Zirconium carbide oxidation: Kinetics and oxygen diffusion through the intermediate layer

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(g m À2 s À1 ) at 1273 K compared to 1173 K was correlated with the preferential oxidation of carbon at the intermediate layer which would leave as CO and/or CO 2 leaving a gap between ZrC and substoichiometric zirconia.
oxidation, zirconia, zirconium/zirconium compounds 1 | INTRODUCTION Zirconium carbide has potential in ultrahigh-temperature applications such as for coatings on hypersonic vehicles 1,2 or as an inert matrix fuel in the nuclear industry. 3,4 ZrC has better properties than other carbides such as a higher thermal conductivity and higher melting point, [5][6][7][8] however, a comprehensive database on its properties is not available and therefore its use is rarely considered. 9 The oxidation of ZrC has been studied [10][11][12][13][14][15][16][17][18][19] under several experimental conditions of temperature and pressure [10][11][12][13][14] but a clear understanding has not yet been achieved due to the large numbers of variables that affect it, such as chemical composition of the initial material (C/Zr stoichiometry), porosity, or grain size. 9,20 A mechanistic model recently proposed by Katoh et al 9 building on the model previously proposed by Shimada 21 showed as an initial stage the formation of an oxycarbide ZrO x C (1Àx) layer 9,10,22 prior to the formation of an oxide layer. This oxycarbide layer has, however, never been experimentally observed, perhaps because the ZrC crystal structure can accommodate up to 60% of oxygen in the crystal lattice without changing its structure. 22 The overall reaction proposed by Katoh et al 9 and Rama Rao and Venugopal 22 is summarized as: What is missing from the model proposed by Katoh et al 9 are the effects of formation of the different zirconia polymorphs and the influence of carbon oxidation on the oxide microstructure with temperature. Carbon is produced during either ZrC oxidation or ZrO x C (1Àx) oxidation and is considered to remain in the oxide layer as inclusions at low temperatures, from 653 < T < 873, or to react with oxygen, above 870 K, leaving the system as CO/CO 2 . 9 The interface characterization between the carbide and the oxide on samples oxidized at 1073 K and the Maltese cross shape development was the topic of our previous publication. 23 The Maltese cross shape of the oxide is induced by crack development at sample corners during the initial stages of the reaction. 23 The failure of corners promotes rapid growth of the oxide in this region. The interface between the carbide/oxide of a hot-pressed ZrC specimen oxidized at 1073 K for 1 hour in air was comprised of a 2-lm-thick amorphous carbon matrix with ZrO 2 nanocrystals embedded in it. Based on this finding, the present work gives deeper understanding of the role of this interface in the reaction mechanism from 1073 to 1373 K for hot-pressed ZrC specimens. Macroscopic characterization via XRD and SEM of the oxide layer at different temperatures was coupled with the use of an isotopic exchange technique where oxygen diffusion was tracked by SIMS analysis using an isotopic tracer ( 18 O).

| EXPERIMENTAL PROCEDURE
High-density ZrC pellets were made using the same procedure described in ref, 23 where the description of Set A, B, and C samples can be found. 23 Commercial ZrC powder (3-5 lm; 90% < 8 lm with 0.2% < Hf < 2%; Grade B; H.C. Starck, Karlsruhe, Germany) has, according to the manufacturer, a carbon concentration of 11.6 wt% (with 11.1% being combined and 0.5% being free carbon). Set B ZrC pellets made from this powder in this study had a carbon concentration of 11.9% with an error ≤0.1% measured with an EMIA 320 V2 carbon and sulfur chemical analyzer (Horiba Scientific, Kyoto, Japan). The commercial ZrC powder analyzed with the same unit showed a carbon concentration of 11.7% with an error ≤0.1%, showing that Set B pellets acquired additional carbon on hot pressing. Set A ZrC pellets presented a carbon content of 11.2%. The same technique was used to quantify the carbon concentration in the oxide layer.
Samples from Set A, hot pressed at 2123 K, were used for characterization of the ZrC and ZrO 2 layers across their interface with a Focused Ion Beam instrument coupled with a Secondary Ion Mass Spectrometer (FEI FIB200-SIMS; FEI Company, Hillsboro, OR). This microscope uses a gallium source for imaging and sputtering. A high current (20 000 pA) was used to sputter the sample cross-sectional surface for 5 minutes, whereas imaging was performed at a current between 1000 and 3000 pA. SIMS chemical analysis was done on a 100 lm square region made of 10 rectangles of dimensions 10 lm 9 100 lm across the interface sputtered at a current of 3000 pA. From each rectangle, secondary negative and positive ions were collected to evaluate the chemical abundance of carbon and oxygen species. On each rectangular area previously analyzed by SIMS, energydispersive X-ray spectrometer (EDX) chemical analysis was also performed with the INCA system (INCA; Oxford Instruments, UK) equipped with an ultrathin polymer window in a LEO Gemini 1525 FEGSEM (Zeiss, UK), at 20 kV. To evaluate the amount of material removed by the action of the FIB-SIMS a nondestructive technique was used: the Zygo NewView 200 3D optical interferometer which enables surface topography characterization. The sputter depth of the gallium source was approximately 0.6 lm in the ZrC side and 1.6 lm in the ZrO 2 side. Set B, 1 cm 3 cubes, hot pressed at 2273 K, were used for kinetic analyses and oxide layer growth measurements. Chemical characterization with EDX on sample cross sections polished and coated with chromium was performed in a JSM 6400 (JEOL, USA). Characterization of the oxide layer was performed by X-ray diffraction (XRD) on a Bruker D2 Desktop (MA, USA), using a Cu Ka source. XRD was performed on oxide fragments or on powders, which were prepared by crushing the oxide layer with an agate pestle in an agate mortar. Quench treatments for kinetic analyses in a chamber-lift furnace were performed in air atmosphere at 1073, 1173, 1273, and 1373 K at times from 15 until 480 minutes. Prior to insertion in the furnace, the samples were weighed and placed in a zirconia or alumina crucible so that the monitoring of weight would not be affected by oxide layer spallation. At 1073 and 1173 K oxidation gave partly oxidized samples and the oxide layer measurements were performed in an optical microscope (Olympus UC30, Tokyo, Japan) on sample cross sections after cutting the samples in half with a diamond-copper saw (Isomet Low Speed Saw; Buehler, Braunschweig, Germany). Oxide thickness was measured by averaging the measurements taken in the middle point of each side. The oxide layer in the samples oxidized at 1273 and 1373 K did not adhere to the carbide core but detached during handling, therefore the oxide thickness was estimated from the residual thickness measured using electronic calipers (accuracy of 0.01 mm) in the centre of the surface. Weight change and surface area measurements were recorded on samples before and after quenching. Kinetic evaluation was performed first by plotting the change in weight normalized per initial surface area and then by plotting the change in weight normalized per carbide core surface area of the carbide after quenching as a function of time. Data were then fitted according to Equations 3 and 4: where DW is the weight change after oxidation (g), A is the surface area (m 2 ), k l and k p are the linear (g m À2 s À1 ) and parabolic (g 2 m À4 s À1 ) rate constants, respectively, and t is the time (seconds). 24,25 The mass gain normalized per initial surface area takes into account the initial area of the manufactured ZrC sample, whereas the mass gain normalized per carbide surface area takes into account the area of the carbide sample core evaluated at each quench time. For experiments at 1273 and 1373 K the carbide core area was measured with the calipers as the oxide was not adherent. The area in this case is evaluated with Equation 5 or 6 depending on the shape of the carbide core which turned from a cuboid shape to a spherical one (see results section in our previous publication 23 ).
where a, b, and c are the dimensions of the cuboid and r in Equation 6 is the radius of the sphere. The carbide area for samples oxidized at 1073 and 1173 K was evaluated by subtracting the dimensions of the partly oxidized cube measured in the centre of each face using caliper from the oxide layer thickness evaluated with the optical microscope. For long oxidation times (>2 hours) the oxide layer grew drastically assuming the typical Maltese cross shape so the oxide thickness was measured in the center of the face of the cross section as this layer showed a compact structure.
In situ XRD analysis was performed on commercial ZrC powder using a high-temperature XRD (HT-XRD); X'pert Multi-Purpose Diffractometer (MPD; Philips, Amsterdam, the Netherlands) under air. Oxidation was simulated by heating the sample in air on a platinum holder (HDK 2.4; Buhler, Germany) at 40 kV and 40 mA, using Ni-filtered CuKa radiation between room temperature and 1306 K, with scans performed every 50 K.
Set C, cut from a Set B sample, was used for a double oxidation experiment using an 16 O followed by 18 O enriched atmosphere in an isotopic exchange set up. The sample was placed on a crucible inside a quartz furnace evacuated to 10 À7 mbar, a flux of 200 mbar of oxygen was inserted when a temperature of about 1060 K was reached. The sample was first exposed to the oxygen atmosphere for 4 minutes in research-grade 16 O (mostly consisting of 16 O plus the natural 18 O abundance of 0.2%), then the furnace was evacuated and cooled before the second oxidation was performed in an atmosphere of 40% enriched 18 O gas at 200 mbar at the same temperature and time as the first oxidation.
FIB-SIMS was used to mill a ramp across the ZrC/ZrO 2 interface using an Oregon-Physics Plasma FIB (Hillsboro, OR) 500 nA/30 keV/Xe beam. This ramp had a slope of 26.6°and width of 150 lm. The roughness of the top surface was 5.2 lm. SIMS and EDX analysis (done in a LEO Gemini 1525 FEGSEM, at 20 kV) were performed on a ramp made with the FEI FIB200-SIMS in the center of this region. This final ramp used for analysis showed a 30°s lope with a width of 45 lm and height of 40 lm. This ramp presented a smoother surface compared to the ramp milled by the Plasma FIB so that the SIMS data collected were less noisy. Point scan EDX was performed and errors were evaluated by averaging the values and taking the standard deviation of the measurements done on the same area. A MATLAB code was used to plot the SIMS data on the ramp. 18 O À isotopic fraction, called here IF, is a useful tool 26 as it represents the oxygen isotope distribution on the surface and limits any sharp change in ion signal intensities due to sample topography or localized charging. 27 IF is evaluated with Equation 7: where 16 O À and 18 O À represents the oxygen ions intensities detected by FIB SIMS. Figure 1A shows the mass gain normalized per initial surface area vs time of samples quenched from 1073 to 1373 K. Data initially were fitted to a parabolic law (Equation 4) as shown in Figure 1B. This first analysis is, however, misleading as it does not take into account the transformation of the carbide core surface area evolution which is known to be of primary importance in metal oxidation. 28 We consider this to be even more important for oxidation which involves a Maltese cross evolution of the oxide as it affects dramatically the carbide core surface area. Figure 1C shows the mass gain normalized per carbide core area vs time. Data for oxidation at 1073 K can be fitted to one kinetic regime, whereas2 regimes are needed for samples oxidized at higher temperature (1173-1373 K). The kinetics at 1073 K are linear, whereas those at 1173, 1273, and 1373 K fit a linear trend up to 2 hours of oxidation (shown in Figure 1D) followed by a rapid change as the oxidation growth accelerates ( Figure 1C). Oxidation at an accelerated rate is referred to as breakaway oxidation and is usually accompanied by loss of a protective oxide layer. 29 In this case, breakaway oxidation occurred when the Maltese cross shape of the oxide fully developed. The oxide growth in this region is severe and is accompanied by shrinkage of the unoxidized carbide core that changes from its initial cubic shape to a spherical one (see Gasparrini et al 23 ). For oxidation times over 2 hours the increase in oxidation was linked to the shrinking of the carbide core which was found in the form of a sphere, at the same time the oxide develops with the characteristic Maltese cross shape. The drastic change in the carbide core from a cubic into a spherical shape, described in our previous publication, 23 is explained with the fact that corners are the points where the oxidation proceeded more rapidly developing with the typical Maltese cross shape. The carbide core surface area is considered the most suitable parameter to be used to derive kinetic analysis when compared with the initial surface area, compare Figures 1B vs 1D, as data points in Figure 1D showed very good agreement with a linear fitting, R 2 ≥ 0.99. From the linear fitting of the data plotted in Figure 1D, it is possible to evaluate the linear rate F I G U R E 2 A, Plot of the linear rate constants (k l ) from Figure 1D  constants, k l , which are shown in Figure 2A. The linear rate constants do not show a clear trend: oxidation at 1073 and 1173 K showed an increase in oxidation rate but at 1273 K a slowdown occurred as the k l is lower than at 1173 K. This slowdown in oxidation kinetics is accompanied by an increase in oxide thickness above 1273 K, as can be seen in Figure 2B,C. Figure 2B shows the oxide thickness vs time from 1073 to 1373 K, the slope of the straight lines fitting the oxide thickness rate are shown in Figure 2C and they are called the oxide thickness linear rate constants k l,oxide . The oxide thicknesses have a similar growth rate at 1073 and 1173 K, however, at higher temperatures the rate of oxide layer growth increased considerably. The slowdown in kinetics at 1273 K which corresponds to an increase in oxide layer thickness was investigated through experimental observations. Specimens oxidized at 1073 and 1173 K presented an adherent oxide layer, which withstood cutting with a diamond saw (see photo in Figure 2E left). Samples oxidized at 1273 and 1373 K instead showed a voluminous oxide layer which was easily damaged during handling. The oxide layer was detached from the carbide core as a gap was present between the oxide and the carbide (see photos in Figure 2E right and Figure 2F).

| Oxidation kinetics
XRD analysis was performed on the bottom side (once in contact with ZrC) and top side (exposed to air) of the oxide layer in samples oxidized at 1273 and 1373 K for 30 minutes as well as on the top surface of the oxide layer formed at 1073 and 1173 K for 30 minutes which was still adherent to the sample. XRD analysis on these samples showed that the oxide layer formed at 1273 and 1373 K was mostly made of m-ZrO 2 , whereas at 1073 and 1173 K the oxide was made of m-ZrO 2 and either t/c-ZrO 2 (see Figure 2D).
A fine black powder was found between the carbide and oxide after oxidation at 1273 K and 1373 K and this could either be free carbon arising from the reaction happening at the interface, as previously reported by Voitovich and Pugach, 16 or substoichiometric zirconia formed by anion vacancies 30 reported to be black 31 which presents the peak at 2h = 30°observed in Figure 2D. The detached oxide layer had a black appearance on the bottom side, where it was once in contact with ZrC, and a white appearance on the top side. This is in agreement with the observation of Shimada et al 32 on ZrC single crystal oxidized at from 0.02 to 2 kPa partial pressure of oxygen, however, in our case the black layer could not be separated from the white layer. In some cases, the oxide was cracked and lifted in the centre as if some gases pushed to make their way out of the bulk, likely CO and/or CO 2 .
The possibility that the oxide at 1073 and 1173 K could be comprised of either t-or c-ZrO 2 is due to the fact that the most common phase in the system is m-ZrO 2 which matches all the XRD peaks present in t-or c-ZrO 2 and ZrO 1.95 plus other peaks, apart from one at 2h = 30°which unfortunately is common with these phases (see PDF 037 1484 33 for m-ZrO 2 , 050 1089 34 for t-ZrO 2 , 049 1642 35 for c-ZrO 2 , and 01 081 1544 36 for ZrO 1.95 ). An experimental observation on samples oxidized at 1073 and 1173 K showed that the oxide formed was compact and stress resistant. For example, during a TGA/DTA experiment at 1073 K, a partially oxidized sample underwent volume expansion and cracked the alumina crucible without any sign of crumbling. As a result it is plausible the peak at 30°is from tetragonal zirconia which is known to improve the strength and toughness of m-ZrO 2 when dispersed within it due to its ability to undergo a stress-induced polymorphic transfomation. 37 Rama Rao et al, 22 however, detected the cubic polymorph of zirconia below 1073 K during ZrC powder oxidation which then transformed to the monoclinic polymorph at higher temperatures. At equilibrium, pure c-ZrO 2 is stable at much higher temperatures than those investigated here, between 2640 K up to the melting point at 2950 K, 38 but other authors found the cubic polymorph during oxidation of ZrC at relatively low temperatures. 39 The identification of the second polymorph in this work is considered to be either t-and/or c-ZrO 2 due to the discrepancies found in literature and the difficulties of differentiating these 2 polymorphs with the available techniques (XRD, TEM) when the monoclinic polymorph is also present. Still it is evident that the second polymorph found in samples oxidized at 1073 and 1173 K enhances the capabilities of zirconia to sustain stresses.
XRD analysis on the crushed oxide layer formed during oxidation at 1273 K and 1373 K showed this to be comprised of m-ZrO 2 (see Figure 2D labeled as 1273 K powder), however, when XRD analysis was performed on the bottom and top sides of the oxide the XRD pattern changed. The bottom/black surface was comprised of both m-ZrO 2 and either t/c-ZrO 2 or substoichiometric ZrO 1.95 . The black color can be explained either by carbon traces or by the presence of an oxygen-deficient m-ZrO 2 layer, identified by Sinhamahapatra et al 31 as ZrO 2Àx . Substoichiometric zirconia could be difficult to imagine in a highly enriched oxygen atmosphere such as atmospheric air. It has been, however, previously reported during zirconium oxidation in an atmosphere of oxygen of 2 9 10 À8 Torr by Ma et al. 40 The substoichiometric layer found by Ma et al, 40 called ZrO x , was sandwiched between zirconium metal and stoichiometric ZrO 2 . This 3-layered structure made of Zr/ZrO x /ZrO 2 was considered energetically more stable to form than an interface Zr/ZrO 2 . 40 In our study, the black layer next to ZrC was identified as substoichiometric zirconia because it well matched the ZrO 1.95 XRD pattern and its black appearance 31 could only be assigned to the presence of ZrO 2Àx and not to carbon traces. Carbon analysis was indeed performed on both the top white side and the bottom black side of the sample: both analyses revealed the same carbon content. Carbon analysis performed on a fragment taken from the white top side of a sample oxidized at 1273 K for 8 hours revealed a carbon content of 0.42 AE 0.01%, whereas the oxide black layer from a sample oxidized at 1273 K for 30 minutes, contained 0.42 AE 0.03% carbon. The sample oxidized for 8 hours was chosen so that it was possible to measure the carbon content (%) on the top side of the oxide layer far from the ZrC side. The sample oxidized for 30 minutes was chosen to have enough black layer to perform multiple analyses. The top side of the oxide was comprised of m-ZrO 2 as can be seen in Figure 2D. At higher temperatures, 1273 K, where the oxidation kinetics is slowed, we see that the intermediate layer is missing and the oxide next to this layer is substoichiometric zirconia. At the same time, the oxide thickness rate increases (see Figure 2C). The volume expansion from cubic to tetragonal and tetragonal to monoclinic is approximately +2% 41 and +4%, 42 respectively, therefore the voluminous and porous appearance of the oxide which grew thicker at 1273 and 1373 K compared to that formed after oxidation at 1073 and 1173 K could be explained by the stresses induced by these transformations. The apparent slowdown in the oxidation kinetics, k l (measured in g m À2 s À1 ) observed at 1273 K (see Figure 2A) could be related to either a mass gain rate decrease or a surface area increase. Results shown in our previous paper 23 showed that the surface area decreased over time during oxidation, therefore the slowdown in kinetics is related to a mass gain rate decrease. In carbides oxidation there is a competition between carbide oxidation and carbon oxidation (see Equations 8 and 9).
During uranium carbide (UC) oxidation, 43 carbon oxidation occurs simultaneously with UC oxidation, 44 however, in the case of ZrC, previous work 18 suggests that CO/CO 2 is produced mostly during the cooling stage. In reference 18 the cracked sample surface was associated with the thermal expansion coefficient mismatch between the carbide and oxide polymorphs during the cooling stage. However, cracks were observed during the heating stage of the reaction using an in situ technique on ZrC 23 and UC. 43 These cracks would offer a route for CO/CO 2 to leave the sample during the heating stage. The mass gain rate decrease observed at 1273 K could be related to the loss of carbon due to carbon oxidation (Equation 9) over carbide oxidation (Equation 8). This occurs when reaction 9 prevails over reaction 8 or when carbon already present in the system is oxidized following reaction 9. Carbon oxidation is thought to prevail in the intermediate layer between ZrC/ ZrO 2 for T = 1273 K following the results achieved on samples oxidized at 1073 K (where a layer of amorphous carbon was detected at the interface carbide/oxide, see Gasparrini et al 23 ). The gap observed between the carbide and oxide for oxidations at 1273 and 1373 K could therefore be induced by preferential oxidation of carbon. Oxygen, when in contact with the intermediate layer made of carbon and zirconia, preferentially oxidizes the carbon that leaves the sample as CO or CO 2 via cracks through the porous oxide layer, as seen by Bellucci et al. 18 The preferential oxidation of carbon promotes an oxygen-deficient zirconia layer, characterized in this study with PDF 01 081 1544 36 for ZrO 1.95, to remain in the carbide/oxide gap. The substoichiometric zirconia is only found on the oxide next to the carbide in little amount, hence why it can only be detected when XRD is directly performed on the black surface of this oxide layer.

| In situ HT-XRD
Formation of t-/c-ZrO 2 below the generally accepted polymorphic stability ranges which start at 1448 K 45 for t-ZrO 2 and 2643 K 45 for c-ZrO 2 was confirmed during an oxidation experiment performed on ZrC powder in a high-temperature XRD. When ZrC powder is heated in a static air environment from room temperature to 1306 K (see Figure 3) the first oxide polymorph formed matched the t-/c-ZrO 2 pattern. The t-/c-ZrO 2 XRD pattern was seen from 891 to 1203 K, whereas for temperatures above this range m-ZrO 2 peaks appeared (XRD peaks were matched with PDF 037 1484 33 for m-ZrO 2 , 050 1089 34 for t-ZrO 2 , 049 1642 35 for c-ZrO 2 and PDF 035 0784 46 for ZrC).
There are several ways in which t-ZrO 2 can be stabilized over m-ZrO 2 including critical crystallite size and the presence of ion impurities or oxygen vacancies. Regarding the critical crystallite size, the formation of t-ZrO 2 before m-ZrO 2 can be explained with the theory of Garvie 47,48 which states that a "critical crystallite size" exists for ZrO 2 . Below a size of 5-16 nm t-ZrO 2 crystals are favored over m-ZrO 2 crystals, whereas above a critical size of 30 nm m-ZrO 2 crystals are favored. This occurs because t-ZrO 2 crystals are stabilized due to their reduced crystal surface free energy 49 when compared with m-ZrO 2 . Previously we showed 23 that the crystallites of ZrO 2 formed were approximately 10 nm in size which agrees well with the theory of Garvie. 48 Another mechanism proposed by different authors for the stabilization of t-ZrO 2 at lower temperatures, even down to room temperature, is the presence of oxygen ion vacancies. 45 The presence of stable tetragonal phase in bulk ZrO 2 has been explained by oxygen ion vacancies within the ZrO 2 lattice supposedly generated either at higher temperature or under vacuum. 45 Srinivasan et al 50 reported that the transformation from tetragonal to monoclinic ZrO 2 is related to the adsorption of gaseous oxygen at relatively low temperature, such as 573 K or on cooling during an HT-XRD study of zirconia. In our case the transformation from tetragonal to monoclinic occurs at high temperature, above 1099 K shown in Figure 3 and could be related to crystal growth or removal of oxygen vacancies from the ZrO 2 lattice. The characterization of a layer of substoichiometric zirconia on hot-pressed ZrC in samples oxidized at 1273 and 1373 K shown in Figure 2D suggests that the first oxide formed during ZrC oxidation is characterized by oxygen vacancies.
Previous studies of ZrC oxidation, typically identify the ZrO 2 crystallites as cubic 22,39,51 rather than tetragonal which, instead, is typically identified in amorphous ZrO 2 oxidation studies. 47,52 Due to this controversy and the similarities in their XRD patterns, as previously explained, both tetragonal and cubic polymorphs may be present in our system.

| Chemical analysis across the ZrC/ZrO 2 interface
A sample cross section (shown in Figure 4A) from set A oxidized in a furnace for 1 hour at 1073 K was analyzed by FIB-SIMS and SEM. Chemical analyses were performed by SIMS and EDX on each rectangle with size 100 9 10 lm highlighted in Figure 4A. SIMS is a surface characterization technique, whereas EDX gives information on the sample bulk. Figures 4B,C, and D show the normalized ions counted during SIMS analysis which are relevant to this system (expressed in fractions of counts per second: cps/cps): (B) carbon, (C) oxygen, and (D) zirconiumrelated species. SIMS analysis showed that on the ZrC side no oxygen was present and in the ZrO 2 side little carbon was found (see Figure 4B,C). In the same way the ions related to ZrC, in this case ZrC 2 (+), showed the highest yield in the ZrC side (see Figure 4D) and dramatically decreased to zero on the ZrO 2 side just 10 lm away from the carbide/oxide interface.
EDX performed on the same region after the FIB-SIMS analysis is shown in Figure 5A. EDX was done by selecting each 100 9 10 lm rectangle as previously done with SIMS, however, it was also performed outside the FIB SIMS sputtered region. Chemical analysis was performed considering all elements: no oxygen was found in the ZrC area and no carbon was found in the ZrO 2 side within the FIB-SIMS sputtered region as shown in Figure 5A (EDX peaks within this region are shown in Figure 5C). EDX performed outside the sputtered region reveals oxygen in the ZrC region and carbon in the ZrO 2 region. Gallium was present as it was used for FIB sputtering, however, it is neglected in the analysis as its abundance was ≤0.54 atomic (%).
The presence of oxygen in ZrC and carbon in the ZrO 2 side outside the FIB sputtered region could be related to contamination due either to the presence of an oxide layer (the sample was kept in air atmosphere) or to sample preparation effects (such as the effect of polishing or the chromium coating). Both SIMS and EDX analysis, however, are in agreement within the FIB-SIMS sputtered region that showed the presence of only ZrC and ZrO 2 on the left and right side of the interface region. EDX is wellknown to lack sensitivity for light elements, such as carbon and oxygen, however, the similarities between the EDX and the SIMS analyses give EDX results credibility and this is why EDX is included in this work. BSEI of sample cross sections ( Figure 5B) show the 3 regions: ZrC (zone 1), intermediate layer (zone 2), and ZrO 2 (zone 3). Two samples from Set B oxidized at 1073 K were analyzed in BSE mode, the intermediate layer on the sample oxidized for 30 minutes was approximately 0.7-6.5 lm wide, whereas the intermediate layer in the sample oxidized for 4 hours at the same temperature was approximately 1.3-9.8 lm wide. An increase in the intermediate layer width occurs with time, however, this has an irregular thickness (see Figure 5B) and so the width is expressed as a range. EDX analysis for a sample oxidized for 30 minutes at 1073 K is shown in Figure 5D; oxygen was deliberately omitted in the analysis done on the ZrC side (zone 1) as the oxygen was found to be related to surface contamination in the analysis shown in Figure 5A. Chromium was also neglected in the analysis as the abundance of 0.51% arises from the chromium coating deposited during sample preparation. Two analyses were performed and the results are summarized in Table 1. EDX analysis shows that Zr and O are present in a stoichiometric ratio 1:2 in the oxide layer but also in the intermediate layer region. This result is in agreement with the observations performed via transmission electron microscopy where the intermediate layer was found to be comprised of ZrO 2 nanocrystals embedded in an amorphous carbon layer. 23 EDX also shows that the intermediate layer is comprised of carbon and ZrO 2 .

| Oxygen tracer diffusion
An oxygen tracer technique was used to determine how oxygen combines with the carbide during ZrC oxidation. Figures 6A,C show the top view of the sample surface and the attempts made to create a ramp across the oxide layer suitable for SIMS analysis. The only successful ramp used for this study is highlighted and shown from the side in Figure 6B. Figures 6D,E show a BSEI and a high magnification ion image of the ramp across the ZrC/ZrO 2 interface sputtered and polished by FIB. Figure 6E is the region used for SIMS analysis. The 3 regions observed: ZrC, intermediate layer and ZrO 2 are labeled as 1, 2, and 3, respectively. EDX chemical characterization on these regions is shown in Table 2. Figures 6F,G show the SIMS elemental mapping: Figure 6F shows the total oxygen abundance map across this region, whereas Figure 6G shows the 18 O À isotopic fraction (IF) distribution on the same area. Figure 6F shows that the total oxygen, sum of both 16 O À and 18 O À ions, is evenly distributed across zone 3 apart from sharp changes F I G U R E 4 A, SEI of a sample cross section oxidized at 1073 K for 1 h (set A), the squared region divided into 10 rectangles of size 100 9 10 lm is the region where FIB-SIMS analysis was performed followed by EDX analysis, the dashed rectangle highlights the interface; normalized values for the (B) carbon-related secondary ions; C, oxygen-related secondary ions; D, zirconium-related secondary ions sputtered from the surface and expressed in cps/cps (counts per second) [Color figure can be viewed at wileyonlinelibrary.com] of intensities due to sample's uneven morphology at cracks and pores. Figure 6G reveals a gradient of 18 O À throughout zone 2, this intermediate layer is 5.8-16.9 lm wide (measured from Figure 6E). To characterize the IF gradient through the intermediate layer, an IF profile was computed by an integrated linescan method in MATLAB and this is shown in Figure 6H. This method consisted in evaluating an averaged value of the IF within a region, highlighted with a black square in Figure 6G, which was chosen as the border between zones 2 and 3 runs parallel to the border between zones 1 and 2. From the overall IF profile across zones 1, 2, and 3 shown in Figure 6H, the IF gradient  | 2647 across zone 2 was isolated and highlighted with a box in Figure 6H. This was normalized to 1 and is shown in Figure 6I. This profile was fitted using the Fick's second law of diffusion for a semi-infinite media, considering a constant source of gas 27 (Equation 10): where C 0 (x) is the isotopic fraction which is normalized to the natural 18 O isotopic abundance, C bg is equal to 0.2% and the gas tracer concentration C g during the second anneal is equal to 40%. The parameter x represents the thickness of the intermediate region where the diffusion profile is measured, this is highlighted with the black box in Figure 6H, where x = 0 represents the border between zone 3 and 2 within the rectangle shown in Figure 6G; t represents the time of sample exposure to the oxidizing gases and D is the diffusion coefficient. The obtained diffusion coefficient D was = 9 9 10 À10 cm 2 s À1 with R 2 = 0.93. The diffusion coefficient for oxygen through this intermediate region in between ZrC/ZrO 2 is larger than the grain-boundary diffusion coefficients which is approximately D B = 1 9 10 À11 cm² s À1 evaluated by Brossmann   18 O gradient is present in zone 3 and therefore it is plausible that during the second oxidation step, either 18 O passed through an almost stoichiometric zirconia layer without significantly reacting with it or no diffusion gradient is present here due to the porous nature of the oxide layer. Confirmation of the stoichiometric nature of ZrO 2 is given by EDX analysis on the oxide layer just a few micrometers away from the intermediate layer (see Table 2). The porous and cracked nature of this oxide indicates that oxidation proceeded along grain boundaries, 23 and cracks are clearly visible in Figures 6D,E. Closer to the intermediate layer, zone 2, cracks are less pronounced compared with the cracks seen by SEM on polished surfaces which extend to 20 lm from the carbide/oxide interface (compare cracks in Figures 6E,D). SIMS analysis suggests that oxidation proceeded with inward formation of the oxide layer by oxygen penetration through cracks. The cracks present in the oxide layer mostly followed the grain boundaries (see Gasparrini et al 23 Figure 1D). Diffusion is usually described with a parabolic behavior, in this case, however, the overall reaction rate was observed to be linear. Linear reaction rates can be ascribed to either a surface reaction or a diffusion mechanism through a protective layer of constant thickness. 29 Oxidation at 1173, 1273, and 1373 K followed linear kinetic up to approximately 2 hours where a drastic oxidation was related to the ZrC core change in shape from a cube to a sphere. Increasing the temperature to 1273 and 1373 K affected both the oxide morphology and the intermediate layer, as shown in Figure 7 bottom row. The oxide at 1273 and 1373 K was made of m-ZrO 2 and it was voluminous compared to the oxide formed at 1073 and 1173 K as the oxide thickness linear rate constants increased considerably (see Figure 2C). The voluminous nature of the oxide at 1273 and 1373 K can be explained with the volume expansion occurring between t/c-ZrO 2 and m-ZrO 2 which is usually reported to be approximately 4%. 42 Between ZrC and the oxide, a gap replaced the intermediate layer which was characterized at 1073 K. The oxide surface at 1273 K at the gap was characterized as substoichiometric zirconia (shown in Figure 7 as a yellow/gray ZrO 2Àx layer), with no carbon uptake between this region and the top oxide surface. The decrease in linear rate constant, k l (g m À2 s À1 ), at 1273 K compared to 1173 K was related to the loss of carbon. Carbon could leave the system as CO and/or CO 2 due to preferential oxidation of carbon at the intermediate layer, reaction (9) prevailing over reaction (8), leaving a substoichiometric layer of ZrO 2 near the interface ZrC/ ZrO 2 .
T A B L E 2 Chemical composition of the ramp shown in Figure 6E: ZrC (zone 1), intermediate layer (zone 2), and ZrO 2 (zone 3) for ZrC sample oxidized at 1073 K in an isotopic exchange setup for 4 + 4 min first in 16   5. At the gap on samples oxidized at 1273 and 1373 K the oxide layer was black and it was identified as substoichiometric zirconia as no carbon uptake was detected in the black oxide formed at 1273 K next to the ZrC side compared to the top white surface of the oxide layer at the same temperature. 6. Samples oxidized at 1273 and 1373 K showed a gap between ZrC and ZrO 2Àx and the oxide was voluminous and made of m-ZrO 2 . On the contrary, the oxide formed by oxidation at 1073 and 1173 K strongly adhered to the carbide core and was comprised of m-and t/c-ZrO 2 . 7. The voluminous and heavily cracked structure of the oxide at 1273 K and 1373 K demonstrates its nonpassivating nature and explains the oxide thickness increase at these temperatures. Linear kinetics were followed by a drastic increase in oxidation after 2 hours of oxygen exposure for T = 1173-1373 K. This change was experimentally linked to the carbide core having its initial cubic shape evolving to a spherical one. 8. Cracking of the oxide and cyclic cracking of the intermediate layer is key for understanding the oxidation mechanism of ZrC. An analytical model and a finite element modeling (FEM) approach will be developed to assess the extent of stresses in the oxide during oxidation. 9. Rapid oxidation produced voluminous and heavily cracked oxides for oxidation from 1073 to 1373 K, hence, ZrC is not suitable for applications in oxygen environments in this range of temperatures.