Platinum Metals Rev., 2006, 50, (2), 69–76 69

Nickel-based superalloys have been the princi-pal high-temperature structural materials for gasturbine engines. Their properties have beenimproved significantly by alloying additions, direc-tional solidification and by the use of single crystals(1). However, gas turbine engines have developedto the point where their operating temperatures arenow close to the melting temperatures of thesealloys. A new base material is therefore required ifhigher material temperatures are to be achieved.

Much contemporary research on high-tempera-ture structural materials is centred on intermetalliccompounds. Several reviews have addressed thepotential for intermetallic alloys (2–7). Amongintermetallics, rhodium-based L12 compoundsoffer advantages for high-temperature structuralapplications. First, the melting points are 300 to700 K higher than those of nickel-based superal-loys (8). Secondly, the L12 crystal structure offersthe possibility of enhanced ductility and excellentworkability as a result of the large number of pos-

sible slip systems. Finally, the two-phase γ/γ′-typemicrostructure formed in nickel-based superalloyscan also be produced in rhodium-based alloys(9–11).

A preliminary study on the mechanical proper-ties of the L12 intermetallic compounds Rh3X (X =Ti, Nb, Ta) is reported elsewhere (12). Rh3Tishows good ductility up to 30% in compression,over a wide temperature range from room tempera-ture to 1673 K, and both Rh3Nb and Rh3Ta show apositive temperature dependence of strength (astress anomaly) at around 1273 K. However, bycontrast with pioneering work on the mechanicalproperties of the rhodium-based L12 compounds,few studies on the physical properties of thesecompounds are found in the literature.

Key parameters for the design of high heat-fluxalloy structures for high-temperature serviceinclude thermal conductivity and thermal expan-sion (13, 14). Thermal conductivity data arerequired to determine the feasibility and the basic

DOI: 10.1595/147106706X106182

Thermophysical Properties of Rh3X forUltra-High Temperature ApplicationsTHERMAL CONDUCTIVITY AND THERMAL EXPANSION OF L12 INTERMETALLIC COMPOUNDS OFRHODIUM WITH TITANIUM, ZIRCONIUM, HAFNIUM, VANADIUM, NIOBIUM AND TANTALUM

By Yoshihiro TeradaDepartment of Metallurgy and Ceramics Science, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8552, Japan;

E-mail: terada@mtl.titech.ac.jp

and Kenji Ohkubo, Seiji Miura and Tetsuo MohriDivision of Materials Science and Engineering, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan

Thermal conductivity and thermal expansion were measured for the L12 intermetallic compoundsRh3X (X = Ti, Zr, Hf, V, Nb, Ta) in the temperature range 300–1100 K to evaluate the feasibilityof applying the compounds as ultra-high temperature structural materials. The thermalconductivities of Rh3X are widely distributed over the range 32–103 W m–1 K –1 at 300 K, butthe differences between the thermal conductivities diminish at higher temperatures. A trendis observed in that the thermal conductivity of Rh3 X is greater if the constituent X belongs toGroup 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 concentratedaround 10 × 10–6 K–1 at 800 K. CTE values of Rh3X decrease as X appears lower in the PeriodicTable. It is demonstrated that Rh3Nb and Rh3Ta are suitable for ultra-high temperature structuralapplications due to their higher thermal conductivities and smaller CTE values.

Platinum Metals Rev., 2006, 50, (2) 70

design parameters of structural materials. Therapid heat transfer afforded by high thermal con-ductivity enables efficient cooling which preventsthe occurrence of life-limiting heat-attack spots.Higher operating temperatures can thus be sus-tained. Thermal expansion data are also required,with a view to minimising the thermal expansionmismatch in joints and thermal stress in compo-nents. Lower thermal expansion is desirable toavoid fatigue through thermal cycling, since ther-mal stress depends directly on the magnitude ofthe thermal expansion.

Rhodium-based compounds Rh3X have L12 crys-tal structure, Table I, with constituent X belongingto Groups 4 and 5 in the Periodic Table (15). Thisstudy is designed to establish a basic data set forthe thermal conductivity and the thermal expan-sion of the L12 intermetallic compounds Rh3X (X= Ti, Zr, Hf, V, Nb, Ta).

Thermal ConductivityThe thermal conductivities of Rh3X at 300 K

are summarised in Figure 1, where the thermalconductivity is plotted as the column height in thePeriodic Table configuration. The largest thermalconductivity is found in Rh3Nb and the smallest inRh3Ti. The following inequalities are observed:

λ[Rh3Ti] < λ[Rh3V] (i)λ[Rh3Zr] < λ[Rh3Nb] (ii)λ[Rh3Hf] < λ[Rh3Ta] (iii)

where λ[Rh3X] represents the thermal conductivi-ty of Rh3X. λ[Rh3X] is therefore larger when X

belongs to Group 5, rather than Group 4. Thethermal conductivity of an intermetallic com-pound reaches a maximum at the stoichiometriccomposition, and decreases monotonically withincreasing deviation from stoichiometry (16, 17).The hypothetical thermal conductivity of stoichio-metric single-phase L12 Rh3Hf is expected to beslightly greater than the experimental value for Rh-23.5 at.% Hf.

We have previously surveyed the thermal con-ductivities of B2 aluminides (FeAl, CoAl, NiAl),titanides (FeTi, CoTi, NiTi), and gallides (CoGa,NiGa) at ambient temperature (16). An empiricalrule was found for compounds AB,, that thermalconductivity decreases monotonically withincreasing horizontal distance, in the PeriodicTable, of constituent A from constituent B, that is:

λ[FeAl] < λ[CoAl] < λ[NiAl]λ[FeTi] > λ[CoTi] > λ[NiTi]λ[CoGa] < λ[NiGa]

The empirical thermal conductivity rule observedfor B2 compounds is also observed in Rh3X withthe L12 crystal structure.

Figure 2 shows the thermal conductivities ofRh3X as a function of temperature. A continuousdecrease in thermal conductivity with increasingtemperature is observed for Rh3Nb, Rh3Ta andRh3Zr, the thermal conductivities of which at 300K are greater than 80 W m–1 K–1. By contrast, aconsiderable increase in thermal conductivity withincreasing temperature is observed below 900 K

Fig. 1 A Periodic Table matrix showing the magnitudeof thermal conductivity of Rh3X at 300 K. Note that thevalue for Rh3Hf is obtained using an off-stoichiometricspecimen

50 W

m– 1

K– 1

Table I

Composition and Phase Characteristics of Rh3XIntermetallic Compounds

Compound Nominal Composition range ofcomposition, L12 phase at 1573 K,

at.% at.%

Rh3Ti Rh-25.0Ti 22.0–27.0 TiRh3Zr Rh-25.0Zr 22.7–27.7 ZrRh3Hf Rh-23.5Hf 19.0–24.0 HfRh3V Rh-25.0V 23.1–33.8 VRh3Nb Rh-25.0Nb 21.1–28.0 NbRh3Ta Rh-25.0Ta 23.1–29.5 Ta

for Rh3Ti, which has a much smaller thermal con-ductivity at 300 K. The thermal conductivities ofRh3Hf and Rh3V are somewhat insensitive totemperature. The thermal conductivities of Rh3Xare widely distributed in the range 32 to 103 W m–1 K–1 at 300 K; the values converge toaround 65 W m–1 K–1 at 1100 K.

The temperature coefficient of thermal con-ductivity, k, in the temperature range 300–1100 Kcan be roughly estimated by using the followingequation:

k = (1/λ300 Κ)(dλ/dT)≈ (1/λ300 Κ){(λ1100 Κ–λ300 Κ)/(1100–300)} (iv)

where λ300 Κ and λ1100 Κ are the thermal conductiv-ities at the temperature indicated by the subscript.The temperature coefficients obtained for Rh3Xare plotted against λ300 K in Figure 3. The plots forintermetallic compounds with crystal structures ofL12, B2, and others already reported (18, 19) arealso shown in Figure 3, together with data for puremetals (20–22). Note that the data for pure metalsin which lattice transformation or magnetic trans-

formation occurs in the temperature range300–1100 K are excluded. It is well known that thethermal conductivity of h.c.p. metals is anisotrop-ic, so data for polycrystalline materials are adoptedfor the h.c.p. metals.

The pure metals are generally characterised byhaving larger thermal conductivities with smallertemperature coefficients, whereas intermetalliccompounds have relatively smaller conductivitieswith larger coefficients. An overall tendency,which can be seen from Figure 3, is that the ther-mal conductivity and temperature coefficient areinversely correlated in metallic materials. No nega-tive k is observed for conductivities below 20 Wm–1 K–1, whereas above 90 W m–1 K–1 hardly anypositive k is found.

The thermal conductivity of Rh3Ti is almostequal to those of conventional L12 compoundssuch as Ni3Al and Ni3Ga, whereas the temperaturecoefficient of Rh3Ti is much greater. Rh3Nb, Rh3Taand Rh3Zr are characterised by greater thermalconductivities and negative temperature coeffi-cients. Their thermal conductivities are nearly

Platinum Metals Rev., 2006, 50, (2) 71

Fig. 2 Thermal conductivityversus temperature for Rh3X,where X is Nb, Ta, Zr, Hf, Vand Ti. Note that the valuefor Rh3Hf is obtained usingan off-stoichiometricspecimen of Rh-23.5Hf

THE

RM

AL

CO

ND

UC

TIV

ITY,

λ, W

m– 1

K– 1 100

50

TEMPERATURE, K

500 1000 1500

equal to that of NiAl, which is well recognised as acompound of high thermal conductivity (4, 16). Inaddition, a negative temperature coefficient is quiterare among intermetallic compounds, being identi-fied solely in FeTi and Ni3Ti other than Rh3X (X =Zr, Nb, Ta). The thermal conductivities of Rh3Vand Rh3Hf are a little smaller than that of NiAl.However, it may be noted that they have relativelylarger thermal conductivities among intermetalliccompounds.

The thermal conductivity of an intermetalliccompound is correlated quantitatively with thoseof the constituents of the compound through

Nordheim’s relation (23). The high thermal con-ductivities of Rh3X may be partly due to the highthermal conductivity of pure rhodium, the thermalconductivity of which at 300 K is 150 W m–1 K–1.

Thermal ExpansionThermal expansion (∆L/L) results for Rh3X are

shown in Figure 4. All the dilatation curves are asmooth function of temperature, with no suddenslope changes. The curves in Figure 4 reveal thatthe thermal expansion of Rh3Hf is slightly smallerthan those of either Rh3Ti or Rh3Zr over the tem-perature range 300–1100 K.

Platinum Metals Rev., 2006, 50, (2) 72

Fig. 3 Correlation between thermal conductivity at 300 K for Rh3X and its temperature coefficient. Data for puremetals (20–22) and intermetallic compounds (18, 19) are also included

TEM

PE

RAT

UR

E C

OE

FFIC

IEN

TO

F TH

ER

MA

LC

ON

DU

CTI

VIT

Y, k

,104

K– 1

25

20

15

10

5

0

–5

–10

3 5 7 10 20 30 50 70 100 200 300 500 700 1000

THERMAL CONDUCTIVITY AT 300 K, λ300 K,W m–1 K–1

Rh3X

f.c.c.b.c.ch.c.p.L12

B2other crystal structures

The difference in ∆L/L is less than 10 % at anytemperature. Also, the data indicate that Rh3Ta hasa smaller thermal expansion than those of Rh3V orRh3Nb. The slope of the curve of ∆L/L vs. tem-perature is the coefficient of thermal expansion(CTE). The slight upward curvature in everydilatation curve indicates that the CTE of Rh3Xincreases with increasing temperature.

CTE values, α, for Rh3X at 800 K are sum-marised in Figure 5, plotted as column heights onthe Periodic Table matrix. The smallest CTE isfound for Rh3Ta, whereas Rh3V shows the largest.The following inequalities are observed:

α[Rh3Ti] > α[Rh3Zr] > α[Rh3Hf] (v)α[Rh3V] > α[Rh3Nb] > α[Rh3Ta] (vi)

Thus the trend is that the CTE values of Rh3Xdecrease as constituent X is positioned lower in thePeriodic Table. The deviation from stoichiometryhas little influence on the CTE values of intermetal-lic compounds, as demonstrated in NiAl (24–26)and Ni3Al (26). Therefore, a hypothetical CTEvalue for stoichiometric Rh3Hf with the L12 singlephase is expected to be approximately equal to thatof the experimental value for Rh-23.5 at.% Hf.

The CTE values of pure metals are well knownto vary inversely with melting points (27). Figure 6shows the correlation between the CTE at 800 Kand the melting points for Rh3X. Data for inter-metallic compounds with L12, B2 and D019

structures, obtained by this group (28), are alsoshown in Figure 6, together with literature data

Platinum Metals Rev., 2006, 50, (2) 73

Fig 4 Thermal expansionof Rh3 X during heatingfrom 300 to 1100 K. Theheating rate is 10 K/min.Note that the curve forRh3Hf is obtained using anoff-stoichiometric specimen

Fig. 5 A Periodic Table matrix showing the magnitude ofthe coefficient of thermal expansion, α, of Rh3X at 800 K.Note that the value for Rh3Hf is obtained using an off-stoichiometric specimen

5 ×

10– 6

K– 1

TEMPERATURE, K

∆L/L

, %

∆L/L

, %

300 400 500 600 700 800 900 1000 1100

1.0

0.5

0

1.0

0.5

0

Platinum Metals Rev., 2006, 50, (2) 74

(22, 29) for pure metals. Since the CTE for h.c.p.metals is usually anisotropic, the CTE data forpolycrystal were adopted for the h.c.p. metals.

In Figure 6, all the plots for pure metals andintermetallic compounds including Rh3X fall on acommon curve, irrespective of crystal structure.The CTEs of Rh3X are concentrated around 10 ×10–6 K–1, approximately equal to that of pure Rhand two-thirds as great as the CTE of convention-al intermetallic compounds such as NiAl andNi3Al. From Figure 6, it can be seen that the small-er CTE values for Rh3X correlate well with thehigher melting points of the compounds.

The interatomic force in metallic materials ischaracterised by cohesive energy, Ecoh, which is the

difference between the potential energy of atomsin the gas state and that in crystal of the material.The cohesive energy in an intermetallic compoundis expressed as the sum of the sublimation energyof the alloy, Esub, and the heat of formation of theordered structure, ∆H (30):

Ecoh = Esub + ∆H (vii)

Table II summarises the Ecoh, Esub and ∆H datafor Rh3X. The Esub values were obtained from thedata source (31) and the ∆H values were calculatedfrom Miedema’s formula (32, 33). For comparison,Table II also gives data for conventional inter-metallic compounds. It is apparent that thecohesive energy of the intermetallic compounds

Fig. 6 Correlation between the coefficient of thermal expansion at 800 K and the melting point for Rh3X. Data forpure metals (22, 29) and for intermetallic compounds (28) are also included

CO

EFF

ICIE

NT

OF

THE

RM

AL

EX

PAN

SIO

N, α

,10– 6

K– 1

MELTING POINT, Tm, K

40

30

20

10

1100 2000 3000 4000 5000

Rh3Xf.c.c.b.c.c.h.c.p.L12B2D019 structures

Platinum Metals Rev., 2006, 50, (2) 75

originates mostly from the sublimation energyrather than from the heat of formation of theordered structure. The greater cohesive energy ofRh3X is correlated with the greater interatomicforce, resulting in the higher melting points andsmaller CTE values of the compounds. The CTEvalues of Rh3Nb and Rh3Ta are particularly smallamong the Rh3X compounds, reflecting theirgreater cohesive energies.

ConclusionsThe thermal conductivity and thermal expan-

sion of the L12 intermetallic compounds Rh3X (X= Ti, Zr, Hf, V, Nb, Ta) were surveyed to evalu-ate their feasibility as ultra-high temperaturestructural materials. Thermal properties were mea-sured at temperatures 300–1100 K. Results aresummarised as follows:[i] There is a noticable trend in the thermal con-ductivity of Rh3X, becoming greater if X belongs toGroup 5 rather than to Group 4 in the PeriodicTable. Thermal conductivity and its temperaturecoefficient are inversely correlated for metallicmaterials. Rh3Nb, Rh3Ta and Rh3Zr are charac-terised by greater thermal conductivities and smallertemperature coefficients; Rh3Ti by a lower conduc-tivity and a higher coefficient of thermal expansion.[ii] The dilatation curves for Rh3X are charac-terised by slight upward curvature, indicating thatthe coefficient of thermal expansion (CTE)increases with increasing temperature. The CTEof Rh3X decreases as constituent X moves down-ward in the Periodic Table. The smaller CTEvalues for Rh3Nb and Rh3Ta are ascribed to theirhigher cohesive energies.

Thus, by virtue of their high thermal conductiv-ities and small CTEs, Rh3Nb and Rh3Ta are themost suitable of the Rh3X compounds for ultra-high temperature structural applications.

References

Table II

Thermodynamic Properties of Rh3X and Other Intermetallic Compounds

Compound Cohesive Sublimation Heat ofenergy, energy, formation,

Ecoh, Esub, ∆H,kJ mol–1 kJ mol–1 J mol–1

Rh3Ti 584 533 51Rh3Zr 641 566 75Rh3Hf 637 571 66Rh3V 571 544 27Rh3Nb 643 598 45Rh3Ta 655 611 44

Ni3Al 436 403 33Ni3Si 459 433 26NiAl 426 378 48FeAl 403 371 32

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Platinum Metals Rev., 2006, 50, (2) 76

Yoshihiro Terada is an Associate Professor inthe Department of Metallurgy and CeramicScience, Tokyo Institute of Technology. Hismain activities are in the thermal andmechanical properties of metallic materialsfor high-temperature applications.

Kenji Ohkubo is a Technician in the Divisionof Materials Science and Engineering,Hokkaido University. His major field ofinterest is the determination andcharacterisation of thermal properties inmetallic materials.

Seiji Miura is an Associate Professor in theDivision of Materials Science andEngineering, Hokkaido University. Hisresearch interest is the development ofintermetallic alloys for ultra-hightemperature applications.

Tetsuo Mohri is a Professor in the Divisionof Materials Science and Engineering,Hokkaido University. His major field ofinterest is the first-principles study of phasestability, equilibria and transformation formetallic systems.

The Authors

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