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 Wearâ??See Friction and Wear Testing.
Acceleration of Freesettling Particles.
Activated Sintering, Earlystage Shrinkage.
Activation Energyâ??See Arrhenius Relation.
Adsorptionâ??See BET Specific Surface Area.
Agglomerate Strength.
Agglomeration Force.
Agglomeration of Nanoscale Particlesâ??See Nanoparticle Agglomeration.
Andreasen Size Distribution.
B
Ball Millingâ??See Jar Milling.
Bearing Strength.
Bell Curveâ??See Gaussian Distribution.
Bendingbeam Viscosity.
Bending Test.
BET Equivalent Sphericalparticle Diameter.
BET Specific Surface Area.
Bimodal Powder Packing.
Bimodal Powder Sintering.
Binder Burnoutâ??See Polymer Pyrolysis.
C
Cantileverbeam Testâ??See Bendingbeam Viscosity.
Capillarity.
Capillarityinduced Sinteringâ??See Surface CurvatureDriven Mass Flow in Sintering.
Capillary Pressure during Liquidphase Sinteringâ??See Mean Capillary Pressure.
Capillary Riseâ??See Washburn Equation.
Capillary Stressâ??See Laplace Equation.
Case Carburization.
Casson Model.
Cementedcarbide Hardness.
Centrifugal Atomization Droplet Size.
D
Darcyâ??s Law.
Debindingâ??See Polymer Pyrolysis, Solvent Debinding Time, Thermal Debinding Time, Vacuum Thermal Debinding Time, and Wicking.
Debinding Master Curveâ??See Master Decomposition Curve.
Debinding Temperature.
Debinding Timeâ??See Solvent Debinding Time, Thermal Debinding Time, Vacuum Thermal Debinding Time, and Wicking.
Debinding by Solvent Immersionâ??See Solvent Debinding Time.
Debinding Weight Loss.
Delubricationâ??See Polymer Pyrolysis.
Densification.
Densification in Liquidphase Sinteringâ??See Dissolutioninduced Densification.
E
Effective Pressure.
Ejection Stressâ??See Maximum Ejection Stress.
Elastic Behaviorâ??See Hookeâ??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 Densityâ??See Sintered Ductility.
F
Feedstock Formulation.
Feedstock Viscosityâ??See Suspension Viscosity and Viscosity Model for Infectionmolding Feedstock.
Feedstock Viscosity as a Function of Shear Rateâ??See Cross Model.
Feedstock Yield Strengthâ??See Yield Strength of ParticlePolymer Feedstock.
Fiberfracture from Buckling.
Fiberfracture Probability.
Fiber Packing Density.
Fickâ??s First Law.
Fickâ??s Second Law.
Fieldactivated Sintering.
G
Gasabsorption Surface Areaâ??See BET Specific Surface Area.
Gasatomization Cooling Rate.
Gasatomization Melt Flow Rate.
Gasatomization Particle Size.
Gasgenerated Final Pores.
Gas Permeabilityâ??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 Modelingâ??See Cooling Rate in Molding.
Herring Scaling Law.
Hertzian stressâ??See Elastic Deformation Necksize Ratio.
Heterodiffusionâ??See Mixedpowder Sintering Shrinkage.
I
Impregnationâ??See Infiltration Pressure.
Inertialflow Equation.
Infiltration Depth.
Infiltration Pressure.
Infiltration Rate.
Inhibited Grain Growthâ??See Zener Relation.
Initialstage Liquidphase Sintering Stressâ??See Sintering Stress in Initialstage Liquidphase Sintering.
Initialstage Neck Growth.
Initialstage Sinteringâ??See Surface DiffusionControlled Neck Growth.
Initialstage Sintering Modelâ??See Kuczynski Neckgrowth Model.
J
Jar Milling.
Jet Mixing Time.
K
Kawakita Equation.
Kelvin Equation.
Kelvin Modelâ??See Viscoelastic Model for PowderPolymer Mixtures.
KFactor.
Kingery Intermediatestage Liquidphase Sintering Modelâ??See Intermediateâ??stage Liquidphase Sintering Model.
Kingery Model for Pressureassisted Liquidphase Sinteringâ??See Pressureassisted Liquidphase Sintering.
Kingery Rearrangement Shrinkage Kineticsâ??See Rearrangement Kinetics in Initialstage Liquidphase Sintering.
Kissinger Method.
Knoop Hardness.
Knudsen Diffusionâ??See Vapor Mean Free Path.
L
Laminar Flow Settlingâ??See Stokesâ?? Law.
Laplace Equation.
Laplace Numberâ??See Suratman Number.
Laser Sintering.
Lattice Diffusionâ??See Vacancy Diffusion.
Lifschwiz, Slyozov, Wagner Model.
Ligament Pinchingâ??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 Atomizationâ??See Gasatomization Melt Flow Rate.
Master Decomposition Curve.
Master Sintering Curve.
Master Sintering Curve for Grain Growthâ??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 Energyâ??See Surfaceenergy variation with Droplet Size.
Neckcurvature Stress.
Neck Growth Early in Liquidphase Sintering.
Neck Growthinduced Shrinkageâ??See Shrinkage Relation to Neck Size.
Neck Growth Limited by Grain Growth.
Neckgrowth Modelâ??See Kuczynski neckgrowth Model.
O
Openpore Content.
Optimal Packing Particlesize Distributionâ??See Andreasen Size Distribution.
Optimal Mixer Rotational Speed.
Ordered Packing.
Osprey Processâ??See Spray Deposition.
Ostwald Ripening.
Oxide Reduction.
P
Packing Density for Lognormal Particles.
Particle Cooling in Atomizationâ??See Newtonian Cooling Approximation.
Particle Coordination Numberâ??See Coordination Number and Density.
Particle Diffusion in Mixing.
Particle Fracture in Milling.
Particle Packing.
Particleshape Index.
Particle Sizeâ??See Equivalent Spherical Diameter and Mean Particle Size.
Particlesize Analysisâ??See Sieve Progression.
Particle size and Apparent Density.
Q
Quantitativemicroscopy Determination of Surface Areaâ??See Surface Area by Quantitative Microscopy.
Quasi3dimensional Energygoverning Equation for Powder Injection Moldingâ??See Energygoverning Equation for Powder Injection Molding.
Quasi3dimensional Pressuregoverning Equation for Powder Injection Modelingâ??See Pressuregoverning Equation in Powder Injection Molding.
Quasi3dimensional Pressuregoverning Equation for Powder Injection Molding with Sliplayer Modelâ??See Pressuregoverning Equation in Powder Injection Molding with Sliplayer Model.
Quasi3dimensional Pressuregoverning Equation for Powder Injection Molding with Slipvelocity Modelâ??See Pressuregoverning Equation in 2.5 Dimensions for Powder Injection Molding with Slipvelocity Model.
R
Radial Crush Strengthâ??See Bearing Strength.
Radiant Heating.
Raleigh Instability.
Random Packing Density.
Random Packing Radialdistribution Function.
Reactioncontrolled Grain Growthâ??See Graingrowth Master Curve, Interfacial Reaction Control, and Interfacecontrolled Grain Growth.
Reactionrate Equationâ??See Avrami Equation.
Reactive Synthesis.
Rearrangement Kinetics in Liquidphase Sintering.
Recalescence Temperature.
S
Saddlesurface Stressâ??See Neckcurvature Stress.
Scherrer Formula.
Screen Sizesâ??See Sieve Progression.
Secondary DendriteArm Spacing.
Secondary Recrystallizationâ??See Abnormal Grain Growth.
Secondstage Liquidphase Sintering Modelâ??See Intermediatestage Liquidphase Sintering Model.
Secondstage Sintering Densificationâ??See Intermediatestage Sinteringdensity Model.
Secondstage Sintering Pore Eliminationâ??See Intermediatestage Pore Elimination.
Secondstage Sintering Surfacearea Reductionâ??See Intermediatestage Surfacearea Reduction.
Sedimentation Particlesize Analysisâ??See Stokesâ?? Law Particlesize Analysis.
T
Tap Densityâ??See Vibrationinduced Particle Packing.
Temperature Adjustments for Equivalent Sintering.
Temperature Dependenceâ??See Arrhenius Relation.
Terminal Densityâ??See Finalstage Sintering Limited Density.
Terminal Neck Sizeâ??See Neck Growth Limited by Grain Growth.
Terminal Neck Size in Sinteringâ??See Limiting Neck Size.
Terminal Pore Sizeâ??See Finalstage Pore Size.
Terminal Settling Velocityâ??See Stokesâ?? Law.
Terminal Sinteringâ??See Trappedgas Pore Stabilization.
Terminal Velocityâ??See Acceleration of Freesettling Particles.
U
Ultrasonic Velocity.
V
Vacancy Concentration Dependence on Surface Curvature.
Vacancy Diffusion.
Vacuum Debindingâ??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 Densityâ??See Archimedes Density.
Weber Number.
Weibull Distribution.
Wetting Angle.
Wicking.
Work Hardeningâ??See Strain Hardening.
Work of Sinteringâ??See Master Sintering Curve.
X
Xray Line Broadeningâ??See Scherrer Formula.
Y
Yield Strength in Viscous Flowâ??See Bingham Viscousflow Model.
Yield Strength of Particleâ??Polymer Feedstock
Youngâ??s Equationâ??See Contact Angle and Wetting Angle.
Youngâ??s Modulusâ??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.