Thermophysical Properties of Rh3X for Ultra-High Temperature Applications
Thermophysical Properties of Rh3X for Ultra-High Temperature Applications
THERMAL CONDUCTIVITY AND THERMAL EXPANSION OF L12 INTERMETALLIC COMPOUNDS OF RHODIUM WITH TITANIUM, ZIRCONIUM, HAFNIUM, VANADIUM, NIOBIUM AND TANTALUM
Thermal conductivity and thermal expansion were measured for the L12 intermetallic compounds Rh3X (X = Ti, Zr, Hf, V, Nb, Ta) in the temperature range 300–1100 K to evaluate the feasibility of applying the compounds as ultra-high temperature structural materials. The thermal conductivities of Rh3X are widely distributed over the range 32–103 W m−1 K−1 at 300 K, but the differences between the thermal conductivities diminish at higher temperatures. A trend is observed in that the thermal conductivity of Rh3X is greater if the constituent X belongs to Group 5 rather than to Group 4 in the Periodic Table. The coefficient of thermal expansion (CTE) values of Rh3X increase slightly with increasing temperature; values are concentrated around 10 × 10−6 K−1 at 800 K. CTE values of Rh3X decrease as X appears lower in the Periodic Table. It is demonstrated that Rh3Nb and Rh3Ta are suitable for ultra-high temperature structural applications due to their higher thermal conductivities and smaller CTE values.
Nickel-based superalloys have been the principal high-temperature structural materials for gas turbine engines. Their properties have been improved significantly by alloying additions, directional solidification and by the use of single crystals (1). However, gas turbine engines have developed to the point where their operating temperatures are now close to the melting temperatures of these alloys. A new base material is therefore required if higher material temperatures are to be achieved.
Much contemporary research on high-temperature structural materials is centred on intermetallic compounds. Several reviews have addressed the potential for intermetallic alloys (2–7). Among intermetallics, rhodium-based L12 compounds offer advantages for high-temperature structural applications. First, the melting points are 300 to 700 K higher than those of nickel-based superalloys (8). Secondly, the L12 crystal structure offers the possibility of enhanced ductility and excellent workability as a result of the large number of possible slip systems. Finally, the two-phase γ/γ′-type microstructure formed in nickel-based superalloys can also be produced in rhodium-based alloys (9–11).
A preliminary study on the mechanical properties of the L12 intermetallic compounds Rh3X (X = Ti, Nb, Ta) is reported elsewhere (12). Rh3Ti shows good ductility up to 30% in compression, over a wide temperature range from room temperature to 1673 K, and both Rh3Nb and Rh3Ta show a positive temperature dependence of strength (a stress anomaly) at around 1273 K. However, by contrast with pioneering work on the mechanical properties of the rhodium-based L12 compounds, few studies on the physical properties of these compounds are found in the literature.
Key parameters for the design of high heat-flux alloy structures for high-temperature service include thermal conductivity and thermal expansion (13, 14). Thermal conductivity data are required to determine the feasibility and the basic design parameters of structural materials. The rapid heat transfer afforded by high thermal conductivity enables efficient cooling which prevents the occurrence of life-limiting heat-attack spots. Higher operating temperatures can thus be sustained. Thermal expansion data are also required, with a view to minimising the thermal expansion mismatch in joints and thermal stress in components. Lower thermal expansion is desirable to avoid fatigue through thermal cycling, since thermal stress depends directly on the magnitude of the thermal expansion.
Rhodium-based compounds Rh3X have L12 crystal structure, Table I, with constituent X belonging to Groups 4 and 5 in the Periodic Table (15). This study is designed to establish a basic data set for the thermal conductivity and the thermal expansion of the L12 intermetallic compounds Rh3X (X = Ti, Zr, Hf, V, Nb, Ta).
The thermal conductivities of Rh3X at 300 K are summarised in Figure 1, where the thermal conductivity is plotted as the column height in the Periodic Table configuration. The largest thermal conductivity is found in Rh3Nb and the smallest in Rh3Ti. The following inequalities are observed:
where λ[Rh3X] represents the thermal conductivity of Rh3X. λ[Rh3X] is therefore larger when X belongs to Group 5, rather than Group 4. The thermal conductivity of an intermetallic compound reaches a maximum at the stoichiometric composition, and decreases monotonically with increasing deviation from stoichiometry (16, 17). The hypothetical thermal conductivity of stoichiometric single-phase L12 Rh3Hf is expected to be slightly greater than the experimental value for Rh-23.5 at.% Hf.
We have previously surveyed the thermal conductivities of B2 aluminides (FeAl, CoAl, NiAl), titanides (FeTi, CoTi, NiTi), and gallides (CoGa, NiGa) at ambient temperature (16). An empirical rule was found for compounds AB, that thermal conductivity decreases monotonically with increasing horizontal distance, in the Periodic Table, of constituent A from constituent B, that is:
The empirical thermal conductivity rule observed for B2 compounds is also observed in Rh3X with the L12 crystal structure.
Figure 2 shows the thermal conductivities of Rh3X as a function of temperature. A continuous decrease in thermal conductivity with increasing temperature is observed for Rh3Nb, Rh3Ta and Rh3Zr, the thermal conductivities of which at 300 K are greater than 80 W m−1 K−1. By contrast, a considerable increase in thermal conductivity with increasing temperature is observed below 900 K for Rh3Ti, which has a much smaller thermal conductivity at 300 K. The thermal conductivities of Rh3Hf and Rh3V are somewhat insensitive to temperature. The thermal conductivities of Rh3X are widely distributed in the range 32 to 103 W m−1 K−1 at 300 K; the values converge to around 65 W m−1 K−1 at 1100 K.
The temperature coefficient of thermal conductivity, k, in the temperature range 300–1100 K can be roughly estimated by using the following equation:
where λ300 K and λ1100 K are the thermal conductivities at the temperature indicated by the subscript. The temperature coefficients obtained for Rh3X are plotted against λ300 K in Figure 3. The plots for intermetallic compounds with crystal structures of L12, B2, and others already reported (18, 19) are also shown in Figure 3, together with data for pure metals (20–22). Note that the data for pure metals in which lattice transformation or magnetic transformation occurs in the temperature range 300–1100 K are excluded. It is well known that the thermal conductivity of h.c.p. metals is anisotropic, so data for polycrystalline materials are adopted for the h.c.p. metals.
The pure metals are generally characterised by having larger thermal conductivities with smaller temperature coefficients, whereas intermetallic compounds have relatively smaller conductivities with larger coefficients. An overall tendency, which can be seen from Figure 3, is that the thermal conductivity and temperature coefficient are inversely correlated in metallic materials. No negative k is observed for conductivities below 20 W m−1 K−1, whereas above 90 W m−1 K−1 hardly any positive k is found.
The thermal conductivity of Rh3Ti is almost equal to those of conventional L12 compounds such as Ni3Al and Ni3Ga, whereas the temperature coefficient of Rh3Ti is much greater. Rh3Nb, Rh3Ta and Rh3Zr are characterised by greater thermal conductivities and negative temperature coefficients. Their thermal conductivities are nearly equal to that of NiAl, which is well recognised as a compound of high thermal conductivity (4, 16). In addition, a negative temperature coefficient is quite rare among intermetallic compounds, being identified solely in FeTi and Ni3Ti other than Rh3X (X = Zr, Nb, Ta). The thermal conductivities of Rh3V and Rh3Hf are a little smaller than that of NiAl. However, it may be noted that they have relatively larger thermal conductivities among intermetallic compounds.
The thermal conductivity of an intermetallic compound is correlated quantitatively with those of the constituents of the compound through Nordheim's relation (23). The high thermal conductivities of Rh3X may be partly due to the high thermal conductivity of pure rhodium, the thermal conductivity of which at 300 K is 150 W m−1 K−1.
Thermal expansion (ΔL/L) results for Rh3X are shown in Figure 4. All the dilatation curves are a smooth function of temperature, with no sudden slope changes. The curves in Figure 4 reveal that the thermal expansion of Rh3Hf is slightly smaller than those of either Rh3Ti or Rh3Zr over the temperature range 300–1100 K.
The difference in ΔL/L is less than 10% at any temperature. Also, the data indicate that Rh3Ta has a smaller thermal expansion than those of Rh3V or Rh3Nb. The slope of the curve of ΔL/L vs. temperature is the coefficient of thermal expansion (CTE). The slight upward curvature in every dilatation curve indicates that the CTE of Rh3X increases with increasing temperature.
CTE values, α, for Rh3X at 800 K are summarised in Figure 5, plotted as column heights on the Periodic Table matrix. The smallest CTE is found for Rh3Ta, whereas Rh3V shows the largest.
The following inequalities are observed:
Thus the trend is that the CTE values of Rh3X decrease as constituent X is positioned lower in the Periodic Table. The deviation from stoichiometry has little influence on the CTE values of intermetallic compounds, as demonstrated in NiAl (24–26) and Ni3Al (26). Therefore, a hypothetical CTE value for stoichiometric Rh3Hf with the L12 single phase is expected to be approximately equal to that of the experimental value for Rh-23.5 at.% Hf.
The CTE values of pure metals are well known to vary inversely with melting points (27). Figure 6 shows the correlation between the CTE at 800 K and the melting points for Rh3X. Data for intermetallic compounds with L12, B2 and D019 structures, obtained by this group (28), are also shown in Figure 6, together with literature data (22, 29) for pure metals. Since the CTE for h.c.p. metals is usually anisotropic, the CTE data for polycrystal were adopted for the h.c.p. metals.
In Figure 6, all the plots for pure metals and intermetallic compounds including Rh3X fall on a common curve, irrespective of crystal structure. The CTEs of Rh3X are concentrated around 10 × 10−6 K−1, approximately equal to that of pure Rh and two-thirds as great as the CTE of conventional intermetallic compounds such as NiAl and Ni3Al. From Figure 6, it can be seen that the smaller CTE values for Rh3X correlate well with the higher melting points of the compounds.
The interatomic force in metallic materials is characterised by cohesive energy, Ecoh, which is the difference between the potential energy of atoms in the gas state and that in crystal of the material. The cohesive energy in an intermetallic compound is expressed as the sum of the sublimation energy of the alloy, Esub, and the heat of formation of the ordered structure, ΔH (30):
Table II summarises the Ecoh, Esub and ΔH data for Rh3X. The Esub values were obtained from the data source (31) and the ΔH values were calculated from Miedema's formula (32, 33). For comparison, Table II also gives data for conventional intermetallic compounds. It is apparent that the cohesive energy of the intermetallic compounds originates mostly from the sublimation energy rather than from the heat of formation of the ordered structure. The greater cohesive energy of Rh3X is correlated with the greater interatomic force, resulting in the higher melting points and smaller CTE values of the compounds. The CTE values of Rh3Nb and Rh3Ta are particularly small among the Rh3X compounds, reflecting their greater cohesive energies.
The thermal conductivity and thermal expansion of the L12 intermetallic compounds Rh3X (X = Ti, Zr, Hf, V, Nb, Ta) were surveyed to evaluate their feasibility as ultra-high temperature structural materials. Thermal properties were measured at temperatures 300–1100 K. Results are summarised as follows:
[i] There is a noticable trend in the thermal conductivity of Rh3X, becoming greater if X belongs to Group 5 rather than to Group 4 in the Periodic Table. Thermal conductivity and its temperature coefficient are inversely correlated for metallic materials. Rh3Nb, Rh3Ta and Rh3Zr are characterised by greater thermal conductivities and smaller temperature coefficients; Rh3Ti by a lower conductivity and a higher coefficient of thermal expansion.
[ii] The dilatation curves for Rh3X are characterised by slight upward curvature, indicating that the coefficient of thermal expansion (CTE) increases with increasing temperature. The CTE of Rh3X decreases as constituent X moves downward in the Periodic Table. The smaller CTE values for Rh3Nb and Rh3Ta are ascribed to their higher cohesive energies.
Thus, by virtue of their high thermal conductivities and small CTEs, Rh3Nb and Rh3Ta are the most suitable of the Rh3X compounds for ultra-high temperature structural applications.
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Yoshihiro Terada is an Associate Professor in the Department of Metallurgy and Ceramic Science, Tokyo Institute of Technology. His main activities are in the thermal and mechanical properties of metallic materials for high-temperature applications.
Kenji Ohkubo is a Technician in the Division of Materials Science and Engineering, Hokkaido University. His major field of interest is the determination and characterisation of thermal properties in metallic materials.
Seiji Miura is an Associate Professor in the Division of Materials Science and Engineering, Hokkaido University. His research interest is the development of intermetallic alloys for ultra-high temperature applications.
Tetsuo Mohri is a Professor in the Division of Materials Science and Engineering, Hokkaido University. His major field of interest is the first-principles study of phase stability, equilibria and transformation for metallic systems.