Journal of Materials Science

, Volume 15, Issue 9, pp 2345–2353 | Cite as

A theoretical model of the manfacture of reaction-bonded silicon nitride with particular emphasis on the effect of ambient reaction temperature and compact size

  • G. S. Hughes
  • C. McGreavy
  • J. H. Merkin
Papers

Abstract

An analysis of the exothermic, irreversible silicon-nitrogen reaction, based on the particle-pellet model, is presented using mixed type boundary conditions to represent external resistances. The mathematical model incorporates a sharp ″cut-off″ in the reaction and takes into account its transient behaviour. The resulting system of partial differential equations is solved numerically using an explicit finite difference scheme. The effects of varying the ambient reaction temperature and compact size on the temperature distribution inside the nitriding compact and on the solid product formation rate, are examined. The results obtained are in acceptable agreement with previous experimental research by other workers, which illustrates how the model adequately represents the silicon-nitrogen reaction.

An investigatory report on the validity of the Arrhenius equation for determining the thermal activation energy of this reaction is also presented.

Keywords

Silicon Nitride Arrhenius Equation Finite Difference Scheme Transient Behaviour Type Boundary 
a

characteristic dimensions of the compact,m

C

concentration of the gas within the compact, mol m−3

CA

molar concentration of the product in the compact, mol m−3

CAO

maximum concentration of the product, 1.6×104 mol m−3

Cf

concentration of the gas surrounding the compact, mol m−3

Cp

specific heat of solid reactant, 1250 J kg−1K−1

De

effective diffusion coefficient, 2×10−6 m2 sec−1

E

activation energy of reaction, 5.5×105 J mol−1

ΔH

heat of reaction, −7.5×105 J mol−1

h

heat transfer coefficient, Wm−2 K−1

Ke

effective thermal conductivity, 6.6 Wm−1 K−1

∂/∂n

derivative normal to the surface of the compact

r(C, T)

reaction rate per unit area, kg m−2 sec−1

rp

mean particle size,m

sg

specific area of the compact, 7.142×102 m2 kg−1

T

absolute temperature within the compact, K

Tc

temperature at the centre of the compact, K

Tf

initial and surrounding temperature, K

Ts

temperature at the surface of the compact, K

t

time, sec

u

dimensionless concentration of the gas in the compact

UA

CA/CAO

V*

dimensionless space

v

dimensionless temperature in the compact

X

conversion factor, defined by Equation 7

x

dimensionless space variable within the compact

ε

void fraction of the compact, x0.4

ρb

bulk density of the compact, 1400 kg m−3

τ

dimensionless time

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References

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Copyright information

© Chapman and Hall Ltd 1980

Authors and Affiliations

  • G. S. Hughes
    • 1
  • C. McGreavy
    • 2
  • J. H. Merkin
    • 1
  1. 1.Department of Applied Mathematical StudiesUniversity of LeedsLeedsUK
  2. 2.Department of Chemical EngineeringUniversity of LeedsLeedsUK

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