Table I
Solutions with minimum least-squares residuals of n, k, and t for a 15-day tarnish film on Ag at λ0 = 2967 Å with Φ0 = 55°, 65°, and 75°. Specimen J915A. Substrate: n = 1.57, k = 1.07.
Initial value | Final solution |
---|
|
|
---|
n | k | t | n | k | t |
---|
1.9 | 0.05 | 30 Å | 1.655 | 0.012 | 33 Å |
1.9 | 0.05 | 40 | 1.669 | 0.002 | 32 |
1.9 | 0.05 | 50 | 1.634 | 0.029 | 34 |
1.7 | 0.05 | 30 | 1.635 | 0.028 | 34 |
1.7 | 0.05 | 40 | 1.606 | 0.049 | 36 |
1.7 | 0.05 | 50 | 1.558 | 0.081 | 39 |
1.7 | 0.1 | 30 | 1.673 | 0.0 | 32 |
1.7 | 0.1 | 40 | 1.623 | 0.037 | 35 |
1.7 | 0.1 | 50 | 1.595 | 0.056 | 37 |
1.7 | 0.2 | 30 | 1.616 | 0.041 | 35 |
1.7 | 0.2 | 40 | 1.615 | 0.043 | 35 |
1.7 | 0.2 | 50 | 1.554 | 0.083 | 39 |
1.6 | 0.05 | 35 | 1.626 | 0.034 | 35 |
1.55 | 0.1 | 40 | 1.595 | 0.057 | 37 |
1.5 | 0.15 | 50 | 1.517 | 0.104 | 42 |
1.5 | 0.05 | 30 | 1.586 | 0.062 | 37 |
1.5 | 0.05 | 40 | 1.561 | 0.079 | 39 |
1.3 | 0.2 | 55 | 1.587 | 0.062 | 37 |
Table II
Solutions with minimum least-squares residuals of n, k, and t for a 15-day tarnish film on Ag at λ0 = 3023 Å with ϕ0 = 55°, 65°, and 75°. Specimen J915A.
Initial value | Final solution |
---|
|
|
---|
n | k | t | n | k | t |
---|
1.6 | 0.05 | 30 Å | 1.523 | 0.022 | 37 Å |
1.6 | 0.05 | 40 | 1.516 | 0.029 | 37 |
1.6 | 0.05 | 50 | 1.480 | 0.056 | 40 |
1.8 | 0.05 | 30 | 1.448 | 0.077 | 43 |
1.8 | 0.05 | 40 | 1.505 | 0.037 | 38 |
1.8 | 0.05 | 50 | 1.541 | 0.007 | 35 |
1.4 | 0.05 | 30 | 1.521 | 0.024 | 37 |
1.4 | 0.05 | 40 | 1.497 | 0.043 | 39 |
1.4 | 0.05 | 50 | 1.480 | 0.056 | 40 |
1.6 | 0.1 | 30 | 1.534 | 0.014 | 36 |
1.6 | 0.1 | 40 | 1.511 | 0.033 | 38 |
1.6 | 0.1 | 50 | 1.514 | 0.030 | 37 |
1.6 | 0.2 | 30 | 1.511 | 0.032 | 38 |
1.6 | 0.2 | 40 | 1.480 | 0.055 | 40 |
1.6 | 0.2 | 50 | 1.497 | 0.043 | 39 |
Table III
Solutions with minimum least-squares residuals of n, k, and t for a 64-day tarnish film on Ag at λ0 = 2967 Å with ϕ0 = 45°, 55°, 65°, 75°, and 85°. Specimen J915A.
Initial value | Final solution |
---|
|
|
---|
n | k | t | n | k | t |
---|
1.4 | 0.01 | 250 Å | 1.791 | 0.189 | 108 Å |
1.4 | 0.01 | 200 | 1.799 | 0.185 | 106 |
1.4 | 0.01 | 150 | 1.804 | 0.182 | 105 |
1.5 | 0.07 | 150 | 1.804 | 0.182 | 105 |
1.5 | 0.07 | 200 | 1.817 | 0.174 | 103 |
1.5 | 0.07 | 250 | 1.799 | 0.185 | 106 |
1.4 | 0.15 | 150 | 1.791 | 0.189 | 108 |
1.4 | 0.15 | 200 | 1.825 | 0.169 | 102 |
1.4 | 0.15 | 250 | 1.804 | 0.182 | 106 |
Table IV
Solutions for film parameters with minimum least-squares residuals and a lower limit on thickness when k≤0. Specimen J915A.
Wavelength | Stage of film growth |
---|
|
---|
15 days (35–43 Å) | 21 days (43–62 Å) | 28 days (52–64 Å) | 33 days (56–81 Å) |
---|
|
|
|
|
---|
n range | k range | n range | k range | n range | k range | n range | k range |
---|
5790 Å | 1.63–1.92 | 0.10–0.16 | 1.57–2.06 | 0.07–0.13 | 1.79–2.11 | 0.10–0.13 | 1.63–2.16 | 0.07–0.12 |
5461 | 1.64–1.92 | 0.12–0.17 | 1.57–2.04 | 0.08–0.15 | 1.78–2.08 | 0.11–0.14 | 1.64–2.15 | 0.08–0.14 |
4358 | 1.68–1.92 | 0.20–0.26 | 1.61–2.04 | 0.17–0.25 | 1.80–2.04 | 0.17–0.21 | 1.67–2.08 | 0.18–0.26 |
4047 | 1.64–1.86 | 0.30–0.37 | 1.57–1.92 | 0.25–0.36 | 1.75–1.96 | 0.33–0.39 | 1.63–1.99 | 0.27–0.37 |
3650 | 1.45–1.59 | 0.37–0.45 | 1.41–1.64 | 0.29–0.41 | 1.53–1.67 | 0.33–0.39 | 1.47–1.71 | 0.28–0.38 |
3341 | 1.66–1.79 | 0.11–0.15 | 1.62–1.84 | 0.05–0.11 | 1.75–1.90 | 0.09–0.12 | 1.66–1.94 | 0.12–0.16 |
3131 | 1.35–1.40 | 0.21–0.25 | 1.41–1.50 | 0.15–0.21 | 1.48–1.53 | 0.16–0.19 | 1.47–1.57 | 0.15–0.20 |
3023 | 1.44–1.55 | 0 −0.08 | 1.43–1.61 | 0 −0.14 | 1.55–1.65 | 0 −0.08 | 1.50–1.59 | 0 −0.14 |
2967 | 1.50–1.63 | 0.03–0.11 | 1.46–1.68 | 0.02–0.16 | 1.60–1.72 | 0.01–0.09 | 1.53–1.75 | 0.01–0.15 |
2894 | 1.52–1.66 | 0.04–0.12 | 1.48–1.72 | 0.02–0.14 | 1.53–1.61 | 0.03–0.11 | 1.54–1.79 | 0.12–0.25 |
Table V
Solutions with minimum least-squares residuals of n, k, and t obtained when n and k were assumed to remain constant for the 15-, 21-, 28-, and 33-day tarnish films. Specimen J915A.
λ0 (Å) | n | k | 15 days | 21 days | 28 days | 33 days |
---|
5790 | 1.99 | 0.12 | 33 | 44 | 56 | 62 |
1.93 | 0.11 | 34 | 46 | 58 | 64 |
1.84 | 0.10 | 37 | 49 | 62 | 68 |
2.05 | 0.13 | 32 | 43 | 54 | 59 |
5461 | 1.92 | 0.13 | 35 | 46 | 58 | 64 |
1.83 | 0.12 | 37 | 49 | 62 | 69 |
1.83 | 0.12 | 37 | 49 | 61 | 68 |
1.82 | 0.12 | 37 | 49 | 62 | 69 |
Table VI
Comparison of solutions using the exact Drude and approximate equations for a 7-day film on Ag. Specimen J915A.
Wavelength | t | Exact n | Approx. n | Exact k | Approx. k |
---|
5790 Å | 12 Å | 2.327 | 2.293 | 0.258 | 0.305 |
14 | 2.010 | 1.975 | 0.209 | 0.242 |
16 | 1.797 | 1.765 | 0.165 | 0.190 |
5461 | 12 | 2.317 | 2.281 | 0.321 | 0.368 |
14 | 2.014 | 1.975 | 0.267 | 0.299 |
16 | 1.805 | 1.770 | 0.214 | 0.236 |
4358 | 12 | 2.204 | 2.167 | 0.351 | 0.382 |
14 | 1.976 | 1.938 | 0.308 | 0.333 |
16 | 1.807 | 1.769 | 0.267 | 0.284 |
4047 | 12 | 2.113 | 2.067 | 0.529 | 0.547 |
14 | 1.907 | 1.861 | 0.470 | 0.480 |
16 | 1.752 | 1.708 | 0.413 | 0.416 |
3650 | 12 | 1.794 | 1.753 | 0.666 | 0.652 |
14 | 1.644 | 1.604 | 0.592 | 0.572 |
16 | 1.531 | 1.495 | 0.522 | 0.499 |
3341 | 12 | 1.913 | 1.848 | 0.137 | 0.095 |
14 | 1.803 | 1.739 | 0.129 | 0.091 |
16 | 1.716 | 1.655 | 0.125 | 0.086 |
3131 | 12 | 1.400 | 1.399 | 0.488 | 0.491 |
14 | 1.386 | 1.385 | 0.487 | 0.490 |
16 | 1.376 | 1.375 | 0.487 | 0.490 |
3023 | 12 | 1.471 | 1.474 | 0.008 | 0.012 |
14 | 1.394 | 1.395 | 0.057 | 0.061 |
16 | 1.323 | 1.321 | 0.083 | 0.086 |
2967 | 12 | 1.645 | 1.653 | 0.063 | 0.069 |
14 | 1.548 | 1.553 | 0.128 | 0.136 |
16 | 1.453 | 1.452 | 0.173 | 0.184 |
2894 | 12 | 1.683 | 1.690 | 0.022 | 0.026 |
14 | 1.581 | 1.585 | 0.083 | 0.09 |
16 | 1.489 | 1.489 | 0.124 | 0.132 |
Table VII
Solutions with minimum least-squares residuals of n, k, and t for an 80-day tarnish film on Ag at λ0 = 2967 Å with ϕ0 = 45°, 55°, 65°, 75°, 85°. Specimen J915B.
Initial value | Final solution |
---|
|
|
---|
n | k | t | n | k | t |
---|
1.6 | 0.05 | 34 Å | 1.57 | 0.005 | 33 Å |
1.6 | 0.05 | 36 | 1.55 | 0.018 | 34 |
1.6 | 0.05 | 38 | 1.54 | 0.028 | 35 |
1.6 | 0.05 | 40 | 1.53 | 0.036 | 36 |
1.6 | 0.05 | 42 | 1.57 | 0.009 | 33 |
1.6 | 0.05 | 44 | 1.58 | 0.002 | 33 |