POWDER COMPACT STRUCTURE.
PART 3. THEORETICAL ANALYSIS OF SINTERING
IN POWDER COMPACTS WITH INHOMOGENEOUS POROSITY
A. V. Galakhov
Translated from Novye Ogneupory, No. 10, pp. 83 – 92, October 2014.
Original article submitted July 17, 2014.
Publications devoted to theoretical analysis of powder compact sintering are reviewed taking account of parti
cle packing inhomogeneity within it. The methods used for resolving the problem are conditionally divided
into analytical and numerical. It is shown that in order to obtain results agreeing with experimental observa
tions more extensive possibilities may be realized using numerical methods in combination with computer
modeling of particle packing. Examples are provided of implementing the method applied to oxide ceramic
Keywords: powder compact, structure, inhomogeneity, sintering, numerical methods.
NUMERICAL METHODS WITHIN THE SCOPE OF A
PHYSICAL MODEL OF SINTERING
The basis of sintering physical theory is the idea of diffu-
sion mass transfer in an assembly of particles in contact. This
mass transfer gives rise to an attempt of a collection of pow-
der compact particles in contact to reduce their surface en
ergy. As the main analytical relationships it is normal to use
equations describing mass transfer within the vicinity of two
particles in contact (Fig. 16). The form of these equations
was proposed by founders of the theory Ya. I. Frenkel’ 
and G. C. Kuczinski . The dependence of contact neck
radius x on sintering time t has the form 
= gdDr/kTt, (9)
where g is surface energy; d is atom size (lattice spacing); D
is volumetric diffusion coefficient of migrating atoms; r is
Since the first publication these equations have under
gone significant changes, connected only with the geometry
of diffusion mass transfer . As a rule in these models sta-
tistical configuration of these particles of regular shape is
considered entirely, normally described by analytical curves.
Use of numerical approximation for describing the shape of
particles in contact makes it possible to extend this analysis
to a configuration of particles with arbitrary shape. This ap
proach has been used in . A geometric model of an ob
ject, and a scheme for approximating its shape and results of
calculations are shown in Fig. 17. A sintered object (see
Refractories and Industrial Ceramics Vol. 55, No. 5, January, 2015
1083-4877/15/05505-0456 © 2015 Springer Science+Business Media New York
Part 1 of the article published in Novye Ogneupory No. 5 of
2014, Part 2 in No. 6 of 2014, and beginning of Part 3 in No. 9 of
FGBUN A. A. Baikov Institute of Metallurgy and Materials Sci
ence, Russian Academy of Sciences, Moscow, Russia.
Fig. 16. Diagram of mass transfer in the vicinity of two particles in