Computational Algorithm Predicting Surface Computational Algorithm - - PowerPoint PPT Presentation

Computational Algorithm Predicting Surface Computational Algorithm Predicting Surface Morphology Evolution During Electropolishing

Joel Thomas1, Charles Reece2 and Stanko R. Brankovic1,*

1Cullen College of Engineering

University of Houston Houston TX

2Jefferson National Laboratory

Newport News VA Newport News, VA

*Stanko.Brankovic@mail.uh.edu

Mathematical Theory of Electropolishing

      t b t b exp ) (                M j b t b 2 exp ) (    important M nF :    for b(t) important:

• C. Wagner, J. Electrochem. Soc., 101, 225 (1954).

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6th SRF Materials Workshop

• Feb. 18-20, 2010 Tallahassee

Scaling Analysis of AFM Data

Width

    l i h i h l l w 1 2 ] ) ( [ 1 ) (

Surface W

sat

w

 i l 1

Log Length Scale Log

l



Log Length Scale

c

l

: ANALYSIS SCALING . , ~ , const w w l l For ; l w l l For

sat C C

   



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6th SRF Materials Workshop

• Feb. 18-20, 2010 Tallahassee

*F. Family, T. Vicsek, J. Phys. A 18, L75 (1985).

AFM Results and Discussion for Cu Surface

5 7 ) ( l ) ( ) ( ; ) ( 5 . 7 ) ( t f t const t m const t lC       

grains ize of the lateral s lC 

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6th SRF Materials Workshop

• Feb. 18-20, 2010 Tallahassee
• S. Shivareddy, S.-E. Bae and S. R. Brankovic, Electrochem. Solid State Lett., 11, 1 (2008).

: case l l For 

AFM Results and Discussion for Cu Surface

: case l l For 

: case l l For

C



: case l l For

C



    l t l l  

l  1 2

    l , const l l

C

  , ,             t w t w exp ) (

m l const

C

  5 . 15 2   

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6th SRF Materials Workshop

• Feb. 18-20, 2010 Tallahassee

  

Synergy Between Scaling Formalism and Mathematical Theory of Electropolishing

Bt t      ) (

Mathematical Theory of Electropolishing

Scaling Functions (Electropolishing)

  ) (

B    1 1

           t l l w t l l w

C C

exp ) , ( ) , (

) / ln( l l B l

C C

  2 1

 

          

C C C

l t l l w t l l w 2  exp ) , ( ) , (

) / ln( 1       a l B 

 

C

l 2

1

00073 . ) / ln( 2



      s B a l l

C C

 

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6th SRF Materials Workshop

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Results Analysis:  vs. l for l lC and  =f(t)

B = 0.00058 B = 0.00058 ± ± 0.00008 0.00008 B’=0 00074 B’=0 00074 ± 0 00008 0 00008 B = 0.00072 B = 0.00072 ± ± 0.00003 0.00003 B =0.00074 B =0.00074 ± 0.00008 0.00008

Th ti l E ti t B 0 00073 -1

Bt t     ) (

) / ln( l l B l

C

    2 1 1

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6th SRF Materials Workshop

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Theoretical Estimate: B = 0.00073s-1 lC  2

Simulation Algorithm for Cu Electropolishing

I (t 0) Image 2D FFT

Algorithm (lC, B, )

Image (t=0) wavelength selection

1

Image 2D FFT wavelength selection

                      l B l l l

w l C C C w l

2 ln 2 1 1 ; 2 2

             

C w l

l t b t b l l 2 exp ) ( 2 2   

          t c t c exp ) (

   

C

l 2

Inverse FFT new data matrix after time t Image (t)

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6th SRF Materials Workshop

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Simulation Algorithm - Results

0.35

t) f(l, w  f(t) wsat 

0 Sec 50 Sec 100 Sec

0.25 0.3 0.1

w / m

0.15 0.2

wsat / m

1 10

l / m

20 40 60 80 100 0.1

t/

 

l / m t/ sec

1

115 2 exp ) ( ) (



            l t w t w

C sat sat



C

l m lC  3 . 5 

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6th SRF Materials Workshop

• Feb. 18-20, 2010 Tallahassee

1

115 .



 ms  

Simulation Algorithm - Results

6.0 0.675

Bt f(t)      const t lC  ) (

5.4 5.6 5.8 0.660 0.665 0.670 0.675



Linear Fit

(Slope = -0.000363)

4.8 5.0 5.2

lC/ m

0.645 0.650 0.655



10 20 30 40 50 60 70 80 90 100 4.6

t / sec

20 40 60 80 100 0.635 0.640

t / sec t / sec

m lC  3 . 5 

• 1

s B 00038 . 

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6th SRF Materials Workshop

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Real Time Simulations of the Cu Surface Morphology Evolution During Electropolishing Morphology Evolution During Electropolishing

(2+1) D surface

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6th SRF Materials Workshop

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( )

Summary

S i i bi i f li l i d h i l

$

• Synergistic combination of scaling analysis and mathematical

theory of electropolishing yields the scaling functions that can be conveniently used for development of the simulation algorithm predicting surface morphology evolution during l t li hi electropolishing.

• The simulation algorithm shod be generally applicable for

any electropolishing process including Nb and should help in

• verall optimization of polishing process (time current etc )
• verall optimization of polishing process (time, current, etc..)
• The

quantitative evaluation

• f

the material preparation/processing and resulting polishing results should be possible using this algorithm. p g g

• The quantitative evaluation of current distribution effects

(primary and secondary) during electropolishing of Nb SRF cavities should be possible using this algorithm

• Polishing of Cu SRF like shape modules/shells and subsequent

coating with Nb layer using electrochemical deposition ?

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6th SRF Materials Workshop

• Feb. 18-20, 2010 Tallahassee