Journal of Alloys and Compounds 403 (2005) 217–222

Enthalpies of formation in the Al–Ni–Ru system by direct reaction synthesis calorimetry Hsin-Ning Su, Philip Nash ∗ Thermal Processing Technology Center, Illinois Institute of Technology, Chicago, IL 60616, USA Received 18 April 2005; accepted 18 May 2005 Available online 1 August 2005

Abstract The enthalpies of formation of ternary compounds in the Al–Ni–Ru system have been determined by high temperature reaction calorimetry. The composition dependence of the enthalpy of formation and lattice parameter of the compounds with B2 structure were determined in the region of 0.40 ≤ Al ≤ 0.5 mole fraction. Unusual behavior is observed for the composition dependence of the enthalpy of formation suggesting that formation of a miscibility gap in the B2 phase field occurs. For some compositions, the experimental enthalpy data therefore represent the formation enthalpy of the metastable B2 phase. © 2005 Elsevier B.V. All rights reserved. Keywords: Enthalpy; Heat of formation, Al–Ni–Ru; Miscibility gap; B2 phase; Calorimeter; Enthalpy; Heat of formation; Wagner–Schottky; Miedema; Thermocalc; Calphad; Defect

1. Introduction The Al–Ni–Ru system is of practical interest since the RuAl intermetallic compound has shown potential for high temperature application [1] and partial substitution for ruthenium by nickel could provide the ability to tailor the properties [2] because of the extensive B2 phase field that some claim [3] extends from NiAl to RuAl. The B2 structure can be visualized as an ordered bcc lattice. Unlike a bcc lattice one type of atom occupies the body-centered position and another type occupies the cube corners. This results in only one lattice point per unit cell and the lattice is therefore primitive cubic. When the composition deviates from stoichiometry constitutional defects must be introduced to preserve the crystal structure. The simple cubic lattice on which the Al atoms reside may be designated ␤ and the corresponding transition metal lattice may be designated ␣. In NiAl, it is well established that on the Al-rich side of stoichiometry vacancies are present on the ␣ sublattice [4]. On ∗

Corresponding author. E-mail address: [email protected] (P. Nash).

0925-8388/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2005.05.032

the Ni-rich side, the excess Ni atoms occupy the ␤ sublattice creating anti-structure defects. In the RuAl compound, the constitutional defect structure appears different from NiAl but is not well understood [5]. Due to the different constitutional defect structure between NiAl and RuAl, it is not straightforward to define the B2 phase field between NiAl and RuAl in the Al–Ni–Ru phase equilibria. The available phase equilibria data indicate that the B2 phase field between NiAl and RuAl exhibits either a miscibility gap [6–9] or complete miscibility [3,10]. It would be very helpful if enthalpy of formation data and lattice parameter data are available to help resolve the issue of the continuity of the B2 phase field and to provide data to thermodynamically optimize the Al–Ni–Ru system by the Calphad method. This paper reports on determinations of enthalpies of formation and precise lattice parameter measurements in the B2 phase field of this system.

2. Experimental procedure The heats of formation were determined using a high temperature reaction calorimeter with a typical accuracy

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of ±1 kJ/mol [11]. The measurements were made with the calorimeter set at 1373 ± 2 K, and using a protective argon atmosphere. The calorimeter was calibrated using pure copper. Samples were produced by mixing elemental powders in a mortar in the required molar ratio, and pressing them into a small pellet. Typical sample weight was about 100 mg. The nickel and iron powders used were reduced in hydrogen at 873 K prior to preparation of the samples to remove oxygen and carbon, which would be a source of errors. The enthalpy of reaction is measured in two steps.
HReaction is obtained first by dropping the pellet into the calorimeter from room temperature. A minimum of six separate samples were measured. The pellets were subsequently removed and again dropped from room temperature into the calorimeter to obtain the heat content of the compound,
HHeat content . The difference between the two measurements yields the heat of formation at 298 K. The results are averages of the six individual measurements. With the standard deviations from the reaction and heat content experiments designated as δ1 and δ2 and from the calibration as δ3 the overall uncertainty in the measurements, δ, was determined 1/2 from δ = (δ21 + δ22 + δ23 ) . Material from the reacted compound was used to obtain an X-ray diffraction pattern to confirm that the reacted sample was the desired compound.

3. Enthalpy of formation calculation By using direct synthesis, the standard enthalpy of formation,
Hf298 K , is calculated from: aAl(s,298 K) + bNi(s,298 K) + cRu(s,298 K) = Ala Nib Ruc(1373 K)

(1)

∆H Reaction

Ala Nib Ruc(s,298 K) = Ala Nib Ruc(1373 K)

∆H Heat content

d-spacing. The lattice parameter was calculated using seven to nine peaks. The Nelson–Riley method was used for correcting for systematic errors [12].

5. Prediction of enthalpies of formation For comparison with our experimental results we have used Miedema’s semi-empirical model extended for ternary alloys [13] to calculate the standard enthalpy of formation,
Hf298 K :
Hf298 K = CA fBA
H inter (A in B) + CA fCA
H inter (A in C) + CB fBC
H inter (B in C) CA and CB are the molar ratios of A and B elements, respectively, in the corresponding compounds, fBA the degree of surface contact of an A atom with B neighbors, while fCA is the degree of surface contact of an A atom with C neighbors.
Hinter is interfacial enthalpy.

6. Enthalpy of formation results The enthalpies of formation of the Al–Ni–Ru compounds and measured lattice parameters are listed in Table 1, together with values calculated in this work based on Miedema’s model. It can be observed that as the Al content increases, the enthalpy tends to be more exothermic. The Miedema model predicts less exothermic values than the measured values for all compositions. Fig. 1 shows the enthalpy results for compounds in the supposed B2 phase region between NiAl and RuAl. Figs. 2 and 3 show the enthalpies of formation of compounds along constant 45 at.% Al indicated as Al0.45 Ni(0.55−X) RuX and 50 at.% Al indicated as Al0.50

(2) From reactions (1) and (2), we get aAl(s,298 K) + bNi(s,298 K) +cRu(s,298 K) = Ala Nib Ruc(s,298 K) The standard enthalpy of formation is thus obtained.
Hf298 K =
HReaction −
HHeat content
HReaction and
HHeat content are molar enthalpy changes for reactions (1) and (2).

4. Lattice parameter calculation X-ray diffraction was performed using Cu Ka radiation. Scans were taken over a 2θ range of 5–120◦ . A NIST alumina reference material was used as a standard to correct

Fig. 1. Enthalpies of formation in B2 phase field of Al–Ni–Ru system.

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Table 1 Summary of high temperature reaction calorimetry results and Miedema’s semi-empirical model results in the Al–Ni–Ru system Compound


H formation (experimental; kJ/mol)

Structure analysis by XRD


H formation (calculated by Miedema’s model; kJ/mol)

Lattice parameter (nm)

Al0.50 Ni0.50 Al0.50 Ni0.10 Ru0.40 Al0.50 Ni0.20 Ru0.30 Al0.50 Ni0.30 Ru0.20 Al0.50 Ni0.35 Ru0.15 Al0.50 Ni0.40 Ru0.10 Al0.50 Ni0.45 Ru0.05 Al0.50 Ru0.50 Al0.45 Ni0.10 Ru0.45 Al0.45 Ni0.20 Ru0.35 Al0.45 Ni0.30 Ru0.25 Al0.45 Ni0.35 Ru0.20 Al0.45 Ni0.45 Ru0.10 Al0.40 Ni0.40 Ru0.20 a Al0.40 Ni0.50 Ru0.10 a Al0.82 Ni0.12 Ru0.06 a

−61.8 ± 1.1 −62.0 ± 1.3 −63.1 ± 0.8 −61.5 ± 1.1 −58.2 ± 2.0 −55.9 ± 2.1 −58.7 ± 2.4 −54.5 ± 1.2 −56.1 ± 0.8 −56.9 ± 1.9 −58.1 ± 1.5 −57.6 ± 0.6 −55.5 ± 1.2 −51.6 ± 1.0 −49.5 ± 1.4 −31.5 ± 1.5

B2 B2 B2 B2 B2 B2 B2 B2 B2 B2 B2 B2 B2 B2 B2 –

−50 −43 −38 −37 −39 −41 −50 −44 −43 −39 −38 −38 −42 −38 −38 −19

0.2887 0.2972 0.2956 0.2931 0.2914 0.2902 0.2891 0.2988b 0.2971 0.2956 0.2942 0.2931 0.2904 0.2936 0.2872 –

Calorimeter temperature set at 1373 K. a Reacted sample was not predominantly B2 phase. b Data from reference [5].

Ni(0.50−X) RuX , respectively. All alloys in these sections exhibited B2 phase X-ray diffraction patterns. There is a decrease in the enthalpy of formation of the B2 compound around 0.1 mole fraction of Ru indicating a reduction in stability which will likely result in a miscibility gap. The effect diminishes on reducing the Al concentration below stoichiometry. This results in negative curvatures for the enthalpy–composition relations characteristic of systems exhibiting miscibility gaps. The relation observed in the enthalpy results of constant Al content in the Al–Ni–Ru system is quite different from the linear relations previously reported in the Al–Ni–Fe system [15]. Some of the experimental data on enthalpy of formation of B2 phase obtained in this work represent the metastable enthalpy curve since at 298 K we should have phase separation but this did not occur because the transformation is kinetically constrained. Fig. 2. Enthalpies of formation of Al0.45 Ni(0.55−X) RuX .

7. Three-dimensional curve fitting for enthalpies of formation result Since the enthalpy of formation is composition dependent, the enthalpies of formation determined in this study (in the range 0.4 ≤ Al mole fraction ≤ 0.5), were fitted as a threedimensional surface with the following polynomial equation: z = a + b × y + c × y2 + d × y3 + e × y4 + f × x + g × xy + h × xy2 + i × xy3 + j × xy4

Fig. 3. Enthalpies of formation of Al0.50 Ni(0.50−X) RuX [14].

where z is the enthalpy of formation, x the Ru mole fraction and y is the Ni mole fraction. a–j are coefficients of the fitted polynomial equation. The obtained coefficients are shown in Table 2. The result based on the fitting equation together with the experiment result and absolute error between fitting and experiment are listed in Table 3 where the maximum absolute

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Table 2 Coefficients of fitted equation of enthalpy of formation Coefficient

Value

a b c d e f g h i j

−60 −991 6267 −13179 9180 11 1782 −8030 8000 3713

Equation is valid in the mole fraction range of 0.4–0.5 Al. Sample standard deviation of absolute error = 0.78. Table 3 Comparison of enthalpies of formation of B2 phase between experimental result and fitted result Compound

Al0.50 Ni0.50 Al0.50 Ni0.10 Ru0.40 Al0.50 Ni0.20 Ru0.30 Al0.50 Ni0.30 Ru0.20 Al0.50 Ni0.35 Ru0.15 Al0.50 Ni0.40 Ru0.10 Al0.50 Ni0.45 Ru0.05 Al0.50 Ru0.50 Al0.45 Ni0.10 Ru0.45 Al0.45 Ni0.20 Ru0.35 Al0.45 Ni0.30 Ru0.25 Al0.45 Ni0.35 Ru0.20 Al0.45 Ni0.45 Ru0.10 Al0.40 Ni0.40 Ru0.20 Al0.40 Ni0.50 Ru0.10


H formation (kJ/mol) Experimental

Calculated from curve fit

−61.8 ± 1.1 −62.0 ± 1.3 −63.1 ± 0.8 −61.5 ± 1.1 −58.2 ± 2.0 −55.9 ± 2.1 −58.7 ± 2.4 −54.5 ± 1.2 −56.1 ± 0.8 −56.9 ± 1.9 −58.1 ± 1.5 −57.6 ± 0.6 −55.5 ± 1.2 −51.6 ± 1.0 −49.5 ± 1.4

−62.2 −61.8 −63.4 −60.9 −58.9 −57.4 −57.8 −54.6 −55.9 −57.6 −57.4 −56.4 −54.4 −52.8 −49.5

Absolute error (difference between experiment and fitted value; kJ/mol)

Fig. 4. Lattice parameters of Al0.50 Ni(0.50−X) RuX [16].

0.4 0.2 0.3 0.6 0.7 1.5a 0.9 0.1 0.2 0.7 0.7 1.2 1.1 1.2 0

a Denoted as the maximum error between experiment and calculation result.

Fig. 5. Lattice parameters of Al0.45 Ni(0.55−X) RuX [16].

error is 1.5 kJ/mol for Al0.50 Ni0.40 Ru0.10 and in most cases the fitting error is within the experimental error range. Since the available experimental data are only within the range where Al mole fraction is between 0.4 and 0.5, the equation is therefore only valid in the same range. The purpose of the surface fitting is to provide a tool for interpolation of the data.

8. Lattice parameter result Figs. 4 and 5 show the lattice parameters of Al0.50 Ni(0.50−X) RuX and Al0.45 Ni(0.55−X) RuX , respectively. No indication of phase separation to two B2 structures was observed on any of the XRD patterns although the presence of a small amount of another phase was observed in some cases (Figs. 6 and 7). The higher Ru content leads to a larger lattice parameter as expected because the atomic radius of Ru is larger than Ni (atomic radius of Ru is 0.134 nm and Ni atom is 0.124 nm). The positive deviation from Vegard’s

Fig. 6. XRD patterns of Al0.50 Ni(0.50−X) RuX .

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Fig. 9. Schematic of proposed vertical section of Al–Ni–Ru system at constant 50 at.% Al. Fig. 7. XRD patterns of Al0.45 Ni(0.55−X) RuX .

rule observed for compounds with Ru mole fraction larger than 0.15 in Fig. 4 and all compounds in Fig. 5 suggest the lattice parameter is affected not only by the atomic sizes but also another effect which leads compounds to be less stable and thus larger lattice parameters are observed than expected. This effect also indicates unusual alloying behavior and provides indirect support for the miscibility gap.

9. Al–Ni–Ru phase equilibrium The liquidus surface for the Al–Ni–Ru ternary system [17,18] shows no monovariant trough bisecting the B2 phase region which means there is no three phase equilibrium between liquid and two separate B2 phase compositions. This indicates that at least close to the solidus the B2 phase exhibits complete miscibility. The work of Vjunitsky et al. [9] as shown in Fig. 8 indicates the existence of a misci-

bility gap at 900 ◦ C. In this work, the heats of formation suggest that there is a miscibility gap; however, no evidence for phase separation was found from X-ray diffraction (Fig. 7). If two separate B2 phase compositions exist, the differences in lattice parameters of the two B2 compositions would give rise to a small angular separation, which could be difficult to observe. One possible explanation for these observations is that the miscibility gap may close before melting, as shown schematically in Fig. 9. Also, the phase separation may require extended annealing if the phase transformation is kinetically constrained. The schematic vertical ternary section provides a consistent interpretation of the experimental results from this work and references [6,7,9,17,18] but not that of Petrovoj [10]. Harte et al. [19] interpreted alloys between NiAl and RuAl as being cored, rather than comprising two distinct phases. If the cores for all compositions are all Ru-rich compared to the interdendritic region, then the form of the vertical section shown is Fig. 9 would be correct. If Ni-rich cores appear on the Ni-rich side and Ru-rich cores on the Ru-rich side, the solidus/liquidus would exhibit a minimum. Some very recent work on a NiAl–3 at.% Ru alloy [20] indicates Ru-rich dendrite cores and Ni-rich interdendritic regions confirming the form of the liquidus shown in Fig. 9.

10. Summary

Fig. 8. Partial isothermal section of Al–Ni–Ru system at 900◦ , obtained by Vjunitsky et al. [9].

Enthalpies of formation for a number of compositions in the Al–Ni–Ru system were measured by direct synthesis calorimetry. Thermodynamic evidence supporting the occurrence of a miscibility gap in the B2 phase field of Al–Ni–Ru was obtained in the form of enthalpy of formation–composition curves exhibiting negative curvatures over part of the composition range between NiAl and RuAl.

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Acknowledgement The support of NSF under Grant no. 0209624 is gratefully acknowledged.

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