Graham S. Arnold, "Absorptivity of several metals at 10.6 μm: empirical expressions for the temperature dependence computed from Drude theory," Appl. Opt. 23, 1434-1436 (1984)
Simple expressions for the temperature-dependent absorptivity at 10.6 μm have been computed for silver, aluminum, gold, copper, lead, and tungsten by means of a straightforward application of the Drude model and experimental dc conductivity data over a wide temperature range. The results of these computations are in reasonable agreement with experimental data where such are available.
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Room Temperature Drude Parameters Used to Calculate 10.6-μm Absorptivities of Metals (Second Entry in Each Case is the Best-Fit Value of Ordal et al.4) and Coefficients Obtained by Least-Squares Fits of the Form 100 × A(T) = ∑aiTi); Notation: 1.2(3) = 1.2 × 103
Metal
ωp/1016 (rad/sec)
τ × 1014 (sec)
Phase
a0
a1
a2
Ag
1.43
3.49
solid
−6.88(−3)
1.59(−3)
liquid
1.30(0)
1.64(−3)
1.37
3.66
solid
−7.03(−3)
1.59(−3)
liquid
1.30(0)
1.66(−3)
Al
2.23
0.801
solid
1.47(−1)
3.20(−3)
liquid
2.91(0)
1.76(−3)
2.24
0.821
solid
1.34(−1)
3.13(−3)
liquid
2.88(0)
1.70(−3)
Au
1.37
2.47
solid
9.43(−2)
2.34(−3)
liquid
3.46(0)
1.48(−3)
1.32
2.46
solid
9.54(−2)
2.36(−3)
liquid
3.46(0)
1.50(−3)
Cu
1.17
1.25
solid
1.92(−1)
3.88(−3)
1.20
1.91
solid
−2.83(−3)
2.59(−3)
Pb
1.12
0.322
solid
7.16(−1)
1.25(−2)
liquid
9.93(0)
2.47(−3)
1.17
0.366
solid
4.67(−1)
1.14(−2)
liquid
8.88(0)
2.25(−3)
W
0.869
1.29
solid
−2.50(−1)
7.29(−3)
−9.25(−7)
0.912
1.23
solid
−2.10(−1)
7.16(−3)
−9.09(−7)
Table II
Comparison of Room Temperature Absorptivities from Least-Squares Fits with Experimental Values (Literature Values at 10 μm)
Comparison of Temperature Dependence of Reflectivities from Least-Squares Fits with Experimental Values a
−dR/dT × 105 (K−1)
Metal
This work
Decker and Hodgkin (at 9 μm)
Ag
1.59
2 ± 0.7
Al
3.20
3 ± 0.5
Cu
2.59–3.88
1.4 ± 0.5
Tabulated experimental value for silver is the average of 2.2 ± 0.7 for a temperature change from 150 to 52.3°C and 1.8 ± 3.5 for a temperature change from 52.3 to 31.7°C. Tabulated experimental value for copper is for a temperature change from 73 to 25.7°C after heating to 160°C.13 Experimental uncertainty for copper is taken from Ref. 9; uncertainty for aluminum is arbitrarily assigned to that of copper.
Table IV
Drude Parameters and Calculated Absorptivities for Molten Metals a
Relaxation time values for this work were obtained from straight-line interpolation or extrapolation from temperatures nearest to those reported in Ref. 12; A(T) from least-squares fits.
Tables (4)
Table I
Room Temperature Drude Parameters Used to Calculate 10.6-μm Absorptivities of Metals (Second Entry in Each Case is the Best-Fit Value of Ordal et al.4) and Coefficients Obtained by Least-Squares Fits of the Form 100 × A(T) = ∑aiTi); Notation: 1.2(3) = 1.2 × 103
Metal
ωp/1016 (rad/sec)
τ × 1014 (sec)
Phase
a0
a1
a2
Ag
1.43
3.49
solid
−6.88(−3)
1.59(−3)
liquid
1.30(0)
1.64(−3)
1.37
3.66
solid
−7.03(−3)
1.59(−3)
liquid
1.30(0)
1.66(−3)
Al
2.23
0.801
solid
1.47(−1)
3.20(−3)
liquid
2.91(0)
1.76(−3)
2.24
0.821
solid
1.34(−1)
3.13(−3)
liquid
2.88(0)
1.70(−3)
Au
1.37
2.47
solid
9.43(−2)
2.34(−3)
liquid
3.46(0)
1.48(−3)
1.32
2.46
solid
9.54(−2)
2.36(−3)
liquid
3.46(0)
1.50(−3)
Cu
1.17
1.25
solid
1.92(−1)
3.88(−3)
1.20
1.91
solid
−2.83(−3)
2.59(−3)
Pb
1.12
0.322
solid
7.16(−1)
1.25(−2)
liquid
9.93(0)
2.47(−3)
1.17
0.366
solid
4.67(−1)
1.14(−2)
liquid
8.88(0)
2.25(−3)
W
0.869
1.29
solid
−2.50(−1)
7.29(−3)
−9.25(−7)
0.912
1.23
solid
−2.10(−1)
7.16(−3)
−9.09(−7)
Table II
Comparison of Room Temperature Absorptivities from Least-Squares Fits with Experimental Values (Literature Values at 10 μm)
Comparison of Temperature Dependence of Reflectivities from Least-Squares Fits with Experimental Values a
−dR/dT × 105 (K−1)
Metal
This work
Decker and Hodgkin (at 9 μm)
Ag
1.59
2 ± 0.7
Al
3.20
3 ± 0.5
Cu
2.59–3.88
1.4 ± 0.5
Tabulated experimental value for silver is the average of 2.2 ± 0.7 for a temperature change from 150 to 52.3°C and 1.8 ± 3.5 for a temperature change from 52.3 to 31.7°C. Tabulated experimental value for copper is for a temperature change from 73 to 25.7°C after heating to 160°C.13 Experimental uncertainty for copper is taken from Ref. 9; uncertainty for aluminum is arbitrarily assigned to that of copper.
Table IV
Drude Parameters and Calculated Absorptivities for Molten Metals a
Relaxation time values for this work were obtained from straight-line interpolation or extrapolation from temperatures nearest to those reported in Ref. 12; A(T) from least-squares fits.
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