Louis Harris and Arthur L. Loeb, "Conductance and Relaxation Time of Electrons in Gold Blacks from Transmission and Reflection Measurements in the Far Infrared*," J. Opt. Soc. Am. 43, 1114-1118 (1953)
The electrical conductivity of gold blacks is evaluated from reflection and transmission measurements in the far infrared. For sufficiently thin samples and sufficiently large wavelengths a closed expression is derived, relating the electrical conductivity of the gold black directly to the absorption and transmission coefficients. It is found that the electrical conductivity varies with wavelength, and for wavelengths larger than 105 microns this variation is attributed to a relaxation effect. The relaxation time of electrons in gold blacks is found to agree closely with that in bulk gold.
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a. Observed reflection and transmission of gold black deposits at different wavelengths; calculated πa/λ values for the deposits, assuming different densities.
Reliability of data is ~1 percent. Equation (9) not applicable. x is the ratio of the density of bulk gold to that of the gold black deposit.
Table II
Reduced conductivity per square, and absorption per unit transmission for different densities of gold black deposits.
Sample
λ
μcσa
AIT
calculated
observed
microns
x=150
x=500
x=150
x=500
53
105
1.8
1.4
2.4
2.4
2.4
345
2.3
2.0
2.3
2.3
2.35
455
2.7
2.4
2.7
2.7
2.7
57
105
1.2
1.0
1.1
1.2
1.2
345
1.3
1.3
1.3
1.3
1.3
455
1.5
1.5
1.5
1.4
1.5
58
105
1.2
1.0
1.2
1.3
1.3
345
1.4
1.4
1.5
1.5
1.5
455
1.7
1.6
1.7
1.7
1.7
52
105
0.33
0.33
0.33
0.33
0.33
345
0.41
0.41
0.41
0.41
0.41
455
0.42
0.42
0.42
0.42
0.42
x is the ratio of the density of bulk gold to that of the gold black deposit. μcσa is the reduced conductivity per square of deposit. A is the fraction absorbed. T is the fraction transmitted.
x is the ratio of the density of bulk gold to that of the gold black deposit.
Tables (4)
Table I
a. Observed reflection and transmission of gold black deposits at different wavelengths; calculated πa/λ values for the deposits, assuming different densities.
Reliability of data is ~1 percent. Equation (9) not applicable. x is the ratio of the density of bulk gold to that of the gold black deposit.
Table II
Reduced conductivity per square, and absorption per unit transmission for different densities of gold black deposits.
Sample
λ
μcσa
AIT
calculated
observed
microns
x=150
x=500
x=150
x=500
53
105
1.8
1.4
2.4
2.4
2.4
345
2.3
2.0
2.3
2.3
2.35
455
2.7
2.4
2.7
2.7
2.7
57
105
1.2
1.0
1.1
1.2
1.2
345
1.3
1.3
1.3
1.3
1.3
455
1.5
1.5
1.5
1.4
1.5
58
105
1.2
1.0
1.2
1.3
1.3
345
1.4
1.4
1.5
1.5
1.5
455
1.7
1.6
1.7
1.7
1.7
52
105
0.33
0.33
0.33
0.33
0.33
345
0.41
0.41
0.41
0.41
0.41
455
0.42
0.42
0.42
0.42
0.42
x is the ratio of the density of bulk gold to that of the gold black deposit. μcσa is the reduced conductivity per square of deposit. A is the fraction absorbed. T is the fraction transmitted.