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By K. K. Kelley, W. W. Weller

This report contains experimentally determined heat capacity data for four crystalline sulfides -- AsS , GeS , NiS , and Ni3 S₂ -- over the temperature range from 50 ° to 298.15 ° K. The heat capacity data were used to evaluate the entropies of the sulfides at 298.15 ° K. Entropies of formation from the metals and rhombic sulfur and from the metals and diatomic sulfur gas are also included .

Jan 1, 1964

By G. L. Humphrey

Although silicon carbide has been an important manufacture refractory for many years, knowledge of its thermodynamic values has been seriously lacking. In fact, some of the very properties that make it a useful substance, particularly chemical inertness, obstruct determination of its heats of formation and reaction. This paper reports the results of new measurements of the heats of combustion and formation, low-temperature heat capacity, entropy at 298.16°K., and heat-content and entropy increments between 298° and l,800°K. Two varieties of silicon carbide were studied -the common, hexagonal (type II) and cubic. The data are combined to obtain heat and free-energy-of-formation functions, which are given in tabular form. It is shown that the cubic variety is the more stable at temperatures to at least 1,800°K but, because of the inherent difficulties and errors in the heat-of-formation determinations at 298°K, it was not found possible to specify the free-energy difference accurately. The mechanism of silicon carbide formation from silica and carbon is not known and is not ascertainable from thermodynamic data. It appears improbable, however, that it can be a single-step reaction. Some reactions involving silicon monoxide gas and metallic Silicon, as possible intermediates in silicon carbide formation, are considered and shown to be thermodynamically feasible.

Jan 1, 1952

By H. E. Criner, M. G. Driessen

Maurice Rey—The influence of cyclone diameter upon the fineness of separation is an important point which, however, cannot be discussed adequately if the injection pressure or the rate of flow are not specified. Perhaps some light can be thrown on the matter by using the formulas derived by Dahlstrom. Let us consider several geometrically similar cyclones where the apertures e and b are equal and proportional to the diameter D and which are operated with the same pressure drop. Eq 8 of Dahlstrom's paper can be written: Q Q = K D'. " or. if F is constant: Q = K D18 K is a constant of proportionality. Introducing this value of Q in eq 13 gives elimination efficiency = K D ,41 Elimination efficiency, in the terminology of Dahl-strom, means the diameter of particles, in microns, which divide equally between the underflow and the overflow. This denomination is regrettable and it would be preferable to call it diameter of separation or characteristic size or any other name connoting a size rather than an efficiency. Whatever the name used, the above equation shows a slow increase in the fineness of separation when the diameter of the cyclone decreases. For example, if a 14-in. cyclone gives a 400-mesh separation (37 microns), geometrically similar cyclones, having the same pressure drop will give separations at the sizes shown below.

Jan 1, 1951

By M. G. Driessen, H. E. Criner

Maurice Rey—The influence of cyclone diameter upon the fineness of separation is an important point which, however, cannot be discussed adequately if the injection pressure or the rate of flow are not specified. Perhaps some light can be thrown on the matter by using the formulas derived by Dahlstrom. Let us consider several geometrically similar cyclones where the apertures e and b are equal and proportional to the diameter D and which are operated with the same pressure drop. Eq 8 of Dahlstrom's paper can be written: Q Q = K D'. " or. if F is constant: Q = K D18 K is a constant of proportionality. Introducing this value of Q in eq 13 gives elimination efficiency = K D ,41 Elimination efficiency, in the terminology of Dahl-strom, means the diameter of particles, in microns, which divide equally between the underflow and the overflow. This denomination is regrettable and it would be preferable to call it diameter of separation or characteristic size or any other name connoting a size rather than an efficiency. Whatever the name used, the above equation shows a slow increase in the fineness of separation when the diameter of the cyclone decreases. For example, if a 14-in. cyclone gives a 400-mesh separation (37 microns), geometrically similar cyclones, having the same pressure drop will give separations at the sizes shown below.

Jan 1, 1951

By J. L. Goen

The Saint Joseph Hospital of Bellingham is located on a site underlain by glacial outwash. The construction of a five-story tower addition above an existing two-story wing was supported by five large trusses that impose a 1600 kips (7117 kN) column load on five pile caps in the courtyard of the hospital and on the new pile caps inside the existing MRI laboratory. The exterior columns of the trusses and the new parking garage addition were supported on conventional auger cast piles installed with conventional equipment. Helical Pulldown® micropiles were selected for use in the courtyard and the MRI laboratory because lightweight installation equipment (maximum unit weight of 7.5 kips (33.3 kN)) had to be used and it was required that no spoils be produced. The installation equipment was lifted into the courtyard by the jobsite crane. Sixty Helical Pulldown micropiles were installed for the pile caps in the courtyard. The pile caps inside the hospital were supported on 240 Helical Pulldown micropiles. Initial compression test indicated an allowable load for the micropiles to be 55 kips (244 kN). However, retest at a later date resulted in an increased allowed design load to be 85 kips (378kN) reducing the number of micropiles required by more than fifteen percent.

Jan 1, 2004

By E. G. King

Existing thermodynamic data for compounds of the rare-earth metals are few in number and often inaccurate because, in the past, it was difficult to obtain samples that were pure enough and reasonable in cost--a situation that is rapidly improving. This paper reports the results of low-temperature heat-capacity and high-temperature heat-content measurements for cerous fluoride (CeF3) and supplies the first such published data for a rare-earth fluoride. The low-temperature heat-capacity data cover the temperature range 51°-298° K. and serve to evaluate the entropy at 298.15° K. The high-temperature heat-content data cover the temperature range 298°-1,799° K., including the temperature and heat of fusion. The results are assembled for ready use in thermodynamic calculations. Cerous fluoride is one of the important intermediate compounds in the production of cerium metal.

Jan 1, 1959

By H. H. Johnson, Eric W. Johnson

A newly developed ac technique was used to measure the electrical-resistivity changes associated with both cyclic stressing and subsequent annealing of high-purity and OFHC copper. The early stage of push-pull fatigue was explored at 293° and 4.2°K, with stresses chosen for an expected fatigue life of 2 to 8 X 105 cycles. For high-purity copper, fatigue at 293°K was accompanied by an initial increase in resistivity. After about 5000 stress cycles, no further increase was observed. Annealing studies showed that the resisticity increment could be accounted for solely in terms of an increased dislocation density, to about 2 x 1010 disl pev sq cm. Fov 42°K fatigue, however, the resistivity increased continually, with no evidence of saturation, as approximately (No. of stress cycles)1/4. This is intevpreted to result from both dislocation multiplication and vacancy production; estimated vacancy concentrations are 10-4 to 10-9. The continuous resistivity increase was inhibited by interspersed annealing treatments at 293°K, which also raised the level of the stress-strain curve. These effects are attributed to annealing of vacancies into dislocation loops. In contrast, OFHC copper fatigued at 4.2°K showed saturation of electrical vesistivity after only a few hundred cycles, and it appeared that vacancies annealed out completely between 77° and 293°K. MaNY observations suggest that both dislocation multiplication and point-defect production are important aspects of fatigue deformation. An increase in dislocation density with number of stress cycles has been demonstrated or implied by several experimental techniques, including optical metallography with lithium fluoride,' electron microscopy with copper,2 thermal conductivity of Cu-Zn alloys,3 and peak-stress measurements during cycling at constant plastic strain amplitude.4,5 At low amplitudes and/or stresses saturation of fatigue hardening and dislocation density occurs early in the expected fatigue life,4-6 frequently by a few hundred cycles. The evidence for point-defect production is somewhat less extensive, but it is nonetheless persuasive. Rosenberg7 reported briefly that, for equal stresses, copper fatigued at liquid-hydrogen temperature displays an increase in electrical resistance some ten times that which accompanies unidirectional stressing. Further, the extra resistance saturates after a few hundred stress cycles, and does not anneal significantly until a temperature of about 170°K is attained.' Point-defect production during fatigue is also suggested by 1) the softening during cyclic stressing of initially strain-hardened polycrystal-line copper9, 2) the strong temperature dependence of the yield strength of fatigue-hardened mono- and polycrystalline copper,579"0 and 3) the influence of intermediate annealing upon slip-band formation in copper fatigued at 90°K.8 It is evident that characterization of the fatigued state requires a knowledge of both point-defect and dislocation densities. For this purpose electrical-resistivity measurements are useful, but they are difficult to perform because of geometric limitations. Push-pull fatigue is necessary to obtain a macroscopic ally uniform deformation over the specimen cross section; however, the specimen must then have a low slenderness ratio to avoid plastic buckling, while the standard dc resistivity technique requires a very slender specimen for

Jan 1, 1965

By G. B. Craig, H. E. Rosinger, W. J. Bratina

NUMEROUS studies have been reported on how the mechanical properties of a bcc metal are affected by interstitial solute atoms in the temperature range where appreciable diffusion occurs in finite time. Only recently, though, has work on an "interstitial-free" iron been reported, this by Leslie and sober,' on an Fe-0.15 pct Ti alloy. The data was limited to a maximum temperature of 296°K. This work presents a systematic study of the flow stress and the activation volume of a similar material as a function of plastic deformation over the temperature range 253" to 473°K. The material studied was Ferrovac E iron containing 0.01 wt pct C and 0.0002 wt pct N annealed at 870°C for 1 hr, and the same iron with an addition of 0.15 wt pct Ti annealed at 870°C for 80 hr; cooling rates being 75°C per hr. In the latter alloy depletion of interstitials in the a-iron matrix associated with the second phase formation was expected. The temperature dependence of the flow stress was measured at 6 = 3.33 x 10-5 sec-1 from 253" to 473°K as a function of the deformation in 0.01 intervals from 0.03 to 0.12 strain. Results for two strains, 0.03 and 0.09 are shown in Fig. 1. The flow stress increased and reached a maximum in the Ferrovac E iron with increasing temperature, but showed a consistent gradual decrease in the Ferrovac E-0.15 pct Ti alloy. A yield point and Luders region, observed in Ferrovac E, was absent in the Ferrovac E-0.15 pct Ti alloy. Also, the Ferrovac E exhibited a serrated stress-strain behavior in the temperature range 330" to 400°K; dynamic strain-aging characteristics were absent for the titanium alloy. The activation volume was determined over the same temperature range by the method of stress relaxation at constant strain. Results are shown in Fig. 2. At the temperatures of serrated stress-strain behavior in Ferrovac E the activation volume was found to increase toward infinity and, as the temperature rose, to decrease, to about 100 to 200 v/b3. By contrast, the activation volume for the Ferrovac E-0.15 pct Ti alloy tended to increase continuously from the initial value of approximately 300 at 300°K to more than 800 at 473°K. Above 400°K, then, the corresponding activation volume values of Ferrovac E were less than that of the Ferrovac E-0.15 pct Ti alloy. The activation volumes, Fig. 2, appear to depend on dislocation-interstitial interaction in Ferrovac E and on dislocation-dislocation interaction in Ferrovac E-0.15 pct Ti alloy. The gradual increase in the latter metal is associated with thermally activated motion of dislocation segments.' The decrease of the activation volume in Ferrovac E above 400°K is probably related to the diminishing effect of interstitials on dislocations. Here, the interstitials can be moved along with a dislocation without appreciable drag. As indicated in Fig. 1, removal of interstitials

Jan 1, 1970

By P. Niessen, S. J. Bercovici

RECENTLY Aust et al.&apos; proposed a model of non-equilibrium grain boundary segregation based on a vacancy gradient induced uphill diffusion process of solute to grain boundaries. According to their proposal, solute atoms which are attracted to vacancies would, during the cooling of a sample, migrate with vacancies toward grain boundaries (vacancy sinks) and thereby enhance the solute concentration in boundary regions. For solute atoms which are not attracted to vacancies no such boundary solute enrichment would be expected. These concepts were given experimental support by boundary and bulk mi-crohardness measurements of various thermally treated dilute zinc and lead alloys and also doped aluminum oxide. The underlying assumption in their work was that solute enrichment in boundary regions is indicated by higher microhardness values. From thermodynamic considerations1&apos;2 it appears that the solid-liquid solute distribution coefficient (K), defined as the concentration of solute in the solid to the concentration of solute in the liquid at equilibrium, indicates whether attractive or repulsive forces exist between vacancies and solute atoms. K < 1 indicates a solute-vacancy attractions, K > 1 indicates no, or a repulsive, vacancy-solute interaction. This note is to report on observations of different grain boundary etching phenomena in high purity zinc alloys. These phenomena appear to depend on whether a K < 1 or K > 1 solute is present. In experiments designed to measure directly the solute enrichment in grain boundary regions, samples of zone refined zinc with 0.1 at. pct solute additions were cooled from 380°C at a rate of 3°C per min. A surface layer of approximately 50 was then removed from the samples by chemical polishing. The samples&apos; surfaces were then protected by a chromating treatment such that in a subsequent etch only grain boundary regions were dissolved. The dissolved regions were approximately semicircular troughs, 10 µ in width. The grain boundaries were usually in the middle, i.e., at the bottom, of this trough. For zinc containing the K < 1 solutes cadmium and aluminum, the grain boundary was always indicated by a ridge as shown in Fig. 1. For pure zinc, and zinc containing the K > 1 solutes copper and gold, a groove at the bottom of the trough indicated the boundary position, Fig. 2., To test if these different grain boundary etching behaviors were possibly connected with the segregation process discussed above, the Zn-Cd alloy was again heated to 380°C and quenched into brine. After surface protection and etching it was found that this specimen no longer exhibited the grain boundary ridges but rather grain boundary grooves as shown in Fig. 2. It would appear, therefore, that the boundary ridge is a consequence of a process occurring during the slow cooling of the samples. From absorption spectrophotometric analysis it was found that for slowly cooled samples containing K < 1 solutes, the solute/zinc ratios of the material from the boundary trough were consistently considerably higher than the solute/zinc ratios of the bulk alloys. This boundary region solute enrichment was not observed in quenched samples. It is concluded therefore, that the boundary ridge shown in Fig. 1 is directly or indirectly connected with nonequilibrium solute segregation.

Jan 1, 1970

By P. W. Erickson

Development of the Twin Buttes mine entailed the largest known preproduction stripping job in the history of mining. It linked earthmovers and conveyor belts in a new approach to development of a pit that may reach, or even exceed, dimensions of 1 x 1-1/2 miles at the surface and go as deep as 1800 feet. The orebody to be stripped was covered by an average of 460 feet of alluvial gravels, which presented an initial stripping job of great magnitude. The initial pit layout and the original time schedule established early in 1965 called for the excavation and disposal of about 250,000,000 tons of alluvial overburden before the end of 1969. Allowing about a year for equipment delivery, this schedule left four years to do the job averaging about 62-1/2 million tons per year. In 1964 when The Anaconda Company undertook the development of Twin Buttes, it was recognized that special planning was necessary for the disposal of waste material and tailings. Environ- mental control was a prime consideration and is particularly sensitive in the Twin Buttes area due to the proximity to residential developments. Disposal of the 250,000,000 tons of alluvium, as well as future rock and tailing waste material, presented a problem which Anaconda engineers resolved by designing a plan to spread out much of the alluvium over an extended area, including a massive 11- 1/2 mile dike system which will impound mill tailing in three basins. The tailing will be impounded behind these-dikes to avoid wind exposure and blowing. The dikes also serve as a

Jan 1, 1974

By E. G. King

Cerium and thorium sulfides have found use as crucible materials for melting certain radioactive metals. However, thermodynamic treatment of these sulfides has been hampered by lack of experimentally derived entropy values. This Bureau of Mines report describes heat-capacity measurements between 51° and 298° K, and entropy evaluations at 298.15° K, for cerium monosulfide (CeS), cerium sesquisulfide (Ce2S3), and thorium disulfide (THS2). The entropy values, with Literature results for the heats of formation, are used to obtain free energies of formation at 298.15°K. MATERIALS The samples used in this work were supplied by Prof, Leo Brewer of the Department of Chemistry, University of California. The methods of preparation and some of the physical and chemical properties of these sulfides were given by Eastman and coworkers.3 4/ Chemical analyses, conducted in our laboratory, gave the following results:

Jan 1, 1959

By L. Xiao

Using K-oleate as a collector and alizarin red S (ARS) as a modifying agent, selective depression of dolomite from francolite was achieved in alkaline medium (pH> 9.0). Interestingly. ARS was also found to depress igneous apatite in alkaline medium in oleate flotation of apatite and calcite. Adsorption of ARS alone on dolomite was found to be higher than that on francolite. Complimentary adsorption experiments of ARS and K-oleate showed that oleate adsorption was increased in the presence of ARS on francolite but not on dolomite. K-oleate adsorbs on both francolite and dolomite and causes precipitation of calcium and magnesium oleate. Such precipitates can be pre-vented when ARS is present. The results are explained in terms of competitive adsorption for the active sites on francolite and dolomite by oleate and ARS, and their interactions with dis-solved mineral species in solution.

Jan 1, 1988

A rough simulated borehole has been developed for the installation and dynamic testing of rock bolts a the WASM Dynamic Test Facility. The rough simulated borehole is used for rock bolts that are sensitive to equipment installation technique or borehole geometry (particularly friction rock stabilisers and resin encapsulated bolts). An extensive axial test program has quantified a difference between the static and dynamic capacity (kN/m of embedment) for friction rock stabilisers once sliding starts. The 47mm split tube bolt has a 50% reduction in embedment capacity (but with significant variation) dissipating 2.7kJ/100mm of sliding per meter of embedment, and the Omega (inflatable) bolt had a 70% reduction in embedment capacity dissipating 6.2kJ/100mm of sliding per meter of embedment. The Omega bolt dynamic capacity remainder at least equivalent to the split tube bolt static capacity.

May 1, 2009

A knowledge of airway friction factor (K-factor) is necessary to designing mine ventilation systems for least cost and optimum effectiveness. The friction factor used must be accurate and reliable to estimate correctly roadway resistances and pressure sources for required flows. Though the resistance to flow offered by mine airways has been an object of study over the last half century, no accurate relation has yet been established from which the prediction of the resistance of a projected airway can be made. In Kentucky, only limited and incomplete data on local K-factors are available. Therefore, there is a need for field investigations to determine these values in-situ for existing mining conditions. The author describes a study concerning K-factor that was carried out in ten coal mines, located in eastern and western Kentucky. The results of these investigations are presented in both tabular and graphical form.

Jan 1, 1991

By Tom Westgarth

As papers are placed before you upon large gas-engines in Belgium and Germany, it was considered that some information should be given upon the same subject in Great Britain. I therefore agreed to compile these notes, which I have made very short in view of the somewhat full nature of the other papers presented to this meeting, and considering the complete nature of the many publications which have been made recently upon the subject of large gas-engines. I give below Tables I. to VI., showing the number and particulars of large gas-engines which have been built or are building by British makers, and in view of the growing size of gas-engines I have concluded that engines of less than 500 h.p. cannot now he included in the category of large gas-engines, and therefore I have not considered engines under that power. Table I.—-" Oechelhauser " Type Gas-Engines. Built or Building by William Beardmore Co., Limited, Glasgow Indicated ! Engines. Horse-Power Type. Nature of Work. Gas Used. 6 2,500 Twin cylinder. Dynamo. Producer. 1 in Single cylinder. Rolling-mill. Producer. 4 1,250 Twin cylinder. Dynamo. Producer. 2 1,250 Single cylinder. Dynamo. Producer. 4 625 Single cylinder. Dynamo. Producer. 1 625 Single cylinder. Rolling-mill. Producer. 1 625 Single cylinder. Air compressor. Producer. 2 500 Single cylinder. Air compressor. Producer. 7 500 Single cylinder. Cement-mill driving Producer. Total, 28 engines ; 32,600 indicated horse-power. * Presented at the Joint Meeting of the Iron and Steel Institute and the American Institute of Mining Engineers, London, July, 1906, and here published under a mutual agreement between the Councils of the two Institutes.

Jan 1, 1907

By M Byrne, P Newman, M Lindqvist

SomincorÆs Neves Corvo Mine, one of the largest copper producers in Europe, is currently constructing a paste backfill plant in order to replace cemented rockfill in its bench and fill stopes and possibly replace hydraulic sandfill in the drift and fill stopes. A 250 m flow loop was constructed at the mine and the flow properties of various paste blends were investigated. Cycloned tailings and total tailings were both pumped successfully as pastes and were also combined with waste rock for additional testing. The pressure losses in 102 mm and 154 mm diameter pipeline were recorded at flowrates up to 60 m3/hr and are presented at slumps from 120 mm to 250 mm. The data showed the sensitivity of paste mixtures to slight changes in consistency, confirming the need for accurate control during paste production and distribution. The flow results clearly showed the different paste behaviour between cycloned and total tailings pastes and the change in properties at low and high slumps. In addition to pressure loss data, strength testing was done on 38 mm and 82 mm diameter samples. Further strength testing is ongoing at the mine using fly ash as a supplement to cement, reducing the overall binder cost. Preliminary engineering for the underground distribution system is briefly discussed, with reference to the siting of the plant. The Neves Corvo Mine is particularly shallow and alternative methods to pumping were sought in order to ensure sufficient hydraulic head for underground distribution. The comparison of options had to take into account the capital and operating costs, the operation of the plant and the impact on the future expansion of paste fill utilisation at Neves Corvo.

Jan 1, 1998

By Maurizio Siepi, Stefano Trevisani, Pagliaccim Federico, Daniele Vanni

"Abstract: The paper describes a large innovative project completed in 2012-20123 by Trevi Group, to develop equipment capable to install ultra-deep diaphragm wall. The project highlights the capacity of SOILMEC to design and build a new hydromill able to reach an unprecedented depth of 250 m, including new devices for monitoring and correct the verticality. The entire project can take advantage of the long and solid experience matured by Trevi and Rodio (now part of Trevi Group), developing in house or, else, select the elements necessary for a high quality product in the ground.The paper describes the results of different systems used to monitor and control the verticality and the twist of panel during excavation, together with the method used to pour concrete. Finally, the results of verification coring and lab tests on concrete samples recovered at various depths are discussed. The test field has been supervised by representatives of three of the major Italian Universities, and lasts almost one year from August 2012 to June 2013.The verification holes made use of an innovative combination of directional drilling and coring, to check the quality of the plastic concrete for the full length of the panel. The data confirmed that the test panel has high quality concrete, meeting or exceeding to the prefixed requirements.With this test, super-deep cut-off walls reaching depths of 250 m have become a reality. This would change the perspectives of dam engineering both for existing dams rehabilitation and for new dams design and construction. With the execution of this test panel, the technology of milled concrete cutoffs has made a ”quantum leap”, pushing the limit of practicable dams."

Jan 1, 2014

By Halter L. Gould

Since the turn of the century there has been a marked increase in population, industrial and economic growth, and in energy requirements in the United States. During this time our energy needs have been met largely by natural gas and petroleum, but as our reserves of these materials are depleted, we are going to depend more and more on our large reserves of coal. The mining of coal for electrical power production has increased at a rapid rate during the past decade. Over half the coal produced in the United States in 1971 came from mines utilizing surface mining operations (Paone, et al, 1974). Surface mining is expected to increase as the rising cost of oil places more demand on coal for energy. About 57 percent of the coal reserves in the United States lie in the area west of the 100th meridian. About one-quarter of this can be mined by current surface methods. This would involve the disturbance of approximately 1.5 million acres (600,000 hectares). By the year 2000, projections indicate disturbance of about 200,000 acres, or 300 square miles, in the West. Mined areas receiving more than 250 mm of annual precipitation can usually be revegetated without irrigation if the spoils are properly shaped, the surface layer consists of suitable plant growth media, and proven techniques in rehabilitating disturbed rangeland are applied. Areas receiving less than 250 mm of annual rainfall or with high evapotranspiration rates pose a more difficult problem. Revegetation of these areas can probably be accomplished only with major inputs of water and good management (National Academy of Science, 1974).

Jan 1, 1978

By Louis Frost

"Dominion No. 17 Colliery, of the Dominion Coal Company, Limited, is located in the district of New Victoria, N.S., at the entrance to Sydney harbour.This Colliery was opened in 1882 to work a submarine area of the Harbour seam (see Figure 1). It was closed in 1921 and the mine, which has a make of water of approximately 250 gallons per minute, was allowed to fill.No. 18 Colliery, situated almost a mile to the east, was opened in 1938 to work the Phalen seam in this area with the intention, later, of driving a cross-measure tunnel to mine the section of the Harbour seam lying between No. 17 Colliery and the Princess Colliery of the Nova Scotia Steel and Coal Company, Limited.In 1945 it became necessary to open this area in the Harbour seam and a cross-measure tunnel was driven from the existing workings of No. 18 Colliery in the Phalen seam, which underlies the Harbour seam at a depth of 500 feet.The tunnel was started in 1946 and completed in 1948. The cost of opening this section, which contained only 6 1/2 million tons of coal, made imperative the recovery of all the available coal and precluded the maintenance of the large barriers that had been left in No. 17 Colliery for impounding the water, especially as the maintenance of these barriers would have meant the loss of 885,000 tons of coal, or 12.3 per cent of the whole tonnage available. Therefore, a study was made to determine the best means to dewater the 250 million gallons of water lying in the old No. 17 Colliery."

Jan 1, 1952

By Gerhard Bockstiegel

Kuczynski&apos;s formula has been derived for the case of nonspherical particles. TWO formulae of Kuczynski&apos;s type have been derived, one describing the increase in tensile strength, the other describing the progress of shrinkage of a powder compact. It has been strength,shown that the exponents of all three formulae each contain two magnitudes of different physical characters, viz, the geometrical factor a and the kinetic factor ß. The interrelationships between the three exponents are stated. SOME years ago Kuczynski1 experimentally showed that the radius, x, of the area of contact between very small spherical metal particles and a metallic block is related to the time of sintering, t, by the following equation x = constant tk [11 where k has the value 1/5 or 1/7. Assuming that the metal particles were perfect spheres and the metallic block was perfectly flat, he derived the foregoing equation from theoretical considerations of the process of material transport in metals, and he showed that exponent k is different for different mechanisms of transport, e.g., k = 1/2 for viscous flow (according to Frenkel2), k = 1/3 for evaporation and condensation, k = 1/5 for volume diffusion, and k = 1/7 for surface diffusion. From this Kuczynski concluded that the mechanism of transport was either volume diffusion or surface diffusion, depending on whether the value of k, as found in his experiments, was 1/5 or 1/7. Subsequently. Cabrera8 corrected Kuczynski&apos;s calculations with regard to surface diffusion, showing that the theoretical value of exponent k is 1/5 for both volume and surface diffusion. He supposed that the different experimental values of k were due to slight differences in the shape of the metal particles. An exponential relationship similar to the aforementioned was found by Okamura, Masuda, and Kikuta,4 Masuda and Kikuta, and Takasaki8 when studying the rate of shrinkage on powder compacts during sintering. The authors measured the shrinkage by means of the fraction w = Vp — V./Vp — V,,,, where V,, is the volume of the green compact, V, is the volume of the sintered compact, and V,,, is the volume of the compact in its densest state. This fraction, w, they found, is related to the time of sintering, t, by the equation w == constant tm. [21 Further, Bockstiegel, Masing, and Zapf7 observed that the tensile strength, s, of sintering iron powder compacts can also be related to the time of sintering, t, by an equation of the foregoing type, i.e., s = constant tn. [3] For exponent n the values 0.28 (S=2/7) and 0.35 ( 2/5) were obtained, and the authors pointed out that there might exist a simple interrelation between exponent n as found in their experiments and exponent k in Kuczynski&apos;s equation. The authors supposed that 2k = n, since the strength of adhesion between a metal sphere and a block (as in Kuczyn-ski&apos;s experiments) must approximately be proportional to their contact area, p. x2. Theoretical Considerations This paper is an attempt to correlate the fundamental experiments of Kuczynski&apos;s type with the results obtained with powder compacts as represented by Egs. 2 and 3. In particular, the paper is to show how the rate of sintering is influenced by the geometry of the sintering particles and by the type of material transport. As the geometry of particles conglomerating in a powder compact is very complex, some simplifying assumption has to be made, of course, in order to adapt the problem to mathematical treatment. In the following paragraph a suitable simplification is introduced, and Kuczynski&apos;s formula is derived for the case of nonsphcrical particles. Relation Between Area of Contact and Sintering Time—As the face of contact between two particles in a sintering powder compact is not necessarily a circle (as in the case of spheres sintering to a block), Kuczynski&apos;s formula is modified as follows: Let the perimeter of the face of contact be described by means of polar coordinates R, 4, as shown in Fig. la, so the area of contact, f, is determined by f= 1/2 . S112p[R(Æ) ]2 dÆ [4] Then, let the two particles be intersected by a plane perpendicular to area f. The intersection is shown in Fig. lb. According to the nomenclature in this figure, the distance, h, between the surfaces of the two particles is a function of T and Æ: h = h(r,Æ). For the particular case of spherical particles, as in Kuczynski&apos;s theory, this function becomes: h = constant r2. It shall be assumed here that in the close neighborhood of their

Jan 1, 1957