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By H. L. Miaw, A. M. Gaudin, D. W. Fuerstenau

A quantitative method for evaluating density of slime coatings has been developed and applied to formation of iron oxide slime coatings on quartz and on corundum. Slime coating density is related to flotation recovery and to properties of the electrical double layer at mineral surfaces. IN spite of considerable study, the nature of slime coatings in flotation is still not completely understood. However, phenomena that control floc-culation and dispersion of colloidal systems are now interpreted in terms of electrical double layers.",' Colloids will flocculate even though the particles carry the same charge, but when two dispersed colloids of opposite charge are mixed. flocculation ensues even more rapidly. Analogous phenomena seem responsible for slime coating on minerals in flotation systems. To shed new light on the issue it was considered desirable to devise a tool that would measure slime coatings. The usual method has been to examine photographs of presumably representative surfaces, after. an intervening washing in running water. But such an examination is non-quantitative, and the changes in chemical environment represented by the washing may have removed the slime coatings that existed during flotation. To provide the possibility for a correlation with electrical double layer phenomena, the experiments were made with quartz, corundum, and iron oxide, for which elec-trokinetic data are available.'-" Since the properties of the electrical double layers of these oxides depend on the pH of the solution, pH will be the most important variable. Furthermore, because the zero point of charge for silica, iron oxide, and alumina occurs at pH 3.7, 8, and 9.5, respectively, the relative charge on the slime and mineral can be changed over wide ranges. Because of its practical importance in quartz flotation, iron oxide powder was chosen as the slime. Also, its uniform composition, contrasting color, and ease of analysis make experimentation simple. In this investigation, correlation was sought between the effect on flotation recovery of slime addition and slime coating density. Materials and Methods Details are available in a thesis by Miaw." The quartz was selected from pure Brazilian crystalline quartz, crushed, sized (65/150 mesh) acid-cleaned, washed, and stored in conductivity water. The corundum (synthetic alumina of high purity prepared by Linde Co., Chicago) was crushed, sized (65/100 mesh) deslimed, boiled in nitric acid, washed, and stored in conductivity water. The iron oxide slime, reagent-grade ferric oxide (—400 mesh) from Allied Chemical & Dye Corp., was heated to 160°C, cooled, and stored in a vacuum desiccator. In the electron microscope the slime particles appeared to be about 0.3µ in size, but their large specific surface (87,900 cm per g, by gas-adsorption method, using krypton) suggests that the actual particles are smaller than 0.3r. Had they been perfect nonporous spheres, they would have had a diameter of 0.13µ.

Jan 1, 1959

By Kanchan K. Sen

The North Shore Connector (NSC) project will extend the Allegheny County Port Authority?s Light Rail Transit System from downtown Pittsburgh below the Allegheny River to the North Shore via twin bore tunnels. Jet grouting, diaphragm walls, and soil mixing were selected as cost-effective technically viable ground improvement and support of excavation techniques. Jet grouting was specified to provide break-out (egress) and break-in (ingress) block sections at the tunnel boring machine (TBM) launching and receiving pits. Jet grout treatment was also used adjacent to buildings with shallow foundations and below retaining walls along the tunnel alignment. A new method for measuring jet grout column diameter based on electrical resistivity was employed on the project. New equipment was introduced in the U.S for constructing soil mix temporary support of excavation using a soil-mix technique termed Cutter Soil Mixing (CSM) due to the use of two vertical cutting wheels that have evolved from diaphragm wall trench cutter technology. The system allows for continuous water tight soil mix panel construction including steel beams. This paper highlights some applications of jet grouting and various support of excavation systems (e.g. slurry walls, cement bentonite walls and CSM walls), including new innovative techniques (e.g. Cyljet and CSM) used under the constraints of an urban environment.

Jan 1, 2010

By S. J. Parry, D. M. Evans, D. L. Buchanan

The reef is a PGE-enriched sulphidic zone, stratigraphically associated with and overlapping the C1d chromitite layer, that was formed by magmatic processes at the 1e-1d subunit boundary. Two distinct patterns of PGE enrichment are related to the presence or absence of Cr2O3 oversaturation during sulphide liquation that occurred during a complex sequence of changes at this boundary

Apr 1, 1996

By Robert H. Peters

Groundfall accidents have been the leading cause of fatalities in the underground coal mining industry for many years. Statistics from the Mine Safety and Health Administration (MSHA) indicate that approximately half of the victims of these fatal accidents were in an area where no devices had been installed to support the mine's roof. This report was prepared by the U.S. Bureau of Mines to summarize the opinions of 268 coal miners, 29 rust-line supervisors, and 30 MSHA inspectors concerning why people go under unsupported roof, and how to prevent this behavior. Interviews were conducted at six minesites.

Jan 1, 1991

By J. -P. Chilès

The discrete Gaussian model is a very popular change-of-support model for estimating block grade distributions. It is designed for a stationary random function Z(x) that is regarded as the transform of a stationary random function Y(x) with Gaussian marginal. It is based on an assumption that is not fully true and thus constitutes an approximation to the exact solution. We examine the effect of this approximation on the modelling of the marginal distribution of block values of a lognormal random function. The initial discrete Gaussian model and a variant of that model are considered.

Jan 1, 2014

By K. Sugawara, Y. Hirakawa, A. Sato

The rock mass properties such as deformability and permeability are highly dependent on the existence of cracks. The Ratio of Crack Opening Dependency (RCOD) was proposed as a new index to evaluate the deformability of infinite jointed rock mass. The RCOD is defined as the ratio of total amount of crack opening and the total deformation of jointed rock mass. The theoretical relation between the RCOD and the effective compliance of jointed rock mass is discussed and confirmed through two-dimensional numerical analysis by the SC-DDM, together with the applicability to the rock engineering. Les propriétés de masse rocheuse telles que la déformabilité et la perméabilité sont très dépendantes de l'existence de fissures. Le rapport de dépendance d'ouverture des fissures a été proposé comme un nouvel index d'évaluation de la déformabilité de masse rocheuse à assemblage infini. Le rapport de dépendance d'ouverture des fissures est défini comme étant le pourcentage de quantité totale d'ouverture des fissures et de déformation totale de la masse rocheuse assemblée. Le rapport théorique entre le rapport de dépendance d'ouverture des fissures et la compliance efficace de masse rocheuse assemblée sont traités et confirmés au travers d'une analyse numérique à deux dimensions par SC-DDM en même temps que l'applicabilité à l'ingénierie des roches. Die Felsmasseneigenschaften wie Verformbarkeit und Durchlässigkeit sind hochgradig abhängig von dem Vorhandensein von Rissen. Das Verhältnis der Riss-Öffnungsabhängigkeit (RCOD) wurde als neuer Index der Verformbargkeit von infinit zerklüfteter Felsmasse vorgeschlagen. Der RCOD wird als Verhältnis der Gesamtmenge der Rissöffnungen und der Gesamtverformung der zerklüfteten Felsmasse definiert. Die theoretische Beziehung zwischen RCOD und der effektiven Verformbarkeit von zerklüfteter Felsmasse wird diskutiert und durch zweidimensionale numerische Analyse mit SC-DDM bestätigt, zusammen mit der Anwendbarkeit auf Bergbautechnik.

Jan 1, 2003

By C. A. Jeffrey

The Dirtlow Rake vein deposit, which is up to 12 m thick, contains a range of paragenetically linked replacement mineralisation styles typical of many Mississippi Valley-type deposit environments. The main ore zone lies within the solution collapse breccia domes, the more southerly of which has recently been well exposed, allowing its relationship to the associated mineral-hosting structures to be studied. The domes were largely formed during early silicification, propagated by dissolution collapse and infilled by subsequent fluorite-barite mineralisation. The location of pipes and pervasive replacement was also controlled by early silicification. Structurally controlled bow tie shears were formed as a result of fluid access at fracture-bedding plane intersections. The nature and distribution of the mineralisation styles indicate that the degree of fluid access, residence time of solutions in contact with the wallrock and susceptibility of the limestone to silicification each played a major role in dictating mineralisation

Jun 19, 1905

By R. Dekkers, J. Plessers

The feasibility of using hydrogen to obtain clean steels is investigated. High hydrogen contents are generally considered as detrimental due to the risk of flakes, bubbles and breakouts during casting. Hydrogen can nonetheless be removed by degassing of the steel. The results of industrial campaigns, where total oxygen content and hydrogen content were monitored, are presented. High resolution microscopy of inclusions and laboratory experiments on the rate of inclusion removal by CaO-Al2O3 slags at different partial hydrogen have been carried out. So far, evidence that hydrogen may influence inclusions or the steel cleanliness is not clear. Keywords: hydrogen, cleanliness, inclusions.

Jan 1, 2004

By Y. Nien Wang, Moe Amini, Heiner Sander, Max John

INTRODUCTION As the population increased along the coast route (California Route 1), and the people’s need to have guaranteed access increased, the landslides and related road closures began to have serious adverse economic impacts. Landslides were causing major long-term road closures about every 10 years on average. In 1983, ground movement at Devil’s Slide caused Highway 1 to be closed for an extended period of time which caused significant economic loss to the surrounding coastal communities. A number of options for bypassing the slide area were considered, and the Martini Creek inland bypass was selected for design. Subsequent litigation led to the creation of the Devil’s Slide Tunnel Study in 1996. The results of this study indicated that a tunnel alternative would be competitive with the inland bypass. The final decision was left to the citizens of San Mateo County, who approved the tunnel alternative in the November, 1996 election After completion of environmental studies and the processing of legal challenges, the final environmental document was finished in 2001. The preferred tunnel alternative was designated to proceed for final design and construction. PROJECT DESCRIPTION The Devil’s Slide Tunnels consists of a separated two-lane road, one lane in each direction, which passes through twin tunnels and over twin bridges and then connects with the existing non-separated, two-lane road at each end. The total length of the project is approximately 1900 meters consisting of four main project divisions, which are described below, going from south to north. 1.Operations and Maintenance Center (OMC) area, 2.Southern approach roadways to the South Portals (250 meters), including the South Rock Cut,

Jan 1, 2005

By John H. Johnson

This report covers the third and final year of work conducted under U. S. Bureau of Mines Grant G0166027, "Monitoring of Mine Air Pollutants". The report discusses work performed in three areas. These are the White Pine Mine (WPM) Experimental Unit, diesel mine-vehicle tailpipe emissions monitoring, and mine ambient air concentration data analysis. The WPM experimental unit was used to study diesel exhaust stratification in an 80 foot long dead-end heading while loading ore with a Wagner ST-5D scoop train LHD. The MTU Mine Air Monitoring Laboratory (MAML) was used to gather temperature and CO2 concentration data at 10 locations. Three different ventilation conditions were compared. The data substantiate the presence of strong buoyant forces of the hot exhaust gases which result in temperature stratification in dead-end headings. The diesel mine-vehicle tailpipe emissions monitoring study involved laboratory measurements of diesel undiluted exhaust pollutant concentrations by the portable tailpipe emissions measurement apparatus (EMA) assembled for in-mine use. The results were compared with simultaneous measurements by standard laboratory exhaust monitoring instruments. These results indicate that accurate field source quality control measurements can be obtained for CO2, CO and NO but NO2 results were low for all engine conditions. The mine ambient air concentration data analysis study included analysis of diesel pollutant concentration data in the Orchard Valley Mine air and comparison of the results with data collected earlier in the White Pine and Brushy Creek mines. The analysis included preparation of lognormal frequency distributions and calculations of C02-based concentration ratios and correlations. In the three mines compared, pollutant concentrations are distributed quite similarly, and the concentrations appear to be controlled to present standards.

Jan 1, 1979

By D. Schleiss

Reduced access to knowledgeable workers is creating challenges for operations. We are doing more 4D Operations - dirty, dull, dangerous, and distant. Personnel costs in these environments are high, and it is not always possible to get the people where you need them. Integrated Operations is a strategy to integrate people, process, and technology for faster and better decision making. Adopting an integrated operations approach can help to relocate personnel, improve collaboration, and align objectives to deliver reduced costs and improved performance. In this paper, the authors will highlight the required infrastructure to enable an Integrated Operations platform. Key decision points for enabling this technology for both Greenfield projects and existing mines will be discussed. Furthermore, the benefits and improved return on investment that result from deployment of an Integrated Operations strategy will be presented.

Jan 1, 2014

By Lorenzo Pellegrini

The respect of EPB reference pressure during TBM advance and hyperbaric activities, the complete and effective filling of the annular gap between tunnel lining extrados and the excavation section and a well organized monitoring system, to control surface settlements and ground distortion, are items of utmost importance in EPB tunnelling process. The paper describes how these concepts have been applied while excavating in the difficult underground conditions found at Sao Paulo (Brazil) during the execution of the Sao Paulo Metro Line 4-Lot 1. In this project, the annular gap has been filled by two components type, cement grouting. The back feed of the extensive monitoring campaign carried out to check the surface settlements during the excavation and hyperbaric maintenance operations will also be described in the paper.

By P M. Ashley, M Muller

Massive sulphide ZnPbCuAg deposits in the Halls Peak district of north-eastern NSW are of the submarine volcanogenic type. They occur as a number of small lenses enclosed in shale and epiclastic rocks, in association with felsic volcanics of early Permian age. The deposits crop out in steep terrain near the eastern edge of the New England plateau. Local relief of 700 m and slopes up to 50¦, coupled with an average annual rainfall of about 1000 mm has led to local severe land sliding in previously mined areas. Mining from the 1890s to the 1960s has also resulted in unconstrained drainage of heavy metal-bearing acid waters and physical dispersion of finer grained metalliferous sediments into the Chandler River. Waters emanating from the main landslide area, from underground workings and draining scattered unconfined stockpiles of massive sulphide ore have pH values of 3 to 4 and contain elevated contents of Zn, Cu, Pb, Cd and Fe. Chemical mobility of heavy metals into streams occurs under low pH conditions with Zn exhibiting the greatest dispersion. Increasing pH conditions downstream cause precipitation of Fe phases and coprecipitation of heavy metals. Physical dispersion of secondary metal-bearing minerals into the surrounding creeks results in wt% levels of Cu, Pb and Zn in the stream sediments thereby exceeding the regional background values by one to three orders of magnitude. Areas disturbed by mining are characterised by lack of vegetation, biomagnification of heavy metals into algae and lower plants, and partial recolonisation by metal-tolerant grass species (Snow Grass, Poa sieberana; Blady Grass, Lomandra longifolia). Rehabilitation measures will have to include landslide stabilisation, impervious sealing or removal of sulphidic materials, import of topsoil and revegetation by metal-tolerant, slow-growing native grass and shrub species.

Jan 1, 1995

By W. Pawlak, J. Janiak, C. Rodkiewicz, B. Ignasiak

"There is a general consensus that, in order to widen the utilization of Western Canadian coals, a major effort must be devoted to their transportation, utilization of fines, beneficiation and mining techniques. It is postulated that the concept studied extensively over the last four years at Alberta Research Council (ARC), and based on a combination of hydraulic mining, selective agglomeration with bitumen and/ or heavy oil, pipeline transportation and oil recovery from agglomerates, offers a particularly attractive solution to the problems associated with extraction, beneficiation, transportation and utilization of Western bituminous and subbituminous coals. Results of preliminary experimental work on the feasibility of pipeline agglomeration of metallurgical coal and hydraulic transportation of agglomerates are presented and discussed in the context of conventional agglomeration techniques in stirred tanks. IntroductionAlberta is endowed with enormous reserves of low-sulphur coals which could attract considerable attention of potential customers, but the remote location of this province handicaps its competitiveness on the world market. It is known that Alberta's Cretaceous, particularly metallurgical, coals differ significantly from their Carboniferous counterparts; current R&D work on indigenous coals should continue to expand in order to encourage overseas client s to use these coals more extensively.There is a genera l consensus that, in order to widen the utilization of Western coals, a major effort must be devoted to their transportation, utilization of fines, beneficiation and mining techniques."

Jan 1, 1986

By Robert E. McIvor

"The design/optimization of the pump and cyclones to maximize grinding circuit efficiency first requires a concise understanding of, and clearly defined specifications for, desired grinding circuit performance. Subsequently, the pump and cyclone performances that provide the desired grinding circuit performance can be defined. Once the performance requirements of each process unit are determined, selection of physical equipment parameters that will deliver those performances can be carried out.The Functional Performance Equation shows that there are two distinct efficiencies in closed circuit ball milling. One of these, “Circuit Classification System Efficiency” (CSE), is the fraction of “coarse” material inside the ball mill upon which grinding energy is deliberately expended, versus the remaining fraction of “fines” or finished size material inside the mill, upon which grinding energy is wasted (on over-grinding). The role of the pump and cyclones is to maximize CSE, which is the desired grinding circuit performance. The obtainable target CSE for any given circuit can be estimated, for example, by referring to a plant data base of CSE’s. Design/optimization guidelines then allow us to specify the pump and cyclone performances that will achieve the target CSE.This paper outlines the step-by-step, systematic method of pump and cyclone selection which maximizes CSE. Numerous examples of its successful application are provided.THE FUNCTIONAL PERFORMANCE EQUATIONObservation of the feed and product size distributions going into and discharging from the mill in grinding circuits with low versus high circulating load ratios initially led to the definition of “Circuit Classification System Efficiency” (or CSE, McIvor, 1988a), and subsequently the discovery of the Functional Performance Equation (McIvor, 1988b; McIvor et al, 1992). The CSE is the fraction or percentage of “coarse” (usually in reference to the plus P80) size material inside the mill, versus “fines” or product size material finer than the circuit P80. It can be readily calculated by taking the average of the percentage of said coarse material in the mill feed and mill discharge streams. As this also represents the percentage of the mill energy expended on targeted, coarse size material, it is directly proportional to overall grinding circuit efficiency and production rate. This is all clearly expressed in the Functional Performance Equation for ball milling circuits, for which the derivation has often been presented (e.g. McIvor, 2006)."

Jan 1, 2011

Why A Friction Hoist? B EFORE discussing the equipment, it would be instructive to review the factors that influenced the management of Opemiska Cop-per Mines to purchase a friction hoist rather than a conventional double drum hoist. The mine required that 250 tons per hour be hoisted from a depth of 2,100 feet. They also specified that the top speed should not exceed 1800 feet per minute. Eight ton capacity skips in balance and a maxi-mum hoisting speed of 1725 feet per minute would meet the required <Output on a duty cycle as follows: Loading time Creep away from loading pocket Accelerate (at 2.5 ft/sec2) 10 seconds 5 seconds 11.5 seconds Full speed run Decelerate (at 2.5 ft/sec2) Creep into dump Cycle time Trips per hour Tons per hour 72 seconds 11.5 seconds 5 seconds 115 seconds 31 31x8 = 248

Jan 1, 1962

This paper describes the economic study of longwall versus bord and pillar mining using all continuous miners for a colliery located at the South Coast district of New South Wales, Australia. In this district longwall mining appears to be a better economic proposition than bord and pillar. The internal rate of return on investment is found to remain approximately constant for each method irrespective of life. The economic importance of percentage extraction of coal is shown to be small for high values of minimum rates of return, becoming more significant as the minimum rate of return decreases.

Jan 1, 1980

By A. Taylor, J. Shelegey, H. Sullivan, J. Doucet

"Historically, performance at Vale’s Clarabelle Mill was measured by Mill throughput and Mill recovery. After the economic collapse in 2008, a series of reviews were performed to drive improvements in business efficiency. These identified that product quality (e.g., concentrate grade, variability in concentrate grade) had a profound impact on downstream processes and suggested that improved control of these parameters would generate the greatest value for the customer (the Copper Cliff Smelter) and the company (Vale). Consequently, a movement was initiated to transform the Mill operating philosophy to consider customer needs as paramount. Systems and strategies used to drive the transformation are described. In 2011, an unexpected furnace failure resulted in decreased capacity at the Copper Cliff Smelter. In response, a two-stage change in production strategy was developed at Clarabelle. The first stage was to modify the ore blend feeding Clarabelle so that the concentrate grade could be significantly increased with minimal impact on recovery. The second stage was a circuit modification to ensure the elevated concentrate grade could be sustained. Execution of the first stage was complete five days after the failure and the second stage was complete within 10 weeks. Steps involved in each stage are outlined and the overall benefits are presented.INTRODUCTION Clarabelle Mill is located in Copper Cliff, Ontario, Canada (approximately 350 km north of Toronto). The Mill treats copper (Cu) and nickel (Ni) sulphide ores. The primary diluents are pyrrhotite (Po) and non sulphide gangue rock (Rk). The process description of the circuits at Clarabelle is documented in the paper by Taylor, Doucet, Blanchette, Barrette & Lawson (2012) in this Proceedings and will not be repeated. The Mill treats ore containing Cu, Ni and platinum group elements (PGE’s) and produces two concentrates; a Cu concentrate and a bulk Cu/ Ni Concentrate (referred to as nickel concentrate). The Cu concentrate is sold to market while the Ni concentrate is thickened at the Mill and pumped to Vale’s smelter complex in Copper Cliff Ontario for further processing. Since commissioning in 1971, Clarabelle Mill has undergone many circuit changes to suit the changing needs and wants of our customers, both internal and external. The Mill processes ores of varying quality, based on mineralogy and size and until 2009 the Mill daily performance was primarily based on throughput. The second key performance indicator (KPI) of “good” or “bad” performance was quality of the concentrate and third; Mill metal recoveries. There were other plant level KPIs such as flotation feed grind size, slurry densities and mass flows to the separation circuit, but for the most part each day was good or bad depending on how many tons were processed through the Mill."

Jan 1, 2012

By Luciano R. G. Santos

Keywords: biosorption, cadmium, copper, biomass, spent zeolite. The majority of the industrial activities produce some kind of solid wastes. In this work two industrial residues (spent zeolite and wood sawdust) were chemically modified to increase their heavy metals sorption capacities. Manilkara longifolia (a Brazilian plant known as parajú) sawdust was first treated with NaOH and modified with different citric acid concentrations (0.6-1.2 mol/L) at 120°C, for 90 min. Infrared spectroscopy confirmed the presence of carboxylate groups in the wood structure as result of their mixing. Similarly, spent zeolites were also submitted to a chemical treatment (NaOH) to remove carbon deposited during oil cracking and to recover its sorption capacity. Batch experiments carried out at ambient temperature showed that both materials present sorption capacity for copper and cadmium comparable to weak acid ion exchange resins. A maximum of 78 mg-Cd/g and 59.7 mg-Cu/g as well as 29.9 mg-Cd/g and 14.6 mg-Cu/g were observed for the sawdust and the zeolite, respectively. The results were modeled according to the Freundlich and Langmuir equilibrium isotherms and compared with results of other studies.

Jan 1, 2005

By J. Gurland

A method of measuring the degree of contact between grains of 1 phase in multiphase alloys is derived. It is shown that the number and the areas of contacts between grains can be determined by metallographic analysis. Relations between the area of contact, the dihedral angle, and the mean free path of spherical grains are developed. It is often desirable to interpret the mechanical behavior of alloys in terms of structural features observed under the microscope. A quantitative description of microstructures of multi-phase alloys requires consideration of geometrical and topological factors such as the amount, size, and shape of grains and the continuity of the constituent phases. The number and dimensions of grains may be metallographically determined by applying the methods described by Smith and Guttman1 and by Fullman2 in their papers on the measurement of particle size and internal boundaries in opaque bodies. The present work intends to show that the same methods can be used to evaluate some of the parameters of phase continuity; namely, contiguity, number of contacts, and areas of contact of grains of 1 phase. Application of these concepts may be found in such problems as the calculation of electrical conductivity of 2-phase alloys, or the evaluation of the length of fracture path through grains of a brittle phase more or less dispersed in a matrix. I. DEFINITION The following definitions and derivations are based on 2-phase alloys, of which the units of the microstructure are grains. Contiguity is defined as the average fraction of surface area shared by 1 grain of a phase with all neighboring grains of the same phase. In a 2-phase alloy of constituents A and B, the contiguity of phase B is given by: where Cb is the contiguity of phase B aBß is the average area of contact between a grain of phase B and adjacent grains of phase B, aAB is the average area of contact between a grain of phase B and adjacent grains of phase A. The contiguity is a measure of the average degree of contact between grains of phase B in the 2-phase mixture. The ratio varies from 0 to 1 as the distribution of phase B changes from a completely dispersed to a fully agglomerated structure. Smith and Guttman1 have shown that the relative areas of 2 kinds of interfaces in a volume are directly proportional to the number of interfaces of each type intersected by a random line. The lines can be drawn on metallographically prepared surfaces as long as these are random sections through the sample. The contiguity ratio of phase B then becomes: Cb = 2NBB/NAB + 2N BB [2] where: NBB is the number of interfaces between grains of phase B intersected per unit length of random line. Nab is the number of interfaces between grains of phase B and grains of phase A intersected per unit length of random line. The factor 2 arises in Eq. [2] because each interface B-B is associated with 2 grains of B-phase, whereas the interface A-B involves only 1 grain of B-phase. The calculations of contiguity do not require any assumption as to volume fraction, particle size, or particle shape. Fullman2 gives an expression for the determination of the mean free path between particles. The mean free path PB between grains of phase A, i.e., through grains or agglomerates of phase B, may be found from the relationship: PB =2fB/NAB [3] where fB is the volume fraction of phase B. The calculation of the mean free path is independent of grain shape and grain size distribution. The calculation of the number of contacts and of contact area requires assumptions of grain shape, grain size, and contact shape. In the case of uni-

Jan 1, 1959