scaling law in transient stage in solidification

8/6/2019 Scaling Law in Transient Stage in Solidification

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Scaling Law in Transient Stage in

Solidification

G. H. MengOct. 27, 2006


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Terminology

Scaling law

A very common view is that these scaling relations are nothing morethan the simplest approximations to the available experimental data,

having no special advantages over other approximations.

solidificationThe transition of a liquid or gas into a solid. IUPAC

Solid forms from itself meltIn Refs solidification crystal growth


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Constraint and Unconstraint Solidification

Constraint solidification i.e. directional

solidification

Thereafter as DS

Unconstraint solidification i.e. free

solidification

Thereafter as FS


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Characteristic lengths of physical processes

VlT

E!

V

DlD!

G

TlT

0(!

(,

+!

pcd0

0

0

T

d

(

+!

Solute diffusion process

Thermal diffusion process

Surface energy effect

For an undercooled melt

For DS of an alloy

For pure materials

For alloy solidification


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Origin of Pattern Formation

Destabilization of previous patterns

Planar solid/liquid interface in DS

Sketch of the sphere crystal in FS


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Scaling law in transient stage in FS

5/3~ tx

5/2ty5/3tx

Self-similar scaling behavior for the arms which form in radial Hele-

Shaw flow with anisotropic surface energy

X longitudinal coordinate

Y transverse coordinate

V(t) monotonously decreases

R(t) monotonously increases

)()(

2

2

0

tVtR

Dd!

W


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Unstable of Planar Pattern in DS

Constitutional undercooling principle

M-S linear kinetic principle

Weak non-linear principle

TDll !

Mm PPP

Subcritical and supercritical bifurcation


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Experimental Procedure

Alloy SCN-0.64wt%Ace.

Preparation

SCN distillation plus zone refining

dryness distillation Ace. circumfluence (KMnO4) distillation

Melted in vial with gas tight cusp

Thickness of the sample: 0.1mm

Experimental equipment


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Evolution of interface morphology

TD ll ! TD kll !

Planar Cellular Dendritic

cb

T

a

DdllL 0w


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Experimental Results

Finite space

180s 795s 960s 1290s1260s1200s 1380s

G=10.0K/mm

V=1.0Qm/s

t=0s


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Experimental results

Two haracteristic lengths are denoted as Pi

and second Pj, respectively.

m

m

j

i

QP

QP

63

394

!

!

Interface morphology in transient stage during

directional solidification in SCN-0.64wt%Ace alloy. G=10.0K/mm

m

m

j

i

QP

QP

75

345

!

!

V=0.8Qm/s V=1.0Qm/s


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Calculated and experimental results

Succinonitrile

Melting point 331.24K

Entropy of fusion 11.21J/mol K

Density of solid 1.016X103kg/m3

Density of liquid 0.970x103kg/m3

Thermal conductivity of liquid 0.223J/m s K

Thermal conductivity of solid 0.224J/m s K

Surface energy 8.95X10-3J/m2

Succinonitrile-Acetone

Diffusion coefficient 1.27x10-9m2/s

Liquidus slope -2.22K/mol pct Ace.

Equilibrium partition ratio 0.1

The physical properties of SCN-Ace

Calculated results according M-S theory

Filled squares: second characteristic length

Filled triangles: first characteristic length

1 2 3 4 5

10

100

1000

10000

1 2 3 4 5

10

100

1000

10000

1 2 3 4 5

10

100

1000

10000

Wavele

ngth,Qm

Velocity, Qm/s

Pmin

Pmax


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Scaling law in transient stage in DS

V=0.8Qm/s

Pic=237Qm; Pie=394Qm

Pjc=113Qm; Pje=63Qm

V=1.0Qm/s

Pic=224Qm; Pie=345Qm

Pjc=101Qm; Pje=75Qm

GTkl

TkdVDl

l

dl

T

D

Tji

Dj

/

)/(/2

68.1

58.10

0

00

2/1

2/1

0

(!

(!

!

!

!

PP

P


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Summery

Scaling law is power-law;

Scaling law is common in solidification;

Scaling law is dependent on the parameters;

Scaling law is limited by the spatial condition.


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Thank you!

scaling law in transient stage in solidification

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