Overview

The only handbook of mathematical relations with a focus onparticulate materials processing The National Science Foundation estimates that over 35% ofmaterials-related funding is now directed toward modeling. In part, this reflects the increased knowledge and the high cost ofexperimental work. However, currently there is no organizedreference book to help the particulate materials community withsorting out various relations. This book fills that important need, providing readers with a quick-reference handbook for easyconsultation. This one-of-a-kind handbook gives readers the relevantmathematical relations needed to model behavior, generate computersimulations, analyze experiment data, and quantify physical andchemical phenomena commonly found in particulate materialsprocessing. It goes beyond the traditional barriers of only onematerial class by covering the major areas in ceramics, cementedcarbides, powder metallurgy, and particulate materials. In manycases, the governing equations are the same but the terms arematerial-specific. To rise above these differences, the authorshave assembled the basic mathematics around the following topicalstructure: Powder technology relations, such as those encountered inatomization, milling, powder production, powder characterization, mixing, particle packing, and powder testing Powder processing, such as uniaxial compaction, injectionmolding, slurry and paste shaping techniques, polymer pyrolysis, sintering, hot isostatic pressing, and forging, with accompanyingrelations associated with microstructure development andmicrostructure coarsening Finishing operations, such as surface treatments, heattreatments, microstructure analysis, material testing, dataanalysis, and structure-property relations Handbook of Mathematical Relations in Particulate MaterialsProcessing is suited for quick reference with stand-alonedefinitions, making it the perfect complement to existing resourcesused by academic researchers, corporate product and processdevelopers, and various scientists, engineers, and techniciansworking in materials processing.

Full Product Details

Author:   Randall M. German (Center for Advanced Vehicular Systems, Mississippi State University ) ,  Seong Jin Park
Publisher:   John Wiley & Sons Inc
Imprint:   Wiley-Interscience
Volume:   3
ISBN:  

9780470368725

ISBN 10:   0470368721
Pages:   350
Publication Date:   06 January 2009
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Electronic book text
Publisher's Status:   Active
Availability:   Available To Order  
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Table of Contents

PARTIAL TABLE OF CONTENTS Foreword. About the Authors. A Abnormal Grain Growth. Abrasive Weara??See Friction and Wear Testing. Acceleration of Free-settling Particles. Activated Sintering, Early-stage Shrinkage. Activation Energya??See Arrhenius Relation. Adsorptiona??See BET Specific Surface Area. Agglomerate Strength. Agglomeration Force. Agglomeration of Nanoscale Particlesa??See NanoparticleAgglomeration. Andreasen Size Distribution. B Ball Millinga??See Jar Milling. Bearing Strength. Bell Curvea??See Gaussian Distribution. Bending-beam Viscosity. Bending Test. BET Equivalent Spherical-particle Diameter. BET Specific Surface Area. Bimodal Powder Packing. Bimodal Powder Sintering. Binder Burnouta??See Polymer Pyrolysis. C Cantilever-beam Testa??See Bending-beamViscosity. Capillarity. Capillarity-induced Sinteringa??See SurfaceCurvature-Driven Mass Flow in Sintering. Capillary Pressure during Liquid-phase Sinteringa??SeeMean Capillary Pressure. Capillary Risea??See Washburn Equation. Capillary Stressa??See Laplace Equation. Case Carburization. Casson Model. Cemented-carbide Hardness. Centrifugal Atomization Droplet Size. D Darcya??s Law. Debindinga??See Polymer Pyrolysis, Solvent DebindingTime, Thermal Debinding Time, Vacuum Thermal Debinding Time,and Wicking. Debinding Master Curvea??See Master DecompositionCurve. Debinding Temperature. Debinding Timea??See Solvent Debinding Time, ThermalDebinding Time, Vacuum Thermal Debinding Time, andWicking. Debinding by Solvent Immersiona??See Solvent DebindingTime. Debinding Weight Loss. Delubricationa??See Polymer Pyrolysis. Densification. Densification in Liquid-phase Sinteringa??SeeDissolution-induced Densification. E Effective Pressure. Ejection Stressa??See Maximum Ejection Stress. Elastic Behaviora??See Hookea??s Law. Elastic deformation Neck-size Ratio. Elastic-modulus Variation with Density. Elastic-property Variation with Porosity. Electrical-conductivity Variation with Porosity. Electromigration Contributions to Spark Sintering. Elongation. Elongation Variation with Densitya??See SinteredDuctility. F Feedstock Formulation. Feedstock Viscositya??See Suspension Viscosity andViscosity Model for Infection-molding Feedstock. Feedstock Viscosity as a Function of Shear Ratea??SeeCross Model. Feedstock Yield Strengtha??See Yield Strength ofParticle-Polymer Feedstock. Fiber-fracture from Buckling. Fiber-fracture Probability. Fiber Packing Density. Ficka??s First Law. Ficka??s Second Law. Field-activated Sintering. G Gas-absorption Surface Areaa??See BET Specific SurfaceArea. Gas-atomization Cooling Rate. Gas-atomization Melt Flow Rate. Gas-atomization Particle Size. Gas-generated Final Pores. Gas Permeabilitya??See Kozeny-Carman Equation. Gate Strain Rate in Injection Molding. Gaudin-Schuhmann distribution. Gaussian Distribution. Gel-densification Model. H Hall-Petch Relation. Hardenability Factor. Hardness. Hardness Variation with Grain Size in Cemented Carbides. Heating-rate Effect in Transient Liquid-phase Sintering. Heat Transfer in Sintered Materials. Heat-transfer Rate in Modelinga??See Cooling Rate inMolding. Herring Scaling Law. Hertzian stressa??See Elastic Deformation Neck-sizeRatio. Heterodiffusiona??See Mixed-powder SinteringShrinkage. I Impregnationa??See Infiltration Pressure. Inertial-flow Equation. Infiltration Depth. Infiltration Pressure. Infiltration Rate. Inhibited Grain Growtha??See Zener Relation. Initial-stage Liquid-phase Sintering Stressa??SeeSintering Stress in Initial-stage Liquid-phaseSintering. Initial-stage Neck Growth. Initial-stage Sinteringa??See SurfaceDiffusion-Controlled Neck Growth. Initial-stage Sintering Modela??See Kuczynski Neck-growthModel. J Jar Milling. Jet Mixing Time. K Kawakita Equation. Kelvin Equation. Kelvin Modela??See Viscoelastic Model for Powder-PolymerMixtures. K-Factor. Kingery Intermediate-stage Liquid-phase SinteringModela??See Intermediatea??stage Liquid-phaseSintering Model. Kingery Model for Pressure-assisted Liquid-phaseSinteringa??See Pressure-assisted Liquid-phaseSintering. Kingery Rearrangement Shrinkage Kineticsa??SeeRearrangement Kinetics in Initial-stage Liquid-phaseSintering. Kissinger Method. Knoop Hardness. Knudsen Diffusiona??See Vapor Mean Free Path. L Laminar Flow Settlinga??See Stokesa?? Law. Laplace Equation. Laplace Numbera??See Suratman Number. Laser Sintering. Lattice Diffusiona??See Vacancy Diffusion. Lifschwiz, Slyozov, Wagner Model. Ligament Pinchinga??See Raleigh Instability. Limiting Neck Size. Limiting Size for Sedimentation Analysis. Liquid and Solid Compositions in Prealloy Particle Melting. M Macroscopic Sintering Model Constitutive Equations. Magnetic Coercivity Correlation in Cemented Carbides. Mass Flow Rate in Atomizationa??See Gas-atomization MeltFlow Rate. Master Decomposition Curve. Master Sintering Curve. Master Sintering Curve for Grain Growtha??SeeGrain-growth Master Curve. Maximum Density in Pressure-assisted Sintering. Maximum Ejection Stress. Maximum Grain Size in Sintering. Maximum Lubricant Content. N Nabarro-Herring Creep-controlled Pressure-assistedDensification. Nanoparticle Agglomeration. Nanoparticle Melting-point Depression. Nanoscale Particle-Agglomerate Spheroidization. Nanoscale Particle-size Effect on Surface Energya??SeeSurface-energy variation with Droplet Size. Neck-curvature Stress. Neck Growth Early in Liquid-phase Sintering. Neck Growth-induced Shrinkagea??See Shrinkage Relationto Neck Size. Neck Growth Limited by Grain Growth. Neck-growth Modela??See Kuczynski neck-growthModel. O Open-pore Content. Optimal Packing Particle-size Distributiona??SeeAndreasen Size Distribution. Optimal Mixer Rotational Speed. Ordered Packing. Osprey Processa??See Spray Deposition. Ostwald Ripening. Oxide Reduction. P Packing Density for Log-normal Particles. Particle Cooling in Atomizationa??See Newtonian CoolingApproximation. Particle Coordination Numbera??See Coordination Numberand Density. Particle Diffusion in Mixing. Particle Fracture in Milling. Particle Packing. Particle-shape Index. Particle Sizea??See Equivalent Spherical Diameterand Mean Particle Size. Particle-size Analysisa??See Sieve Progression. Particle size and Apparent Density. Q Quantitative-microscopy Determination of Surface Areaa??SeeSurface Area by Quantitative Microscopy. Quasi-3-dimensional Energy-governing Equation for PowderInjection Moldinga??See Energy-governing Equation forPowder Injection Molding. Quasi-3-dimensional Pressure-governing Equation for PowderInjection Modelinga??See Pressure-governing Equation inPowder Injection Molding. Quasi-3-dimensional Pressure-governing Equation for PowderInjection Molding with Slip-layer Modela??SeePressure-governing Equation in Powder Injection Molding withSlip-layer Model. Quasi-3-dimensional Pressure-governing Equation for PowderInjection Molding with Slip-velocity Modela??SeePressure-governing Equation in 2.5 Dimensions for PowderInjection Molding with Slip-velocity Model. R Radial Crush Strengtha??See Bearing Strength. Radiant Heating. Raleigh Instability. Random Packing Density. Random Packing Radial-distribution Function. Reaction-controlled Grain Growtha??See Grain-growthMaster Curve, Interfacial Reaction Control, andInterface-controlled Grain Growth. Reaction-rate Equationa??See Avrami Equation. Reactive Synthesis. Rearrangement Kinetics in Liquid-phase Sintering. Recalescence Temperature. S Saddle-surface Stressa??See Neck-curvatureStress. Scherrer Formula. Screen Sizesa??See Sieve Progression. Secondary Dendrite-Arm Spacing. Secondary Recrystallizationa??See Abnormal GrainGrowth. Second-stage Liquid-phase Sintering Modela??SeeIntermediate-stage Liquid-phase Sintering Model. Second-stage Sintering Densificationa??SeeIntermediate-stage Sintering-density Model. Second-stage Sintering Pore Eliminationa??SeeIntermediate-stage Pore Elimination. Second-stage Sintering Surface-area Reductiona??SeeIntermediate-stage Surface-area Reduction. Sedimentation Particle-size Analysisa??SeeStokesa?? Law Particle-size Analysis. T Tap Densitya??See Vibration-induced ParticlePacking. Temperature Adjustments for Equivalent Sintering. Temperature Dependencea??See Arrhenius Relation. Terminal Densitya??See Final-stage Sintering LimitedDensity. Terminal Neck Sizea??See Neck Growth Limited by GrainGrowth. Terminal Neck Size in Sinteringa??See Limiting NeckSize. Terminal Pore Sizea??See Final-stage Pore Size. Terminal Settling Velocitya??See Stokesa??Law. Terminal Sinteringa??See Trapped-gas PoreStabilization. Terminal Velocitya??See Acceleration of Free-settlingParticles. U Ultrasonic Velocity. V Vacancy Concentration Dependence on Surface Curvature. Vacancy Diffusion. Vacuum Debindinga??See Vacuum Thermal Debinding. Vacuum Distillation Rate. Vacuum Flux in Sintering. Vacuum Thermal Debinding. Vapor Mean Free Path. Vapor Pressure. Vibration-induced Particle Packing. Vickers Hardness Number. W Washburn Equation. Water-atomization Particle Size. Water Immersion Densitya??See Archimedes Density. Weber Number. Weibull Distribution. Wetting Angle. Wicking. Work Hardeninga??See Strain Hardening. Work of Sinteringa??See Master Sintering Curve. X X-ray Line Broadeninga??See Scherrer Formula. Y Yield Strength in Viscous Flowa??See BinghamViscous-flow Model. Yield Strength of Particlea??Polymer Feedstock Younga??s Equationa??See Contact Angle and WettingAngle. Younga??s Modulusa??See Elastic Modulus. Z Zener Relation. Zeta Potential. Appendix. References.

Reviews

Suited for quick reference with stand alone definitions. It is theperfect complement to existing textbooks since it will simply cut to the key relations. (Alamogordo Daily News, 16 March 2011)

Author Information

Randall M. German, PhD, is the CAVS Chair Professor ofMechanical Engineering and Director of the Center for AdvancedVehicular Systems at Mississippi State University. He holds anHonorary Doctorate from the Universidad Carlos III de Madrid inSpain, is a Fellow of APMI and ASM, holds the Tesla Medal, and islisted in various issues of Who's Who. His accomplishments comprise850 published articles, twenty-three issued patents, nineteenedited proceedings, and fourteen books, including SinteringTheory and Practice (Wiley). Seong Jin Park, PhD, is Associate Research Professor inthe Center for Advanced Vehicular Systems at Mississippi StateUniversity. He is the recipient of numerous awards and honors, including Leading Scientists of the World and OutstandingScientists Worldwide, both awarded by the InternationalBiographical Centre in 2007. Dr. Park is the author of over 190published articles and three books, holds four patents, and createdfour commercialized software programs. His areas of specializationand interest include materials processing technology, numericaltechnology, and physics.

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