Optical properties (at a wavelength of 684.5 nm) - thermophysics.ru

Optical properties (at a wavelength of 684.5 nm) and radiance temperatures at
the melting point of group VIIIb transition metals cobalt, nickel, palladium and
platinum 1 .
Claus Cagran 2 , Boris Wilthan 2 , Gernot Pottlacher 2
1 Work to be presented at ECTP 2005,Bratislava; intended for publication in High Temp.-
High Press.
2
Institute of Experimental Physics, Graz University of Technology, Petersgasse 16,
8010 Graz, Austria, Email: pottlacher@tugraz.at

ABSTRACT
The optical constants (index of refraction n and extinction coefficient k) and normal spectral
emissivity of liquid cobalt, nickel, palladium and platinum were measured by a Division-of-
Amplitude-Photopolarimeter (DOAP) operating at a wavelength of 684.5 nm. The polarimeter
is part of a pulse-heating apparatus using resistive self-heating of conducting specimens from
room temperature to the end of the liquid state in less than 50 µs. Temperature during this
experiments (except for nickel) was simultaneously determined by a fast optical pyrometer
operating at a center wavelength of 650 nm utilizing Planck’s radiation law. Additionally,
results for radiance temperatures at melting at 684.5 nm calculated from emissivity and the
melting temperature are presented for all four materials. The melting-point emissivities
(normal spectral) / radiance temperatures at 684.5 nm, as determined by averaging several
experimental results for each material, are: 0.346 / 1623.1 K for cobalt, 0.365 / 1595.8 K for
nickel, 0.360 / 1678.8 K for palladium, and 0.364 / 1858.9 K for platinum, respectively. The
results for all determined optical properties are given as melting-point values as well as linear
least-squares fits to the liquid state. Based on uncertainties arising from polarimetry,
pyrometery and sample conditions, the combined uncertainty for emissivity and optical
constants (with a coverage factor of k = 2) is estimated and reported.
INTRODUCTION
Ever since Drude proposed his theory and a formula for the optical properties of metals based
on free charge carriers in 1900 [Drude 1900], lots of efforts have been taken to determine
[i.e., Palik 1990] and interpret [e.g., Roberts 1955] the optical constants N = n – ik (N –
complex index of refraction, n – (real or classical) index of refraction, k – extinction
coefficient) of metals and metal surfaces.
According to Palik 1990 (subpart 1) four general methods are used for obtaining experimental
data from which optical constants can be deduced: the Kramers-Kronig method, the
reflectance method, ellipsometry, and the use of electron-loss spectroscopy. Out of these four
techniques, data obtained by the Kramers-Kronig method and electron-loss spectroscopy are
found to be more accurate than by the remaining two methods. Nevertheless, all four methods
are not basically restricted to the solid state of the metals under investigation but
measurements in the liquid state are often avoided or omitted (due to the high chemical
2

eactivity of liquid metals and hence the arising ambiguities in data interpretation). Therefore,
data for n and k in the liquid state are very sparse in literature.
A couple of years ago, an ellipsometric measurement device was added to the experimental
pulse-heating setup at Graz University of Technology (TUG). The purpose of this
ellipsometer was the determination of normal spectral emissivity to increase the accuracy of
pyrometrical obtained temperatures during pulse-heating experiments on metals and alloys.
Pulse-heating uses the passage of a large current pulse over a conducting sample (cylindrical
or rectangular shaped wires) which are resistively self-heated at rates up to 10 8 K/s. As a
consequence, typical experimental durations are about 50 µs at this high heating rates. During
this short period, samples can be heated from room temperature up to the end of the stable
liquid phase (boiling point), which is one of the main advantages of this containerless
technique.
Due to the time-scale used throughout pulse-heating experiments, the used ellipsometer
cannot use any rotation devices or moving parts. Therefore, a µs-Division-of-Amplitude-
Photopolarimeter (DOAP) is used whose basic concepts, utilizing the Stokes formalism for
polarized light, have first been pointed out by Azzam (1982) and later on adopted and applied
by Krishnan (1992).
Unlike the other four methods mentioned above, the DOAP enables the time resolved
measurement of optical properties n and k during such pulse-heating experiments in the liquid
state. The anticipated (normal spectral) emissivity can be calculated in a second step as a byproduct
from the optical constants.
Over the last few years a wide variety of pure metals have been investigated concerning
emissivity at melting and its behaviour in the liquid phase and the results have been partially
published elsewhere [Cagran 2002, Cagran 2004].
EXPERIMENTAL
As mentioned in the introduction, the optical constants n and k as well as normal spectral
emissivity are obtained with a DOAP system which itself is a part of a resistive pulse-heating
apparatus at the Institute of Experimental Physics (IEP-TUG). More detailed information as
well as a schematic drawing of the system can be found in [Seifter 2002, Cagran 2002].
The basic principle of this device is to detect (time resolved) the change in polarization of an
initially polarized laser beam of known polarization upon refection from a sample surface.
The Stokes formalism of polarized light uses the division of the overall light intensity into
3

four independent components (thus the name of the DOAP) which are recorded separately.
Out of these four so-called ‘Stokes parameters’, the state of polarization after reflection can be
evaluated with help of the knowledge of the initial polarization. In a second step, n and k can
be related to the polarization of the reflected light and the spectral normal reflectivity, R ⊥ , of
the sample material is obtained with
2 2
( n2
− n1
) + k2
2 2
( n + n ) + k
R⊥ =
(1)
2
1
2
where n 2 and k 2 are the optical constants of the material under investigation and n 1 is the
refractive index of the ambient atmosphere (air or nitrogen).
In turn, normal spectral emissivity ε for opaque materials can be deduced from reflectivity by:
2 2
( n2 − n1
) + k2
4n1n2
=
2 2
2 2
( n + n ) + k ( n + n ) + k
ε 1−
R = 1−
(2)
⊥
=
⊥
2
1
In our experiment, the measurement of the optical properties and emissivity is limited to
normal incidence and to the laser wavelength used within the DOAP system, nominally
λ = 684.5 nm. The laser wavelength of the DOAP was chosen from commercially available
solid state laser diodes to match the wavelength of the main pyrometer (λ = 650 nm) as close
as possible. Although the emissivity measurement improves the pyrometric temperature, a not
yet exactly specified uncertainty is implied by the difference in wavelengths.
More in-depth details on the DOAP and the data evaluation can are shown in Seifter (2002)
and in Cagran (2003).
Additionally, radiance temperatures, T r , for all materials under investigations can be
calculated with knowledge of emissivity, ε, its wavelength, λ (in our case 684.5 nm), and the
melting temperature, T m , of the material with:
2
c2
1
T
r
= ⋅
(3)
λ ⎛ ⎛ c ⎞ ⎞
⎜
2
exp − ⎟
⎜
⎜
⎟ 1
⎝ λ ⋅Tm
⎠ ⎟
ln⎜1+
⎟
⎜ ε ⎟
⎜
⎟
⎝
⎠
c 2 deontes Planck’s second radiation constant, and its value is c 2 = 1.4388 mK [Henning
1977].
2
1
2
RESULTS AND DISCUSSION
Wired shaped metal samples (cylindrical cross-section of nominally ∅ = 0.5 mm and an
average length of about 45 mm) have been used for all four investigated group VIIIb metals.
4

Some of the samples have been treated with high grade abrasive paper and acetone prior to
the experiment to remove thin surface layers (i.e. oxides, nitrides, etc.) and organic
substances, e.g., fat. Further material specifications can be found in Tab. 1.
The surface treatment prior to the experiments and the initial surface structure of the sample
material (which is mainly a result of the wire drawing) can drastically change the solid state
optical properties/emissivity of the sample material as ε, n, and k are in our experiments
dominated by the surface. Therefore, one can almost produce any solid state value for these
properties by changing the surface (roughness, structure). This effect vanishes not until
melting is reached and smoothening of the surface due to surface tension generates
reproducible conditions for each material 1 . As a result, the DOAP is primarily intended for
measurements at melting and in the liquid state; reported values for the solid state are shown
for completion and to outline the overall behaviour of ε, n, and k before T m .
All results presented in figures in the following are mean values of several independent
measurements (the exact number of experiments for each metal is stated in the corresponding
section).
Cobalt: Experimental results (average of 6 independent measurements) for optical properties n
and k and normal spectral emissivity for solid and liquid cobalt are presented in Fig.1. The
values of n, k, and ε at melting and linear least-squares fits for the liquid state as well as the
radiance temperature calculated according to Eq.(3) can be found in Tab. 2 and Tab. 3.
1 To determine reproducible solid state values, the material under investigation has to undergo special treatments
(tempering under inert gas (or vacuum) at different temperatures for some hours) and special measurement
conditions have to be used (vacuum chamber or non-reactive inert gas atmosphere). As such procedures can not
be applied to each sample at TUG and solid state values are not of primary interest, reported results are restricted
to liquid state data only.
5

normal spectral emissivity
at 684.5 nm
optical constants n and k
at 684.5 nm
0.525
0.500
0.475
0.450
0.425
0.400
0.375
0.350
0.325
0.300
0.275
800 1000 1200 1400 1600 1800 2000 2200 2400 2600
radiance temperature at 650 nm, K
5.25
5.00
4.75
4.50
4.25
4.00
3.75
k
3.50
3.25
3.00
2.75
2.50
2.25
2.00
n
1.75
800 1000 1200 1400 1600 1800 2000 2200 2400 2600
radiance temperature at 650 nm, K
a
b
Figure 1: Normal spectral emissivity (a) and optical properties n and k (b) at 684.5 nm of cobalt at
melting and in the liquid state versus radiance temperature. (a): open circles: emissivity data of this
work (average of 6 independent measurements); solid line: linear least-squares fit to the liquid state;
full up-triangle: literature data of [Kaschnitz 1998a] interpolated for 684.5 nm. (b): solid squares:
index of refraction, n, data of this work; open down-triangles: extinction coefficient, k, data of this
work; dashed lines: linear least-squares fits to the solid state.
The emissivity value at melting observed within the recent measurements is in good
agreement with the literature data published by Kaschnitz (1998a). Figure 1a exhibits the
typical ε drop at melting due to smoothening of the surface (as described in the preceding
section). No literature data for comparison have been found for n and k of cobalt. All three
properties show a slight increase throughout the liquid state.
Nickel: Experimental results (average of 6 independent measurements) for optical properties n
and k and normal spectral emissivity for solid and liquid nickel are presented in Fig.2. The
6

values of n, k, and ε at melting and linear least-squares fits for the liquid state as well as the
radiance temperature calculated according to Eq.(3) can be found in Tab. 2 and Tab. 3.
Note: As the radiance temperature of nickel almost equals the onset temperature of the
pyrometer at λ = 650 nm, measurements have been carried out using another pyrometer
operating at 1570 nm. Since plotting optical properties and emissivity at 684.5 nm versus
radiance temperatures obtained at a completely different wavelength is not significant, values
for nickel are shown versus temperature assuming a constant emissivity from melting
throughout the liquid state (emissivity in liquid state / emissivity at melting = ε/ε m = 1). This
assumption can be supported by the emissivity results in Fig. 2a.
0.525
0.500
normal spectral emissivity
at 684.5 nm
optical constants n and k
at 684.5 nm
0.475
0.450
0.425
0.400
0.375
0.350
0.325
1200 1400 1600 1800 2000 2200 2400
temperature (assuming ε/ε m
=1), K
4.50
4.25
4.00
3.75
3.50
3.25
k
3.00
2.75
2.50
2.25
2.00
n
1.75
1200 1400 1600 1800 2000 2200 2400
temperature (assuming ε/ε m
=1), K
a
b
Figure 2: Normal spectral emissivity (a) and optical properties n and k (b) at 684.5 nm of nickel at
melting and in the liquid state versus temperature (assuming a constant emissivity, ε/ε m =1, throughout
the liquid state). (a): open circles: emissivity data of this work (average of 6 independent
measurements); solid line: linear least-squares fit to the liquid state; solid up-triangle: literature data of
[Kaschnitz 1998b] interpolated for 684.5 nm. (b): solid squares: index of refraction, n, data of this
work; open down-triangles: extinction coefficient, k, data of this work; open square/solid down
7

triangle: literature data of n/k for the solid state of nickel at λ = 688.8 nm taken from [Palik 1990];
dashed lines: linear least-squares fits to the solid state.
The emissivity value at melting (Fig. 2a) observed within the recent measurements is again in
good agreement with the literature data published by Kaschnitz (1998b), whereas n and k
show an interesting contradiction: the solid state values of n are (within the stated
uncertainties) in good agreement with the value reported by Palik (1990) which does not hold
for k. The interesting fact is that as all reported properties change at melting, k in the liquid
state compares quite good to the solid state value from Palik (1990). This alternating
behaviour of n and k is believed to result from the already mentioned solid state surface
structure. For liquid nickel, the two optical constants show a slight decrease throughout the
liquid state whereas emissivity increases slightly.
Palladium: Experimental results (average of 6 independent measurements) for optical
properties n and k and normal spectral emissivity for solid and liquid palladium are presented
in Fig.3. The values of n, k, and ε at melting and linear least-squares fits for the liquid state as
well as the radiance temperature calculated according to Eq.(3) can be found in Tab. 2 and
Tab. 3. Recently obtained thermophysical properties of solid and liquid palladium can be
found in a corresponding article [Cagran 2005].
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normal spectral emissivity
at 684.5 nm
optical constants n and k
at 684.5 nm
0.525
0.500
0.475
0.450
0.425
0.400
0.375
0.350
0.325
1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200
radiance temperature at 650 nm, K
4.50
4.25
4.00
3.75
3.50
3.25
3.00
2.75
2.50
k b
2.25
2.00
n
1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200
radiance temperature at 650 nm, K
a
Figure 3: Normal spectral emissivity (a) and optical properties n and k (b) at 684.5 nm of palladium at
melting and in the liquid state versus radiance temperature. (a): open circles: emissivity data of this
work (average of 6 independent measurements); solid line: linear least-squares fit to the liquid state;
full up-triangle: literature data of [McClure 1999] interpolated for 684.5 nm. (b): solid squares: index
of refraction, n, data of this work; open down-triangles: extinction coefficient, k, data of this work;
dashed lines: linear least-squares fits to the solid state.
The emissivity value at melting (Fig. 3a) observed within the recent measurements is once
again in good agreement with the literature data published by McClure (1999). As for cobalt,
no literature data for comparison have been found for n and k of palladium. The optical
constants of palladium decrease whereas emissivity shows an increase during the liquid state.
9

Platinum: Experimental results (average of 7 independent measurements) for optical
properties n and k and normal spectral emissivity for solid and liquid platinum are presented
in Fig.4. The values of n, k, and ε at melting and linear least-squares fits for the liquid state as
well as the radiance temperature calculated according to Eq.(3) can be found in Tab. 2 and
normal spectral emissivity
at 684.5 nm
optical constants n and k
at 684.5 nm
0.39
0.38
0.37
0.36
0.35
0.34
0.33
a
0.32
0.31
0.30
0.29
0.28
1400 1600 1800 2000 2200 2400 2600
radiance temperature at 650 nm, K
4.6
4.4
4.2
4.0
k
3.8
3.6
3.4
3.2
b
3.0
2.8
n
2.6
2.4
2.2
1400 1600 1800 2000 2200 2400 2600
radiance temperature at 650 nm, K
Figure 4: Normal spectral emissivity (a) and optical properties n and k (b) at 684.5 nm of platinum at
melting and in the liquid state versus radiance temperature. (a): open circles: emissivity data of this
work (average of 6 independent measurements); solid line: linear least-squares fit to the liquid state;
solid up-triangle: literature data of [McClure 1999] interpolated for 684.5 nm; solid diamond: solid
state literature value extrapolated to melting taken from [Righini, 1980]. (b): solid squares: index of
refraction, n, data of this work; open down-triangles: extinction coefficient, k, data of this work; open
square/solid down triangle: literature data of n/k for the solid state of platinum at λ = 688.8 nm taken
from [Palik 1990]; dashed lines: linear least-squares fits to the solid state.
As can be seen from Figure 4a, platinum exhibits a different emissivity behaviour at melting
compared to the other three materials: ε of platinum does not drop but suddenly increases at
the melting transition. This is caused by the good processability of platinum: drawn wires
10

already have a perfectly smooth, shiny and most notably reproducible surface. Therefore,
results obtained with the DOAP for the solid state are of equal quality as for the liquid state.
Figure 4a reports the recently obtained emissivity results for platinum and both ε at the onset
and after melting shows a good agreement with respective literature data, Righini (1980) for
the solid and McClure (1999) for the liquid. By abrading the platinum wires prior to the
experiment emissivity in the solid can be drastically increased resulting in the experimental
signals observed for the other three presented materials (higher emissivity in solid, drop at
melting). Nevertheless, as shown earlier for silver [Cagran 2003], the observed emissivity
value and behaviour in the liquid is independent from the initial surface roughness.
The different optical behaviour is also noticeable in the results for n and k as both show
opposite trends upon melting. The refractive index increases (as with the other three
investigated materials) but the extinction coefficient drops at T m . A comparison of the recently
obtained solid state values regarding n and k shows a decent agreement with data published by
Palik (1990) for pure platinum.
For liquid platinum, an increase during the liquid state can be observed for all three
investigated optical properties.
Radiance temperatures: To complete the set of optical properties, radiance temperatures at
melting (at 684.5 nm) have been calculated for all four materials according to Eq. 3. The
individual results can be found in Tab. 2. No comparison of these radiance temperatures with
literature data is provided as the measurement wavelength is not very common and no
significant data are available. Nevertheless, as emissivity is in good agreement with literature
data, radiance temperatures are also expected to be accurate.
UNCERTAINTIES
An in-depth analysis of the uncertainty according to GUM (Guide to the expression of
Uncertainty in Measurement) [GUM 1999] for all feasible thermophysical properties is
currently under development for the pulse-heating system used at TUG. These results will be
incorporated and published as soon as the analysis is completely finished. Meanwhile, the up
to now used estimation of uncertainties has to be applied to the recent measurements which
already incorporates expanded relative uncertainties with a coverage factor of k = 2, as
demanded by the concept of GUM. This recent estimation is based on the reproducibility and
scatter of the measurements. Typically, the signal-to-noise ratio of a single experiment does
11

not exceed ± 6 %. By averaging several different measurements to minimize the noise of the
emissivity signals and applying a linear least-squares fit to the liquid phase behaviour of
normal spectral emissivity, the uncertainty can be reduced up to a factor of 2, thus one yields
an uncertainty of ± 3 %. With respect to GUM and k=2, the uncertainty for normal spectral
emissivity is given with ± 6 % for all materials with the exception of cobalt for which a
uncertainty of ± 8 % (due to a weaker signal/noise ratio) should be given.
A similar argumentation is used when estimating the uncertainty of optical constants n and k
and as a result an uncertainty of ± 6 % (± 8 % for cobalt) is estimated for both optical
constants.
CONCLUSIONS
Optical properties measurements using a µs-DOAP on liquid cobalt, nickel, palladium, and
platinum are presented within the recent work. The results for refractive index n, extinction
coefficient k, normal spectral emissivity ε and radiance temperature at melting T r,m (all
properties at 684.5 nm) are given in graphs as well as in tables for all investigated materials.
From comparison of these data with literature values, it can be seen that the DOAP is also
capable of determining the optical constants of liquid metals.
All four materials exhibit an increase in normal spectral emissivity throughout the liquid state
and thus fit seamlessly into categorization of materials with respect to their liquid state
behaviour of ε as already published earlier in [Cagran 2002].
The results for optical constants in the liquid state are a novelty, as literature data are even
sparse for solid materials but almost no published data exist for the liquid phase. As a future
outlook it can be thought of adding data of optical constants to the standard set of available
optical data determined at TUG.
ACKNOWLEDGEMENTS
The present work is partially supported by the Austrian ‘Fonds zur Foerderung der
wissenschaftlichen Forschung (FWF)’, Vienna, Grant 15055.
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TABLES
Table 1: Summary of material information for cobalt, nickel, palladium, and platinum specimens
Material Supplier Purity Treatment Lot #
Cobalt (Co) Alfa Aesar 99.995% n/a 06079
Nickel (Ni) Advent Research Materials 99.98% annealed Gi1136
Palladium (Pa) Alfa Aesar 99.9% n/a F28J28
Platinum (Pt) Advent Research Materials 99.99+% annealed Gi1800
Table 2: Summary of normal spectral emissivity results at 684.5 nm and radiance temperatures for
liquid cobalt, nickel, palladium, and platinum.
T m : melting temperatures taken from [Bedford 1996]; ε(T m ): normal spectral emissivity at T m ; T r,m :
radiance temperatures at melting (at 684.5 nm); ε(T): linear fit for emissivity in the liquid state; ΔT:
nominal temperature range of validity of ε(T).
Note: all temperatures for ε(T) and ΔT are radiance temperatures at 650 nm except for nickel
(indicated by * , see text).
Material T m [K] ε(T m ) T r,m [K] ε(T) ΔT [K]
Cobalt (Co) 1768.0 0.346 1623.1 0.333 + 8.275×10 -6·T r 1630 < T r < 2650
Nickel (Ni) 1728.0 0.365 1595.8 0.345 + 1.145×10 -5·T * 1728 < T * < 2450
Palladium (Pa) 1828.0 0.360 1678.8 0.306 + 3.226×10 -5·T r 1680 < T r < 3150
Platinum (Pt) 2041.3 0.364 1858.9 0.339 + 1.326×10 -5·T r 1660 < T r < 2500
Table 3: Summary of refractive index and extinction coefficient results at 684.5 nm for liquid cobalt,
nickel, palladium, and platinum.
n(T m ): refractive index at T m ; n(T): linear fit for n in the liquid state; k(T m ): extinction coefficient at T m ;
k(T): linear fit for k in the liquid state; ΔT: nominal temperature range of validity of ε(T).
Note: all temperatures for ε(T) and ΔT are radiance temperatures at 650 nm except for nickel
(indicated by * , see text).
Material n(T m ) n(T) k(T m ) k(T) ΔT [K]
Cobalt (Co) 3.126 2.631 + 3.030×10 -4·T r 4.130 3.999 + 8.021×10 -5·T r 1630 < T r < 2650
Nickel (Ni) 2.949 3.202 - 1.465×10 -4· T * 4.029 4.230 - 1.166×10 -4·T * 1728 < T * < 2450
Palladium (Pa) 2.793 2.934 - 8.347×10 -5·T r 4.104 4.810 - 4.188×10 -4·T r 1680 < T r < 3150
Platinum (Pt) 2.881 1.567 + 7.070×10 -4·T r 4.044 3.717 + 1.761×10 -4·T r 1660 < T r < 2500
13

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