Composition Dependence of Normal Spectral Emissivity of Liquid Ni–Al Alloys

Abstract

Ni–Al alloys are good candidates for the fabrication high-efficiency gas turbine blades. The Ni–Al system is also important as a solution for AlN crystal growth. To accurately model the casting process for turbine blade fabrication and design solution growth techniques for AlN, the thermophysical properties of the liquid alloy are required. In this study, the normal spectral emissivity of Ni–Al liquid alloys was measured using the electromagnetic levitation technique under a static magnetic field. Both the melting temperature of Cu and the eutectic temperature of the Ni–C system were used as fixed temperature points for spectrometer calibration to obtain the radiance of liquid Ni–Al alloys. The composition dependence of the normal spectral emissivity of liquid Ni–Al alloys had a maximum at ~40–50 mol%Al-Ni. The Ni–Al binary system had a stable intermetallic compound of NiAl with a melting temperature of 1911 K. The short range chemical ordering could be attributed to strong bonding between Ni and Al atoms, which affected the scattering cross section of the conduction electrons even in the liquid state; hence, the normal spectral emissivity had a maximum at ~40–50 mol%Al-Ni.

1. Introduction

High-efficiency gas turbines for thermal power plants and aircrafts require heat-resistant alloys, and Ni–Al alloys have been widely used for fabrication of such turbine blades. For accurate modelling of the casting process of the alloy, the thermophysical properties of Ni–Al alloys in the liquid state are needed. We recently investigated liquid Ni–Al alloys as the solution for AlN crystal growth. Al could be stably maintained in the Ni–Al solution even at high temperatures; therefore, the moderate driving force of the AlN formation reaction could be controlled by choosing the chemical composition of the solution and growth tempertaure.¹⁾ To design the solution growth technique for AlN, the thermophysical properties of the liquid Ni–Al alloys are needed. In previous work, our group developed a high-temperature thermophysical property measurement system called PROSPECT,^2,3,4,5,6) which uses electromagnetic levitation with a static magnetic field. The density of the liquid Ni–Al alloys was previously measured using PROSPECT.⁷⁾ Emissivity is an important parameter to understand the heat transfer phenomenon by radiation; it is also required to measure the heat capacity using laser modulation calorimetry as the laser absorptivity.^8,9) Therefore, in this study, we measured the normal spectral emissivity of liquid Ni–Al alloys using the PROSPECT system.

2. Experimental

Details of the experimental procedures have been described in previous papers,^5,10,11) therefore only a brief outline is provided here. The normal spectral emissivity ε(λ, T) is defined as the ratio between the normal spectral radiance emitted from a sample R_s(λ, T) and from a blackbody R_b(λ, T) as:   

$$\epsilon (\lambda ,T)=\frac{R_{\mathrm{s}}(\lambda ,T)}{R_{\mathrm{b}}(\lambda ,T)}.$$(1)

Prior to the measurement of radiation from the liquid Ni–Al sample, a multichannel spectrometer was calibrated using a quasi-blackbody. A schematic diagram of the quasi-blackbody used in this study is shown in Fig. 1(a). The quasi-blackbody was made of graphite and had a cavity at the center of the top face. The cavity was 5 mm in diameter and 50 mm in depth. The melting temperature of Cu (1357.8 K) was as that for ITS-90¹²⁾ and the eutectic temperature of the Ni–C binary system (1599.7 K)¹³⁾ were used as fixed points to calibrate the spectrometer over the applied experimental temperature range. The cavity was surrounded by a metal bath consisting of pure Cu or 7-mol%C-containing Ni to ensure a homogenized temperature distribution in the blackbody; then, the cavity radiation was observed using a multichannel spectrometer (spectral range: 530–1100 nm; USB2000, Ocean Optics Inc., Florida). The Cu, Ni, and C used in the blackbody had a purity of 99.99 mass%. The emissivity of the blackbody cavity was estimated to be 0.999.¹⁴⁾ Figure 1(b) shows the experimental apparatus for the emissivity measurements using PROSPECT. For the calibration of the multichannel spectrometer, the blackbody and solenoidal coil replaced the sample and levitation coil as shown in Fig. 1(b). The blackbody was inductively heated by the solenoidal coil under a normal pressure of 5 vol%H₂-Ar. The spectrometer was calibrated at the fixed points that appeared as a plateau during the heating process. The normal spectral radiance from the blackbody was obtained by Planck’s law.

Fig. 1.

Schematic diagrams of (a) the quasi-black body and (b) experimental apparatus for emissivity measurement using the electromagnetic levitation technique under a static magnetic field. (Online version in color.)

The normal spectral emissivities of liquid Ni–Al alloys were measured using the PROSPECT system through the same optical path as the spectrometer calibration experiment shown in Fig. 1(b). The Ni–Al alloy samples were prepared by arc-melting of a mixture of Ni (99.99 mass%) and Al (99.99 mass%). The pre-melted sample was placed on a sample holder made from sintered BN, and the chamber was then evacuated to 10⁻² Pa using a turbo molecular pump coupled with a rotary pump. After evacuation, the chamber was filled with 5 vol%H₂-Ar and He gases. These gases were purified by a deoxidation column containing heated metallic Mg as an oxygen getter. Prior to levitating the sample, a metallic Ti film was heated to remove residual oxygen in the chamber. This procedure was effective for preventing oxidation of the Ni–Al sample.

The sample was levitated by applying a radio-frequency current to the levitation coil. A vertical static magnetic field of 4 T was applied to the sample droplet to suppress surface oscillation and translational motion of the droplet using a super-conducting magnet. Temperature control was realized by exposing the droplet to a He gas flow. The sample temperature was measured using a single-color pyrometer (temperature range: 450–2500°C, spectral range: 1.45–1.8 μm; IGA140/MB25, IMPAC Pyrometers, LumaSense Technologies, Germany). The temperatures were calibrated using the liquidus temperature of each alloy,⁷⁾ and temperatures other than the liquidus temperature were determined by assuming that the normal spectral emissivity of the sample has no temperature dependence at the pyrometer wavelength (1.6 μm). The levitated droplet was monitored using a high speed camera (MC 1310, Mikrotron, Germany) to confirm that no oxide form on the droplet during experiment.

3. Results

Intensity profiles of the radiation from the blackbody containing Cu and 7 mol%C-Ni during the heating process were observed using a spectrometer at a wavelength of 940 nm, as shown in Figs. 2(a) and 2(b), respectively. A plateau corresponding with the melting temperature of Cu or the eutectic temperature of Ni–C was observed. The intensity profiles during heating process around the fixed point were measured three times for each blackbody. The normal spectral radiance at the fixed points was calculated by Planck’s law. The relationship between normal spectral radiance and the output count of the spectrometer is shown for 800 to 1000 nm in Fig. 3. The normal spectral radiance of the Ni–Al droplet was measured using the same spectrometer, and it was calibrated using the linear relationships.

Fig. 2.

Intensity profiles of the radiation from the quasi-blackbody contained (a) Cu and (b) 7 mol%C-Ni observed using a spectrometer during heating process.

Fig. 3.

Relationship between normal spectral radiance and output count intensity of the spectrometer.

Figures 4(a) and 4(b) show the wavelength dependence of the normal spectral emissivity of liquid Ni and the temperature dependence of the normal spectral emissivity at a wavelength of 940 nm for liquid Ni, respectively, along with literature data.^{5,15,16,17,18)} The vertical dashed line in Fig. 4(b) presents the melting temperature of Ni. The obtained data agreed with literature within an expanded uncertainty range, as shown by the error bars in Fig. 4(b).

Fig. 4.

(a) The wavelength dependence of the normal spectral emissivity, (b) the temperature dependence of the normal spectral emissivity at a wavelength of 940 nm for liquid Ni. A vertical dashed line in Fig. 4(b) presents the melting temperature of Ni. (Online version in color.)

Figure 5 shows the wavelength dependence of the normal spectral emissivity of the liquid Ni–Al alloys. The temperatures of each sample are shown in Fig. 5. The normal spectral emissivity of the liquid Ni–Al alloys slightly decreased with increasing wavelength in this wavelength region, except for 80 mol%Al-Ni.

Fig. 5.

Wavelength dependence of the normal spectral emissivity of liquid Ni–Al. (Online version in color.)

Figure 6 shows the temperature dependence of the normal spectral emissivity for the liquid Ni–Al alloys at a wavelength of 940 nm. Each vertical dashed line presents the liquidus temperature for each alloy. The normal spectral emissivities were constant with temperature within the experimental temperature region, as shown in Fig. 6. As explained in the Experimental section, temperatures other than the liquidus temperature were determined by assuming that the normal spectral emissivities of the liquid Ni–Al alloys have no temperature dependence at the pyrometer wavelength of 1.6 μm. Hence, it should be pointed out that the obtained results are consistent with the assumptions, although the wavelengths is different each other. Except for the liquidus temperature, some uncertainty remains for the true temperature measurement.

Fig. 6.

Temperature dependence of the normal spectral emissivity of liquid Ni–Al at a wavelength of 940 nm. Each vertical dashed line presents the liquidus temperature of each alloy. The emissivity values including twice the standard deviation are shown in the figure. (Online version in color.)

The error bars in Figs. 4(b) and 6 indicate expanded uncertainty for each data point, as evaluated using the Guide to the Expression of Uncertainty in Measurement.¹⁹⁾ The uncertainty of the normal spectral emissivity measurement (u(ε)) is expressed as:   

$$\begin{array}{l}{u}^2(\epsilon )={\left({\displaystyle \frac{\partial \epsilon }{\partial a}}\right)}^2{u}^2(a)+{\left({\displaystyle \frac{\partial \epsilon }{\partial X_{\mathrm{s}}}}\right)}^2{u}^2(X_{\mathrm{s}})\\ \hspace{1em}\hspace{1em}\hspace{1em}+{\left({\displaystyle \frac{\partial \epsilon }{\partial T}}\right)}^2{u}^2(T_{\text{Fluctuation}})+{\left({\displaystyle \frac{\partial \epsilon }{\partial T}}\right)}^2{u}^2(T_{\text{pyrometer}}),\end{array}$$(2)

where u(a) is the uncertainty of the calibration coefficient obtained from Fig. 3, u(X_S) is the standard deviation of the output intensity for the spectrometer, u(T_Fluctuation) is the standard deviation of the temperature measurement of the sample, and u(T_pyrometer) is the accuracy of the pyrometer. As an example, the uncertainty analysis for pure Ni at 1537 K and 940 nm are given in Table 1. Table 1 shows that u(T_pyrometer) is the dominant factor in the normal spectral emissivity measurement.

Table 1. Uncertainty analysis sheet of the normal spectral emissivity measurement for pure Ni at 1573 K at a wavelength of 940 nm.

Factor	Standard uncertainty	Sensitivity coefficient	Contribution
Uncertainty of slope of calibration line: u(a)	1.01 × 10−3 Wm−1μm−1	2.60 × 10−1 W−1m2μm	2.63 × 10−4
Variation of detected radiance from sample: u(XS)	2.22 × 101 (counts)	5.17 × 10−5	1.14 × 10−3
Standard deviation of temperature measurement: u(TFluctuation)	2.17 × 10−1 K	−2.10 × 10−3 K−1	4.55 × 10−4
Accuracy of pyrometer: u(Tpyrometer)	4.44 K	−2.10 × 10−3 K−1	9.31 × 10−3
Combined uncertainty: u(ε)			9.39 × 10−3
Expanded uncertainty: 2u(ε)			1.88 × 10−2
Emissivity of Ni: ε			0.327
Uncertainty			5.74%

Figure 7 shows the composition dependence of the normal spectral emissivity for the liquid Ni–Al alloys at 1873 K at a wavelength of 940 nm. For 10, 70, and 80 mol%Al-Ni, the normal spectral emissivity at 1873 K was obtained via extrapolation, with the assumption that the normal spectral emissivity had no temperature dependence up to 1873 K. The normal spectral emissivity of pure Al was obtained from literature.²⁰⁾ As shown in Fig. 6, the normal spectral emissivity of the Ni–Al alloys had a maximum value at ~40–50 mol%Al-Ni.

Fig. 7.

Composition dependence of the normal spectral emissivity of liquid Ni–Al at a wavelength of 940 nm. (Online version in color.)

4. Discussion

For comparison with the experimentally obtained values, we calculated the normal spectral emissivity of liquid Ni–Al alloys based on the Drude model. In the Drude model, the normal spectral emissivity can be obtained from the density, the electric conductivity, and the electron number per atom of the liquid Ni–Al alloy. The normal spectral emissivity is expressed using the refractive index n and extinction coefficient k as:   

$$\epsilon =\frac{4n}{{(n+1)}^2+k^2}.$$(3)

The n and k are expressed as:   

$$n^2-k^2=1-\frac{{\omega }_p{}^2{\tau }^2}{1+{\omega }^2{\tau }^2},$$(4)

  

$$2nk=\frac{{\omega }_p{}^2\tau }{\omega (1+{\omega }^2{\tau }^2)}.$$(5)

Here, ω_p is the plasma angular frequency and τ is the relaxation time. The ω_p and τ are expressed as:   

$${\omega }_p{}^2=\frac{N{e}^2}{m{\epsilon }_0},$$(6)

  

$$\tau =\frac{m}{{\rho }_{\text{el}}N{e}^2}.$$(7)

Here, N is the number of free electrons per unit volume, m is the electron mass, e is the elementary charge, ε₀ is the permittivity of vacuum, and ρ_el is the electrical resistivity. Five groups reported the electrical resistivity of liquid Ni–Al^{21,22,23,24,25)} alloys, as shown in Fig. 8, and the reported data were in general agreement with each other. Antropov et al. reported the electrical conductivity over a wide composition range,²²⁾ and their reported electrical resistivity was used in this calculation. N can be obtained from the number of free electrons per atom and the density of the alloy. The number of free electrons per atom for pure Al and Ni at zero electron temperature were 3.0 and 1.4, respectively, from first-principles study.²⁶⁾ Here, N of the Ni–Al alloys was estimated assuming that N varied linearly with mole fraction. The density of the liquid Ni–Al was measured in our previous work.⁷⁾ The values used for the calculation are summarized in Table 2.

Fig. 8.

Composition dependence of the electrical resistivity of liquid Ni–Al. (Online version in color.)

Table 2. Values used for calculation of normal spectral emissivity of liquid Ni–Al based on the Drude model.

Al content mol%	Electron number per atom	Density kg/m3	Electrical resistivity Ωm
0	1.40	7746	9.10 × 10−7
3	1.45	7572	1.04 × 10−6
7	1.51	7341	9.71 × 10−7
10	1.56	7168	9.09 × 10−7
12	1.59	7053	9.51 × 10−7
16	1.66	6822	9.57 × 10−7
18	1.69	6707	9.99 × 10−7
21	1.73	6535	1.03 × 10−6
25	1.80	6305	1.07 × 10−6
30	1.88	6019	1.14 × 10−6
36	1.98	5675	1.13 × 10−6
40	2.04	5447	1.16 × 10−6
45	2.12	5162	1.26 × 10−6
50	2.20	4877	1.24 × 10−6
59	2.34	4366	1.12 × 10−6
70	2.52	3744	8.50 × 10−7
79	2.66	3236	6.63 × 10−7
100	3.00	2058	4.03 × 10−7

Permittivity of vacuum: 8.85 × 10⁻¹² F/m

Electron mass: 9.11 × 10⁻³¹ kg

Elementary charge: 1.60 × 10⁻¹⁹ C

The composition dependence of the normal spectral emissivity of liquid Ni–Al alloys was calculated using the Drude model and presented together with the experimental data in Fig. 7. The experimentally obtained composition dependence could be closely reproduced using the Drude model. Both experimental and calculated values had a maximum at ~50 mol%Al-Ni. The Ni–Al binary system has a stable intermetallic compound, NiAl, with a melting temperature of 1911 K.²⁷⁾ Recently, we reported that the excess volume of liquid Ni–Al alloys has a minimum at ~50 mol%Al-Ni.⁷⁾ In addition, the local structure of the liquid Ni–Al alloys was investigated via X-ray diffraction and computational simulations.^28,29,30,31) The results indicated that the position of the local maximum of the first peak of the partial pair distribution function between Ni and Al atoms is smaller than that between the Ni and Ni atoms and between the Al and Al atoms. From these reports, we considered that the short-range chemical ordering, attributed to the strong bonding between Ni and Al atoms, could affect the scattering cross section of the conduction electrons. An increase in the scattering cross section of the conduction electrons causes an increase in the electrical resistivity. The probability that the nearest neighbors are hetero atoms has a maximum at 50 mol%Al-Ni, thus, the electrical resistivity has a maximum at the composition as shown in Fig. 8. The emissivity increases with increasing the electrical resistivity as shown by Eqs. (3), (4), (5), (6), (7), therefore, the normal spectral emissivity had a maximum at ~40–50 mol%Al-Ni as shown in Fig. 7.

5. Conclusion

The normal spectral emissivity of liquid Ni–Al alloys was measured using the PROSPECT system. The melting temperature of Cu (1357.8 K) and the eutectic temperature of Ni–C (1599.7 K) were used as fixed points to calibrate the spectrometer. The normal spectral emissivity of the liquid Ni–Al alloys showed negligible temperature dependence within the investigated temperature range. The composition dependence of the normal spectral emissivity of liquid Ni–Al alloys had a maximum at ~40–50 mol%Al–Ni. The results agreed with the normal spectral emissivity calculated by the Drude model. We considered that short range chemical ordering, attributed to strong bonding between the Ni and Al atoms, affected the scattering cross section of the conduction electrons, even in the liquid state; hence, the normal spectral emissivity of liquid Ni–Al alloys had a maximum at ~40–50 mol%Al-Ni.

Acknowledgments

This work was supported by Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Numbers 26249113, 18J11474 and 20H02633, Foundation for Promotion of Material Science and Technology of Japan (MST Foundation) and ISIJ Research Promotion Grant.

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