TEM study of the reaction mechanisms involved in the carbothermal reduction of hafnia

Abstract

The synthesis of HfC_xO_y oxycarbides through the carbothermal reaction of hafnia with carbon black was undertaken. The obtained powders at different rates of advancement were studied by TEM and XRD in order to investigate the reaction mechanisms involved during such a transformation. The contact between the two starting reactants is shown to be non-reactive, attesting to the transformation operating through solid–gas reactions. The hafnia phase is destabilized by the CO_(g) rich atmosphere and is consumed by the migration of ledges at the surface of the crystals acting as a zipper mechanism that liberates HfO_(g) and CO_2(g) species. The carbon dioxide thus released is used in return to oxidize the carbon black forming carbon monoxide through the Boudouard equilibrium. The liberated HfO_(g) then reacts with the ambient CO_(g) to form the oxycarbide phase which is shown to nucleate in the carbon black areas. The oxycarbide nuclei display a core–shell microstructure which is formed by a single crystal core embedded in an oxygen rich amorphous phase. During the final stage of the reaction, the atmosphere, which, saturated in CO_(g), progressively reduces the oxygen rich gangue until it finally disappears. The accurate determination of the cell parameter of the oxycarbide phase during the reaction indicates that the first formed compound is nearly saturated in carbon, comparable to the metallic carbide. The small change in the lattice parameter indicates that the chemical composition is very restricted, so the solid solution of oxygen within the hafnium oxycarbide seems to be very limited.

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1. Introduction

Zirconium, titanium and hafnium carbides (group IV transition metal carbides) possess a mixture of properties which allow them to be classified as Ultra-High Temperature Ceramics (UHTC) (high hardness, high electrical conductivity, high melting point, high corrosion resistance and a good wear resistance).^1–3 These properties enable them to be used as thermal barriers in the aerospace industry, as materials for solar energy exploitation, as a melting pot and as wear resistant coatings.^1–4 Similar to the other group IV transition-metal, the hafnium carbide (HfC_x) presents a rocksalt type structure well known for its vasoconstrictrice behavior due to the occurrence of variable amount of carbon vacancies on the octahedral site (0.50–0.59 < x < 0.98–1).^5,6

Several synthesis methods were developed to produce carbide coatings: reactive magnetron sputtering,⁷ low-pressure chemical vapor deposition (LPCVD)⁸ and carbide powders by mechanosynthesis.^9,10 Recently, non-conventional routes have been developed in order to obtain HfC powders whose size grading is fine. Sacks et al.¹¹ used a mixture of metal alkoxide and carbon sources (phenolic resin or glycerol) to obtain powders which were subsequently pyrolysed. A heat treatment in the range of 1200–1800 °C under flowing argon allows carbides to be produced. The final material was shown to be sub-stoichiometric and some oxygen was found, substituted with carbon, forming oxycarbide compounds with HfC_xO_y formulae. At 1475 °C, the crystallite size (∼50 nm) was determined from XRD spectra using the Scherrer Equation. More recently, 100–200 nm grain size carbides (pure at ∼97%) were obtained by pyrolysing HfCl₄ and citric acid monohydrate¹² at 1600 °C and near-stoichiometric carbides with sub-micron grain sizes were fabricated¹³ by using a method of the electro-deoxidation of hafnium dioxide (HfO₂) and graphite powder.

These methods, however, are generally used to produce limited quantities of carbides. In this context the most common way to synthesize carbide powders at the industrial scale is the carbothermal reduction, this process being well suited to producing large amounts of powders with a good reproducibility. Many authors have undertaken kinetics and thermodynamics studies on the carbothermal reduction of zirconia (ZrO₂)^14–17 and titanium dioxide (TiO₂),^18,19 but the Hf–C system has been much less studied. In particular, the carbothermal reduction of hafnia (HfO₂) by carbon black has never been investigated by a structural approach and, particularly, by transmission electron microscopy (TEM). However, with a melting point near 3950 °C, hafnium carbide (HfC_x) is one of the most refractory materials. In addition, it is interesting to note that the hafnium carbide can form a substitution solid solution with zirconium carbide.²⁰ Indeed, on the one hand hafnia is isostructural with ZrO₂ which is often present as an impurity in zirconia powders samples and on the other hand HfO₂–ZrO₂ dioxide powders can be mixed up to get oxycarbides showing intermediate compositions together with associated melting temperatures.

The carbothermal reduction consists of the reaction of a metal oxide powder and carbon (carbon black or graphite) to form a carbide phase with the release of carbon monoxide following:

MO_x(s) + (x + 1)C_(s) = MC_(s) + xCO_(g) (1)

Zhelankin et al.²¹ first reported the increase of the unit cell parameter of non-stoichiometric HfC_x hafnium carbides with the increase of the carbon amount (x). It is however now well known that in the case of carbothermal reactions an oxycarbide phase with a HfC_xO_y formulae is formed, at least before the reaction towards the final stoichiometric carbide.^11,13,22 The linear correlation, according to Vegard’s law, between the lattice parameter and the composition of the oxycarbide phase was established by Constant et al.²³ Finally, the formation of an intermediate monoclinic oxycarbide was suggested by Liu et al.,²² but this fact was never confirmed by other authors who suggested a cubic structure.

This contribution presents the results of the first structural and microstructural study carried out by coupling TEM and XRD to investigate the reaction mechanisms involved during the carbothermal transformation of hafnia. The results obtained will be discussed in light of results obtained on this system by other authors. In addition, they will also be compared to those obtained in a previous study dedicated to the TEM study of the reaction mechanisms involved in the carbothermal reduction of zirconia, which can be considered as a very similar chemical system.²⁴

2. Experimental procedure: synthesis protocol of the oxycarbide powders and characterization

In order to get comparable results with previous TEM studies devoted to the carbothermal reduction of zirconia²⁴ and rutile,²⁵ the same carbon black was used for the carbothermal reduction of the hafnia powders (commercial amorphous carbon black, 99.25 at.%, Prolabo, France). However, as several studies in the literature have highlighted the influence that the initial grain size of the dioxide has on the size of the obtained oxycarbide grains, we chose hafnia powders showing nanometer-sized crystals. These starting powders, provided by the Centre de Transfert des Technologies Céramiques (CTTC) of Limoges (France), required an initial heat treatment under air at 600 °C for 4 h (Vectar furnace, Chesterfield, United Kingdom) in order to eliminate some chlorine impurities (Cl = 0.90 at.%). After treatment, the purity was close to 99.9%, including a restricted amount of zirconia impurities (Zr < 0.5 at.%). For the synthesis of the oxycarbide phase, the starting reactants were weighed in fixed proportions, fitting to the theoretical eqn (1). They were then mixed in a low speed planetary ball mill (Pulverisette 6, Fritsch, Germany) using ten balls (100% tungsten carbide) with a diameter of 1.0 mm. The blending sequence was composed of 5 pulses of 1 min at 200 rpm interrupted by pauses of 5 min to avoid heating. Then, the mixture was treated in a graphite furnace (AET Technologies, Rambouillet, France) under flowing argon (30 L h⁻¹).

In order to understand the mechanisms involved in the carbothermal reduction of hafnia, it was necessary to observe samples selected at different steps of the reaction process. The advancement (named ξ) could be controlled by measuring the weight loss of the sample. This reaction rate has been determined as the “experimental weight loss” over “theoretical weight loss” ratio. The theoretical weight loss is 22.72% for the chosen stoichiometry. The different advancements obtained by varying the heating treatments, i.e. the dwelling time and the temperature, are reported in Table 1.

Table 1 The different heat treatments and their corresponding advancements ξ

Advancement ξ	Temperature (°C)	Dwelling time
0.12	1650	No dwell
0.42	1650	30 min
0.70	1650	1 h
1	1650	2 h
1	1650	8 h
1	1800	1 h

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The crystallized phases in the oxycarbide samples were identified by X-ray diffraction (D5000, Siemens AG, Munich, Germany) for angles (2θ) ranging between 10° and 125° (step: 0.020°, step time: 1.6 s) using Cu Kα₁–Kα₂ radiation. A second diffractometer was used to determine the lattice parameters of the oxycarbide phase (D8 Advance Bruker, Karlsruhe, Germany) equipped with a front Johansson germanium monochromator which allows the selection of Cu Kα₁ radiation. The lattice parameters were refined by the method of Le Bail using the Fullprof® software.²⁶ This kind of refinement provides knowledge of the space group of each crystallized phases present in the sample. However, this method does not require knowledge of the atomic positions. It is generally used to determine new structures and allows the prediction of the symmetry, comparing the fit of the profile to different space groups,²⁷ and it is then used for the accurate determination of the lattice parameters. Beforehand, for a quantitative exploitation of the XRD data and, in particular, to get reliable values for the cell parameter measurements, an internal standard (Al₂O₃ corundum) was mixed with a ratio of 50 wt% to the synthesized oxycarbide powders in order to correct the sample position.

Transmission electron microscopy (TEM) characterizations were performed with a JEOL 2010 and a TEM-STEM JEOL 2100 microscope (JEOL, Tokyo, Japan) operating at 200 kV. TEM samples were generated by crushing powders in an agate mortar with water. A small drop containing some of the grains was deposited on a copper grid and covered by holey carbon film.

3. Results

3.1 The starting reactants: ξ = 0

The starting hafnia powder crystallized under its monoclinic form (JCPDS file no. 00-043-1017) as shown by the X-ray diffraction pattern provided in Fig. 1a. The hafnia grain size, assumed to be spherical, was determined using the Fullprof® software. The contribution of the instrumental resolution function (IRF) was determined by a previous study performed with a perfectly crystallized lanthanum hexaboride standard (LaB₆). The contribution of the Gaussian function, approached to a zero value, and the determination of the integral width of the Lorentzian part allowed us to measure a hafnia grain size of ∼17 nm ± 1 nm. The laser granulometry results show a bimodal distribution of grain size centered on values of 20 nm and 170 nm. The TEM study confirms that the hafnia powder is made up of two distinct populations. The elementary particles corresponding to the crystallites show a diameter of 15–20 nm, which is very similar to that measured by XRD (Fig. 1b). The selected area electron diffraction (SAED) pattern (insert in Fig. 1b) presents a quite continuous diffraction ring, in agreement with the grain size observed, and confirms the monoclinic cell (space group P2₁/c) as shown by the occurrence of the (100) first tenuous rings. It also reveals that the elementary crystallites are strongly aggregated, forming ball shaped aggregates (see circled regions in Fig. 1c) the size of which do not exceed 100–200 nm. The latter are connected by low energy bonds forming larger agglomerates. The carbon black presents a typical microstructure, corresponding to interconnected spherical balls of ∼100 nm (Fig. 2a) having quite a smooth surface (Fig. 2b). The SAED pattern is composed of two diffuse continuous rings. The first ring attests of the periodicity of the carbon planes along the c axis, whereas the second reveals a beginning of organization within the (001). These carbon planes are rolled up around the center of the particle showing a 2-dimensional organization characteristic of turbostratic carbon.

Fig. 1 Characterization of the hafnia starting powder. (a) X-Ray diffraction pattern of the initial hafnia powder, (b) TEM general view of the hafnia powder and its SAED pattern, (c) TEM view of aggregates (1) and agglomerates (2) in starting hafnia powder.

Fig. 2 Observation by TEM of the carbon black starting powder. (a) General overview, (b) enlargement on carbon balls and their SAED pattern.

3.2 The progressive transformation from the reactants towards the final oxycarbide product

Fig. 3a presents the X-ray diffraction patterns obtained from the synthesized powders corresponding to the different values of ξ reported in Table 1. All X-ray patterns have been normalized in intensity based on the (113) peak of the corundum standard. Starting from ξ = 0 and moving to ξ = 0.7, it is shown that the intensity of the diffraction peaks of hafnia decrease when the ξ value rises, while, oppositely, the intensity of the oxycarbide diffraction peaks progressively increase. This observation attests that the progressive consumption of the hafnium dioxide during the reaction is concomitant to the formation of the oxycarbide phase. The oxycarbide phase that appears from ξ = 0.12 and the final powder (ξ = 1) is a single phase compound of oxycarbide. All patterns can be indexed with the JCPDS data file of the hafnium carbide with the Fm3̄m space group (JCPDS file no. 00-039-1491), however it ought to be noted that the diffraction peaks of the oxycarbide phase are slightly shifted towards lower angles of 2θ as the ξ value increases. This information is more conveniently evidenced with the high 2θ angle (511) diffraction peaks (see the framed area in Fig. 3a and its corresponding enlargement in Fig. 3b) for which the phenomenon is emphasized. For the ZrO₂–C system, this peak shift corresponds to a progressive modification of the lattice parameter, with the value of the cell parameter rising with the advancement. In this case also, such a phenomenon is linked to the progressive substitution of the oxygen by carbon atoms in the hafnium carbide crystal lattice, the radius of oxygen (R_O = 0.67 Å) being inferior to that of carbon (R_C = 0.74 Å). However, it is worth noting that compared to the ZrO₂–C system, the peak shift is limited, indicating that the lattice parameter evolution is weak. Fig. 3c displays the evolution of the oxycarbide phase lattice parameter a obtained by the Le Bail refinement. It is to be noted that the values of the cell parameters, obtained at ξ = 1 (a_HfCxOy = 4.6378 Å ± 0.0005), correspond to that of a nearly stoichiometric carbide (a_HfC = 4.638 Å ± 0.005).²⁸

Fig. 3 X-ray diffraction results obtained either on reactants or products at different ξ values. (a) X-Ray diffraction patterns of the starting hafnia and of the different powders obtained at different advancements of the reaction, mixed with an internal standard (Al₂O₃). (b) Enlargement of the framed area in (a) corresponding to the (511) diffraction peak of the hafnium oxycarbide. (c) Evolution of the hafnium oxycarbide lattice parameter with respect to the advancement ξ. (d) Enlargement of the (111) diffraction peak of the hafnium dioxide.

Concerning the hafnia, it is also interesting to compare the XRD patterns acquired from the starting reactant (ξ = 0) with the one acquired at ξ = 0.12, i.e. solely after a heating at 1650 °C without any dwelling (Table 1). Owing to the low advancement at ξ = 0.12, the amount of hafnia is not really changed but the shape of the diffraction line profile shows a drastic change (Fig. 3d). Whereas the full-width half-maximum (FWHM) of the diffraction peaks is very large at ξ = 0 (FWHM = 0.2235°), it harshly decreases at ξ = 0.12 (FWHM = 0.0432°), with the line profile being similar to the resolution function of the apparatus. This suggests that the crystal size of hafnia suddenly rises from ∼17 nm to a few hundreds of nanometers at least from the beginning of the dwelling. This assumption is confirmed by the TEM study of the evolution of the hafnia with an increasing ξ value (Fig. 4). At ξ = 0.12, the hafnia is characterized by 400 to 500 nm crystallites, explaining the evolution of the diffraction peak profiles. This grain size is very similar to that of the aggregates previously evidenced in the hafnia starting powder. Fig. 4 also shows that the crystal size of hafnia progressively decreases with an increasing ξ value, and that the crystals progressively acquire a facetted shape (automorphous character). The crystalline facets were indexed with electron diffraction experiments (Fig. 5). Starting from the 4 fold cubic axis, the corresponding images show that the (100) and (010) faces are identified as being edge on while the two others faces are oblique, as wedge fringes are observed parallel to the 〈110〉 type directions. A rotation of the crystal around the b* axis reveals the appearance of ledges at the periphery of the crystal (see circled area in Fig. 5b), which are finally viewed edge on in Fig. 5c. These ledges are formed by the same planes as the crystalline faces limiting the studied crystal, i.e. the (11̄1) and (111). The same ledges are also observed at the nanometric scale in high resolution images (Fig. 5d). As will be discussed further on, these ledges are structural features which can be considered as being at the origin of the destabilization process of the hafnia crystals. Fig. 3a shows that the hafnia has almost disappeared at ξ = 0.70 and should be absent at ξ = 0.8, as was the case for the zirconia in the ZrO₂–C system. From a thermodynamic view point, it is concluded that the hafnia amount is the rate limiting factor for the carbothermal reaction. Finally, it is noticeable that, in contrast with the ZrO₂–C system,²⁴ the automorphous oxycarbide crystals are dislocation free, regardless of the advancement of the reaction.

Fig. 4 TEM observations of the morphological evolution of starting reactants during the reaction: hafnia (a) ξ = 0, (b) ξ = 0.12, (c) ξ = 0.42, (d) ξ = 0.7; carbon black (e) ξ = 0, (f) ξ = 0.42.

Fig. 5 Tilting experiments to determine the indexation of the crystalline faces and ledges at the surface grain of the hafnia crystals (ξ = 0.42) (a) image and its associated SAED pattern under [001̄] zone axis. (b) Image and its associated SAED pattern under [101̄] zone axis. (c) Image and its associated SAED pattern under [102̄] zone axis. (d) High resolution image obtained with the [101̄] zone axis and showing the existence of ledges at the nanometric scale.

The carbon balls also show a change in the morphology with the ξ value. Starting from ξ = 0, which shows rounded carbon balls of 300 nm (Fig. 4e), the diameter of the spheres decrease (Fig. 4f) and the periphery of the particles no longer remains smooth, showing the disruption of the external graphitic layers attesting to the destabilization process of carbon black.

Finally it can be noted that whatever the advancement, no reaction products were ever seen at the contact between the carbon and the hafnia (Fig. 6). The contact between the reactants remains non-reactive, despite the evidence of the destabilization of the hafnia crystallites, attested to by the presence of numerous ledges on its surface (see the small black arrows in Fig. 6). The HfC_xO_y oxycarbide is not present between the two reactants but it nucleates within the carbon black regions (Fig. 6 see dashed-line arrows). Each nucleus of oxycarbide consists of “core–shell” type particles (Fig. 7a and b) where the core is composed of a single crystal of oxycarbide embedded in an amorphous gangue (Fig. 7c). Chemical analyses were performed, as well as a mapping of the same region in a STEM mode (Fig. 7d). It is clearly shown that oxygen is present in the core shell structures. The estimation of the oxycarbide composition, based on its cell parameter, is that it is rich in carbon, the oxygen amount is certainly very high in the external amorphous layer, as was already the case around the Zr-oxycarbides nucleus.²⁴

Fig. 6 TEM observations, performed at ξ = 0.42, showing the contact between a hafnia crystallite and the neighboring carbon black balls. The hafnia crystallite shows numerous ledges on its surface (see black arrows). The nucleation sites of the oxycarbides are situated within the carbon black areas of the sample (see dashed-line arrows).

Fig. 7 TEM observations showing the nucleation site of the oxycarbides (ξ = 0.42). (a) TEM overview of a nucleation site. (b) Enlargement on a nucleus located within the carbon black. (c) High resolution TEM image of the nuclei covering layer and its associated SAED pattern. (d) EDX mapping of the nucleation site in a STEM mode.

The oxycarbide crystallites grow as the advancement of the reaction increases (Fig. 8), with the external embedding layer being present and persisting until ξ = 0.70. In some regions of the sample, this external rim surrounding the oxycarbide particle crystallized, as shown by the typical Moiré effects observed in the high magnification images (Fig. 9). This phenomenon was also observed during the carbothermal reduction of ZrO₂ by carbon black²⁴ but at higher rates of advancement of the reaction (above ξ = 0.80). Such an external rim disappeared at ξ = 1 (Fig. 10) and remnants of it were observed as isolated islands grafted onto the oxycarbide surface (Fig. 10c). At the end of the reaction, all the hafnia particles had disappeared (see also Fig. 3a). However, some residual carbon was present (Fig. 10a), meaning that the final carbide is sub-stoichiometric in carbon. All oxycarbide crystals display the same facetted morphology (Fig. 10c), even if those involved in agglomerates (Fig. 10b) display more rounded shapes, which is probably due to a coalescence phenomenon or pre-sintering features. The grain size distribution appears uniform. It does not exceed 400 nm and the average size is around 300 nm.

Fig. 8 TEM observation of a hafnium oxycarbide particle at ξ = 0.7. (a) General overview. (b) Enlargement of the rim of the crystal showing the presence of an amorphous layer in the circled region of (a).

Fig. 9 TEM observation of an oxycarbide particle showing the crystallization of its external surrounding layer as HfC_xO_y nanocrystallites (ξ = 0.7). (a) General overview. (b) Enlargement of the rim corresponding to the rectangular area reported in (a) showing a typical Moiré effect.

Fig. 10 TEM observation of a hafnium oxycarbide particle at ξ = 1. (a) TEM overview of the final product containing hafnium oxycarbide and residual free carbon. (b) Observation of agglomerates in the final powder. (c) Enlargement of a hafnium oxycarbide particle and its corresponding SAED pattern (d).

4. Discussion

The TEM study of the final product highlights the presence of residual free carbon, so that the hafnium oxycarbide is sub-stoichiometric in carbon like the other carbide or oxycarbide compounds of the group IV transition metals.

The observations carried out by TEM on samples selected at different rates of advancement of the reaction show that the contact between hafnia and carbon black is a non-reactive interface. In addition, the nucleation of the oxycarbides is strictly localized in the carbon black aggregates. This suggests that this carbothermal reaction is not a solid–solid reaction in which the product is generally developed between the reactants. Instead, the reactants need to be forwarded by a gaseous vector towards the oxycarbide formation area. The purely reconstructive character of the carbothermal reduction of hafnia does not allow the production of particles which have a size lower than 100 nm. The average size of the final product being around 300 nm is comparable with those obtained by other authors using other synthesis methods.^12,13,22 Even at low values of the reaction rate (ξ = 0.12), the grain size distribution of the oxycarbide is important, so the carbothermal route seems to be inappropriate for synthesizing nanometer scale oxycarbides.

The nanometer sized crystallites of hafnia have not allowed smaller sized oxycarbides to be obtained. In fact, the detailed study of the evolution of the hafnia crystallites reveals an abrupt coarsening of the powder during the heating-up of the furnace. It is thus concluded that even if hafnium dioxide is not the thermodynamically stable form during the synthesis conditions (a reductive atmosphere), a grain growth phenomenon arises through the coalescence of elementary particles within the aggregates in order to reduce the surface energy of the dioxide powder. The coalescence then occurs at lower temperatures than the carbothermal reaction, meaning that its Gibbs energy is much lower than that required for the carbothermal reaction. The same behavior was already evidenced in the case of the carbothermal reduction of rutile.²⁵ This result seems to demonstrate that in carbothermal reactions, the original size of the dioxide crystals is not a factor in controlling the expected size of the oxycarbides.

At ξ = 0.12, the hafnia crystallites show rounded shapes, while at ξ = 0.42 they have acquired facetted automorphous habits decorated with ledges. These particular microstructures are similar to those observed in zirconia, prepared using a carbothermal reduction.²⁴ Their occurrence could then be interpreted the same manner, the presence of such structural ledges being associated with the destabilization process of the dioxide compound with the contact of the CO_(g) rich atmosphere.²⁵ Indeed, the particularity of the destabilization mechanism involved in zirconia is related to its structure and the same process should operate in hafnia, the latter being isostructural with zirconia. Summarily, in these compounds the {111} and {100} reticular planes corresponding to the ledges are associated with the more dense planes of the structure. However, it ought to be noted that these planes are very specific as they correspond to an alternation of the anionic and cationic layers in the direction normal to these planes. If a {111} or {100} anionic layer is in contact with the surrounding CO_(g) rich atmosphere, the hafnia surface will be reduced, releasing some carbon dioxide. However, the underlying cationic layer will then be in direct contact with the reducing atmosphere and could constitute a passivation layer which stops the reaction. The only way to continue the destabilization phenomenon is to break the chemical bonds directly at the level of the crystalline ledges. This process, which permits the release of the hafnia component (hafnium and oxygen) in the form of gaseous species, is accompanied by the migration of the ledges on the surface of the particle (see the arrows in Fig. 5d). From the SSUB5 database²⁹ and using the Thermo-Calc software, the equilibrium constants for the potential reactions between Hf_(s), Hf_(g), HfO_(g), HfO_2(g), HfO_(s) and HfC_(s) were determined and used to draw the volatility diagram of the Hf–C–O system. Fig. 11 shows, at 1650 °C, the logarithm of the HfO_x pressure as a function of the logarithm of the carbon monoxide pressure. We can easily assume that around the hafnia particles the carbon monoxide pressure is higher than 10 Pascal. This value, indeed, corresponds to the boundary of the stability domains of Hf_(g) and HfO_(g). Therefore, the most thermodynamically stable form in our temperature conditions seem to be the gaseous species HfO.

Fig. 11 Volatility diagram of the Hf–C–O system at 1650 °C as a function of the carbon monoxide pressure.

The solid–gas reaction accounting for the destabilization of hafnia can then be written as follows:

HfO_2(s) + (z + x)CO_(g) = HfO_(g) + CO_2(g) (2)

On the carbon black reaction sites, a disruption of the graphitic layers was observed on the surface of the carbon balls. Carbon seems to react with the surrounding atmosphere of carbon dioxide to produce an emission of carbon monoxide according to the eqn (1):

zC_(s) + zCO_2(g) = 2zCO_(g) (3)

the carbon monoxide thus liberated is simultaneously used to destabilize the hafnia through reaction (2). The HfO liberated is transported through the gas medium to the nucleation site of the oxycarbide, and the co-condensation of HfO_(g) and CO_(g) leads to the formation of a hafnium oxycarbide phase which nucleates heterogeneously within the amorphous carbon (Fig. 6 and 7). Eqn (4) describes not only the destabilization phenomenon of HfO₂ but also the nucleation of the oxycarbide phase and corresponds to the global equation of the carbothermal reaction.

HfO_2(s) + (z + x)CO_(g) → HfC_xO_y(s) + zCO_2(g) (4)

At the vicinity of the nucleation site, the co-condensation of HfO_(g) and CO_(g) gives local rises of high amounts of oxygen, which can explain the formation of the amorphous gangue, which is rich in oxygen, that surrounds the oxycarbide crystals in the early stage of the reaction. When the hafnium dioxide vanishes near ξ = 0.7, the carbon excess within the sample continues to pump the oxygen from this amorphous layer by the Boudouard equilibrium and, when its composition becomes that of the oxycarbide, the external layer crystallizes (Fig. 9). This result is then very similar to that observed in the ZrO₂–C system.²⁴

The Rietveld refinements performed to accurately determine the cell parameters were carried out on the global XRD diagrams, including the refinement of the atomic positions. The results indicated that, whatever the advancement rate of the reaction, the oxycarbide shows a face-centered cubic structure with an Fm3̄m space group and they do not confirm the occurrence of a monoclinic intermediate phase.²² The low shift of the (511) hafnium carbide peak and the small increase of its lattice parameter are conducive to a limited modification of the composition during the reaction. The lattice parameter increases only slightly by 0.05% between ξ = 0.12 and ξ = 1, with the advancement value following a linear function. This result contrasts with that obtained for the ZrO₂–C system.²⁴ In this system, a small increase in the cell parameter by 0.06% was observed between ξ = 0.2 and ξ = 0.8 (the composition was then assumed to be constant), while a drastic increase of the cell parameter by 0.2% was observed between ξ = 0.8 and ξ = 1. This two-step formation of the oxycarbide phase was also accompanied by a singular evolution of the crystalline habit of the oxycarbides from automorphous dislocation-free crystals to xenomorphous dislocation-bearing crystals. In the case of HfO₂–C, the oxycarbide is formed through a one-step process and its morphology does not evolve as ξ increases. The crystalline habit corresponds to that of the primary automorphous and dislocation-free oxycarbide of the ZrO₂–C system. As the hafnium oxycarbide is nearly stoichiometric in carbon at the earliest stage of the reaction, there is no need for dislocations. Indeed, their presence in the ZrO₂–C system has been justified by the fact that the enrichment in carbon of the ZrC_xO_y oxycarbides above ξ = 0.8 was assisted by the dislocation motion.²⁴

This result suggests that the solid solution of oxygen within the hafnium oxycarbide is very limited compared to that in the zirconium oxycarbide. Complementary investigations are now in progress to accurately determine the extent of this solid solution in the HfC_xO_y compounds based on the thermodynamic calculation of phase diagrams performed with the CALPHAD method and comprehensive experimental studies to measure the solid solutions obtained in both ZrO₂–C and HfO₂–C systems.

5. Conclusions

This microstructural approach undertaken on the Hf–C system allows us to compare the results obtained with the mechanisms involved during the carbothermal reduction of zirconia, which is isostructural with hafnia.

The numerous similar points between the two systems are as follows:

• The interface between the dioxide and carbon black is non-reactive and the reaction proceeds through solid–gas reactions.

• The oxycarbide phase nucleates in the carbon black area forming some core–shell microstructures exhibiting a crystal core embedded within an amorphous gangue which is rich in oxygen and crystalizes near ξ = 0.7.

• This gangue then disappears between ξ = 0.7 and ξ = 1, when the hafnia is consumed, thanks to the progressive reduction of the oxycarbide which is continued due to the carbon excess.

The main difference between the two systems concerns the growth of the oxycarbide phase. While in the ZrO₂–C system the oxycarbides are obtained through a process involving two steps, in the HfO₂–C system only one generation of oxycarbide is formed, its composition being rich in carbon at the early stage of the reaction. This result highly suggests that oxygen solubility is very low in HfC_xO_y compared to ZrC_xO_y.

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Footnote

† Present address: Center for Nanotechnology Innovation@NEST, Istituto Italiano di Tecnologia, Piazza San Silvestro 12, 56127 Pisa, Italy.

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