Institute of Metallurgy, Clausthal University of Technology, Clausthal-Zellerfeld, Germany

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1 Hai-Lin Chena, b, Rainer Schmid-Fetzera a Institute of Metallurgy, Clausthal University of Technology, Clausthal-Zellerfeld, Germany b Thermo-Calc Software AB, Stockholm, Sweden The Mg C phase equilibria and their thermodynamic basis H.-L. Chen, R. Schmid-Fetzer, Int. J. Mat. Res. 103 (2012) 1-8. The Mg C binary phase equilibria and thermodynamic data are critically evaluated in this work. The necessity is demonstrated to meticulously evaluate the original experimental literature instead of relying on erroneous statements in a previous review that had led to a completely different phase diagram. The two Mg carbides, Mg2C3 and MgC2, are both shown to be metastable based on the examination of the thermodynamic data and the original experimental work on their formation and decomposition. Using the Calphad method, a thermodynamic description of the Mg C system is developed. The stable phase diagram at 1 bar was calculated without assuming any binary interaction parameters. The solubilities of C in liquid Mg, having recently been measured to be tens of ppm between 800 C and 900 C, verify the calculated phase diagram. The metastable Mg2C3 and MgC2 phases were also modeled and their descriptions were directly derived from the thermodynamic data. The complete Mg C description allows the calculation of metastable phase equilibria involving these carbides by suspending graphite and diamond. Keywords: Mg C; Phase equilibria; Thermodynamic assessment 1

2 1. Introduction Magnesium alloys have the potential to serve, beyond lightweight alloys, as functional as well as biomaterials [1, 2]. Carbon in Mg alloys is relevant for some grain refining techniques, for the interactions of SiC and other C-compound reinforcements at the interface to the alloy and other applications. The focus of this investigation is on the phase equilibria in the Mg C system. In our recent work [3], the carbon solubility in liquid magnesium has been measured for the first time by means of GD-OES (Glow discharge optical emission spectrometry). This work proceeds to develop a thermodynamic description and a consistent calculation of the Mg C phase diagram using the Calphad method. The Mg C phase diagram had not been well determined at all. Novak [4] reported the existence of two carbides, Mg2C3 and MgC2, which was confirmed by subsequent researchers [5 9]. It will be detailed later in this study that Nayeb-Hashemi and Clark misinterpreted the reports of the earlier experimental work in their assessment of the Mg C system, as summarized in their erroneous statement [10]: "According to [46Ehr] (i.e., Ref. [6]) and [48Irm] (i.e., Ref. [8]), the MgC2 is stable below 600 C and decomposes to Mg2C3 + C near 600 C. The stability range of Mg2C3 appears to be between 600 to 660 C, and it decomposes to Mg vapor and C near 660 C". The thermodynamic data measured by Irmann using acid solution calorimetry [8], however, indicated that the two carbides would be unstable (at least at room temperature). But Nayeb-Hashemi and Clark [10] only stated that the acid solution calorimetry was generally not highly reliable and the results needed to be confirmed. It will be detailed in this work that neither MgC2 nor Mg2C3 is stable in the Mg C system at 1 bar. The very first Mg C phase diagrams found in the literature appeared in two review papers [11, 12], both pointing to original work by the group of Shul'zhenko [13, 14]. The existence of a compound MgC was claimed and moreover to be the only one being stable at atmospheric pressure. At higher pressure MgC and MgC2 are shown at 7.7 GPa and only MgC2 at 10 GPa. The existence of MgC had never been reported elsewhere. 2

3 Hu et al. [15] recently conducted a thermodynamic modeling of the Mg C system, which appeared to be essentially based on the erroneous summarizing statement in the review by Nayeb-Hashemi and Clark [10]. Thus, similar stability ranges of the carbides MgC2 and Mg2C3 appear in the calculated phase diagram [15]. Furthermore, their theoretically calculated solubility of C in liquid (Mg) is larger by a many orders of magnitude compared to our most recent experimental data [3]. On that background, it is the purpose of this study to show that these currently available Mg C phase diagrams are not accepted. A thermodynamic description will be developed based on a meticulous analysis of the original experimental literature and incorporating the recent experimental solubility data for a consistent calculation of the Mg C phase diagram. 2. Assessment of literature data 2.1. Solid phases Table 1 presents the crystallographic data of all accepted solid phases in the Mg C system. The early work of Irmann [8] and Hajek et al. [16] investigated the sesqui-carbide Mg2C3 but failed to solve its crystal structure. The phase was then tentatively assumed to be hexagonal. Fjellvag and Karen [17] reinvestigated the crystal structure of Mg2C3 by means of neutron diffraction and reported an orthorhombic structure instead. The compound was reported to be the first example of a carbide structure having exclusively C3 carbon groups and its atomic occupations were determined from Rietveld refinement. In their investigation, powder samples had been prepared by reaction of Mg dust with n-pentane at ~680 C and a relatively pure product (90 % Mg2C3) was obtained with carbon and MgO as impurities. The work of Fjellvag and Karen [17] on Mg2C3 was rated to be more reliable than the early work in Refs. [8, 16] considering the better experimental technique and the relatively purer samples. Because of the high reactivity and thermal instability [9, 16], the crystal structure of the Mg dicarbide MgC2 had remained unsolved for many years. Franck et al. [5] and Bredig [18] 3

4 previously investigated the crystal structures of some dicarbides, MgC 2, CaC 2, SrC 2 and BaC 2. It was found that MgC 2 was not isotypic with the tetragonal forms of the other three carbides and its structure appeared to be of lower symmetry. The structure, however, could not be determined from XRD patterns, although they were very satisfactory. Having not noticed the work of Refs. [5, 18], Rueggeberg [7] reported that MgC 2 was isotypic to CaC 2 in a slightly later investigation. Bredig [19] afterwards argued that it was not possible to ascribe a facecentered tetragonal (fct) crystal lattice (which could and should be transformed to body centered tetragonal (bct)) such as that of calcium carbide to magnesium MgC 2. There were some indications that MgC 2 might instead be isotypic with the metastable crystal form III [18] of calcium carbide. Karen et al. [20] recently determined the crystal structure of MgC 2 using neutron diffraction and Rietveld refinement. This phase was reported to have a primitive tetragonal structure (Pearson symbol: tp6; space group: P4 2 /mnm). The lattice parameters determined by Karen et al. [20] given in Table 1 noticeably disagree with those determined by Rueggeberg [7], but agree well with those measured by Irmann [8]. Irmann [8] had probably used a larger face-centered tetragonal unit cell, which can be transformed to a bodycentered tetragonal with a fct = (2) 1/2 a bct and c fct = c bct. Magnesium containing C 70 fullerides with compositions of Mg x C 70 at 1 < x < 5 were prepared via solid state reaction of pristine C 70 powder and Mg metal heated at K for h. A single phase fulleride was obtained only at x = 5. Mg 5 C 70 was found to be an Mgsaturated phase and XRD revealed a simple orthorhombic structure. The Mg-fullerides transform into amorphous-like structures for reaction temperatures higher than 480 C and/or reaction times longer than 200 h [21]. The metastable phase Mg 5 C 70 will not be included in the present thermodynamic modeling. The existence of the monocarbide MgC was claimed in two review papers [11, 12], both pointing to original work by the group of Shul'zhenko [13, 14]. The original papers [13, 14] 4

5 could not be retrieved even after substantial effort by Ukrainian colleagues. The first review [11] presents three isobaric phase diagram sections at atmospheric pressure, at 7.7 GPa and at 10 GPa, taken from Ref. [14]. The diagram at 1 atm shows only the single compound MgC, stable up to 2900 K where it decomposes into L+graphite. The NaCl structure type with a = pm was also mentioned for MgC. That high stability of MgC is incompatible with all other studies, showing that (metastable) Mg 2 C 3 decomposes into the stable two-phase equilibrium (Mg)+graphite. The MgC phase has not even been mentioned in any other study. It is noted that the melting point of pure Mg in the diagram at 1 atm [11] is completely off, 1045 K instead of 923 K. In the two high-pressure diagrams the additional phase MgC 2 appears, claimed to exhibit a rhombic low-temperature and a cubic high-temperature modification. The second review [12] only presents the phase diagram at 7.7 GPa, taken from Ref. [13]. However, none of the invariant temperatures in that diagram agree with the ones in the first review [11], e.g K vs K for the decomposition of MgC 2, shown as one of the few non-dashed lines. The diagram in the second review [12] also shows erroneous phase field descriptions (Gas+diamond instead of Liq+graphite). In view of all these inconsistencies and the fact that the source of these data in Refs. [13, 14] cannot be judged the existence of the monocarbide MgC is not accepted. Lattice parameters of pure Mg (hcp_a3) and C (graphite) are taken from Pearson s handbook [22]. Diamond is metastable at ambient temperature and ambient pressure. Lattice parameters of diamond at 60 GPa is taken from the compilation of Massalski et al. [23] Thermodynamic data Thermodynamic properties of both MgC 2 and Mg 2 C 3 were determined, as given in Table 2. The standard enthalpy of formation, f H 298, was measured by Irmann [8] using acid solution calorimetry as being endothermic, and J mol-atoms 1, respectively. The compilation of NIST-JANAF Thermochemical Tables [24] (as well as Thermochemical Data 5

6 of Elements and Compounds [25]) collected similar data of enthalpy of formation of both Mg carbides, with reference to the work of Furukawa et al. [26], while it is not clear if these data also originated from the work of Irmann [8], which is presumably the only experimental source. Values of the absolute entropy S 298 were also documented for both carbides [24 26], while it is not clear how they were measured or calculated since low-temperature Cp measurements are not reported. The heat capacities above room temperature were tabulated in Ref. [24] with reference to Ref. [26], while Ref. [25] gave the polynomial expressions, Eqs. (1) and (2), with reference to another compilation [27]. Recalculation using the polynomials turns out that they are essentially the same as the tabulated values. Reviewing the similarity in the parameters (on the mol-atoms scale) in Eqs. (1) and (2) it appears that these data probably originate from estimations, since no reference on original experimental data could be found. Cp (Mg2C3) = T T 2 (J K 1 mol-atoms 1, K) (1) Cp (MgC2) = T T 2 (J K 1 mol-atoms 1, K) (2) Hu et al. [15] recently calculated the enthalpy of formation of Mg2C3 at 0 K using ab-initio method. The crystal structure that must have been assumed for the VASP calculations is not given in Ref. [15]. The slightly positive values of +0.7 kj mol-atoms 1 for Mg2C3 significantly differs from the experimental data of Irmann [8], which were not mentioned by Hu et al. [15]. In their thermodynamic modeling, both MgC2 and Mg2C3 were assumed to be stable phases at room temperature. Their assessed enthalpy of formation for MgC2 is kj mol-atoms 1, which is also significantly different from the experimental data of Irmann [8]. No thermodynamic data associated with liquid was available in literature Thermal stability of Mg2C3 and MgC2 The formation of the two magnesium carbides, Mg2C3 and MgC2, had been confirmed by many investigators [4 9, 17, 20]. However, MgC2 and most likely also Mg2C3 are metastable in the Mg C phase diagram at 1 bar as demonstrated by the findings of Refs. [8, 9, 16]. The 6

7 reported temperatures for decomposition involving graphite correspond to irreversible kinetic experiments and have nothing to do with the equilibria associated with them. These key experimental data are summarized in Table 3. It was explicitly stated by Irmann [8] that it was impossible to synthesize the two carbides from the elements, Mg and C. This is consistent with the measured endothermic enthalpy of formation (see Table 2), even though the solution calorimetry in hydrochloric acid may be generally not highly reliable. The largest error was noted to be not in the calorimetric measurement but in the chemical analysis of the samples, which could not be prepared as pure carbide. All preparation routes involve Mg (in the form of metal, powders, or vapor) and hydrocarbons or organic Mg Compounds. Best results are obtained using Mg and acetylene, C 2 H 2, for MgC 2 (best purity 70 % MgC 2, rest mainly graphite) or pentane, C 5 H 12, for Mg 2 C 3 (best purity 85 % Mg 2 C 3, rest mainly graphite) in optimized process routes [8]. As an exception to the organic route, Schneider and Cordes [9] formed Mg 2 C 3 and MgC 2 as reaction products from MgCl 2 (+NaCl) + CaC 2 in iron crucibles under argon. They deduced the type of the carbides, and their formation rate, indirectly from the C 2 H 2 /C 3 H 4 ratio in the reaction gas evolved, acetylene for MgC 2 or allylene, C 3 H 4, for Mg 2 C 3. Reaction of MgCl 2 + CaC 2 proceeds at C (i.e. above the MgCl 2 +CaCl 2 eutectic) but not at 600 C, or, with addition of NaCl, at C (i.e. above the NaCl+MgCl 2 +CaCl 2 eutectic). MgC 2 forms as transient product in the low temperature range (with NaCl) and transforms to Mg 2 C 3 which subsequently and, with increasing temperature, decomposes into the elements. The carbides have not been isolated or investigated using XRD or other direct means. They report a "thermal stability limit" of Mg 2 C 3 at a temperature from 740 to 750 C, which might be a misleading term since it does not relate to an equilibrium value but to hypothetical complete and instantaneous decomposition of Mg 2 C 3 into the elements, obtained from the extrapolation of their kinetic decomposition curves to zero time and 100 % decomposition. The value is consistent with the findings of Irmann [8] and Hajek et al. [16], also the relatively higher 7

8 stability of Mg 2 C 3 compared to MgC 2. Direct evidence of the metastability of MgC 2, relative to Mg 2 C 3 + C, is given by the fact that no trace of the reverse reaction, Mg 2 C 3 (s) + C(gr) 2 MgC 2 (s) occurs after 90 h at C, even though graphite was present in beneficial finest dispersion in the sample, formed from in-situ decomposed transient MgC 2 [9]. In the following some simple thermodynamic considerations will also demonstrate that the carbide Mg 2 C 3 is metastable in the Mg C phase diagram. In view of the very small, or even vanishing, mutual solubilities of C (graphite) and Mg (solid/liquid) and disregarding C p corrections, the Gibbs energy of formation may be well approximated using the values in Table 2 as f G(Mg 2 C 3 ) = T (J mol-atoms 1 ). Thus, f G >> 0 at any realistic temperature and the carbide is not stable. Considering the error bar given by [8] one may assume a lower value of f H = 8000 J mol-atoms 1 and search for a higher value of f S since that value is not based on direct experimental data. Realistic values for carbides range between f S = 0.73 R and R, the latter, positive, value is for the metastable cementite, Fe 3 C. Assuming that value as an estimate one obtains f G(Mg 2 C 3 ) = T with f G(Mg 2 C 3 ) < 0 above 1590 C. If one stretches the limit and assumes f S = + R, twice as high as for any known carbide, the formation temperature, calculated from f G(Mg 2 C 3 ) = T, decreases to 690 C. That is, Mg 2 C 3 would be stable, relative to Mg and C, above 690 C, becoming even more stable with increasing temperature. We know, however, from the experimental data in Table 3 that Mg 2 C 3 is not stable at 670 C or higher temperature. That exercise demonstrates that there are no realistic thermodynamic data making Mg 2 C 3 stable at any temperature Mutual solubility between Mg and C There is no report of solid solubility of C in Mg and it has been believed to be negligible [10]. This is probably a very reasonable assumption since it could be shown that near the melting 8

9 point the solubility is extremely small even in liquid Mg. By means of GD-OES, the present authors measured the C solubility in pure liquid Mg for the first time [3]. The Mg C alloys were carefully prepared by melting pure magnesium (99.99 wt.%) in pure graphite crucibles ( %) and letting them directly react to form saturated liquid solutions. The liquid alloys were then frozen by quenching and subjected to dedicated GD-OES analysis for composition measurements. The solubilities were determined to be in the order of tens of ppm-w, from about 20 ppm-w at 800 C up to 64.8 ppm-w at 900 C. These data are within the scope of expectation of a very small C solubility in liquid Mg. The solubility Mg in C (graphite and diamond) can be simply assumed to be zero by taking into account their atomic sizes and the general knowledge that few elements can be dissolved in C. 3. Thermodynamic modeling The mutual solid solubility between Mg and C is considered to be negligible. In order to avoid arbitrary positive interaction parameters, both Mg (hcp_a3) and C (graphite as well as diamond) are modeled as pure stoichiometric elements. The liquid phase was treated as a substitutional solution and modeled by the Redlich Kister polynomial [28]. The unary thermodynamic descriptions of Mg (hcp_a3 and liquid) and C (graphite, diamond and liquid) were taken from the SGTE compilation [29]. The interaction parameters between Mg and C in the liquid need to be determined by thermodynamic optimization. The only set of experimental data on the C solubility in liquid Mg [3] can be used for this purpose. It turns out that these data can be well reproduced by treating liquid as an ideal solution and the interaction parameters of liquid were thus assigned to be zero. The two metastable carbides, Mg2C3 and MgC2, are taken into account in the present modeling. It is useful to generate Gibbs energy equations for the two carbides using thermodynamic data, since that allows metastable calculations (with graphite and diamond 9

10 suspended) in the Mg C and Mg C H system. With heat capacity, standard enthalpy of formation, and absolute entropy being available, the two phases are modeled as stoichiometric phases using an absolute reference state at K. G MgmCn ( T) n G (298 K) m G (298 K) A B T C T ln( T) D T E T F T o,gra o,hcp C C A* B T C T ln( T ) D T E T F T (3) From Eq. (3), the expression for heat capacity can be given in Eq. (4). Comparing Eq. (4) with the polynomial expressions Eqs. (1) and (2), the four coefficients C, D, E and F can be directly determined from the heat capacity. 2 2 C p ( T) C 2D T 6E T 2F T (4) The other two coefficients, A * and B, can be evaluated from the standard enthalpy of formation ( f H 298 ) and the absolute entropy (S 298 ). In general, these two coefficients should be evaluated by also taking into account the phase equilibria data. In this case, however, no reliable (metastable) phase equilibria data relevant to Mg 2 C 3 and MgC 2 are available for this purpose. Therefore, the Gibbs energy descriptions of Mg 2 C 3 and MgC 2 are completely determined from thermodynamic data and presented in Table 4. It is important to include the gas phase in the Mg C binary system modeling because not only Mg is relatively volatile but also the partial pressures are relevant for melting technology. Moreover, that forms the basis for metastable equilibrium calculations involving hydrocarbons, such as acetylene, pentane or allylene in combination with the solid carbides in the Mg C H system. The gas phase is described as an ideal gas mixture of the species C, C2, C3, C4, C5, Mg and Mg2, and its Gibbs energy per mole of species in the gas is given Table 4. The Gibbs energy functions of the individual gas species are recalculated from the corresponding data for f H 298, S 298, and C p given by Binnewies and Milke [25] in the same manner as described in Eqs. (3) and (4). 10

11 4. Mg C phase diagram and discussion Figures 1 and 2 represent the stable Mg C phase diagram at 1 bar calculated according to the current thermodynamic assessment, in the whole composition range and enlarged on the Mgrich side, respectively. The calculated boiling point of pure Mg agrees well with the reference value 1093 C at 1 bar [25]. The calculated graphite sublimation is 3793 C at 1 bar, slightly different from the value of 3782 C in Ref. [25]. This is because the Gibbs energy data of graphite were accepted from Ref. [29] and not from Ref. [25]. The liquid phase is modeled as a substitutional solution. It is found that the graphite liquidus data, or solubility of C in liquid magnesium, from our recent work [3] can be well reproduced by treating liquid as an ideal solution. It is not meaningful to introduce interaction parameters for a better fitting based on the limited composition range data. No compounds are present in the stable Mg C phase diagram. Therefore, the experimentally verified stable Mg C phase diagram at 1 bar is basically identical to the one extrapolated from unary thermodynamic data. Two invariant reactions occur in the binary system at 1 bar pressure: Graphite + Gas = Liquid, at C, 633 ppm-a or 313 ppm-w carbon in Liquid (5) Liquid = Graphite + (Mg), at C, 4 ppm-a or 2 ppm-w carbon in Liquid. (6) These reaction temperatures are virtually the same as the boiling and melting temperatures, respectively, of pure magnesium because of the very small carbon solubility in Liquid. The two metastable carbides, Mg2C3 and MgC2, are included in this assessment. Since no reliable metastable phase equilibria data are available, their Gibbs energy functions are derived exclusively from thermodynamic data. In order to represent their degree of metastability quantitatively, Fig. 3 shows the calculated Gibbs energies of formation of Gas, Liquid, Mg2C3 and MgC2 at 500 C, relative to pure Mg (Hcp_A3) and C (Graphite) at the 11

12 same temperature and 1 bar. It can be seen that both Mg2C3 and MgC2 are rather unstable at 500 C relative to the stable phases (Mg) and graphite (or even diamond). The value for the Gibbs energy of formation of Mg2C3, 12.2 kj mol-atoms 1 at 500 C, decreases only slightly to 11.6 kj mol-atoms 1 at 600 C due to the reasonably assessed entropy values in Table 2. At all temperatures that value is above 10 kj mol-atoms 1, relative to the stable elements, and the Gibbs energy of formation of MgC2 is even more positive. In fact, only if both Graphite and Diamond are suspended, may the two carbides form in a calculated metastable phase diagram. Considering all the facts in the original experimental work [8, 9, 16] it is evident that the summarizing statement in the first assessment of the Mg C system [10], as cited literally in the introduction, is erroneous. Neither can MgC2 be accepted to be stable below 600 C nor Mg2C3 to be stable between 600 C and 660 C as an equilibrium phase in the phase diagram. However, these decomposition temperatures have obviously guided the recent thermodynamic calculation of the Mg C phase diagram [15], reproducing 597 C and 657 C as equilibrium decomposition temperatures of MgC2 and Mg2C3, respectively. The results of the kinetic decomposition experiments [8, 6] are even plotted in that most recently published thermodynamic modeling work as "data points" in the phase diagram, Fig. 3 of Ref. [15], where the composition was probably taken from the inhomogeneous "carbide+graphite+mg" samples. That is unacceptable since these data relate to kinetic decomposition experiments, as detailed above. The construction of the phase diagram calculated by Hu et al. [15] is due to the following peculiarities. The calculated stability of both compounds Mg2C3 and MgC2 in the phase diagram of Ref. [15] at room temperature is due to the assumption of an almost zero value of fh, way off the experimental error bar. The calculated peritectic decomposition of Mg2C3 at 657 C results from the assumption of a gigantic carbon solubility in liquid magnesium thus stabilizing the liquid phase. The liquid composition in equilibrium with graphite at 660 C read from Fig. 3 of Ref. [15] is 16.5 at.% C, compared to at.% C in 12

13 the present Fig. 2. At 1000 C these solubility values are 21.6 at.% C [15], compared to 0.03 at.% C in the present Fig. 2. These enormous differences are due to the fact that an extremely large negative interaction parameter in the liquid phase had been assumed by Hu et al. [15], 0 L C,Mg L = J mol 1, compared to the value zero in the present assessment, which is the only one validated by direct experimental solubility data. 5. Conclusion A thermodynamic description of the Mg C binary system was obtained using the Calphad method based on a critical evaluation of all original experimental data. The stable Mg C phase diagram at 1 bar is presented by means of thermodynamic calculation which is entirely different from the one proposed by Hu et al. [15]. In the present modeling no interaction parameters in the liquid phase were assumed and the resulting very small solubility of C in liquid Mg is verified by recent experimental data [3]. Compared to that, the theoretically calculated solubility by Hu et al. [15] is larger by many orders of magnitude. Furthermore, the two Mg carbides, Mg2C3 and MgC2, were both shown to be metastable phases in this work while they had been treated as stable phases by Hu et al. [15] due to unrealistically assumed thermodynamic parameters. Clearly, no reactions at binary Mg/graphite interfaces are expected to form any compound in an alloy sample at any temperature. The incorporation of the gas phase species and the descriptions of the Gibbs energy of Mg2C3 and MgC2 in the current thermodynamic description enable calculations of metastable phase equilibria associated with Mg2C3 and MgC2, in the Mg C system or higher-order systems, such as Mg C H. 13

14 References: [1] R.-G. Guan, T. Zhao, L.-L. Wang, T. Cui: Adv. Mater. Res (2009) [2] T. Narushima: Metals for Biomedical Devices, Woodhead Publishing Limited, Cambridge (2010). [3] H.-L. Chen, N. Li, A. Klostermeier, R. Schmid-Fetzer: J. Anal. At. Spectrom. 26 (2011) [4] J. Novak: Z. Phys. Chem. 73 (1910) 513. [5] H.H. Franck, M.A. Bredig, K.-H. Kou: Z. Anorg. Chem. 232 (1937) 110. [6] P. Ehrlich, Unpublished research, FIAT Rev. Ger. Sci., Inorganic Chemistry Part II, ( ) 191, as quoted in Ref. [10] from M. Hansen, K. Anderko: Consititution of Binary Alloys, 2nd ed., New York, McGraw-Hill Book Comp. (1958). [7] W.H.C. Rueggeberg: J. Am. Chem. Soc. 65 (1943) 602. [8] F. Irmann: Helv. Chim. Acta 31 (1948) [9] A. Schneider, J.F. Cordes: Z. Anorg. Chem. 279 (1955) 94. [10] A.A. Nayeb-Hashemi, J. B. Clark: Phase diagrams of binary magnesium alloys, ASM International, Metals Park, Ohio (1988). [11] Yu. A. Kocherzhinski, O.G. Kulik: Powder Metall. Met. Cer. 35 (1996) 470. [12] P.B. Budberg, in: N.P. Lyakishev (Ed.), Binary alloy phase diagram: Handbook, Vol. 1, Mashinostroenie, Moscow (1996) 730. [13] A.A.Shul'zhenko, I.Y. Ignat'eva, N.N. Belyavina, I.S. Belousov: Sov. J. Superhard Mater. 10 (1988) 1. [14] A.A. Shul'zhenko, I. Yu. Ignat'eva, in: Progress in the Synthesis of Ultrahard Materials at the Institute of Ultrahard Materials of the Academy of Sciences of the Ukrainian SSR (1989) 5. [15] B. Hu, Y. Du, H. Xu, W. Sun, W.W. Zhang, D. Zhao: J. Min. Metall. Sect. B-Metall. 46 (2010)

15 [16] B. Hajek, P. Karen, V. Brozek: Collect. Czech. Chem. Commun. 48 (1983) [17] H. Fjellvag, P. Karen: Inorg. Chem. 31 (1992) [18] M.A. Bredig: J. Phys. Chem. 46 (1942) 801. [19] M.A. Bredig: J. Am. Chem. Soc. 65 (1943) [20] P. Karen, A. Kjekshus, Q. Huang, V.L. Karen: J. Alloys Compd. 282 (1999) 72. [21] S. Heguri, T. Hara, M. Kobayashi: Solid State Commun. 148 (2008) 251. [22] P. Villars, L.D. Calvert, Pearson s Handbook of Crystallographic Data for Intermetallic Phases, 2nd ed., ASM International, Metals Park, Ohio (1991). [23] T.B. Massalski, H. Okamoto, P.R. Subramanian, L. Kacprzak, Binary Alloy Phase Diagrams, 2nd ed., ASM International, Materials Park, Ohio (1990). [24] M.W. Chase: NIST-JANAF Thermochemical Tables, 4th ed., National Institute of Standards and Technology, Gaithersburg, Maryland (1998). [25] M. Binnewies, E. Milke: Thermochemical Data of Elements and Compounds, 2nd ed., Wiley-VCH, Weinheim (2002). [26] G.T. Furukawa, M.L. Reilly, et al.: U.S. Nat. Bur. Stand. Report 6928, Appendix B, (1960), as cited by Ref. [24]. [27] O. Knacke, O. Kubaschewski, K. Hesselmann: Thermochemical Properties of Inorganic Substances, 2nd ed., Springer-Verlag, Berlin (1991). [28] O. Redlich, A. T. Kister: Ind. Eng. Chem. 40 (1948) 345. [29] A.T. Dinsdale: Calphad 15 (1991)

16 Correspondence address: Prof. Dr. Rainer Schmid-Fetzer Robert-Koch-Str. 42 Institute of Metallurgy, Clausthal University of Technology, D-38678, Clausthal-Zellerfeld, Germany Tel.: Fax:

17 List of figure and table captions Figure 1: Calculated stable Mg C phase diagram at 1 bar pressure. Fig.2 Mg-rich side of the stable Mg C phase diagram, compared with the experimental data of graphite liquidus from Chen et al. [3]. The narrow Gas+Liquid phase field virtually coincides with the Gas+Liquid+Graphite equilibrium line at 1 bar pressure. Figure 3: Gibbs energies (of formation) of Gas, Liquid, diamond and compounds at 500 C, relative to pure Mg-hcp and C-graphite at same temperature and 1 bar. Table 1: Crystallographic data of accepted solid phases Table 2: Thermodynamic data of Mg C compounds: fh 298 is the standard enthalpy of formation at 25 C, reference state solid Mg and graphite; S 298 is the absolute entropy, and fs 298 is the standard entropy of formation at 25 C. Table 3: Key experimental work on formation and thermal stability of Mg C compounds Table 4: Phase names, models (sublattice formula) and parameters of the Gibbs energy equations 17

18 Table 1: Crystallographic data of accepted solid phases Phase Pearson Lattice symbol/ parameters Comments, References Space group/ (pm) Prototype (Mg) hp2 a = [22] P6 3 /mmc c = Mg Mg 2 C 3 h* op10 Pnnm Mg 2 C 3 a = c = a = c = a = b = c = g cm 3 (exp.) [8] [16] 2.23 g cm 3 (calc.) [17] MgC 2 ti6 a = 486 [7] I4/mmm c = 567 CaC 2 t*12 a = g cm 3 (exp.) [8] - c = the lattice parameters can be transformed - to a = 392 and c = 502 if using a unit cell of 6 atoms tp6 a = g cm 3 (calc.) [20] P4 2 /mnm c =

19 MgC 2 Mg 5 C 70 orthorhombic a = 1684 Metastable C 70 fulleride [21] b = 1462 c = 1384 (C)gr hp4 a = Graphite [22] P6 3 /mmc c = C (graphite) (C)d cf8 Fd-3m C (diamond) a = Diamond, at 60 GPa [23] 19

20 Table 2: Thermodynamic data of Mg C compounds: f H 298 is the standard enthalpy of formation at 25 C, reference state solid Mg and graphite; S 298 is the absolute entropy, and f S 298 is the standard entropy of formation at 25 C. Phase f H 298 S 298 f S 298 Comments, References (kj mol- (J K 1 mol- (J K 1 mol- atoms 1 ) atoms 1 ) atoms 1 ) Mg 2 C Acid solution calorimetry [8] Review [24 26] 0.7*) f H ab initio at 0 K [15] Assessed [This work] MgC Acid solution calorimetry [8] Review [24 26] Assessed [15] Assessed [This work] *) The reported ab-initio value of J mol-atoms 1 is close to the reported Calphadassessed value of J mol-atoms 1 [15]. 20

21 Table 3: Key experimental work on formation and thermal stability of Mg C compounds Phase Investigation Pressure Reference Mg 2 C 3 Mg 2 C 3 Mg 2 C 3 Prepared at C from Mg powder and pentane. Direct reaction reported, not via MgC 2. Decomposition Mg 2 C 3 (s) 2 Mg(l,g) + 3 C(gr), occurs at 670 C in about 12 h and even faster at C. Graphite crucibles sealed in silica tubes, initial vacuum 1.3 mbar. Decomposition Mg 2 C 3 (s) 2 Mg(l,g) + 3 C(gr), rapid at 700 C and 800 C (0.5 1 h). Iron crucibles sealed in silica tubes. < 1 bar [8] p Mg at T [16] p Mg at T [8] MgC 2 Prepared at 450 C from Mg powder and acetylene. 1 bar [8] MgC 2 Decomposition 2 MgC 2 (s) Mg 2 C 3 (s) + C(gr), at 350 C p Mg at T [8] MgC 2 negligibly slow (8 d), rapid at 550 C (2 4 h). Sealed in glass capsules. Formation of MgC 2 (s) does not occur from the reverse reaction, Mg 2 C 3 (s) + C(gr) 2 MgC 2 (s) after 90 h at C [9] 21

22 Table 4: Phase names, models (sublattice formula) and parameters of the Gibbs energy equations Gas: (C, C2, C3, C4, C5, Mg, Mg2) 1 5 P),Gas G C = T T ln(t) T T 1 + R T ln(10 5 P),Gas G C2 = T T ln(t) T T 1 + R T ln(10,gas G C3 = T 42.3 T ln(t) T T 1 + R T ln(10 5 P),Gas G C4 = T T ln(t) + R T ln(10 5 P),Gas G C5 = T T ln(t) + R T ln(10 5 P),Gas G Mg = T T ln(t) + R T ln(10 5 P),Gas G Mg2 = T 24.3 T ln(t) + R T ln(10 5 P) Liquid: (Mg, C) 1 L 0 L C,Mg =ZERO Mg 2 C 3 : (Mg) 2 (C) 3 G = T T ln(t) T T 1 o,mg 2 C 3 Mg:C MgC 2 : (Mg) 1 (C) 2 o,mgc G 2 Mg:C = T T ln(t) T T 1 (Mg): Mg 1 Graphite: C 1 Diamond: C 1 Gibbs energy is given in J mol-formula 1, temperature (T) in Kelvin and pressure (P) in Pascal. 22

23 The Gibbs energies for the pure elements are found in the SGTE compilation [29], and the Gibbs energies for gas species are recalculated from Ref. [25]. Fig. 1 Calculated stable Mg C phase diagram at 1 bar pressure. Fig. 2 Mg-rich side of the stable Mg C phase diagram, compared with the experimental data of graphite liquidus from Chen et al. [3]. The narrow Gas + Liquid phase field virtually coincides with the Gas + Liquid + Graphite equilibrium line at 1 bar pressure. Fig. 3 Gibbs energies (of formation) of Gas, Liquid, diamond and compounds at 500 C, relative to pure Mg-hcp and C-graphite at the same temperature and 1 bar. 23