1. Randall M. German Ph.D., M.S., B.S. Chair Professor Director and
  2. Seong Jin Park Ph.D. Associate Research Professor

Published Online: 7 JAN 2008

DOI: 10.1002/9780470370087.ch16

Mathematical Relations in Particulate Materials Processing: Ceramics, Powder Metals, Cermets, Carbides, Hard Materials, and Minerals

Mathematical Relations in Particulate Materials Processing: Ceramics, Powder Metals, Cermets, Carbides, Hard Materials, and Minerals

How to Cite

German, R. M. and Park, S. J. (2008) P, in Mathematical Relations in Particulate Materials Processing: Ceramics, Powder Metals, Cermets, Carbides, Hard Materials, and Minerals, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470370087.ch16

Author Information

  1. Center for Advanced Vehicular Systems at Mississippi State University, Mississippi State, USA

Publication History

  1. Published Online: 7 JAN 2008
  2. Published Print: 27 AUG 2008

ISBN Information

Print ISBN: 9780470173640

Online ISBN: 9780470370087



  • packing density for log-normal particles;
  • particle-size effect on initial-stage sintering;
  • pore-free composite or mixed-phase density


This chapter contains sections titled:

  • Packing Density for Log-normal Particles

  • Particle Cooling in Atomization—See Newtonian Cooling Approximation

  • Particle Coordination Number—See Coordination Number and Density

  • Particle Diffusion in Mixing

  • Particle Fracture in Milling

  • Particle Packing

  • Particle-shape Index

  • Particle Size—See Equivalent Spherical Diameter and Mean Particle Size

  • Particle-size Analysis—See Sieve Progression

  • Particle size and Apparent Density

  • Particle size by Viscous Settling—See Stokes' Particle Diameter

  • Particle-size Control in Centrifugal Atomization—See Centrifugal Atomization Particle Size

  • Particle-size Distribution—See Andreasen Size Distribution, Gaudin–Schuhman Distribution, Log-normal Distribution, and Rosin–Rammler Distribution

  • Particle-size Effect on Initial-stage Sintering—See Herring Scaling Law

  • Particle-size Effect on Packing Density—See Particle Packing

  • Particle-size Effect on Solubility—See Solubility Dependence on Particle Size

  • Particle-size in Atomization—See Water Atomization Particle Size

  • Particle-size Measurement Error

  • Peak Broadening—See Broadening

  • Peak Stress for Ejection—See Maximum Ejection Stress

  • Pendular-bond Capillary Force

  • Percolation in Semisolid Particles

  • Percolation Limits

  • Perimeter-based Particle Size—See Grain Diameter Based on Equivalent Circle

  • Permeability-based Particle Size—See Fisher Subsieve Particle Size

  • Permeability Coefficient

  • Phase Transformation—See Nucleation Rate

  • Plasma-spraying Particle Size

  • Plastic Flow in Hot Compaction

  • Plastic Flow in Sintering

  • Plastic Working—See Strain Hardening

  • Poiseuille's Equation

  • Poisson's Ratio

  • Polymer-blend Viscosity—See Binder (Mixed-polymer) Viscosity

  • Polymer Pyrolysis

  • Pore Attachment to Grain Boundaries

  • Pore Closure

  • Pore Drag—See Migration of Particles

  • Pore Filling in Liquid-phase Sintering

  • Pore-free Composite or Mixed-phase Density

  • Pore Mobility during Sintering

  • Pore Pinning of Grain Boundaries—See Grain Pinning by Pores in Final-stage Sintering and Zener Relation

  • Pore-separation Distance

  • Pore Separation from Grain Boundaries

  • Pore Size and Grain Size in Final-stage Sintering—See Grain Size to Pore Size in Final-stage Liquid-phase Sintering

  • Pore Size and Grain Size in Intermediate-stage Sintering

  • Pore Size in Final-stage Sintering

  • Pore Size in Viscous-flow Final-stage Sintering

  • Porosimetry—See Washburn Equation

  • Porosity—See Fractional Density

  • Porosity Effect on Ductility—See Sintered Ductility

  • Porosity Effect on Elastic Behavior

  • Porosity Effect on Sonic Velocity—See Ultrasonic Velocity

  • Porosity Effect on Strength—See Sintered Strength

  • Porosity Effect on Thermal Conductivity—See Thermal-conductivity Dependence on Porosity

  • Porosity in Swelling Systems with Limited Solubility

  • Powder-forging Height Strain and Densification

  • Powder Injection-molding Feedstock Viscosity—See Viscosity Model for Injection-molding Feedstock

  • Power-law Creep

  • Prealloyed-particle Sintering—See Liquid and Solid Compositions in Prealloy-particle Melting

  • Prealloyed-powder Liquid-phase Sintering—See Supersolidus Liquid-phase Sintering Shrinkage Rate

  • Precision

  • Pressure-assisted Liquid-phase Sintering

  • Pressure-assisted Sintering Maximum Density—See Maximum Density in Pressure-assisted Sintering

  • Pressure-assisted Sintering Semisolid System—See Viscous Flow in Pressure-assisted Sintering

  • Pressure Effect on Feedstock Viscosity

  • Pressure Effect on Final-stage Sintering by Viscous Flow

  • Pressure-governing Equation in Powder-injection Molding

  • Pressure-governing Equation for Powder Injection Molding with Slip Layer

  • Pressure-governing Equation in 2.5 Dimensions for Powder Injection Molding with Slip Velocity

  • Pressure Gradients in Compaction—See Die-wall Friction

  • Pressure-induced Neck Flattening—See Compaction-induced Neck Size

  • Price Estimation—See Costing and Price Estimation

  • Process Capability

  • Projected Area–based Particle Size—See Equivalent Spherical Diameter

  • Proof Testing—See Weibull Distribution

  • Pycnometer Density