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By H. Lyn Bourne

This is the fifth annual tabulation of mineral royalty information. This tabulation, like the previous editions, includes all of the earlier data. There are also 60 new entries. In addition to royalty information, some entries show the cost of purchased reserves. Two articles relative to the evaluation of minerals reserves appeared in December, 1986. R.H. Paschall (In the Aggregate, ME, p 1139) wrote a good article, although it lacked specific royalty data. However, this author takes exception to two ideas in Paschall's column. Paschall contends that the royalty rate does not affect the mineral appraisal. This present author could not disagree more. Paschall also claims the location of an industrial mineral deposit is the only serious or practical caveat in comparing royalties. Comments received here from readers helped make the list of caveats that are cited each year. The readers will decide which factors influence the mineral value for their commodities of interest. Paschall's point about the relationship of the parties who are negotiating a royalty agreement is important and very well taken. The other article, written by William Vernon (Pit and Quarry, December 1986), gives a step-by-step process on how to conduct a mineral appraisal. The article cites three reasons for an appraisal: transfer rights; collateral for a loan; and taxation. A fourth reason is to establish adequate compensation for reserves lost through condemnation. This author has appeared in several court cases where compensation for loss of mineral reserves through condemnation required a mineral appraisal. Royalty rate becomes an important factor in the appraisal process, although the Pit and Quarry article refers to that part of the valuation equation as "profitability." Both articles were well written and are recommended reading for those interested in mineral valuations. The same caveats that have appeared in previous columns relative to factors that influence the value of reserves are restated. The data in the table serve as a general reference and are not intended to present an absolute scale of reserves costs. Several factors influence the value of any mineral commodity. The factors include: • location/transportation - especially significant for most industrial minerals; • market conditions both for the commodity and the company acquiring the right to mine; • quality or grade of the deposit as it reflects the amount of processing/beneficiation necessary to produce the finished product; and • legislative restrictions and conditions for mining a given material at a given site. These and other factors will significantly influence the cost of reserves. The table shows the range of royalties and the variations in the basis of computing the fees. In a few instances, it gives the cost of acquired reserves based on purchase price and quantitative estimates of the material in place. The table lists the commodity in column 1, and the subsequent columns give: • the location by state, US geographic area, or Canadian province ; • the cost - R for royalty and P for purchased cost; • the year in which the lease or purchase agreement occurred; and • comments or footnotes for more information. The cost column requires more explanation. The units may refer to cubic yards (/cu yd), cubic feet (/cu ft), short tons (/T), or acres (/A). 1 cu yd = 0.76 M2 1cuft = 0.28m3 1 st = 0.9072 t 1 acre - 0.4047 ha or m2

Jan 7, 1987

By A. F. Colombo

Bench-scale research was undertaken to determine if adding ammonia to cyanide leaching solutions would enhance the extraction of copper from an argillaceous Michigan copper ore. Two leaching techniques, (1) rolling using a tumbling bottle and (2) aerating using a modified Buchner funnel, and variations in pulp temperature; were employed in evaluating the effect of ammonia concentration on copper extraction. Under these experimental conditions, the extraction of copper was shown to be independent of ammonia concentration and entirely dependent on cyanide concentration.

Jan 1, 1968

By M J. Nugus

The structural models developed by exploration and mining geologists are most commonly concerned with the ‘main structures’ or key constituents that pertain to the associated mineralisation. To this end, it is recognised that the geological and exploration models, which are developed, are essentially ‘fit for task’ and the scale-related variances are not always realised at an early stage. In fact, in many cases anomalous intercepts along different trends and of variable apparent continuity have often been neglected as ‘back scatter’ and not important. Recognition of the importance of subordinate structures as mineralising hosts suggests that additional opportunities exist outside the primary and main structures. History shows that opportunities are often not realised where gold is hosted in orientations not parallel to the predominant trend of the schistosity, main fault or shear zone.Another reason for the importance of subordinate structures can be understood from their roles in a percolation network. Subordinate structures can access the large fluid fluxes provided by backbone elements, but, as dangling elements, they provide greater opportunities for gold precipitation mechanisms and hence may constitute essential parts of the resource. Therefore, the role, understanding and consideration of the smaller-scale and orthogonal structures should be considered during all facets of exploration, resource development, delineation and mining.

Aug 22, 2011

By Sibin Zhang, Shengli Wu, Youhao Yin, Yuandong Pei, Zhixing Zhao, Jiangshan Shi, Zhengyun Fan

Spraying medium to achieve an energy-saving and emission reduction for iron ore sintering has been researched, such as spraying natural gas, coke oven gas, oxygen, sintering flue gas and gas from annular cooler. This paper focuses on effect of spraying steam on sintering surface on reduction of NOx and dioxin emissions in practical sintering production in Shougang Jingtang. It can be found that, with the increase of sintering bed spraying steam amount, NOx and dioxin of flue gas showed a decreasing trend. As spraying steam 1 t/h for 550 m2 sintering machine in Jingtang, NOx content decreases 2.6–9.5 mg/Nm3, and dioxin decreases 0.007–0.014 TEG ng/Nm3.

Mar 1, 2018

By J. Jolly, R. V. Wheeler

This short note on the probable character of the organic sulfur compounds in coal can do no more than indicate lines of research. We have no new experimental work to describe, nothing comparable in value with the careful studies of American coals by Powell and Parrl and Yancey and Frazer. A study of the manner in which sulfur compounds exist in British coals (and their behavior on heat treatment) is rendered increasingly necessary by the fact that the British reserves of good coking coals of reasonably low sulfur content are fast being depleted. We believe that it is essentially by a study of the modes of formation, occurrence, and decomposition of the various types of inorganic and organic sulfur compounds in coal that it will be possible, with hope of success, to attack the problem of purifying coals, otherwise eminently suitable for coking, from these objectionable ingredients. Sulfur, so far as is at present known, does not normally occur in the free state in the coal conglomerate, but is chiefly distributed, irregularly, in three forms : 1. As primary constituents of the coal conglomerate, organic in nature and probably associated with those molecular complexes that have resulted from the degradation of the proteins of the plant tissues responsible for the formation of the coal mass. These constituents can be classed as "organic sulfur." 2. As metallic sulfides, e.g., iron pyrites. 3. As metallic sulfates, e.g., calcium sulfate and ferrous sulfate. (The occurrence of these compounds varies with the occurrence and degree of degradation of class 2.) It is usually found that sulfur compounds of class 3, the metallic sulfates, are present in coal in small proportions only, amounting to about 1 or 1.5 per cent. of the total sulfur. The compounds in classes 1 and 2 are therefore of more importance. Class 1 alone will receive considera-

Jan 1, 1925

By N. Nakanishi, C. M. Wayman

The effect of small copper additions on the mar-tensitic transformation behavior in Au-47.5 at. pct Cd was studied by measuring electrical resistivity as a function of temperature. The transformation behavior was found to change and transformation start (M,) temperatures for both the ß to ß' and ß to ß' transformations were depressed substantially by the addition of small amounts of copper. Both M, temperatures were lowered approximately 70°C per at. pct Cu. Copper also had the effect of narrowing the transformation hysteresis region (resistivity us temperature), and for the alloy Au-47.5 Cd-1.5 Cu there was little or no hysteresis; in this alloy, the reverse transfmmation upon heating apparently occurs below the thermodynamic equilibrium temperature, To. THE ß phase in the Au-Cd system occurs at the electron/atom ratio 3/2, and is similar to other ß phases in alloys based on copper, silver, or gold. It is of the CsCl type, in which a considerable degree of long-range order persists to the melting temperature.' The phase boundaries of the ß phase are not known precisely below 300° C, but at room tem- perature the phase exists from approximately 46 to 52* at. pct Cd.2 At low temperatures, the ß phase transforms in a diffusionless (martensitic) manner. Alloys having a composition near 47.5 pct Cd transform upon slow cooling to an orthorhombic3 phase, ß', at - 60°C. Alloys having a composition near 49.0 pct Cd, transform at - 30°C into a phase, ß", which has been recently identified as trigonal.4 Alloys having compositions near 48.5 pct Cd will transform into both the 0' and 0" phases over a range of temperatures. The progress of transformations can be observed

Jan 1, 1963

By R. G. Ward

The temperature gradient in the subhearth metal or "salamandern of the iron bhst furnace results in the establishment of gradients in the concentrations of silicon, manganese, carbon, and sulfur. The temperature and compositional variations observed in three blast furnaces are analyzed according to irreversible thermodynamics and the systems appear to be close to the steady state condition. Apparent heats of transport, Q, for silicon, manganese, carbon, and sulfur are found to be respectively -17.5, -5, -2.1, and+22k cal per g mol. In conclusion the significance of thermal diffusion in extraction metallurgy is briefly discussed. INCREASING interest has been shown in recent years in the application of irreversible thermodynamics to metallurgical problems. In particular studies have been made of the transport of matter in thermal gradients1-' and under chemical gradients imposed by a binary solvent However, no detailed example in extraction metallurgy has been reported although gradients are the essence of many extractive processes. The case of the distribution of elements in molten blast furnace iron under a thermal gradient is discussed here. DATA In blast furnace operation the hearth bottom is often extensively destroyed by molten metal, and the metal may penetrate perhaps 10 ft into the furnace foundations forming a "bear" or "salamander". Several hundred tons of molten metal may thus exist beneath the level of the conventional tap hole and remain relatively undisturbed for several years under a thermal gradient. This system is subject to little convective stirring because the temperature decreases from top to bottom, and mechanical stirring due to movements in the stack and to tapping operations is unlikely to penetrate far into the metal. The system may thus be regarded as static

Jan 1, 1963

By A. L. Field

WOOLSEY McA. JOHNSON, Hartford, Conn. (written discussion).¬When ;we regard the number of British thermal units running into the billions that-must be applied to metallurgical slags in the United States, we cannot but conclude that the physical chemistry of-slags is a very important subject when measured in dollars and cents. A further contemplation of the subject shows us that it has been hitherto treated in too purely a practical manner. It is needless to comment at length on the cost of these heat units and on the cost of fluxes to produce these metallurgical slags, for, it amounts to tens of millions of dollars annually. Accordingly, this research is of value to the country. But we must,all balance our results against our efforts. Therefore, while the speaker is unwilling to criticise unduly this meritorious research, lie does criticise it in the interest of the profession for the reason that it seems to him too highly theoretical. The article is much too, scientific to produce results at a minimum cost. Let us explain our meaning. It has been said that there are always two sides to a question. It may be further said that there are always three sides to a question, the two extremes and the middle ground. In any industrial research there are the highly theoretical side, the purely practical side, and the theoretico-practical side. To study a slag and be practical in the studying, there is something needed that represents in the laboratory (or in microcosm) what actually happens macrocosmically in the blast furnace. There is such a thing as the art of metallurgical research occupying the middle ground between theory and practice.

Jan 4, 1917

By Derek J. Lennon

Ground conditions in central Glasgow generally comprise loose granular deposits overlying stiffer soils. CFA piling would normally be preferred for urban sites in these ground conditions, but flighting of the superficial deposits has on occasions resulted in building damage. Over the last five years rotary bored piling with vinyl polymer support fluid has proved to be an economic alternative to bentonite slurry. Two case histories in central Glasgow are described in this paper, one for piles founding in granular soils and one for piles founding into bedrock. A comparison is made between the methods required for disposal of the liquid waste from bentonite and vinyl polymer slurries.

Jan 1, 2006

By Thomas E. Browne

The Electric Power Research Institute Energy Supply Program is developing coal supply forecasts. By coal supply forecasts I mean the future relationships between coal price and production levels. A representative supply curve is shown in Figure l. It will make the rest of my presentation clearer if at this point I give you some background about EPRI and the Energy Supply Program. EPRI is funded by the nation's electric utility industry to develop new technologies for the production and conservation of electricity. Most of the research is conducted by outside contractors. We participate in joint projects with the Department of Energy and other organizations. The Energy Supply Program is one of three "economic" programs. The other two are Energy Demand and Conservation, and Systems. The Systems Program's main function is to provide the means to integrate the output of the other two Programs. The primary function of the "economic" programs is to provide information pertaining to future energy prices, availability, requirements, etc. to the EPRI personnel planning R&D programs. A secondary role that is becoming more and more important is providing information of direct use to the electric utility industry. I should note that the results of all EPRI's contract work are available to the general public. A "Coal Supply Analysis System" is being developed for EPRI by Charles River Associates. To the extent possible it will draw upon existing work, but much additional work needs to be done in the area of coal supply economics.

Jan 1, 1977

By E. Pardo-Igúzquiza, R. A. Olea

The bootstrap is a computer-intensive resampling method for estimating the uncertainty of complex statistical models. We expand on an application of the bootstrap for inferring semivariogram parameters and their uncertainty. The model fitted to the median of the bootstrap distribution of the experimental semivariogram is proposed as an estimator of the semivariogram. The proposed application is not restricted to normal data and the estimator is resistant to outliers. Improvements are more significant for data-sets with less than 100 observations, which are those for which semivariogram model inference is the most difficult. The application is illustrated by using it to characterize a synthetic random field for which the true semivariogram type and parameters are known.

Jan 1, 2015

By N. B. Pilling, R. E. Bedworth

The corrosion of metals is one problem on which time and thought have been expended for many years. In the effort to avert the destructive action of a hostile environment, attention has been directed almost entirely to the conditions under which most metallic structures are called upon to perform, and the extensive and complicated phenomena attending the corrosive action of atmospheric agencies, acting at the ordinary atmospheric temperatures, have been studied, but there is unanimity of opinion regarding many fundamental facts. One neglected phase is the corrosive action of various gases upon metals exposed to temperatures considerably higher than the atmospheric range, and more especially the attack of atmospheric oxygen upon exposed metallic surfaces. That the problem is difficult is connoted by the practical dominance of industrial electric heating by alloys of one type (nickel-chromium). Proprietary interest may account, in part, for the paucity of information available upon even the most general factors determining the behavior of metals and alloys when exposed to such exacting conditions. The present paper gives some conclusions reached as the result of experimental work, extending over several years, on the mechanism and contributory factors of the high-temperature oxidation of a number of simple unalloyed metals; it is free from experimental detail and proof. High-temperature metallic oxidation may be considered as a phase of metallic corrosion. The scheme outlined below, in which corrosive agent and environment are the principal criteria, is one way of analyzing the several groups of corrosion phenomena. Erosion.—Disintegrating or destructive action by physical causes. Corrosion.—Disintegrating or destructive action by chemical causes. Low-temperature Corrosion.—Solid participating phases essentially immobile: (a) Gaseous agent; (b) liquid agent: action electrolytic and action non-electrolytic. High-temperature Corrosion.—Solid participating phases possess diffusive mobility: (a) Liquid agent; (b) gaseous agent: reducing gases, oxidizing gases. (1) Water; (2) miscellaneous elemental and combined oxygen.

Jan 1, 1923

By George Smith

ChillaQoe is situated in latitude 17" S., about 138 miles from the port of Cairns, with which it is now connected by rail. A township has been established on the banks of Chillagoe creek, a perennial stream of irregular volume crossing the field almost at rightrangles, nearly midway between the mining-camps of Calcifer and Mungana, which have been formed at the southeastern and western extremes of the field respectively. This situation was selected because of the water-supply and its proximity to the site most suitable for the erection of reductionworks. By its central position it commands the whole of the mines. The altitude above sea-level is about 1200 ft., whereas that of Calcifer and Mungana is 1400 ft.—a difference sufficient to account for a materially higher temperature at Chillagoe. The surrounding limestone bluffis add by radiation to the heat, and, at the same time, prevent the cool breezes from passing freely through the town; consequently, the temper* ture, which is high throughout the year, and especially so during the summer months, is here ge~ierally very oppressive also. The general trend of the field is southeast and northwest, and its length about 18 miles, with an average width of 5 miles; the approximate area is thus 90 sq. miles. The surrounding mineral-district is, however, much more extensive, and numerous other mines, sprcad over wide areas and producing a variety of minerals, exist in the same or parallel belts of mineralized country, of which Chillagoe proper covers but a very small portion. Immense bluffs of limestone, wollastonite and conglomerate, rising in places to nearly 300 ft., and so~netimes nearly a quarter-mile across, give the field a very picturesque and interesting appearance. The limestone has been classified as Devo-

Jan 1, 1904

By H. F. Bishop, F. A. Brandt, W. S. Pellini

M. S. Fisher and D. R. F. West (Imperial College of Science and Technology, London, England)—It may be of value to compare certain features of the results recorded in this very interesting paper with those of an investigation11 involving determinations of temperature gradients and rates of solidification of steel blocks of 3 in. sq section, cast horizontally in sand molds, some of which contained chills. Castings in plain carbon steels containing up to 0.8 pct C were made and, throughout this range of compositions, both inverse-rate and direct cooling curves, obtained from thermocouples placed within the mold cavity, showed a major arrest, the temperature of which was taken as the "effective liquidus" for the particular steel in question, solidifying under the conditions of the investigation. At the completion of the arrest, the curves showed a comparatively rapid de- crease in temperature. Some of the steels investigated lay within the peritectic region, and a second arrest at 1485°C was detected. In Fig. 15, which shows the effective liquidus temperatures, the limit of the 8 + liquid field has been placed at approximately 0.5 pct C. In inverse-rate curves corresponding to the thermal center of each casting, there was always a discontinuity, viz: an abrupt change of slope, at a temperature about 10 to 20°C below the "liquidus arrest," after which there seemed to be no significant irregularity in the rate of cooling. Curves corresponding to other positions in the casting generally showed some irregularities below the main arrest, probably as a result of heat flow from the solidifying interior. Even the reproducible discontinuity in the curves for the central positions appeared to have no theoretical or practical significance, though it probably corresponded to a stage in the solidification process at which only a relatively small amount of interdendritic liquid remained. Its temperature, rela-

Jan 1, 1953

By R. E. Bedworth, N. B. Pilling

The corrosion of metals is one problem on which time and thought have been expended for many years. In the effort to avert the destructive action of a hostile environment, attention has been directed almost entirely to the conditions under which most metallic structures are called upon to perform, and the extensive and complicated phenomena attending the corrosive action of atmospheric agencies, acting at the ordinary atmospheric temperatures, have been studied, but there is unanimity of opinion regarding many fundamental facts. One neglected phase is the corrosive action of various gases upon metals exposed to temperatures considerably higher than the atmospheric range, and more especially the attack of atmospheric oxygen upon exposed metallic surfaces. That the problem is difficult is connoted by the practical dominance of industrial electric heating by alloys of one type (nickel-chromium). Proprietary interest may account, in part, for the paucity of information available upon even the most general factors determining the behavior of metals and alloys when exposed to such exacting conditions. The present paper gives some conclusions reached as the result of experimental work, extending over several years, on the mechanism and contributory factors of the high-temperature oxidation of a number of simple unalloyed metals; it is free from experimental detail and proof. High-temperature metallic oxidation may be considered as a phase of metallic corrosion. The scheme outlined below, in which corrosive agent and environment are the principal criteria, is one way of analyzing the several groups of corrosion phenomena. Erosion.—Disintegrating or destructive action by physical causes. Corrosion.—Disintegrating or destructive action by chemical causes. Low-temperature Corrosion.—Solid participating phases essentially immobile: (a) Gaseous agent; (b) liquid agent: action electrolytic and action non-electrolytic. High-temperature Corrosion.—Solid participating phases possess diffusive mobility: (a) Liquid agent; (b) gaseous agent: reducing gases, oxidizing gases. (1) Water; (2) miscellaneous elemental and combined oxygen.

Jan 1, 1923

By Lawrence A. Garfield

From the bottom of a shallow fissure the near-naked man-animal hacked out a hand-sized chunk of the red rock-like material which, when beaten between other rocks, could be drawn out to the thinness of a flint edge. Unlike flint, however, it did not shatter when, as the point for a spear or arrow, it went wide of its mark and fell amongst the rocks or tree branches. For this reason and others, the red rock- like material was specially sought and much time was spent in trying to break it from the real-rock in which it grew. Only infrequently was a chunk broken free and in this area many hours had been spent to win but a few fragments. What luck then, to remove so large a piece where before nothing but real-rock dust formed whenever the stone hammer hit. Why did this happen? Did yesterday's food-fire, burning on top the red rock, loosen its hold on the real-rock and cause it to break free when struck with the stone hammer? It is not a matter of recorded history that the first heat assisted extraction of native copper from country rock occurred under the circumstances or in the manner related but it is known that crude mining operations using these techniques were conducted by primitive man. In this way the first mineral production may have been achieved and the original example of rapid excavation unknowingly given to the world. Rapid excavation is not a method of removing rock or ore from an insitu condition nor does the term refer to a type of equipment which is specifically employed in mining and underground construction. It is, rather, the nomenclature currently popular in industry-primarily in underground construction- relating to a comparative rate of performance.

Jan 1, 1971

By Z Lianbi, Z Yibin, Z Youhong, P Bin

Without adequate soil available, it is difficult to rehabilitate a large area of acid mine waste dump with sustainable plant communities, which has a strong potential acid generation. In the present project, paste tailings capping method has been put forward to reconstruct plant ecosystem on acid mine waste rock dump. This rehabilitation method uses paste tailings as capillary break and plant growth media. The tailings used contained 26.3 per cent of particles of less than 20 ¦m which satisfy the requirement of grain of paste tailings preparation. The tailings are not acid- producing materials. In addition to Cu, total contents of Zn, Pb, Cr, Cd, As and Ni in tailings are lower than those in local soil. Paste tailings concentration 70 per cent ~ 72 per cent was prepared by concentrating ten per cent tailings by using polypropylenecrylic sodium as flocculation. The potential pollution risks are low by using paste tailings as capillary break layer. Plants directly grown in the tailings did not particularly accumulate Cu, Zn, Pb, Cr, Cd, As, Ni in roots, stem and leaves, which were 0.01 ~ 1.6 times of those grown in soil.CITATION:Yibin, Z, Lianbi, Z, Bin, P and Youhong, Z, 2012. Study on paste tailings capping ecology reclamation on acid mine waste rock dump, in Proceedings Life-of-Mine 2012 , pp 243-246 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Jul 10, 2012

By Leonel Lopez

Throughout Mexican history, mining has been an important, traditional activity. Before the "Discovery of America," native miners worked a variety of deposits throughout the country, including Mixtec gold and gem mines in Oaxaca State and Aztec gold, silver and copper from mines in Michoacán. The 500th anniversary of Mining in Mexico after the "Discovery of America" was initiated by the Mexican mining sector on April 15, 1991. As early as 1548, when the Guanajuato mining district was discovered, Mexico had become a leading world producer of precious metals. Since then, Mexican mineral production has developed in cycles, responding to changing technological, economic and political conditions. During the 20th century, Mexican mine output reached its peak in the decades of the 1930s and 1940s, when it was producing about 40% of the world's silver, 15% of its lead, 10% of its zinc, 4% of its copper and 3.5% of its gold. In 1990, by way of contrast, these percentages of world output stood at 13.5% for silver, 4.7% for lead, 4.1% for zinc, 3.2% for copper, and 0.43% for gold. The lowest production levels were recorded during the 1960s and 1970s, when Mexicanization of the industry and increasing state controls weakened mineral economics to a point that mineral exploration budgets were sharply reduced or eliminated, along with the industry's future. Only the noble old mining districts continued to supply production, with occasional eruptions of "bonanzas" and new extensions in established mining districts.

Jan 1, 1994

By H Benzer, N A. Aydogan

It is well known that the high pressure grinding rolls (HPGR) can only be operated efficiently under choke feeding conditions in which a material bed is built up between the rollers to ensure interparticle breakage. By increasing the fines amount in the material bed up to a specific level with the recycling load, a uniform material bed is created and higher pressure gradient along the roller width is obtained which results in compact flakes including more fines. Extensive test work has been carried out with an industrial HPGR unit grinding cement clinker in a cement plant in Turkey. During the test work the recycling load of the circuit was changed to achieve different ratios to the fresh feed rate in order to identify the effect of the recycling load on the circuit performance. Six different tests were performed with the circuit at steady state. For each test, samples were collected from HPGR fresh feed and discharge, and total feed, then the particle size distributions of the samples were determined and mass balances around the circuit were calculated. The conclusion was that the reduction ratio of the HPGR increased with increase in recycling load. The flake densities showed the same trend with more compacted flakes being produced for higher recycling loads.

Jan 1, 2009

By A. C. D. Chaklader, Ashok K. Kakar

The basic density equation originally dericed ' to predict the increase in density of a compact of spherical particles with the progressive deformation at the points of contact has been further modified to include the yield strength of the material. This has been done by assuming that the contact areas grow to stable sizes under a fixed stress which is equal to three times the yield strength. The final equation has the form: where Do and D me the initial and final bulk densities of the compact, u is the applied pressure, and Y is the yield strength of the material. This equation was tested with the data obtained on spheres of lead, K-Monel, and sapphire. The calculated yield strength t~alues for lead and sapphire are within the range of values reported in the literature. A few of the earliest hot pressing models proposed to explain the mechanism by Murray, Livey, and williams2 and then by McClelland3 are based on a plastic flow mechanism. However, more recent investigations suggest that the overall densification process is a combination of several mechanisms, such as particle rearrangement, fragmentation, plastic flow, and stress-enhanced diffusional creep. While fragmentation and particle rearrangement are considered to be responsible for the densification in the early stages,"475 it has been concluded that the final stages of hot pressing are controlled by stress-enhanced diffusional creep.516 The manner in which the densification takes place, i.e., by fragmentation, particle rearrangement, plastic flow, or stress-enhanced diffusional creep, would depend upon the type of material, the temperature, and the stress level used during the hot-pressing experiments. Metal compacts can be expected to have a much greater contribution from plastic flow than ceramic oxides. Also, plastic flow would be a significant contributing factor to densification at high temperatures and high stresses. Most of these works, directed towards elucidation of densification mechanism, have dealt with kinetics of the process. The results of most of the authors vary from one another and they have proposed either new empirical or semiempirical equations to fit their data. The densification rate was found to vary with the type of the powder, shape and size of the powder, initial packing density of the compact, and a few other factors such as rate of heating, pressure, and so forth. Beyond the initial stages, the densification process has been considered to be as time-dependent flow, controlled by a diffusional process, e.g., Nabarro-Herring creep. Palm our, Bradley, and johnson' have attempted to use modified creep rate equations to interpret the data of densification under hot-pressing conditions. Beyond the initial stages, however, the densification would be controlled by a process depending upon the temperature, pressure, and size of the powders. It is the authors' belief that such densification cannot be exclusively controlled by a single process and so attempts should be made to study some observable phenomenon like microstructure, yield strength, and so forth. The emphasis of this work has been toward studying the densification problem from a more fundamental point of view. Some of the principal variables, like initial packing density, mode of packing, and size of the powders, have been controlled to a great extent. The total strain produced on pressure application (instantaneous) in such a case can be considered to be due to plastic and elastic deformation. The elastic component of the strain can be determined by decreasing the load to the initial value. The strain remaining then can be correlated with the contact areas produced by deformation and the corresponding applied load. In a previous paper,' the possible deformation behavior of spheres in a compact has been theoretically analyzed and experimentally tested. The change in contact area radius a relative to the particle radius R was related to the bulk density and the bulk strain for simple and systematic modes of packing. Tt was found that a density equation relating the above parameters can be represented by: where D and Do are the bulk densities of the compact at any value of a/R and a/R = 0, respectively. This basic equation should hold for any material as it was derived from geometrical considerations alone. An attempt has been made in this work to include the yield strength in the above density equation, so that a knowledge of the properties of any material can be used in predicting the densification behavior during the hot-pressing process. THEORETICAL CONSIDERATTONS The deformation of two spheres in contact under a static load can be compared to the deformation occurring between a hard spherical indentor and the flat face of a softer metal. Tt has been shown theoretically by both ~encky~ and lshlinskyg and experimentally by ~abor" that, for a material incapable of appreciable work hardening, the mean pressure required to produce plastic yielding (for deformation occurring between flat face and a hemispherical indentor) is approximately equal to three times the elastic limit, Y, of the material (in tension or compression experiments). Tabor has further observed that the same relationship is valid in the case of work-hardening materials, if the elastic limit at the edge of the indenta-

Jan 1, 1969