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By Arthur C. McFarlan

There are two distinct coal fields in Kentucky-the Eastern field constituting a part of the Appalachian coal region and the Western field constituting the southern part of the Eastern Interior region. The outcrop pattern of the State is dominated by the Cincinnati arch. Coal-bearing Pennsylvanian strata occupy a low structural position on either flank, preserved thereby from erosion, which in the past has removed these same beds, though a much thinner succession, from the crest of the arch. General geological relationships are shown in figures 1 and 2. On April 13, 1750, Dr. Thomas Walker discovered the first coal recorded in Kentucky. He entered the State through Cumberland Gap (Cave Gap) and found coal a few miles north.

Jan 1, 1944

By Kenneth N. Han

The effect of anions such as sulfate, chloride, and nitrate on the solubility of rare earth element-bearing phosphates and fluorocarbonates has been examined using relevant thermodynamic data. The study has found that these anions have significant influences on the overall dissolution of rare earth elements (REEs) from various sources in the aqueous media. The thermodynamic calculations in this study have indicated that the speciation of REEs with the anions tends to increase the overall solubility of the REE-bearing minerals. However, in some cases, strong precipitation of REEs with some of these anions causes an adverse effect on the solubility of these elements. It has been found that sulfate ion has the most pronounced effect on the solubility compared to nitrate and chloride, in which the latter two acids exhibited almost identical results. The calculated results have indicated that REE-oxide (hydrated) is the easiest compound to dissolve, followed by carbonate, phosphate, fluoride, sulfate, fluoro-carbonate, and oxalate in that order.

By W. -S. Hwang, R. A. Stoehr, P. Ingerslev

"The flow of molten metal entering complex two-dimensional foundry molds has been modeled using the Simplified Marker and Cell (SMAC) and Solution Algorithm (SOLA) techniques. The molds were for a series of four and three-spoke wheel designs. The computer calculations were compared to physical experiments in which molten cast iron was poured into C02-bonded sand molds. The metal was photographed with a high speed motion picture camera focused through a Pyrex glass window on one face of the mold. To get good agreement between the calculations and the experiments, it was necessary to accurately represent the velocity through the ingate. This was calculated by application of the Bernoulli equation to flow through the feed system. Some difficulties were experienced with mathematical instability, expecially in the three-spoke design with a narrow ingate. This was overcome by using 100% upwind differencing, and over relaxation parameter near 1.0 (i.e. no over relaxation), and variable mesh spacing.IntroductionModeling the flow of molten metal entering molds has the potential for making significant contributions to the design of feed systems. It will supply information to the computer-aided-design systems of the future that will enable the designer to optimize the placement of gates, dimensioning of passages, and designation of casting speeds. Such design criteria have generally been based on application of energy balance (Bernoulli equation) principles to flow in the sprues, runners, and gates. Indeed, this is the easiest way to determine the proper dimensions to give a suitable filling time for a casting of a given size. A number of computer programs, including one by some of the present authors, have integrated such calculations into CAD systems. l Modeling the flow of metal inside the mold cavity requires other techniques that will handle free-surface transient flow. Stoehr and Hwang reported on the application of the Marker-and-Cell (MAC) technique to mold filling problems at the previous conference in this series at Hennicker, N.H. in 1983. 2 Although considerable progress has been made since that time in improving the accuracy, stability, and convenience of these techniques, the shapes to which they were applied remained limited. Also, physical verification of the results of the calculations was limited to water models.The work to be reported in this paper was undertaken with two objectives: (1) to apply these techniques to more complex and realistic shapes, and (2) to verify the results by comparison with flow patterns observed in molten metal poured into actual sand molds."

Jan 1, 1986

By Jorge Cárdenas Miranda, Hector Espinoza

Currently in open pit mining in Peru with double bench, it is a challenge to optimize fragmentation in the drill rows near to the slopes to ensure the performance in the loading and haulage operation along with the process in the plant. That is why the present paper addresses a previously unanalyzed variable on the effect of the discontinuity plane on the fragmentation results. From the numerical mathematical models applied through algorithms in advanced computational tools such as Elfen, it was quantified the improvement in fragmentation results as P80 through a correct pre-split plane both in its extension as well as in its width. The first results show an improvement of 30% in the P80 and ensuring the quality of the walls without damage to the matrix of the final wall. The basis developed in this paper is based on the concept of wave reflection in the free face zones where greater efforts are presented for fragmentation, a similar theory is presented in the variation of initiation sequences that seek a greater area of reflective planes in the form of "V". Cases were evaluated with a percentage of compliance of the pre-split planes from 0 to 100% evaluating the impact on the results and correlated with field information explaining the behavior and validating the benefit. From the quantification of the benefits, this work opens the possibility of focusing resources on optimizing the pre-split process to achieve an improvement in the fragmentation results, giving a greater tool in the decision to optimize the blasting process.

Feb 6, 2023

"Qatar, crude petroleum, production, annualdata MY 1949-51Quality mine, Ark., coal, carbonizing properties TP 667washabilty study RI 496N. Dak., lignite, grindabilty as function ofmoisture, tests, results RI 5167"

Jan 1, 1960

A unity of viewpoint emerged from the workshop. The concept that transmission is via characteristic modes was a common theme in many of the presentations. Also, the confusion an the meaning of monofilar and bifilar to describe these dominant modes was cleared up. But, there was still a healthy divergence of opinion on what constitutes an optimum system. It was generally agreed that further analytical and experimental work is definitely needed. In particular, it was stressed that independent measurements of the constitutive properties of the electromagnetic environment are needed. Also, there was considerable concern that laboratory measurements of rock samples could lead to misleading results for the effective conductivities. Also, there was a general recognition that over simplified propagation theory should not be used to interpret field data. From a theoratical and practical point of view, it was realized that mode coupling plays a vital role in the transmission channel. One must not only understand which and how many propagation modes are excited by the transmitting antenna, but the conversion of energy from one mode type to another must be accounted for. This conversion can either be done intentionally (by fixed mode convertors) or non intentionally (by random wall roughness). In fact, mode conversion can be quite complicated when various propagation paths exist such as when insulated cables, leaky feeders, grounded rails, coal seams, etc. all convey portions of the electromagnetic energy. However, this state of affairs should be regared as an. opportunity for extended communication coverage in mines rather than a limitation of a desig. procedure based on preconceived notions of the dominant propagation mechanism.

Jan 1, 1978

By M. R. Khalesi, S. Bellec, C. Bazin, D. Hodouin

This paper proposes a classification model to predict the split coefficient of gold ore particles as a function of the particle size and gold content. The model is calibrated and validated using data obtained from the sampling of an industrial grinding circuit. Model calibration is based on a complete simulation of the circuit and involves parameters related to the gold grain distribution in the ore as well as a grinding and liberation model. Since cyanide is added into the studied grinding circuit, assumptions related to gold dissolution in the mills are made to allow simulation results which reflect industrial behaviour patterns.

Jan 1, 2011

By F. H. (Sam) Froes, C. Suryanarayana, K. C. Russell, C. M. Ward-Close

"Far from equilibrium synthesis allows development of novel crystal structures and microstructures, leading to achievement of enhanced physical and mechanical properties. A number of ""far from equilibrium"" techniques are reviewed with emphasis on the amount of departure from equilibrium. The ability of two such techniques, mechanical alloying (MAl, and physical vapor deposition (PVD) to develop novel structures are discussed in detail. For the MA process emphasis is placed on intermetallic compound compositions. Solubility extension, beyond rapid solidification (RS) levels, is found in terminal compositions but not for the intermetallics. Nanostructure-sized grains (< 100nm) form which can be retained after ""low temperature"" compaction. On continued milling in many cases the nanometer-sized grains transform to an amorphous structure. Ordering is destroyed by MA, except in those intermetallics with large negative enthalpies of formation. For the PVD process, a review of application to terminal light alloy compositions is presented. This includes a new high-temperature aluminum alloy, layered materials with nanometer spacing, corrosion-resistant magnesium alloys and low-density titanium compositions. IntroductionTo enhance the mechanical property combinations of advanced structural materials innovations in process/synthesis are required [1-6]. In this paper the capability of various ""far from equilibrium"" synthesis techniques [7,8] to produce novel constitutional and microstructural effects, and hence potentially enhanced physical and mechanical properties, in advanced materials is presented. The application of two such methods, mechanical alloying (MA) and physical vapor deposition (PVD) is discussed in detail. For the MA process emphasis is on intermetallic compositions with consideration given to solid solubility extension, microstructural refinement, amorphization, and formation of intermetallic compounds. For the PVD process application to terminal light alloy compositions is discussed."

Jan 1, 1994

By I Govender, T L. Moodley

Tumbling mills are grossly inefficient, using only 5 per cent of the total energy supplied for actual breakage. A significant proportion of this inefficiency is unavoidable owing to geometric limitations; rotating drum systems are prone to exhibiting certain regions (energy barriers) that resist particle entry thereby restricting the transfer of energy. Though such systems are inherently inefficient, improved modelling schemes may lead to slightly enhanced efficiency through better microscale predictions of key breakage drivers (stress, force). Central to achieving such incremental advances is the development of a universally accepted rheology for dense granular flows. Armed with a better understanding of these macro-scale ingredients, classical process modelling offers an efficient, spreadsheet friendly framework for recovering the spatial distributions of the comminution drivers. At this real-time level of process control, it should be possible to tune comminution operations towards more energy efficient configurations – the ultimate goal of this research. The present work employs validated DEM data to recover the full continuum field which will ultimately serve as a basis for calibrating process model outputs based on different rheological hypotheses. Such a continuumbased approach captures tensor properties like the shear stress and strain rate – both of which are necessary to developing a dense granular rheology. Moreover, DEM captures this data at the momentum transfer timescale of 10-6 s – no other measurement technique is capable of this level of spatial and temporal resolution. Importantly, the confidence in this DEM data is strengthened because it has been validated at the continuum scale using Positron Emission Particle Tracking (PEPT) kinematic measurements. Validated DEM data is derived from batch experiments conducted within a 300 mm ID laboratory drum using three and five millimetre glass beads at 60 and 75 percent critical speed; such mill speeds are typically encountered in the tumbling mill industry. Dimensional analysis is conducted using critical rheological parameters (shear rate, shear stress, granular temperature etc), which are key to not only developing a granular rheology but ultimately will be used to tune our mechanistic models.

Aug 24, 2022

By J W. Dong, Y M. Li, J L. Tian, Z H. Jiang

Electroslag remelting is widely used to produce various special steels, mainly because of its ability to provide high cleanliness and excellent homogeneity of ingot. Undoubtedly an optimal slag plays a key role in removing inclusions and enhancing the mechanical properties of a specific special steel. In order to improve the metallurgical performance of the slag in electroslag refining of die steel, a variety of slags have already been developed using traditional trial-and-error methods. Nonetheless, these slags may not be inherently optimal for the specific requirements of actual die steel refining processes. In this work, we have designed a CaF2-CaO-Al2O3-SiO2-MgO quinary slag system using genetic algorithms method aiming to remove the existing large size inclusions (D and Ds type) in high quality die steel. The comprehensive effects of five components (CaF2, CaO, Al2O3, SiO2 and MgO) were studied based on existing fundamental theory. The slag composition was screened considering the parameters such as melting point, electrical conductivity, calcium ion concentration, and appropriate viscosity etc. Furthermore, the candidate optimal slag was applied in the industrial production of die steel by electroslag remelting method. The detection results indicate that majority large inclusions (D and Ds type) have been successfully removed, showing significant advantage to traditional slags. This result has demonstrated the genetic method to be efficient and reliable. In addition, depending on the personalised demand of other steel and alloys, this method allows for the adjustment of the screening frameworks and processes to develop the candidate optimal slags. This method has not been reported previously in the field of electroslag composition design, and compared with the traditional trial-and-error method, the new method will save a lot of time and experimental costs.

Jun 19, 2024

By A Hall, D Kratochvil, P Littlejohn

Economic recovery of gold from complex gold ores, including poly-metallic deposits, is impacted by the presence of cyanide-soluble base metals. These base metals can create both a metallurgical challenge plus waste handling and disposal challenges. Base metals such as Cu and Zn compete for the cyanide reagent and often increase the total cyanide consumption to the point of making precious metals recovery uneconomic. In addition, the accumulation of base metals in cyanide solutions represent a challenge for cyanide detoxification and waste water treatment as these metals report to waste sludge. Such sludge requires safe handling and disposal, with possible long-term liabilities.Base metal interference can be removed with sulfidisation-acidification-recycling-thickening (SART) process technology. SART liberates the base metal from the cyanide complex and precipitates the metal as an insoluble sulfide product that can be recovered as a commercial grade concentrate. With the base metal precipitated, the cyanide can be regenerated as free cyanide and recycled to the gold extraction circuit.BioteQ completed laboratory testing for two projects, one employing cyanide leaching of copper-gold sulfide flotation concentrate and one employing a Merrill Crowe process, to determine the effectiveness of SART to remove and recover Cu and Zn in high-grade sulfide concentrates and to reduce the impact of cyanide-soluble metals on gold recovery and cyanide consumption. This paper will provide an overview of the testing methodology and results along with a review of the potential for SART to be applied to complex gold ores with poly-metallic deposits to improve project economics, operability and waste management.CITATION:Littlejohn, P, Kratochvil, D and Hall, A, 2013. Sulfidisation-acidification-recycling-thickening (SART) for complex gold ores, in Proceedings World Gold 2013 , pp 149-156 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Sep 26, 2013

By Lloyd Williams

1. This investigation shows that the Sewanee bed is the only coal bed being mined in Sequatchie County. Other coal beds are present, but as they do not contain known recoverable reserves, estimates of reserves were made only for the Sewanee bed. 2. Known measured and indicated reserves in the Sewanee bed, based on a minimum thickness of 14 inches and on 1,800 short tons per acre-foot of coal in place, are estimated to be 76 million short tons as of January 1, 1953. Of this total 62 million short tons represent coal 28 inches and more thick. Areas in the bed were omitted from the estimate because available data relative to the bed characteristics were insufficient to permit making an estimate conforming with the definitions of measured and indicated coal adopted for this study. Should future drilling or development prove reserves in these areas, such reserves should be added to the total estimated reserves determined by this investigation.

Jan 1, 1955

By A. W. Deurbrouck

This report describes the preparation characteristics of the significant coalbeds from which samples could be obtained in Webster County, W. Va. In 1964, approximately 825,000 tons of coal was produced in the county, of which 732,000 tons was mechanically cleaned in three preparation plants. The Sewell coal bed accounted for 94 percent of the coal produced. Twelve samples were collected from five coalbeds. Four of the samples would require upgrading to meet metallurgical requirements; two others of just over 8.0 percent ash would require some upgrading. In general the coalbed samples collected in the county were of medium-sulfur and medium-to low-ash content as received or after removal of the sink 1.58-specific-gravity material.

Jan 1, 1966

By H. R. Shell, Robert C. Johnson, Wilbur H. Warwick

Alpha silicon nitride fibers , Si3N4 , were successfully grown in graphite crucibles by a new method utilizing silicates and silicon ( S in equations below) as sources of silicon and using carbon , aluminum , and silicon as reducing agents (R in equations below ) . The basic reaction mechanism is believed to be generally as follows : 1,300 - 1,500 ° C S + R + N₂ SiO + RO + N₂ › 3Si0 + R + 2N₂ _1,300 - 1,500° C 3RO + Si¸N • ( 1 ) ( 2 ) A build - up of coatings on the solid raw- material particles hindered the evolution of silicon or silicon monoxide vapor and thereby slowed down further formation of silicon nitride fibers . Free oxygen in the crucible caused the formation of amorphous silicon dioxide ( SiO2 ) fibers . This problem was solved by passing , entering , and exiting gases through layers of lump graphite inside the reaction vessel . The silicon nitride fibers grew best around 1,400 ° C. Nitrogen flow rates from 4 to 6 liters per minute were adequate . The fiber widths were generally only a few microns whereas their lengths sometimes reached one - quarter inch or more . Chemical and X- ray analyses indicated that bulk fiber samples were usually 80 to 90 percent Si3N4 . The fibers had good oxidation resistance to about 1,260 ° C. Thermal shock resistance was excellent . Electrical resistance was determined .

Jan 1, 1964

By G. Plenge, M. Brittan

"Plant design parameters for gold extraction, leach residence time and cyanide consumption are generally determined from standard bench-scale bottle roll or agitation leach tests. The application of laboratory data to process design has essentially evolved from the testing of oxide or low cyanide-consuming ores. Such scale-up factors may not be appropriate for ores that deplete cyanide and oxygen since this interferes with gold extraction kinetics. High cyanide-consuming ores also exacerbate the differences between the conditions applicable to small batch tests and large continuous operations. Testing a reactive high-sulfide South American ore deposit necessitated the re-evaluation of conventional bench-scale cyanidation procedures. Pulp density can be a major factor affecting the results for plant design purposes and should be treated as a test work variable. As with high clay-bearing ore, where pulp viscosity can hinder mass transfer, minimizing the influence of test equipment on gold extraction kinetics may require low pulp densities. This introduces interpretative complexity since cyanide consumption changes as a function of pulp density. Activated carbon also consumes cyanide, so its effect has to be accounted for in the case of carbon-in-leach (CIL) or carbon-in-pulp (CIP) plant flowsheets. Since cyanide is an expensive reagent, often a major component of plant operating costs, it is important that the scale-up of cyanide consumption from laboratory to plant be representative. The traditional method of reporting cyanide consumption in bench-scale testing is questioned since it takes credit for residual free cyanide in leach tails. The projected plant consumption may be better estimated by using the total cyanide addition in a laboratory test. We propose a test work protocol that categorizes the cyanide consumption into its components but requires more extensive testing to generate design data. The ultimate validation of scale-up factors used by project engineers requires rigorous bench-scale versus commercial plant comparative data. Such data are not readily available.IntroductionMajor factors in the design of a gold processing plant are gold recovery, leach residence time and cyanide consumption. These parameters are important determinants of project revenue and costs and, thereby, potentially of project financial viability. Estimates of the associated design criteria for a commercial plant are normally generated from laboratory cyanidation, carbon-in-leach (CIL) or carbon-in-pulp (CIP) tests using standard procedures (Angove, 2005). The key question is whether the standard laboratory test work procedures developed historically for low reagent consuming ores are appropriate for ores that are highcyanide and oxygen consumers.The present paper examines test procedural factors that can influence the test work results and, therefore, their interpretation for design scale-up purposes. The study refers in particular to a high cyanide-consuming sulfide ore. The ore was being tested to develop scoping level engineering design criteria for a proposed project in South America."

Jan 1, 2015

By K. R. P. Petersen

Paper written on project work carried out in partial fulfilment of M.Sc. Eng.(Metallurgical Engineering) degree The interrelationship between mineral liberation and leaching behaviour of a gold ore is ill defined, mainly due to the complexity of both leaching and mineral liberation. This study presents a neural network approach to modelling the liberation of gold bearing ores. A complete mineralogical analysis of unmilled and milled ores, including gold deportment and gangue content are used as inputs to a self-organizing neural net, which generates order preserving topological maps. The arrangement and shapes of these clusters are coupled to unmilled free gold data to predict gold liberation in milled ores (absolute error: 8.1%). Moreover, the self-organizing maps were diagnostic of the quality of data used, indicating that the relationship between particle size and gangue material content requires further investigation.

Jan 1, 2003

By Andrew Palangio, Blessing Taiwo

Understanding rock mass structural features is essential for optimizing blast design, highwall control, and evaluating post-blast performance in both surface and underground mining operations. This paper presents a comprehensive methodology utilizing image-based structural mapping to accurately characterize geological discontinuities including joints, faults, and lineations captured from both terrestrial and aerial imagery at varying scales. Key structural parameters such as joint orientation, spacing, and apparent in-situ block size are extracted to understand rock mass classification and enhance blast design inputs with greater geotechnical precision. The study introduces a significant enhancement to the existing discontinuity assessment algorithm by integrating a deep learning-assisted detection process. This improvement enables more accurate, quantitative and consistent identification of pre-existing cracks and surface features across complex bench free faces. The enhanced system facilitates better evaluation of how structural features influence blast fragmentation, energy distribution, and slope stability. A case study from a limestone quarry illustrates the use of a derived comminution factor based on the relationship between joint-controlled pre-blast block sizes and post-blast fragmentation to evaluate blast performance and optimize future design strategies. The results highlight the value of structural analysis in reducing overbreak, minimizing underbreak, and improving fragmentation predictability. This paper emphasizes the importance of integrating structural assessments into the blasting workflow to enable a more data-driven, geotechnically informed, and performance-optimized approach to modern blast design and evaluation.

Jan 26, 2026

By Xi Zhang

A technique for fabricating free-standing, high-aspect-ratio porous and pillar-type Ni structures has been developed using wet Si processing. A wafer of (100) Si was initially etched in HF solution to form deep pores with micron-sized diameter. The aspect ratio can exceed 200. By introducing the as-etched Si into a defined aqueous Ni2+ solution, Ni deposits grew rapidly onto the sidewalls and replaced the Si. Long-time immersion allows the Si sidewalls to be completely converted and thus form a metallic Ni structure with high-aspect-ratio pores. It is known that close-packed submicron Si pillars can be formed by oxidizing and subsequent etching of the macropore sidewalls. Treated in the same Ni solution, high-aspect-ratio Ni pillars were correspondingly emerged by replicating the original pillar-type Si structure.

Jan 1, 2006

By Immo H. Redeker

Introduction In October of 1961 Texas Gulf Sulphur Company contacted the Asheville Minerals Research Laboratory, of the North Carolina State University, and requested assistance in the development of a phosphate ore body in Beaufort County. The main: objectives of the work at Asheville were defined as follows. The Laboratory should try to determine on the basis of drill core samples, submitted by Texas Gulf Sulphur Company, the highest grade of phosphate concentrate that could be obtained with high recoveries from North Carolina ore, the thickness of the ore body that could be treated economically in one section, and the quantity of concentrate that could be obtained per acre. The results should be compared with data obtained from the treatment of Florida ores. It was important to use mineral preparation methods during the initial laboratory work that could be verified later by continuous pilot plant operation and could be scaled-up for a commercial plant. The writer was in charge of the project at the Asheville Minerals Research Laboratory and participated in the development of one of North Carolina&apos;s greatest mineral resources from the first drill core examination to the production of the first poundage and tonnage quantities of flotation concentrates. The Lee Creek phosphate mine and mill was put in operation in early 1966 and can produce three million tons of phosphate concentrate a year. Sulfuric- acid, and phosphoric acid plant, diamonium phosphate plant and triple super phosphate plants came on stream in 1967; at that time they were the world&apos;s largest. Now that a phosphate industry has been established in the State, it]

Jan 1, 1971

By William C. Harrigan, William D. Nix

Dynamic measurements of Young&apos;s modulus have been made for poly crystalline Ni-W alloys from room temperature to 800°C. The alloys studied range in composition from pure nickel to Ni-10 at. pct W. The results indicate that Young&apos;s modulus decreases linearly with temperature above the Curie temperature. The rate of change of Young&apos;s Modulus with temperature mas found to range from 104 psi per "C for pure nickel to 0.82 x 104 psi per °C for Mi-10 pct W. At all temperatures the elastic modulus decreases with increcrsing tungsten content up to 1 at. pct W, and increases as the tungsten content is increased above that level. Young&apos;s modulus decreases slightly as the carbon content is increased from 0.002 to 0.09 wt pct C THE knowledge of the elastic modulus of metals and alloys is important for a number of reasons. The first and most obvious reason comes from the need to predict elastic deflections under given loading conditions. A second and somewhat more subtle reason comes from the fact that the elastic properties of an alloy must be known before a proper account of the mechanisms of plastic deformation can be made. This is especially true for high-temperature creep of crystalline solids. Sherby and his coworkers have shown that the high-temperature steady-state creep rates of crystalline solids are inversely related to the elastic modulus1,2 and that the temperature dependence of the elastic modulus must be taken into account if reliable determinations of the activation energy for creep are to be made. In addition, measurements of the elastic constants of solid solutions are needed to allow one to assess the modulus interaction contribution to solid-solution Strengthening.3-5 Pelloux and Grant6 have demonstrated that substantial solid-solution strengthening at room temperature and elevated temperatures occurs when refractory metal solute atoms are added to nickel. While the high-temperature elastic properties of pure nickel have been measured by a number of authors,7-10 the elastic properties of nickel-based refractory metal alloys have not been determined. The purpose of this paper is to report on measurements of Young&apos;s modulus of polycrystalline Ni-W alloys at elevated temperatures. It is expected that these measurements will be valuable to studies of the mechanical properties of nickel-based refractory metal solid solutions. I) EXPERIMENTAL Young&apos;s moduli of polycrystalline samples were determined by a dynamic method in order to reduce high- temperature anelastic and plastic relaxations. The samples were forced in transverse free-free vibration; that is, both ends of the sample were unrestrained and the vibration was transverse to the long axis. The fundamental resonant frequency was determined by the Forster method.11 The analysis of this type of vibration which was formulated by Rayleigh,12 Timo-chenko,13 and pickett,14 and reviewed by Fine," leads where fn is the resonant frequency of the nth mode, r is the radius of the circular cross section. L is the specimen length, ßn is 1.5056 for free-free vibration in the fundamental mode of vibration, 6 is the mass density, and E is Young&apos;s modulus in the axial direction. This equation can be transformed into: E = 9.17605 x 10-6(L/D)E/Lf2 [2] where E is Young&apos;s modulus in psi, L is the length in inches, d is the diameter in inches, W is the weight in grams, and f is the resonance frequency in cps. Eq. [2] was further modified in order to take account of the thermal expansion of the samples. The resulting correct term is: where the thermal expansion coefficients for nickel and tungsten, respectively. Xw is the atom fraction of tungsten in the sample and T is the temperature in "C. The treatment of the thermal expansion coefficient as a linear function of composition seems sufficiently accurate since an error of 25 pct in the expansion coefficient will result in only a 0.3 pct error in the modulus at 1000°C. A) Apparatus. The equipment for this investigation has been described by Lytton et al.16 Several modifications of the equipment have been made. The most significant change involved replacing the detector crystal transducer with a magnetic transducer. A phonographic magnetic transducer was employed as a sensing device since the contact pressure necessary to produce a stable signal is much less than that for a crystal transducer. This magnetic transducer is also not affected by conditions of high temperature and vacuum which are present in these experiments. The vacuum was 10-5 torr at room temperature and about 5 x 10-4 torr at 900°C. This was sufficient to prevent surface contamination of the samples during the tests. The samples were heated in an elliptical furnace with a quartz lamp at one focal line and the sample at the other, as described by Lytton et a1.16 The temperature of the sample was measured by monitoring the

Jan 1, 1969