welter.4 These authors came to the conclusion that failures in hot-rolling were due essentially to the presence of a wide zone of columnar crystals between t'he thin layer of fine crystal5 near the surfaces of the bars and the large but more nearly equiaxed grains of the central core. This macrostructural defect was explained in turn by the probable upward deviation in the temperature of the metal while it was being poured into the molds of the castling machine. More recently, cast shapes of copper were investigated by X. 1'. Allenh and by C. Blazey. Allen examined vertically cast wirebars and hori-zontally cast wedge cakes of electrolytic tough-pitch copper, but only for the distribution of densities; i.e., porosity. Blazey was interested mainly in the mechanism of the variations in electrical conductivity due to cold-work and anneal, but gave introductively an account of the composi-tion and average densities of the tough-pitch horizontally cast Wirebars used. As far as the present writer can tell, no investigation mas under-taken for the sake of presenting a picture of the distribution of mechanical characteristics in the wirebars of copper, or otherwise.

Jan 1, 1938

By M. G. Corson

Until recently, the characteristics of cast copper have seldom been studied and such study as has been made has been inadequate. The prevailing idea seems to be that since pure copper is infrequently used in the cast stlate, there is no reason for trying to establish precise data regarding the properties of the metal in that condition. On the other hand, wrought copper either in the shape of sheets or wire rarely fails in service, except as a result of the action of reducing gases at the annealing temperatures, so there is little incentive to study the properties of the cast shapes —cakes, bars, ingots and billets—for the sake of tracing the causes of failures of the wrought metal to the cast stock. However, about a decade ago, wirebars of American origin often cracked badly while being hot-rolled in mills in Germany. This Icd to four investigations: by E. Seidl and E. Schieboldll by P. Siebe12 by 0. Bauer and G. Sachs,3 and by G. Welter.4 These authors came to the conclusion that failures in hot-rolling were due essentially to the presence of a wide zone of columnar crystals between t'he thin layer of fine crystal5 near the surfaces of the bars and the large but more nearly equiaxed grains of the central core. This macrostructural defect was explained in turn by the probable upward deviation in the temperature of the metal while it was being poured into the molds of the castling machine. More recently, cast shapes of copper were investigated by X. 1'. Allenh and by C. Blazey. Allen examined vertically cast wirebars and hori-zontally cast wedge cakes of electrolytic tough-pitch copper, but only for the distribution of densities; i.e., porosity. Blazey was interested mainly in the mechanism of the variations in electrical conductivity due to cold-work and anneal, but gave introductively an account of the composi-tion and average densities of the tough-pitch horizontally cast Wirebars used. As far as the present writer can tell, no investigation mas under-taken for the sake of presenting a picture of the distribution of mechanical characteristics in the wirebars of copper, or otherwise.

Jan 1, 1938

William Metcalf, Pittsburg, Pa. (communication to the Secretary*): I am greatly pleased that some one has at last reached what I have long regarded as the only rational explanation yet given of the reasons why steel hardens. Mr. Field claims originality; and doubtless he is entitled to it, but not to priority, mhich must be granted to Prof. John W. Langley.' The difference between them is that Langley says " Tension, probably molecular," and Field says " Tension, probably atomic "; in either case the vital thing after solution is tension. Mr. Field's argument carries with it the idea of increase of density with hardness; if he mill study the facts farther he will observe that the case is just the reverse; that is, the greater the hardness the less the specific gravity; it was just this fact that led Langley to his conclusion, in mhich I have always concurred. Field agrees with Langley that the first requisite for perfect hardening is complete solution of the carbon, not combination; and all of the facts agree with this conclusion. The fact that increase of hardness causes reduction of density was first brought to my notice some 40 years ago, when Major William Wade was testing Jones & Laughlin's cold-rolled iron, and I mas his assistant. We found the well-known increase of tenacity, compressive strength, torsional resistance, and hardness. Specific-gravity tests showed that the cold-rolled iron was less dense than the hot-rolled bars. Major Wade was so surprised at this result that he gave me a lot of samples to weigh, saying that he was not satisfied with

Jan 1, 1904

By P. Douglas, G. M. Leak, B. Mills

The sinusoidal surface relaxation technique has been used to measure the surface self-diffusion coefficient of spectroscopically pure nickel over a wide temperature range under a hydrogen atmosphere. A kink in the Arrhenius plot has been observed. In the temperature range T/T 0.98 to 0.80 (T in O K and T, is the melting temperature) the average self diffusion coefficient is given by Below the temperature T/T,- 0.80a decrease in the slope of the log Ds us 1/T plot is observed. This is associated with a diffusion process characterized by a lower activation energy (-20,000 cal mole'') and smaller preexponential term (-10- sq cm sec"). A series of experiments were carried out at T/Tm = 0.61 under a hydrogen atmosphere of higher oxygen partial pressure than for the rest of the experiments. It was found that Ds was significantly depressed due to oxygen adsorption. This evidence supports the opinion that the low temperature process (activation energy -20,000 cal mole-') is unlikely to be due to oxygen adsorption. An interesting feature of the present data is that the transition temperature (T/Tm - 0.80) is a function of orientation. For a small number of crystals of measured orientation the transition temperature was observed to be higher towards the low index (100) pole. Theories of surface diffusion are briefly reviewed and it is concluded that the present reszuts are best explained by invoking a surface roughening process. GJOSTEIN has recently analyzed available surface diffusion data for a wide range of metals. He suggested that two mechanisms were operative for fcc metals, an adatom process at high temperatures and a vacancy process at low temperatures. Results for nickel can be summarized as follows. At low temperatures (T/T, - 0.3 to 0.44) under ultra high vacuum conditions, Melmed2 measured an activation energy Q of 21 kcal mole-' using field electron emission microscopy. At higher temperatures (T/T - 0.7 to 0.9) under a vacuum of 10- ' torr, Maiya and lakel measured y as 39 kcal mole-' using the multiple scratch smoothing technique. The present work was undertaken to try to find out if two distinct processes could be observed. High temperature results give Q about 47 kcal mole-': there is evidence also for a low temperature value of about 20 kcal mole-'. These measurements were all made under a hydrogen atmosphere, in the temperature range 860" to 1412°C. Concurrent with the present study Bonze1 and jostein> have also observed a break in the Arrhenius plot for the (110) surface of nickel. These measure- ments under ultrahigh vacuum conditions using the laser diffraction technique are in excellent agreement with the work reported here under hydrogen annealing conditions. THEORY The available surface relaxation techniques include single and multiple scratch smoothing and grain boundary grooving. The processes have been compared in detail by Gjostein for conditions where surface diffusion dominates6 and Mills et al? where volume diffusion dominates. In summary the relevant points are as follows. Grain boundary grooving gives an average Ds for the two surfaces adjacent to the boundary and this can, to some extent, be simplified by using symmetrical bicrystals. This technique has been used to study the effect of environment on Ds for silver and copper.'-'' Scratch techniques yield Ds values for the small orientation range exposed by the scratches (-2 deg). The multiple scratch process is preferable because the profile rapidly becomes sinusoidal and can then be interpreted theoretically in a relatively simple way. Also corrections for mass transport processes other than surface diffusion can be introduced easily. Mullins" considered a sinusoidal profile described the wavelength of the profile. After time t the profile can be described by the equation The terms A, A', C, and B which account, respectively, for contributions due to evaporation-condensation, diffusion through the gas phase, volume diffusion through the lattice, and surface diffusion are defined as: where Ds = the surface self diffusion coefficient ys = the surface energy per unit area p = the equilibrium vapor pressure over a flat surface pa = the equilibrium vapor density over a flat surface DG= the diffusion coefficient of vapor molecules in the inert gas DM = the mass transfer diffusion coefficient which for a pure cubic metal is Dv/f where Dv is the radiotracer diffusion coefficient and f is the correlation factor H = the molecular volume V = the surface density of atoms, il2'3 M = mass of an evaporating molecule

Jan 1, 1970

Jan 1, 1892