Ebook
Handbook of Mathematical Relations in Particulate Materials ProcessingISBN: 9780470368725
350 pages
January 2009

The National Science Foundation estimates that over 35% of materialsrelated funding is now directed toward modeling. In part, this reflects the increased knowledge and the high cost of experimental work. However, currently there is no organized reference book to help the particulate materials community with sorting out various relations. This book fills that important need, providing readers with a quickreference handbook for easy consultation.
This oneofakind handbook gives readers the relevant mathematical relations needed to model behavior, generate computer simulations, analyze experiment data, and quantify physical and chemical phenomena commonly found in particulate materials processing. It goes beyond the traditional barriers of only one material class by covering the major areas in ceramics, cemented carbides, powder metallurgy, and particulate materials. In many cases, the governing equations are the same but the terms are materialspecific. To rise above these differences, the authors have assembled the basic mathematics around the following topical structure:

Powder technology relations, such as those encountered in atomization, milling, powder production, powder characterization, mixing, particle packing, and powder testing

Powder processing, such as uniaxial compaction, injection molding, slurry and paste shaping techniques, polymer pyrolysis, sintering, hot isostatic pressing, and forging, with accompanying relations associated with microstructure development and microstructure coarsening

Finishing operations, such as surface treatments, heat treatments, microstructure analysis, material testing, data analysis, and structureproperty relations
Handbook of Mathematical Relations in Particulate Materials Processing is suited for quick reference with standalone definitions, making it the perfect complement to existing resources used by academic researchers, corporate product and process developers, and various scientists, engineers, and technicians working in materials processing.
Foreword.
About the Authors.
A
Abnormal Grain Growth.
Abrasive Weara??See Friction and Wear Testing.
Acceleration of Freesettling Particles.
Activated Sintering, Earlystage Shrinkage.
Activation Energya??See Arrhenius Relation.
Adsorptiona??See BET Specific Surface Area.
Agglomerate Strength.
Agglomeration Force.
Agglomeration of Nanoscale Particlesa??See Nanoparticle Agglomeration.
Andreasen Size Distribution.
B
Ball Millinga??See Jar Milling.
Bearing Strength.
Bell Curvea??See Gaussian Distribution.
Bendingbeam Viscosity.
Bending Test.
BET Equivalent Sphericalparticle Diameter.
BET Specific Surface Area.
Bimodal Powder Packing.
Bimodal Powder Sintering.
Binder Burnouta??See Polymer Pyrolysis.
C
Cantileverbeam Testa??See Bendingbeam Viscosity.
Capillarity.
Capillarityinduced Sinteringa??See Surface CurvatureDriven Mass Flow in Sintering.
Capillary Pressure during Liquidphase Sinteringa??See Mean Capillary Pressure.
Capillary Risea??See Washburn Equation.
Capillary Stressa??See Laplace Equation.
Case Carburization.
Casson Model.
Cementedcarbide Hardness.
Centrifugal Atomization Droplet Size.
D
Darcya??s Law.
Debindinga??See Polymer Pyrolysis, Solvent Debinding Time, Thermal Debinding Time, Vacuum Thermal Debinding Time, and Wicking.
Debinding Master Curvea??See Master Decomposition Curve.
Debinding Temperature.
Debinding Timea??See Solvent Debinding Time, Thermal Debinding Time, Vacuum Thermal Debinding Time, and Wicking.
Debinding by Solvent Immersiona??See Solvent Debinding Time.
Debinding Weight Loss.
Delubricationa??See Polymer Pyrolysis.
Densification.
Densification in Liquidphase Sinteringa??See Dissolutioninduced Densification.
E
Effective Pressure.
Ejection Stressa??See Maximum Ejection Stress.
Elastic Behaviora??See Hookea??s Law.
Elastic deformation Necksize Ratio.
Elasticmodulus Variation with Density.
Elasticproperty Variation with Porosity.
Electricalconductivity Variation with Porosity.
Electromigration Contributions to Spark Sintering.
Elongation.
Elongation Variation with Densitya??See Sintered Ductility.
F
Feedstock Formulation.
Feedstock Viscositya??See Suspension Viscosity and Viscosity Model for Infectionmolding Feedstock.
Feedstock Viscosity as a Function of Shear Ratea??See Cross Model.
Feedstock Yield Strengtha??See Yield Strength of ParticlePolymer Feedstock.
Fiberfracture from Buckling.
Fiberfracture Probability.
Fiber Packing Density.
Ficka??s First Law.
Ficka??s Second Law.
Fieldactivated Sintering.
G
Gasabsorption Surface Areaa??See BET Specific Surface Area.
Gasatomization Cooling Rate.
Gasatomization Melt Flow Rate.
Gasatomization Particle Size.
Gasgenerated Final Pores.
Gas Permeabilitya??See KozenyCarman Equation.
Gate Strain Rate in Injection Molding.
GaudinSchuhmann distribution.
Gaussian Distribution.
Geldensification Model.
H
HallPetch Relation.
Hardenability Factor.
Hardness.
Hardness Variation with Grain Size in Cemented Carbides.
Heatingrate Effect in Transient Liquidphase Sintering.
Heat Transfer in Sintered Materials.
Heattransfer Rate in Modelinga??See Cooling Rate in Molding.
Herring Scaling Law.
Hertzian stressa??See Elastic Deformation Necksize Ratio.
Heterodiffusiona??See Mixedpowder Sintering Shrinkage.
I
Impregnationa??See Infiltration Pressure.
Inertialflow Equation.
Infiltration Depth.
Infiltration Pressure.
Infiltration Rate.
Inhibited Grain Growtha??See Zener Relation.
Initialstage Liquidphase Sintering Stressa??See Sintering Stress in Initialstage Liquidphase Sintering.
Initialstage Neck Growth.
Initialstage Sinteringa??See Surface DiffusionControlled Neck Growth.
Initialstage Sintering Modela??See Kuczynski Neckgrowth Model.
J
Jar Milling.
Jet Mixing Time.
K
Kawakita Equation.
Kelvin Equation.
Kelvin Modela??See Viscoelastic Model for PowderPolymer Mixtures.
KFactor.
Kingery Intermediatestage Liquidphase Sintering Modela??See Intermediatea??stage Liquidphase Sintering Model.
Kingery Model for Pressureassisted Liquidphase Sinteringa??See Pressureassisted Liquidphase Sintering.
Kingery Rearrangement Shrinkage Kineticsa??See Rearrangement Kinetics in Initialstage Liquidphase Sintering.
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 Gasatomization Melt Flow Rate.
Master Decomposition Curve.
Master Sintering Curve.
Master Sintering Curve for Grain Growtha??See Graingrowth Master Curve.
Maximum Density in Pressureassisted Sintering.
Maximum Ejection Stress.
Maximum Grain Size in Sintering.
Maximum Lubricant Content.
N
NabarroHerring Creepcontrolled Pressureassisted Densification.
Nanoparticle Agglomeration.
Nanoparticle Meltingpoint Depression.
Nanoscale ParticleAgglomerate Spheroidization.
Nanoscale Particlesize Effect on Surface Energya??See Surfaceenergy variation with Droplet Size.
Neckcurvature Stress.
Neck Growth Early in Liquidphase Sintering.
Neck Growthinduced Shrinkagea??See Shrinkage Relation to Neck Size.
Neck Growth Limited by Grain Growth.
Neckgrowth Modela??See Kuczynski neckgrowth Model.
O
Openpore Content.
Optimal Packing Particlesize Distributiona??See Andreasen Size Distribution.
Optimal Mixer Rotational Speed.
Ordered Packing.
Osprey Processa??See Spray Deposition.
Ostwald Ripening.
Oxide Reduction.
P
Packing Density for Lognormal Particles.
Particle Cooling in Atomizationa??See Newtonian Cooling Approximation.
Particle Coordination Numbera??See Coordination Number and Density.
Particle Diffusion in Mixing.
Particle Fracture in Milling.
Particle Packing.
Particleshape Index.
Particle Sizea??See Equivalent Spherical Diameter and Mean Particle Size.
Particlesize Analysisa??See Sieve Progression.
Particle size and Apparent Density.
Q
Quantitativemicroscopy Determination of Surface Areaa??See Surface Area by Quantitative Microscopy.
Quasi3dimensional Energygoverning Equation for Powder Injection Moldinga??See Energygoverning Equation for Powder Injection Molding.
Quasi3dimensional Pressuregoverning Equation for Powder Injection Modelinga??See Pressuregoverning Equation in Powder Injection Molding.
Quasi3dimensional Pressuregoverning Equation for Powder Injection Molding with Sliplayer Modela??See Pressuregoverning Equation in Powder Injection Molding with Sliplayer Model.
Quasi3dimensional Pressuregoverning Equation for Powder Injection Molding with Slipvelocity Modela??See Pressuregoverning Equation in 2.5 Dimensions for Powder Injection Molding with Slipvelocity Model.
R
Radial Crush Strengtha??See Bearing Strength.
Radiant Heating.
Raleigh Instability.
Random Packing Density.
Random Packing Radialdistribution Function.
Reactioncontrolled Grain Growtha??See Graingrowth Master Curve, Interfacial Reaction Control, and Interfacecontrolled Grain Growth.
Reactionrate Equationa??See Avrami Equation.
Reactive Synthesis.
Rearrangement Kinetics in Liquidphase Sintering.
Recalescence Temperature.
S
Saddlesurface Stressa??See Neckcurvature Stress.
Scherrer Formula.
Screen Sizesa??See Sieve Progression.
Secondary DendriteArm Spacing.
Secondary Recrystallizationa??See Abnormal Grain Growth.
Secondstage Liquidphase Sintering Modela??See Intermediatestage Liquidphase Sintering Model.
Secondstage Sintering Densificationa??See Intermediatestage Sinteringdensity Model.
Secondstage Sintering Pore Eliminationa??See Intermediatestage Pore Elimination.
Secondstage Sintering Surfacearea Reductiona??See Intermediatestage Surfacearea Reduction.
Sedimentation Particlesize Analysisa??See Stokesa?? Law Particlesize Analysis.
T
Tap Densitya??See Vibrationinduced Particle Packing.
Temperature Adjustments for Equivalent Sintering.
Temperature Dependencea??See Arrhenius Relation.
Terminal Densitya??See Finalstage Sintering Limited Density.
Terminal Neck Sizea??See Neck Growth Limited by Grain Growth.
Terminal Neck Size in Sinteringa??See Limiting Neck Size.
Terminal Pore Sizea??See Finalstage Pore Size.
Terminal Settling Velocitya??See Stokesa?? Law.
Terminal Sinteringa??See Trappedgas Pore Stabilization.
Terminal Velocitya??See Acceleration of Freesettling Particles.
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.
Vibrationinduced Particle Packing.
Vickers Hardness Number.
W
Washburn Equation.
Wateratomization 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
Xray Line Broadeninga??See Scherrer Formula.
Y
Yield Strength in Viscous Flowa??See Bingham Viscousflow Model.
Yield Strength of Particlea??Polymer Feedstock
Younga??s Equationa??See Contact Angle and Wetting Angle.
Younga??s Modulusa??See Elastic Modulus.
Z
Zener Relation.
Zeta Potential.
Appendix.
References.
Seong Jin Park, PhD, is Associate Research Professor in the Center for Advanced Vehicular Systems at Mississippi State University. He is the recipient of numerous awards and honors, including Leading Scientists of the World and Outstanding Scientists Worldwide, both awarded by the International Biographical Centre in 2007. Dr. Park is the author of over 190 published articles and three books, holds four patents, and created four commercialized software programs. His areas of specialization and interest include materials processing technology, numerical technology, and physics.