Table 3 Values of Mullins derivative y′ (x) versus x for the various metals.

From: New solution of the partial differential equation of the grain groove profile problem in the case of evaporation/condensation

Metal

C (μm2/s)

Ct (μm)

Values of approximated Mullins derivative y′ (x)

x = 0 μm

x = 0.01 μm

x = 0.1 μm

x = 0.5 μm

x = 1 μm

Co

2.42 × 10−8

0.0242

1

0.9990

0.9020

0.0789

–

Zn (solid)

2.63 × 10−8

0.0263

1

0.9990

0.9092

0.0926

–

Ga

3.89 × 10−8

0.0389

1

0.9994

0.9378

0.2009

0.0726

Ti

4.37 × 10−8

0.0437

1

0.9994

0.9444

0.2394

0.1427

Tl

6.34 × 10−8

0.0634

1

0.9996

0.9613

0.3730

0.1821

Li

1.75 × 10−7

0.1750

1

0.9999

0.9858

0.6996

0.2396

Au

2.50 × 10−7

0.2505

1

0.9999

0.9901

0.7792

0.3685

Cu

6.70 × 10−7

0.6704

1

1.0000

0.9963

0.9110

0.6887

Al

7.54 × 10−7

0.7535

1

1.0000

0.9967

0.9204

0.7176

Cs

7.64 × 10−7

0.7638

1

1.0000

0.9967

0.9214

0.7209

Sr

8.08 × 10−7

0.8081

1

1.0000

0.9969

0.9256

0.7339

Mg

8.51 × 10−7

0.8510

1

1.0000

0.9971

0.9292

0.7454

Zn (liquid)

5.40 × 10−6

5.4015

1

1.0000

0.9995

0.9885

0.9548

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