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Metallurgical and Materials Transactions A

, Volume 32, Issue 3, pp 595–604 | Cite as

Numerical modeling for peritectic solidification of RE123 high T c oxide superconductors

  • Masaki Sumida
  • Takateru Umeda
Article

Abstract

In this article, a numerical solidification model is proposed, which describes peritectic solidification of RE1Ba2Cu3Ox (123, RE: rare earth metals) high T c oxide superconductors. The model was developed under an assumption of growth under mixed control, which involved three stages: decomposition reaction at the interface between the RE2Ba1Cu1O5 (211) particle and liquid, solute transport by diffusion in liquid, and interface kinetics of growing 123 crystal. These stages are combined numerically for an isolated spherical 211 particle and an infinitely planar 123 interface using the bispherical coordinate. Vicinity of the 123 growth front is supposed. The calculation results visualize a time transition of the decrement of the distance between the two solids (211 and 123), the 211 particle radius decrement, and the liquid diffusion field. It is also shown that it is able to estimate the growth rate dependence of the 123/L interface undercooling, and liquid concentrations at the 123/L and the L/211 interfaces, which are deviated from the local equilibrium concentrations. Contribution of each stage to the peritectic reaction and microscopic interface kinetics of the 123 phase are briefly discussed.

Keywords

Material Transaction Interface Reaction Peritectic Reaction Kinetic Coefficient Liquid Concentration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

b

distance between origin and center of sphere

dr211/dt

decomposition rate of 211, cm/s

dt

time-step, s

fL211

volume fraction of 211 particles in liquid

hμ

scale factor of μ

hη

scale factor of η

hø

scale factor of ø

k211

rate constant (cm/s)

kT/211

rate constant (cm/s K)

mL/123

liquidus slope of 123 phase at T P (K/mol)

mL/211

liquidus slope of 211 phase at T P (K/mol)

r211

radius of 211 particle (cm)

r211(i)

initial value of r 211

t

time (s)

z0

the shortest distance between planar 123 and spherical 211 phases (cm)

z0(i)

initial value of z 0

C

solute concentration in liquid

CL,e/123

equilibrium solute concentration in liquid at 123/L interface, mol fraction

CL,e/211

equilibrium solute concentration in liquid at L/ 211 interface, mol fraction

CL,i/123

solute concentration in liquid at 123/L interface, mol fraction

CL,i/211

solute concentration in liquid at L/211 interface, mol fraction

CP

solute concentration at peritectic point, mol fraction

CS/123

solute concentration of 123 solid phase, mol fraction

CS/211

solute concentration of 211 solid phase, mol fraction

C0

initial composition, mol fraction

D

diffusion coefficient in liquid (cm2/s)

G

temperature gradient (K/cm)

J1

diffusion flux at 123/L interface (cm3/s)

J2

solute flux for growth of 123 (cm3/s)

J3

diffusion flux at L/211 interface (cm3/s)

J4

solute flux for decomposition of 211 (cm3/s)

R

growth rate (cm/s)

T

temperature (K)

Ti,123

123/L interface temperature (K)

Ti,211

L/211 interface temperature (K)

TP

peritectic temperature (K)

α

thermal diffusivity (cm2/s)

β123

kinetic coefficient (cm/s)

βT123

kinetic coefficient (cm/s K2)

λ

mean spacing of 211 particles in liquid

σ123

interface supersaturation at 123/L interface

ΔT123

undercooling at 123/L interface (K)

ΔT211

undercooling at L/211 interface (K)

ΔTG

temperature difference between 123/L and L/ 211 interface (K)

ΔTk/123

kinetic undercooling at 123/L interface (K)

ΔTk/211

kinetic superheating at L/211 interface (K)

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Copyright information

© ASM International & TMS-The Minerals, Metals and Materials Society 2001

Authors and Affiliations

  • Masaki Sumida
    • 1
    • 2
  • Takateru Umeda
    • 3
  1. 1.New Energy and Industrial Technology Development OrganizationTokyo
  2. 2.Department of Metallurgy, Graduate School of EngineeringThe University of TokyoTokyoJapan
  3. 3.Department of Metallurgy, Graduate School of EngineeringThe University of TokyoJapan

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