P Berthod
email: patrice.berthod@centraliens-lille.org

Kinetics of High Temperature Oxidation and Chromia Volatilization for a Binary Ni-Cr Alloy

Keywords:

Kinetics of High Temperature Oxidation and Chromia

Volatilization for a Binary Ni-Cr Alloy P.

INTRODUCTION

When exposed to air at high temperature, chromium-containing alloys are covered by an external Cr 2 O 3 layer which protects them against rapid oxidation (Ref. [START_REF] Kofstad | High Temperature Corrosion[END_REF]. Indeed, the progress of oxidation is then controlled by outwards Cr cation diffusion (or inwards oxygen anion diffusion) through this existing chromia scale. Cr 2 O 3 is a stoechiometric oxide, therefore this diffusion is particularly low. Thus, chromia acts as an efficient protective barrier against oxidation and this element is often used to allow the superalloys to resist oxidation as well as other types of high temperature corrosion. For instance, it is the case in molten glasses in which chromium allows the formation by passivation of a protective barrier of chromia (Ref. 2 to 3), the dissolution of which is more limited in molten glass than alumina or SiO 2 scales. Unlike Al 2 O 3 , which develops on the external surface of alumina-forming alloys when oxidized at high temperature, chromia is not stable when the exposition temperature is too high. Indeed, when temperature exceeds 1000°C, the chromia oxide suffers from a volatilization phenomenon. The external part of the Cr 2 O 3 scale is continuously oxidized again into CrO 3 , a new oxide that is volatile and leaves the scale in a gaseous form. This phenomenon can become problematical at very high temperatures, in aeronautics (Ref. [START_REF] Sims | The Superalloys[END_REF] to 5) as well as in other fields where chromia-forming alloys are used, such as Solid Oxide Fuel Cells (SOFCs), as demonstrated in recent works (Ref. 6 to 7). The rate of chromia volatilization is negligible bellow 1000°C but increases with temperature and must be taken into account for very high temperatures. If not, determination of the parabolic constants by thermogravimetry becomes more difficult and leads to values that are too low to represent correctly the real damage caused by oxidation of the alloy. To better predict the lifetime of chromia-forming superalloys at very high temperatures, it could be necessary to state the rates of both mass gain kinetic and chromia volatilization. For temperatures up to 1000°C, the oxidation kinetics follow, each time, the Wagner's law [START_REF] Kofstad | High Temperature Corrosion[END_REF] which can be integrated into equation [START_REF] Martino | [END_REF] for cases where the transient initial oxidation stages can be neglected compared to the following parabolic oxidation:

m Kp dt dm = (1) 2 1 t . Kp . 2 m = (2)
where m is the mass gain per unit surface area induced by Cr 2 O 3 formation (i.e. the mass of oxygen that joined the alloy), Kp is the parabolic oxidation rate constant and t the time, the origin of which is the beginning of the oxidation phenomenon at the considered temperature. For higher temperature one must also estimate the linear speed of volatilization of chromia, i.e. the volatilization constant Kv which appears in the equations ( 3) and (4):

Kv dt dm v = (3) t . Kv m v = (4)
where m v is the mass of chromia that left the alloy per unit surface area in the CrO 3 gaseous form.

Studies concerning chromia volatilization at high temperature began about fifty years ago, relating to its thermodynamic aspects as well as to its rate (Ref. 8 to 11). Relating to the kinetic of chromia volatilization, studies were done using thermogravimetry on iodide chromium, pure chromium, chromia-forming steels or sintered chromia, in different gas mixtures containing oxygen at different pressures. Thus numerous data about the chromia volatilization rate are already available. But it can be also interesting to directly determinate the volatilization constant from the thermogravimetry results obtained on complex superalloys, since volatilization of chromia may depend on the alloy. Indeed, knowing how it varies with the chemical composition of the alloy, or with its microstructure, allows to know how to modify this one in order to minimize chromia volatilization, and therefore to improve its protection against high temperature oxidation. Several techniques are possible. For example thermogravimetric curves can be fitted by calculations on an equation model such as done by Di Martino (Ref. 12) on chromia-forming cobalt-base superalloys. Thanks to the Origin software, he automatically tested successive values of Kv until the theoretic curve based on the equation ( 5) converged to the experimental mass gain curve.

Here another technique was tested and applied to reach more directly the values of both Kp and Kv. This will be done by analyzing the data files issued from the thermobalance according to the differential equation ( 22). A simple alloy was studied here, a Ni-30Cr binary alloy, the solidus temperature of which is high enough to allow test temperatures as high as 1300°C without risk of beginning of fusion. It contains a sole element able to promote a selective oxidation, while the other one is the base element of most chromiaforming superalloys used at very high temperatures.

EXPERIMENTAL METHOD

Synthesis of the Samples and Oxidation Tests

This Ni-30% w Cr alloy was synthesized by foundry under controlled atmosphere (400mbar of pure Argon, H 2 O < 3ppm, O 2 < 2ppm, C n H m < 0.5ppm). The ingot of about 100g was obtained from pure Ni and Cr (> 99.9% w , Alfa Aesar) by induction melting in a copper crucible cooled by water circulation, in which it quickly solidified. Thereafter a treatment of about 2 hours at 1000°C, followed by a slow cooling in furnace, was applied to release the stresses that can appear during the solidification. Parallelepipeds (dimensions of about 2 mm x 10 mm x 10 mm) were cut to obtain the samples for the thermogravimetry tests. Their surfaces were polished with SiC paper from 80 to 1200 grid under water.

Oxidation tests were performed at high temperatures using a Setaram TGA92 thermobalance under a dry industrial air flow (80%N 2 -20%O 2 ) at 1.5 liter/hour (corresponding to a linear flow rate of about 5cm/min). Oxidation exposures were performed during 50 hours at 1000°C, 1100°C, 1200°C and 1300°C. This duration is short enough to avoid the local detachments of the chromia scale that can affect the mass gain curves after 70-75 hours for such alloys, as well as their local consequences for the sub-surface microstructure. But this duration is also long enough to get a sufficiently long parabolic oxidation stage after the initial transient oxidation. The heating and cooling rates were respectively 20°C/min and 10°C/min. The sum of the heating and cooling durations was about 3 hours, as is to say 5% of the whole test duration. The initial temperature was nearly 20°C (i.e. 293K) for all tests since the thermobalance was in an air-conditioned room at this temperature.

Metallographic Study

After oxidation tests all samples were covered with gold using cathodic evaporation, to give a good electrical conductivity to the external oxide layer. Thereafter the external oxide scale was strengthened by an electrolytic deposition of nickel. The samples were cut in two parts using an Accutom-2 saw equipped with a diamond blade. Afterwards they were embedded in a cold resin (Araldite CY230 +Strengthener Escil HY956), and polished, first with SiC paper from 80 to 1200 grid under water, then finished with diamond pastes 6µm and 3µm (DP-Suspension P of Struers).

The samples were observed using an optical microscope to observe the oxidation front of the samples. The thickness of the chromia scale, where it was not lost during cooling after test, was estimated by calculating the average value of about 20 measures performed using a graduated ocular. The interval of uncertainty was defined by the standard deviation.

The samples were also examined using a Scanning Electron Microscope (SEM) Philips XL30 in Back Scattered Electrons mode under a 20kV acceleration voltage. The Energy Dispersive Spectrometry (EDS) device was used to verify the real chemical composition of the obtained alloy and to analyze the external oxide scale.

Moreover, two chromium profiles were performed on each sample (i.e. for each temperature) by Wavelength Dispersion Spectrometry (WDS) using a Cameca SX100 microprobe, in order to estimate the total oxidized chromium. Depth and step of measures depended on the total depth of chromium depletion. The difference between, on the one hand the chromium quantity that left the metallic state, and on the other hand the chromium remaining on the sample as a Cr 2 O 3 oxide, led to estimate by a metallographic way the quantity of volatilized chromium with the form CrO 3 . This was afterwards compared to the value that was mathematically determined from the thermogravimetry results.

Mathematical Processing (transient oxidation)

Before they reached the targeted test temperature, samples encountered a first oxidation during heating. Thereafter, the transient oxidation can be not finished, as shown by the existence of a first linear mass gain before the parabolic or pseudo-parabolic oxidation took place. Indeed, except for 1300°C, all the mass gain curves obtained showed a more or less long initial linear part (of the m = K l .t type). This first double contribution of the preliminary oxidation to the mass gain must be taken into account.

Oxidation of such nickel alloys usually starts with nucleation and growth of both NiO and Cr 2 O 3 , and this transient stage finishes when the Cr 2 O 3 scale becomes continuous. It is assumed here that the oxide formed during the transient oxidation stage is mainly of Cr 2 O 3 since no NiO was detected in the parts of external oxide that remained on surface after test, like it will be seen further. Then it is considered here that the total mass gain that results from the transient oxidation stage is essentially due to Cr 2 O 3 .

The mathematical treatment of the mass curves was started by the determination of the contribution of the transient oxidation to the mass gain. First the recorded files were processed using the Excel 97 software of Microsoft to draw the mass gain curves m = ) t ( f , where m is counted from the time when the temperature reached the stage temperature (t = 0).

The first mass gain induced by oxidation during heating and linear isothermal oxidation is the sum of an Heating part and a Linear part [START_REF] Quadakkers | [END_REF]:

L H 0 m m m + = (6)
Then the value of K l , can be easily determined from the mass gain measured between the beginning of the isothermal stage and the beginning of the parabolic part of the curve. m H was determined from the ) T ( f K l = evolution given by the four values of K l at 1273, 1373, 1473 and 1573K that led to a linear curve ln(K l ) versus 1/T (K -1 ). The Arrhenius constants (K lo and Q) that appear in equation [START_REF] Oishi | Proceedings[END_REF] were determined. An estimated value of m H was obtained with the expression (8) calculated from the Riemann's sum (9) :

T . R Q lo l e . K K - = (7) dt . e . K m H o t 0 ) t ( T . R Q l H ∫ - = (8) ( ) t . e . K m N 1 n t . n . R K 293 . R Q l H H o ∆           = ∑ = ∆ + - ( 9
)
where 293K is the initial temperature, R H the heating rate, t H the heating duration, ∆t the recording time increment (40s), and N the approximate number of recording paths during the heating

t . R K 293 T t t N H test H ∆ - = ∆ ≅ .

Mathematical Processing (determination of Kp and Kv)

When the temperature is not high enough to lead to a significant volatilization of chromia (e.g. 1000°C and less), the Wagner's law can be written (10). This means that the elementary mass gain between t and t+dt is proportional to the ratio of a constant by the existing mass gain, multiplied by the elementary time step dt. The existing mass gain is itself proportional to the oxide thickness and includes the mass gain m o previously obtained during the transient oxidation. These elementary mass gain and existing mass gain are both masses of oxygen that went on the alloy and formed the chromia oxide. When the temperature is significantly higher than 1000°C, the elementary mass loss by volatilization of chromia, which cannot be neglected, is proportional to the elementary time step dt, then equal to -Kv.dt. This loss of chromia is the sum of a loss of chromium -Kv Cr .dt and a loss of oxygen -Kv O .dt. The three losses are bound from one another by equations ( 11), ( 12) and [START_REF] Stearns | [END_REF]. The elementary mass gain of oxygen, dm O , is then the sum, on the one hand of a part proportional to the ratio of a constant which can be noted Kp O by the existing mass of oxygen m O multiplied by the elementary time step dt, and on the other hand of the negative part -Kv O .dt. Thus, the oxygen mass gain per unit surface area is given by ( 14). This equation can also become (15). To do that here, we considered the numerical file

) t ( f m =
, where m is the real mass gain (that also includes the first mass gain due to transient oxidation). For the lowest temperatures and near the end of experiment, the used thermobalance was not always accurate enough to detect the mass change between two successive weight measures (that were separated by only 40 seconds). Then it was decided to keep only one m value of ten to obtain a time step long enough to allow the measure of a more significant mass gain between two successive kept values. In addition, a great dispersion often remained among the kept successive values, a problem due to the lack of precision of the thermobalance again. In order to reduce the dispersion of the successive calculated derived numbers dt dm , without loss of precision, each In fact, Kv also includes the linear volatilization of the platinum thread to which hung the sample in the microbalance. It is the reason why this other contribution was separately determined for all temperatures with short thermogravimetry runs without any sample. Calculated by unit of area this contribution appeared, like it will be seen thereafter, as being almost negligible compared to chromia volatilization since its measured values were 0.93 . 10 -10 , 4.5 . 10 -10 , 26.3 . 10 -10 and 198 . 10 -10 g.s -1 for 1000, 1100, 1200 and 1300°C respectively. However these values, after their conversion into mass loss by sample unit surface area (0.42, 2.2, 11.4 and 91 . 10 -10 g.cm -2 .s -1 ) were subtracted from the measured Kv values to give the final Kv constants. But the contribution of the platinum volatilization was neglected for the determination of the linear K l constants.

RESULTS

Metallographic Study of the As-cast Alloy and of the Oxidized Samples

According to the Cr-Ni binary diagram, the alloy presents a single phase for all temperatures. The latter is Ni-austenite which contains the whole chromium in solid solution. The grain boundaries are not visible but it can be thought that the grain size of this alloy is about 25µm, as observed on similar Ni-30Cr-xC ingots elaborated following the same way. The obtained chemical composition determined by EDS with the SEM is 70 ± 0.5%w Ni and 30 ± 0.5%w Cr (average value ± standard deviation). The surface states of the alloy after 50 hours of oxidation for the four temperatures are illustrated by Fig. 1. The external oxide scale, exclusively of Cr 2 O 3 (verified by EDS analysis on the parts of oxide that remained on samples), often left the alloy surface during the cooling after test, especially for the sample oxidized at 1000°C. Voids also appeared in the subsurface over a depth that increases with temperature. The 20 to 30 measures led to the results that are summarized in Table I, in which the increasing of the oxide thickness with temperature can be seen. Two WDS chromium profiles (weight content) were performed from the extreme surface inwards the bulk for all samples (Fig. 2). The Cr-depletion depths logically increase with temperature, from about 40µm at 1000°C to ten times this value at 1300°C. Lower the temperature is lower the minimal chromium content is.

Thermogravimetry Results

The four thermogravimetry curves obtained are shown in Fig. 3 (only the isothermal part of the mass gain curves). They are logically ordered following the order of the temperatures. Three of them show a global parabolic shape, but they also have a short first linear part with a great slope, except for 1300°C for what the parabolic oxidation was obviously already begun when the targeted temperature was reached. The 1100°C curve also shows a little jump corresponding to a local detachment of the chromia scale, probably due to compressive strains that developed during the oxide growth. Therefore the chromia scale was certainly fissured and allowed oxygen to directly access to the underlying alloy surface again. The little mass gain jump resulted from the local oxidation that became fast again.

The initial linear oxidation at the beginning of the isothermal step was first considered. The slope of the m=f(t) straight lines for 1000, 1100 and 1200°C was determined, from which the values of the K l constants were deduced. For 1300°C, the slope of the straight line tangential to the curve at the first point was taken as an approximate value of the slope of the previous (and unknown) linear oxidation part of the curve. All these values are displayed in the first line of Table II. In a ln(K l ) = f(1/T) Arrhenius graph, it appears that the four points are relatively well aligned (Fig. 4). This means that first the beginning of the parabolic oxidation was very closed to the beginning of the isothermal 1300°C stage, then that the slope of the tangent to the curve can be taken as the K l constant at 1300°C. Second, this linear constant effectively obeys to an Arrhenius law, the activation energy of which was determined in the first line of Table III. Knowing the evolution of K l with temperature, it was possible to calculate indirectly the mass gain before the beginning isothermal stage, according to equation (9). After having added the mass gain obtained during the isothermal linear oxidation (directly measured by the thermobalance), the total mass gain before parabolic oxidation is known for all temperatures (from 1.4 .10 -5 g/cm 2 at 1000°C to 4.5 .10 -4 g/cm 2 at 1300°C).

The parabolic oxidation began when the external chromia scale became continuous all around the sample. Thereafter, the thermogravimetry data file can be exploited according to equation ( 22). This led to the four curves shown in Fig. 5 value can occur. For 1100°C it is clearly due to the little detachment which was already seen on the thermogravimetry curve in Fig. 3. For this curve it led to a particularly great jump, because of the mass gain itself but more because of the derived function (it is obvious when dt dm is plotted as a function of time). The jumps observed on the right of the dt dm . m curves for 1200°C and 1300°C (Fig. 5) are probably due to small detachments of the chromia scale or to another oxidation phenomenon. They can be not obvious on the thermogravimetry curves (Fig. 3) but dt dm is particularly sensitive to them. Indeed plotting the derived function versus time revealed that it effectively corresponds to a jump of dt dm .

On the left of these jumps (i.e. for later times) the points are effectively almost aligned along a straight line. It is particularly true for the highest temperatures, while such an alignment is more difficult to observe for the lowest temperatures because of the greater dispersion of the points. Particularly at 1200 and at 1300°C the points are really aligned along the regression straight line calculated from them. In addition the latter is horizontal for 1000°C and shows a positive slope which is greater when temperature is greater. The deduced values of Kp and Kv are given in Table II, in which a value of Kv after correction from the platinum volatilization is also featuring. The two constants increase with temperature and the variation of their napierian logarithms versus the reciprocal temperature, shows that they follow an Arrhenius law (Fig. 6), the activation energies of which are given in Table III

∆ = ∆ = ∆ = (26)
where t ∆ is the test duration (180,000 seconds).

Table IV shows all these values and it appears that there is for 1000°C a very good correspondence between the chromium mass that left the alloy ( bulk

DISCUSSION

The linearity observed for the curves finally obtained for the second part of the curves displayed in Fig. 5, clearly indicates that m and its derived function dt dm effectively obey the equation ( 22) (in which the term Kp is supposed constant). Then it was always possible to extract from the curve the values of both Kp and Kv for the four tested temperatures. Their comparison with constants reported in previous works show a good agreement with the latter. The Kv values obtained here were first confirmed by the chromium balance sheets, notably for the three lowest temperatures. Second, they are in good agreement with the volatilization constants reported by other authors in Table V. The values of Kp, displayed in Table II, are of the same order of magnitude as most of Kp values obtained for the same temperatures with other chromia-forming alloys, nickel base or cobalt base.

In order to verify the accuracy of the determination of both the parabolic constant Kp and the volatilization constant Kv, each theoretic (or mathematical) curve was plotted together with the real curve measured by thermogravimetry for the same temperature (Fig. 7). The mathematical curves were drawn from the equation ( 22) by calculating for each step the new elementary mass gain according to equation ( 27) in which each elementary mass gain The experimental initial mass gain that already existed at t=0 (due to the transient oxidation) was taken for the first step to avoid an initial division by zero, but it was subtracted thereafter from the whole mathematical curve. It appears in Fig. 7 that the mathematical curves correctly fit the experimental ones, notably on their second part, with notably a good "parallelism" between the ends of the two curves, which is on a great importance for long times predictions. At the opposite, the fit can be a little worse for the first half of the curves, in which some experimental curves presented small defects essentially due to a little detachment of the chromia scale, or in which the expression of Kp is not yet almost constant.

CONCLUSION

The parabolic constant Kp and the volatilization constant Kv, respectively corresponding to the Wagner's law type part of the mass gain kinetic and to the vaporization of chromia into volatile CrO 3 when temperature is higher than 1000°C, were here determined together for a simple binary Ni-30Cr alloy for the 1000-1300°C temperature range, with notably a good agreement with previous results about the volatilization rate of chromia. This procedure, that appeared well adapted for this very simple alloy, allows to extract from classical thermogravimetry files, these two kinetic constants that are both of a great importance to wholly characterize the deterioration of a chromia-forming alloy by oxidation at very high temperatures. But it is possible that it becomes less true for more complex chromia-forming alloys or superalloys since these ones usually also contain other very oxidable elements that can significantly participate to the mass gain without corresponding to the model used here.

  of the chromia volatilization the real value of m O cannot be directly measured during a thermogravimetry test. Indeed, at all times, the elementary mass gain dm or the measured mass gain m are lower than respectively dm O (16) and m O (17) and the difference increases with temperature. Equations (14) and (15) must be rewritten into (18) and (19) where dm and Kv appear instead of dm O and Kv O while m O must remain under Kp O . the test, m and m O increase simultaneously but not with the same rate at all times. Indeed, the mass gain is particularly fast during the first part of the parabolic oxidation (about the first 10 hours)), is assumed to be almost constant, the first member of equation (19) or (20) appears to vary linearly with m. Drawing this quantity versus m may lead to a straight line, for what the ordinate at the origin is which can be simply noted Kp (21), and the slope is Kv. Then, plotting dt dm . m as a function of m theoretically may lead to the values of both Kp and Kv (22).

  dt dm was estimated by the regression coefficient calculated on the interval of ten successive values of m. Therefore the new time step is equal to ten times the measure time step (i.e. 400s). Thereafter the variation of this curve was verified, then the values of Kp and Kv were determined.

  which presents the evolution of dt dm . m versus m -. These new curves first display a great dispersion of the points, notably at 1000°C. But it fortunately becomes less marked when the temperature raises. This dispersion is due to the lack of precision of the thermobalance, especially at the lowest temperatures for which the mass gains between two consecutive measures are too close from one another. Despite of the calculation of the slope of the regression straight line for every ten time steps, a variation of the derived function, and of the dt dm . m values, is observed. Fortunately, this problem almost disappears when temperature increases, because of the faster oxidation and then the higher mass difference between two consecutive measures. Nevertheless, for the three highest temperatures, a jump of the dt dm . m

  sum of chromium present in the Cr 2 O 3 scale ( scale Cr m) and chromium that disappeared in volatile CrO 3 ( vol Cr m ). For 1100 and 1200°C the correspondence is relatively good too: the values of scale can be explained. Indeed, the chromium depletion is sufficiently deep to lead to a not really correct calculation of bulk Cr m in the zones that are near a ridge or a corner of the parallelepiped sample.

+

  , obtained between t = n.dt and t = (n+1).dt, is determined from the previous total mass gain m n , the two constants Kp and Kv previously determined, and the time step dt (40 seconds too).

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .

 1234 Fig. 1. Surface and sub-surface states of the samples after oxidation at 1000°C, 1100°C, 1200°C and 1300°C

Fig. 6 .Fig. 7 .

 67 Fig. 6. Variation of the Kp and Kv measured values versus the temperature in an Arrhenius plotting

  .

	m	=	ρ	.	(	M . M 2	)	.	e	(25)	m	vol Cr	Kv	Cr	.	t	M 2	O Cr 2 M Cr	3	.	. Kv	t	0	.	684	. Kv	t

Table I .

 I Thicknesses of the external chromia scale after the thermogravimetric tests

			after 50 hours at …
	Thickness of the external
	Cr 2 O 3 oxide layer	1000°C	1100°C	1200°C	1300°C
	Average thickness	6.38	12.46	22.90	38.95
	Standard deviation	1.08	1.34	1.23	3.11

Table II .

 II Values obtained for the transient linear oxidation constant K l , the parabolic constant Kp and the volatilization constant Kv

	Oxidation constants	1000°C	1100°C	1200°C	1300°C
	(g/cm 2 /s) Value of the K l constant	5.1

. 10 -8 18 . 10 -8 30 . 10 -8 125 . 10 -8 Value of the Kp constant (g 2 . cm -4 . s -1 ) 2.8 . 10 -12 23 . 10 -12 67 . 10 -12 245 . 10 -12

	Value of the Kv constant	1.3 . 10 -10	89 . 10 -10	168 . 10 -10	367 . 10 -10
	(g . cm -2 . s -1 )

Value of the Kv constant (g . cm -2 . s -1 ) corrected from Pt volatilization 0.9 . 10 -10 87 . 10 -10 157 . 10 -10 276 . 10 -10Table III .

 III Activation energies for the three types of oxidation constants, calculated from the results obtained for the four temperatures (*except 1000°C for Kv)

		Activation energy
	Oxidation constants
		kJ / mol
	K l	167
	Kp	242
	Kv	104*

Table IV .

 IV Chromium balance sheet between the chromium quantity lost by the alloy, chromium present in the remaining chromia scale and chromium lost volatilization

	chromium quantities (mg / cm 2 )	1000°C	1100°C	1200°C	1300°C
	still present in the chromia scale	2.27	4.43	8.15	13.9
	lost by vaporization of chromia into CrO 3	0.01	1.07	1.93	3.40
	sum of the two upper lines	2.28	5.50	10.1	17.3
	chromium having left the alloy
	(calculated on the two Cr WDS profiles)	2.22 to 2.28	8.10 to 9.13	12.7 to 12.9	27.3 to 31.5

Table V .

 V Comparison of the obtained volatilization constants with those reported in previous works

	after 50 hours at 1000°C	after 50 hours at 1100°C
	Kv (10 -10 g.cm -2 .s -1 )	1100°C	1200°C	1300°C
	Hagel (9) *
	Cr 2 O 3 +1%Y 2 O 3	37	124	360
	76mmHg O 2 Stearns et al (13) after 50 hours at 1200°C	after 50 hours at 1300°C
	Preoxidized Cr	83	280	/
	0.115 Torr O 2
	Di Martino (12)
	Co base superalloys	2.3	45	/
	0.2 atm O 2
	This study	87	157	276
	* : calculated from the Kv = 0.214 . exp (-204kJ.mol -1 / R.T) formula

ACKNOWLEDGMENTS

The author thanks Lionel Aranda who performed the thermogravimetry tests, and the Microanalysis Common Service of the Faculty of Science of Nancy, especially Johann Ravaux and Alain Kohler.

Comparison between Kv from Thermogravimetry and Microanalysis Results

A balance sheet was made for chromium. bulk Cr m , the amount of total chromium mass per unit surface area that left the bulk to diffuse towards the oxidation front, was assessed for the four temperatures. It was determined according to equation (23). In fact an approximate value was calculated according to (24). where ρ is the density of the alloy (8.2 g.cm -3 assessed by the ratio of the mass of a 5*5*5mm 3 cube by its volume), % w Cr(bulk) is the weight chromium content in the bulk, % w Cr(e) is the weight chromium content at the depth e from the extreme surface, % w Cr n is the weight chromium content at the depth n.∆e from the extreme surface, and N is the entire value of the ratio of the chromium depletion depth (dd) by the step ∆e.


P Berthod

C Vébert

L Aranda

R Podor

C Rapin

Study of the Carbide Transformations during High Temperature Oxidation of Nickel Base Superalloys

Keywords: Nickel alloys, Carbides, High temperature oxidation, Carbon, Thermodynamic calculations

Microstructure phenomena resulting from high temperature oxidation of three nickel base superalloys were studied by microstructure examinations. Disappearance, nature modification, volume fraction evolution or precipitation of carbides were observed in the alloys near the external surface, depending on the temperature and the chemical composition of the alloys. Thermodynamic calculations allowed to better know what happened to carbon and to quantify its new distribution. The studied alloys lost a more or less great part of their sub-surface carbon content at 1200°C while carbon seemingly diffused deeper in the alloy at 1100°C and 1000°C. The latter part of carbon promoted the coarsening of the pre-existing carbides, some modifications of their natures or the precipitation of new carbides in the matrix, then the occurrence of a new carbides zone.

INTRODUCTION

During exposure to air at high temperature, the more reactive elements contained in a superalloy diffuse towards the oxidation front to be oxidized (Ref. [START_REF] Kofstad | High Temperature Corrosion[END_REF]. When temperature and/or time exposition are high enough, marked concentration gradients appear. This evolution of the local chemical composition can lead to microstructure modifications. Appearance of new phases, such as Ni austenite in αCr + βNiAl alloys due to Al oxidation, or chromium carbides dissolution in Fe-Cr-C alloys, are two examples of such sub-surface microstructure changes which were already studied (Ref. 2). Fig. 1 illustrates, for example, the cases of several Ni-base superalloys strengthened by carbides, after exposure at different high temperatures for a long time. Their microstructures are modified by a disappearance of the initial carbides from the affected zone. A little deeper, it can be observed an obvious chemical modification of the initial carbides (become darker), a coarsening of the latter or a precipitation of new acicular phases. While it is generally easy to detect where metallic elements from disappearing phases have gone, it is much more difficult for other constitutive elements, like carbon, which are lighter or present in very smaller quantities. Such elements are not easy to analyze by microprobe and it is difficult to know what it happened to them. Fortunately, associated to the microstructure examinations, microanalysis of heavier elements, thermodynamic calculations can help to understand where light or rare elements have gone, then to better describe the oxidation phenomena or its consequences on the microstructure.

EXPERIMENTAL METHOD Chemical Composition of the Studied Alloys

The alloys studied here are three simple nickel-base alloys, representing the base of more complex superalloys which are industrially employed in hot processes (Refs. [START_REF] Bradley | Superalloys : A Technical Guide[END_REF][START_REF] Sims | The Superalloys[END_REF]. They all contain nickel, chromium, tantalum and carbon. Table I displays the chemical composition of the alloys. They were synthesized in small quantities by high frequency induction melting under argon gas (ingots of nearly 100g) in a copper cold crucible, in which they quickly solidified.

High Temperature Oxidation Exposures and Samples Preparation

Oxidation tests at high temperatures were performed using a high temperature furnace under a dry industrial air flow (80%N 2 -20%O 2 ) at 1.5 liter/hour (corresponding to a linear flow rate of about 5cm/min). The samples were parallelepipeds (dimensions of about 2 mm x 10 mm x 10 mm), the surface of which was polished with SiC paper from 80 to 1200 grid under water. Oxidation exposures were performed during 100 hours at 1000°C, 1100°C or 1200°C. After oxidation tests all samples were covered using cathodic evaporation of gold, to give a good electrical conductivity to the external oxide layer, allowing thereafter a strengthening of the external oxide layer by an electrolytic deposition of nickel. The samples were cut in two parts using an Accutom-2 saw equipped with a diamond blade, then embedded in a cold resin (Araldite CY230 +Strengthener Escil HY956), and polished, first with SiC paper from 80 to 1200 grid under water, then finished with diamond pastes 6µm and 3µm (DP-Suspension P of Struers).

Microstructure Examinations

A Scanning Electron Microscope (SEM) Philips XL30 used in Back Scattered Electrons (BSE) mode allowed to clearly observe the constitutive phases since the average atomic numbers are sensibly different. In addition, some of them were clearly identified by Wavelength Dispersion Spectrometry (WDS) using a Cameca SX100 microprobe. Furthermore, SEM was also employed to analyze the mean chemical composition of a selected area over the local microstructure, except for carbon. Microprobe was also employed to get concentration profiles through the external zone deteriorated by oxidation.

Image Analysis Measurements

Measurements of the surface fractions of the different phases were realized on SEM photographs (BSE mode), using the AnalySIS software from Soft Imaging System GMBH which allows surface fractions measurements. Volume fractions were assessed from these results, assuming that surface fraction and volume fraction have similar values. Using room temperature densities of the different phases, the mass fraction of each phase was estimated thanks to the equation (1) :

) ( f j mass ϕ = ∑ ϕ ρ ϕ ρ ϕ ϕ i i vol j vol )) ( f . ( ) ( f . i j (1)
where ρϕ i , f mass (ϕ i ) and f vol (ϕ i ) are respectively the density, the mass fraction and the volume fraction of the considered phase ϕ i .

The densities values which were used (in g . cm -3 ) are 8.9 for the matrix, 6.941 for the Cr 7 C 3 carbide, 6.953 for the Cr 23 C 6 carbide and 14.5 for the TaC carbide (Ref. 5).

Thermodynamic Calculations

Thermodynamic calculations were carried out using Thermo-Calc software (Ref. 6) with the SSOL database (SGTE) (Ref. 7), completed with binary and ternary systems (Ref. 8). Thermo-Calc calculations were performed for calculating isothermal and others diagrams for the oxidation zone first to determine an upper limit for the carbon content in the zone where carbides have disappeared. Second, it was also used to calculate the probable carbon content deeper in the alloy, knowing quantitatively both microstructure and the other elements contents from image analysis and microanalysis.

RESULTS

Microstructure of the As-cast Alloys

The alloys present a relatively fine structure which can be characterized by a space between two secondary dendrite arms of about 25µm. The microstructure is constituted by an austenitic nickel matrix containing a part of the other elements and an interdendritic carbides network more or less dense depending on the carbon content (Fig. 2). These grain boundaries carbides are of different types, chromium carbides (M 7 C 3 and M 23 C 6 ) and TaC, for the three alloys. Indeed, WDS measurements (three per carbide for each alloy) showed that the three types of carbides coexist, what is not surprising since solidification and cooling were quicker than in a sand mold for example. Here the high temperature state has only partly evolved from the high temperature equilibrium.

Observation of the Sub-surface Microstructure of the Alloys after Oxidation

After high temperature oxidation for 100 hours, the bulk microstructures of the alloys are generally modified since they have converged to the equilibrium corresponding to both chemical composition and temperature. The three most visible microstructure modifications are the lost of the initial TaC carbides for Alloy A and Alloy B, a stoechiometry change of the chromium carbides for all alloys (rather M 7 C 3 for the highest temperatures and rather M 23 C 6 for the lowest ones) and a little increasing of the chromium carbides for Alloy A. All the samples are affected by both selective oxidation and internal oxidation that were analyzed by microprobe WDS measurements. The external oxide scale is mainly composed of Cr 2 O 3 , sometimes containing also rare little CrTaO 4 inclusions. Internal oxides were clearly identified by microprobe WDS analysis as being CrTaO 4 , sometimes coexisting with voids. On the opposite no nitridation phenomena was observed. Under the external chromia layer the alloys present a more or less deep zone which was affected by oxidation and which may be composed of one or two different parts. The sub-surface microstructure state of Alloy A, Alloy B and Alloy C for all temperatures are respectively illustrated by Fig. 3, Fig. 4 and Fig. 5.

From the external surface one always meets first a zone which lost all its initial carbides during oxidation. The thickness of this carbideless zone obviously depends on the temperature. For alloys tested at 1200°C this zone is directly followed by the bulk which presents an homogeneous microstructure. For alloys exposed to 1100 or 1000°C, the carbideless zone and the bulk are separated by a second part of the affected zone. In that one the carbide system has undergone one or several types of modifications. The different carbides seen for each alloy and each temperature were analyzed by microprobe. This was often difficult because of the small size of the carbides, and sometimes it was possible that the results partly include the matrix present under the carbides. Table II shows the average values and the standard deviation values obtained with three or more results per type of carbide on each sample, to compare with the theoretic atomic Cr/C ratio corresponding to the M 7 C 3 and M 23 C 6 stoechiometries. In some cases, the initial carbides have kept the same shape but their chemical composition has obviously changed since the carbides are here sensibly darker than everywhere else in the bulk (e.g. Alloy B at 1100°C in Fig. 4). In other cases, the carbides have kept their initial chemical composition but have grown during oxidation to finally give both a carbide surface fraction seemingly higher and lightly darker (SEM in BSE mode) because of the coarsened size of these carbides (e.g. Alloy C at 1000°C in Fig. 5). And sometimes at 1000°C, new carbides appeared in the matrix with an acicular and oriented shape (e.g. Alloy A at 1000°C in Fig. 3). Such phenomena were seen and studied earlier for Ni-Cr-C alloys and cobalt-base superalloys (Ref. 9).

All the metallographic measures realized on both zone affected by oxidation and bulk for comparison, are resumed in Table III : the mean depth of the carbideless zone, the mean thickness of the zone where carbides are still here but modified (nature, surface fractions, new precipitation), the nature (determined by WDS micro-analysis) and the mean surface fraction of carbides in this latter zone. For comparison, the mean surface fraction of carbides in the bulk are also reminded. It appears that the depth of the carbideless zone increases with temperature for all the alloys (less than 50µm for 1000°C to about 200µm for 1200°C) while the thickness of the intermediate zone where carbides are still here but modified (thereafter called "new carbides zone"), also increases with temperature from 1000°C to 1100°C to finally disappear at 1200°C. Concerning the new carbides zone, it can be noted first that the total surface fraction of carbides is sensibly higher than in the bulk. Second, the microstructure changes between the bulk and this zone seemingly consist of a shifting from a mix of

Thermodynamic Study of the Carbideless Zone

The carbides initially present in this zone near the extreme surface have totally disappeared from the grain boundaries, where they are sometimes replaced by rare internal CrTaO 4 oxides. It can be considered that only one phase is present here : the matrix. The total absence of carbides in this zone implies that carbon is probably become rare in this carbideless zone. Thermodynamic calculations were of a precious help to quantify the maximal carbon content possible in this zone taking into account the decrease of the chromium content through the carbideless zone. Fig. 6 shows for example the 1100°C isothermal phase diagram computed by Thermo-Calc for the Alloy A, a type of diagram which was already used earlier by Durham et al (Ref. 10) to describe the outwards diffusion path of carbon. In this example, WDS profiles having shown that the chromium content almost linearly decreases through the carbideless zone (from about 30%wt Cr to about 23%wt Cr), the carbon solubility increases from 0.017%wt to 0.035%wt. Then the maximal possible carbon content can represent at the most 20% of the initial carbon content, and that only near the extreme surface.

Such results were obtained for the carbideless zones of all the alloys and all temperatures : it appeared that, in a first approximation, the carbon content in this zone can be considered as negligible compared to the initial one or in other zones having conserved or reached a significant amount of carbides.

Thermodynamic Study of the New Carbides Zone

The microstructure changes previously noted must be related to local modifications of the chemical composition of the alloy, due to the diffusion of its constitutive elements towards others locations. EDS and WDS microanalysis did not show sensible changes of the initial contents of the heavier elements (Ni, Cr, Ta) which can be easily analyzed. Therefore carbon appears as being responsible of these microstructures modifications having led to these new carbides zones. The increasing of the volume fractions of M 23 C 6 inside the new carbides zone compared to the bulk, the shifting from M 23 C 6 to M 7 C 3 or the precipitation of new carbides in the matrix itself seems indicate that this region is obviously become enriched in carbon.

In order to confirm this hypothesis and to better know how many carbon is come in this zone thermodynamic calculations were performed from the locally analyzed Ni-Cr-Ta composition with test of successive values for the carbon content in the [0%wt C ; 1.0%wt C] range until the measured volume fraction (converted in mass fraction) is reached. Table IV presents the results of these calculations.

It appeared always possible to reach the measured carbides volume fractions really measured on the new carbides zones in the alloys after oxidation. On the one hand it appears that the process is diffusioncontrolled and allows the local microstructure to continuously stay to the equilibrium corresponding to the local composition at each time. On the other hand, this microstructure effectively leads to know the local carbon content. The carbon contents determined by the thermodynamic calculation way are obviously higher than the initial ones, of an average of 50% of the carbon content of each alloy before oxidation test.

Discussion

This carbon enrichment of the new carbides zone was not obtained with carbon coming from the bulk. Indeed we verified that the microstructure of the whole bulk was homogeneous and also well corresponded for the same temperature to the thermodynamic stable state calculated from the initial composition. Therefore, the only possible carbon supplier is the carbideless zone which was effectively impoverished in carbon. Following this hypothesis, Table V presents in its first column the maximal carbon mass lost by the carbideless zone per surface unit, considering that nearly all its carbon left it. The last column contains the mass or molar percentage of this carbon which could be go in the neighbor new carbides zone. The maximal possible carbon quantity lost by the carbideless zone per surface unit increases when temperature increases. In addition more carbon is here lost when the initial carbon content is higher (Alloy B and Alloy C compared to Alloy A) while no such rule existed for the depth of the carbideless zone. The part of this carbon having participated to the carbon enrichment of the new carbide zone is of about 100% at 1000°C and decreases with temperature to finally fall to zero at 1200°C.

Thus, it appears that at 1000°C oxidation did not only induce a diffusion of chromium and tantalum, initially present in solid solution as well as in the interdendritic carbides, from the bulk towards the oxidation front. But it was evidenced that, for certain conditions, carbon released by the disappearing carbides diffuses in the opposite way, towards the bulk. The progress with time of this carbon transport obviously leads to a carbon enrichment inside a more internal zone in which this enrichment promotes different possible carbides changes depending on the alloy composition. At 1100°C only a part of this carbon remains in the alloy in which it participates to the carbide transformations to give a new carbides zone, like for 1000°C. The other part of the carbon either quitted the alloy (oxidized into gases) or diffused deeper in the alloy. The second hypothesis appears to be difficult to verify since the carbides existing deeper than the new carbides zone would have not sufficiently changed. It is more true at 1200°C for which no new carbides zone obviously exist and no microstructure change showing a carbon enrichment can be seen anywhere. Then, either carbon has totally quitted the alloy or it diffused on such a wide depth that a carbon enrichment is locally too light to be detected in the microstructure. Carbide surface analysis and thermodynamic calculations become no sufficiently efficient either to affirm that there is no other carbon enrichment deeper or to precise too little carbon content modifications.

Such phenomena were already encountered earlier for others metallic alloys after high temperature oxidation. For example, Singh et al (Ref. 11) also observed a carbideless zone growing from the extreme surface for iron-base alloys containing both aluminum and carbon. They explained that the disappearance of the initial Fe 3 AlC carbides took place simultaneously with a diffusion of the released carbon atoms out to the surface. Durham et al (Ref. 10) studied the dependence of the chromia-forming behavior of iron-base alloys on the coarseness of their chromium carbides. They encountered a dissolution of the finest carbides which acted as reservoirs of chromium for supplying the external chromia scale, then the growth of a carbides-depleted zone. Ennis et al (Ref. 12) also saw, for a nickel superalloy exposed to 900°C for a long time, the formation of a carbideless sub-surface zone. They also explained that the carbon atoms released by the dissolving carbides migrated to the center of their thin specimen to give an enhanced carbide precipitation. In addition Kaya et al (Ref. 13) saw that carburizing atmospheres induced also similar phenomena : both a coarsening and a transformation into the M 7 C 3 stoechiometry for the initial M 23 C 6 carbides of the Fe-Cr-Ni based HK40 alloy. They also observed a coarsening of M 23 C 6 without nature changes and the precipitation of M 7 C 3 .

Thus we found in this work similar phenomena as previously observed for other alloys : disappearance of carbides with growth of a carbideless zone, appearance of a new zone with coarsening, stoechiometry modification or matrix precipitation of carbides, and that related to one or two types of diffusion of carbon atoms released by dissolving carbides. In this work both surface fractions of carbides and the different local carbon contents were furthermore quantitatively determined, respectively by image analysis measurements and deduced from thermodynamic calculations. This lead to precise the part which promoted the visible carbides modifications in the sub-surface of the alloy, and the part which either quitted the alloy or diffused deeper in the alloy with no noticeable changes of the microstructure.

CONCLUSION

When exposed to high temperature oxidation carbide-strengthened superalloys can encounter specific phenomena which can be potentially important for their local mechanical properties near the external surface : growth of a sub-surface zone without carbides, and for temperatures less than 1200°C, appearance of a second zone enriched in carbon and in which the carbide system is coarsened or modified. If such phenomena were encountered earlier, a balance sheet was made in this work which lead to precise the new distribution of carbon in the whole zone affected by oxidation. Thus the mechanisms described in previous works were here found again, with a more quantitative knowledge of the new local carbon contents, not obtained using microanalysis but indirectly determined from thermodynamic calculations. Thermodynamic modeling was precisely revealed as an useful tool, complementary to more classical equipment when oxidation phenomena are studied. It allows to precise the last remaining unknown quantity that is a light element content. Max. solubility of the carbideless zone at its two limits (%wt) :

inner limit : 0.017%C outer limit : 0.035%C MATRIX + M3C2

  TaC+M 23 C 6 (bulk) to only M 23 C 6 or to only M 7 C 3 , from a mix of M 23 C 6 +M 7 C 3 to another mix of less M 23 C 6 and more M 7 C 3 or to only M 7 C 3 . Third, when temperature increases from 1000°C to 1100°C, the nature of carbides in the new carbides zone shifts, from M 23 C 6 to M 7 C 3 or from M 23 C 6 +M 7 C 3 to less M 23 C 6 and more M 7 C 3 .

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .

 123456 Fig. 1.

Table I .

 I Chemical Compositions of the Studied Nickel-Base Alloys

	Alloys		Compositions
		Ni	Cr	C	Ta
	Alloy A	Bal.	30.9	0.2	2.0
	Alloy B	Bal.	31.9	0.4	2.7
	Alloy C	Bal.	30.6	0.4	5.4

Table II .

 II WDS analysis results obtained for the one or two types of chromium carbides seen in the subsurface microstructures of the samples (% at Cr / % at C ratio to compare to 2.33 for M 7 C 3 and 3.83 for M 23 C 6 )

	Alloy		M 7 C 3			M 23 C 6
	Temperature	(average value ± standard deviation)	(average value ± standard deviation)
		% at Cr	% at C	% at Cr / % at C	% at Cr	% at C	% at Cr / % at C
	Alloy A 1200°C
		69.0 ± 1.9	28.3 ± 1.8	2.5 ± 0.2	/	/	/
	M 7 C 3 and rares M 23 C 6
	Alloy A 1100°C
	M 7 C 3 and M 23 C 6	65.3 ± 7.5	24.9 ± 1.2	2.6 ± 0.4	75.9 ± 0.8	22.3 ± 0.8	3.4 ± 0.2
	Alloy A 1000°C
	M 7 C 3 and M 23 C 6	/	/	/	78.4 ± 3.0	21.8 ± 2.7	3.7 ± 0.7
	Alloy B 1200°C
	M 7 C 3	66.9 ± 0.5	28.2 ± 0.8	2.4 ± 0.1	/	/	/
	Alloy B 1100°C
	M 7 C 3	67.8 ± 0.8	23.0 ± 0.1	2.9 ± 0.1	74.9 ± 0.4	20.7 ± 0.5	3.6 ± 0.1
	Alloy B 1000°C
	M7C3 and M23C6	67.0 ± 0.8	22.9 ± 0.1	2.9 ± 0.1	70.4 ± 4.96 18.1 ± 0.4	3.9 ± 0.3
	Alloy C 1200°C
	M 7 C 3	69.4 ± 0.7	25.8 ± 0.7	2.0 ± 0.1	/	/	/
	Alloy C 1100°C
	rare M 7 C 3 and M 23 C 6	70.8 ± 0.3	20.6 ± 0.3	3.4 ± 0.1*	79.0 ± 0.6	16.1 ± 0.3	4.9 ± 0.1*
	Alloy C 1000°C
	M 23 C 6	/	/	/	82.5 ± 1.9	21.6 ± 0.5	3.8 ± 0.1

* : stoechiometry transformation in progress or participation of the matrix under the carbide to the WDS analysis results

Table IV .

 IV Carbon contents of the C-enriched zone determined by calculation; carbides natures and mass fractions calculated with these carbon contents

	Alloy	carbon content in the	theoric carbides for
		C-enriched zone	this calculated %C
	Temperature	(weight %)	(weight fraction %)
	Alloy A 1200°C	/	/
	Alloy A 1100°C	0.260	2.66%wt M 7 C 3
	Alloy A 1000°C	0.289	4.91%wt M 23 C 6
	Alloy B 1200°C	/	/
	Alloy B 1100°C	0.472	5.03%wt M 7 C 3
			0.00%wt M23C6
	Alloy B 1000°C	0.646	4.75%wt M 7 C 3
			3.64%wt M 23 C 6
	Alloy C 1200°C	/	/
	Alloy C 1100°C	0.737	7.97%wt M 7 C 3
	Alloy C 1000°C	0.592	10.28%wt M 23 C 6

Table V .

 V Amount of the carbon lost by the carbideless zone and part of this carbon used for the carbon enrichment of the new carbides zone

	precipitation of new acicular carbides in matrix	nature modification and volume fraction evolution
			of carbides in grain boundaries
	disappearance of carbides
	Alloy	maximal mass lost by	part kept by the C-
		the carbideless zone	enriched zone
	Temperature		(mg / cm 2 )	(%)
	Alloy A 1200°C		0.409	0
	Alloy A 1100°C		0.141	60
	Alloy A 1000°C		0.032	96
	Alloy B 1200°C		0.712	0
	Alloy B 1100°C		0.259	24
	Alloy B 1000°C		0.142	98
	Alloy C 1200°C		0.605	0
	Alloy C 1100°C		0.303	84
	Alloy C 1000°C		0.085	96

ACKNOWLEDGMENTS

The authors thank S. Michon who built the thermodynamic database used here, and the Microanalysis Common Service of the Faculty of Science of Nancy, especially J. Demange, J. Ravaux and A. Kohler.


Patrice Berthod
email: patrice.berthod@centraliens-lille.org

Influence of chromium carbides on the high temperature oxidation behavior and on the chromium diffusion in nickel base alloys

Keywords: Nickel alloys, Chromium carbides, High temperature oxidation, Chromia volatilization, Chromium diffusion

Two simple cast nickel alloys Ni-30Cr-0.2C and Ni-30Cr-0.8C were oxidized at 1000, 1100 and 1200°C. Their behaviors were characterized using thermogravimetry techniques and their parabolic and chromia volatilization constants were determined by analysing the dt dm . m versus m curves. The obtained constants were generally in good agreement with experimental mass gain kinetics and chromium balance sheets. A higher carbon content i.e. a higher carbides density leads to higher values of the transient linear oxidation constant K l , of the parabolic constant K p , and obviously also of the volatilization constant K v . Chromium diffusion coefficients through the zone affected by oxidation were calculated from oxidation kinetics and chromium gradients. They increase when carbide density increases.

INTRODUCTION

The high temperature oxidation of alloys containing a sufficient amount of chromium is limited by the rapid establishment of a continuous Cr 2 O 3 layer on the external surface (Ref. [START_REF] Kofstad | High Temperature Corrosion[END_REF]. Thus chromium, which protects alloys from a too fast oxidation, is often used in industrial superalloys to resist high temperature oxidation by air or by other hot gases (Ref. 2 to 3). This element is also used to protect superalloys against corrosion by molten salts or glasses, by forming an external passivation chromia scale (Ref. 4 to 5). In chromia-forming superalloys chromium is always present in solid solution in the matrix. Since it is also a carbide-former element, Cr can be present in carbides, e.g. in the alloys for which the mechanical strength is provided by interdendritic carbides. For such alloys the distribution of chromium between the matrix and the interdendritic carbides can influence the oxidation behavior by influencing the chromium diffusion towards the oxidation front. Such an effect was earlier seen on complex Ni-base and Co-base chromia-forming alloys (Ref. 6) for which there was a clear dependence of the high temperature oxidation rate on the carbon content i.e. on the density of the carbides network. But this influence remained difficult to explain because of the complex chemical compositions and of the presence of different types of carbides.

Here the influence of the chromium carbides on the high temperature oxidation behavior was studied at 1000, 1100 and 1200°C, for two alloys that can be considered as very simplified versions of real nickel base superalloys reinforced by carbides: an alloy with a low fraction of carbides (Ni-30Cr-0.2C) and another alloy with a higher fraction of carbides (Ni-30Cr-0.8C) (contents given in weight percent). The characterization of the oxidation behavior is achieved by the determination of both the parabolic constant K p and the chromia volatilization constant K v . Indeed knowing the rate of mass loss due to the volatilization of chromia is important too since it allows a more precise determination of K p when the temperature is higher than 1000°C. In addition, the volatilization behavior of chromia may also depend on the chromium carbides density or on the distribution of chromium between matrix and intergranular carbides, and it could be interesting to reveal and to study this possible dependence.

In order to determine K v several techniques are possible. First it is possible to look for a value of K v that allows a good description of the experimental mass gain curve by a { where B is a constant and k' is related to the volatilization rate (Ref. 9 to 10). Here these two constants were determined by analysing the thermogravimetry data using a third method which was earlier presented in detail (Ref. 11), which is based on the equation dt dm . m = m . K K v pand which will be shortly described later in the text. The diffusion rates of chromium for the two alloys were deduced from thermogravimetry results (taking chromia volatilization into account) and chromium contents profiles across the zone affected by oxidation. The obtained diffusion coefficients were studied with respect to the carbides density.

EXPERIMENTAL METHOD

Synthesis of the Alloys and Oxidation Runs

The two alloys Ni-30Cr-0.2C and Ni-30Cr-0.8C (weight percent) were elaborated by casting of ingots (mass ≈ 100g) in a cold crucible with a high frequency induction furnace, under an inert atmosphere (about 400mbar of pure Argon, H 2 O < 3ppm, O 2 < 2ppm, C n H m < 0.5ppm), and from pure Ni and Cr (> 99.9 wt.%, Alfa Aesar) and graphite. Parallelepipeds (dimensions of about 10 mm x 10 mm x 3 mm) were cut to obtain the samples for the thermogravimetry tests. Their surfaces were polished with SiC paper from 240 to 1200 grid under water. Oxidation tests were performed at 1000, 1100 and 1200°C using a Setaram TGA92 thermobalance under a dry synthetic air flow (80%N 2 -20%O 2 ) at 1.5 L/h. The test duration (50 hours) was long enough to get a sufficiently long parabolic oxidation stage after the initial transient oxidation. Temperature and mass gain values were recorded every 40 seconds.

Mathematical Processing

Before they reached the targeted test temperature, the samples encountered a first oxidation during heating, which was followed at the beginning of the isothermal stage by a second part of transient oxidation. The latter gave a linear mass gain (of the { dt . K m l = }-type with K l expressed in g cm -2 s -1 ) before the parabolic oxidation started. Thus, for all tests, the treatment of the mass gain results began with the determination of the linear constant K l . These K l values for an alloy at the three test temperatures, which obviously obeyed an Arrhenius law, allow estimating the mass gain obtained during the heating. This first mass gain can be thereafter added to the isothermal mass gain obtained during the second part of the transient oxidation. Then the initial mass gain m 0 can be known before considering the parabolic or pseudo-parabolic part. This procedure was entirely described in a previous work (Ref. 11). The analysis of the thermogravimetry results for quantifying both the parabolic rate and the volatilization rate were performed considering the equation [START_REF] Kofstad | High Temperature Corrosion[END_REF], which can also be written with a second form (equation 2) in which the first member appears to be a linear function of m :

dm = dt . K dt . m K v p - (1) dt dm . m = m . K K v p - (2)
where m and dm are expressed in g cm -2 , K p in g 2 cm -4 s -1 and K v in g cm -2 s -1 .

Plotting dt dm . m versus m may lead to a straight line, the ordinate at the origin and the slope of which are respectively K p and K v . This can be verified by drawing a mathematical curve which is typical of a mass gain kinetic of a chromia-forming alloy oxidised at T>>1000°C (mass loss due to the volatilization of chromia, Fig. 1 a) or typical of a pure parabolic mass gain kinetic (T<1000°C, absence of chromia volatilization, Fig. 1 b). Such theoretic mass gain curves can be obtained by computing the curves according to equation ( 3) from values arbitrarily given to K p and K v (here the values are chosen to be characteristic of the constants that are usually measured for alloys of the same family) where the next total mass gain m n+1 at the step n+1 (i.e. at t = (n+1) . ∆t where ∆t is the time step) is the sum of the total mass gain m n at the previous step n and of the elementary mass gain dm n+1 calculated according to equation ( 4):

m n+1 = n m + dm n+1 (3) dm n+1 = dt . K dt . m K v n p - (4)
The obtained mathematical curves show that a significant value of K v (that simulates a noticeable volatilization of chromia) leads to a tilted straight line (first curve, Fig. 1 a) while a K v equal to zero (no chromia volatilization) leads on the contrary to a horizontal straight line (second curve, Fig. 1 b). More accurate values of K v were determined first by taking into account the mass loss corresponding to the volatilization of the platinum suspension. The latter was measured by performing tests without samples, that lead to volatilization rates of R susp = 0.93 × 10 -10 g s -1 (1000°C), 4.5 × 10 -10 g s -1 (1100°C) and 26.3 × 10 - 10 g s -1 (1200°C), that allowed to add a R susp . t linear term to the mass gain recorded by the thermobalance, before division by the sample surface. Second, it was seen on samples after oxidation tests that a carbide-free zone grew from the external surface of the sample, with a depth supposed to obey a {d(t)=constant x t }-type diffusion-controlled law (like it was previously observed by microscopy examination for other carbidesreinforced alloys after oxidation during several durations). In order to do not minimize the real mass gain due to the sole oxidation of chromium, the loss of carbon that initially belonged to the disappearing carbides in the alloy was taken into account. This was done by adding to the measured mass gain a term R C (t) calculated according to equation (5), before division by the sample surface and treatment with respect to equation ( 2

) 5
where ρ alloy is the density of the alloy (about 8.2 g cm -3 for the two alloys), S the external surface of the sample, d cfz is the depth of the carbide-free zone measured by microscopy on the sample after the thermogravimetry test, W C alloy is the carbon weight content of the alloy, t the time counted since the beginning of the isothermal stage and ∆t stage the total duration of this stage.

Metallographic Study

The oxidized samples were covered using cathodic evaporation of gold in order to give a good electrical conductivity to the external oxide scale. Thereafter a layer of electrolytic nickel was deposited on the external oxide to protect it from mechanical stresses. Each sample was cut in two parts using an Accutom-2 saw equipped with a diamond blade. It was embedded in an epoxy resin, then polished with SiC paper from 120 to 1200 grid under water. The final polishing was realized using a 1µm-diamond suspension. An optical microscope equipped with a graduated ocular was used to observe the oxidation front of the samples and to measure the thickness of the oxide scale on the areas where it partly remained after test. The oxide thickness was assessed by the calculation of the average value of about twenty measures, and of the interval of uncertainty defined by the standard deviation. The samples were also examined using a Scanning Electron Microscope (SEM) Philips XL30 in Back Scattered Electrons (BSE) mode with an acceleration voltage of 20kV. Its Energy Dispersive Spectroscopy (EDS) device was used to verify the real chemical composition of the obtained alloy (except carbon) and to identify the external oxide layer, as well as the internal oxides when present. Two chromium profiles measurements were performed for each sample by Wavelength Dispersion Spectrometry (WDS) using a Cameca SX100 microprobe, in order to value the total oxidized chromium and the chromium gradients in the zone affected by oxidation.

RESULTS

Characteristics of the Obtained Alloys

The alloys microstructures are composed of a dendritic nickel fcc matrix and of Cr 7 C 3 carbides that are present in the grain boundaries. These chromium carbides are dispersed and in small quantity in the Ni-30Cr-0.2C alloy. They are more present and form a continuous interdendritic network in the Ni-30Cr-0.8C alloy, in which the austenitic dendrites are more visible and characterized by an average space between two successive secondary arms of about 30µm. The obtained chemical compositions, which were measured on 0.2mm 2 areas using the EDS apparatus of the MEB, are given in Table I. The obtained Ni and Cr contents are very close to the targeted ones. The too low carbon contents cannot be measured by SEM/EDS or microprobe but the obtained microstructures showed that the two targeted values, 0.2 and 0.8, were obviously reached too. Indeed, the surface fractions of the chromium carbides observed in the present alloys are very close to the surface fractions obtained earlier on other similar alloys with the same carbon contents (which were measured using spark-source mass spectrometry). It is not surprising since carbon contents are usually well respected for the elaboration procedure that was used here too.

Thermogravimetry Results

The graph presented in Fig. 2 shows the isothermal mass gain curves obtained for the two alloys for the three temperatures. It appears that all curves become parabolic after a first more or less extended linear oxidation part, which is generally longer for the Ni-30Cr-0.8C alloy than for the Ni-30Cr-0.2C alloy. It is a first reason why the mass gain curves of the high carbon alloy are all above than the curves corresponding to the other alloy for the same temperatures. But, in addition, the parabolic oxidation is also often faster for Ni-30Cr-0.8C than for Ni-30Cr-0.2C.

The dt dm . m versus m curves were plotted in Fig. 3 and Fig. 4 for respectively the Ni-30Cr-0.2C and Ni-30Cr-0.8C alloys for 1100 and 1200°C, temperatures that allow a significant rate of chromia volatilization.

As seen earlier on synthetic curves (Fig. 1), all curves begin here (on the right of the graphs) by particularly high points, for the reason given previously. In some cases this also may be due to the very sensitive dt dm factor value, as long as the external chromia scale is not perfectly continuous. The second part of the curve (on the left of the graphs) is almost linear, although the dt dm . m values (more precisely the dt dm values) are more or less scattered. Fortunately, this dispersion becomes smaller when the test temperature increases, as is to say when the mass gain during dt is greater for all times and then less affected by the lack of precision of the thermobalance.

The determination of the K l constants leads to the values given in Table II by which an Arrhenius plot was derived (Fig. 5 a), for determination of the activation energies. For comparison the corresponding values that were previously obtained for a simple Ni-30wt.%Cr binary alloy (Ref. 11) are added. It appears that the K l constant increases with temperature and obviously obeys an Arrhenius law, but it also depends on the carbon content. If for 1000°C K l is lower for the Ni-30Cr-0.2C alloy than for the other alloy, this difference becomes smaller for 1100°C and this order is inverted for 1200°C. Indeed the activation energy should be decreased by the presence of a high quantity of carbides. This becomes more obvious when the results obtained earlier for the Ni-30%Cr alloy (without carbides then close to the Ni-30Cr-0.2C alloy) are taken into account. However, on the 1000-1200°C range it can be considered that K l generally increases with the carbon content. The values of the parabolic constant K p are displayed in Table III, with also three points plotted in a ln(K p ) versus 1/T graph for the two alloys in Fig. 5 b. When carbides are present, the increasing of the parabolic constant with the carbides amount, which was already observed for other alloys (Ref. 6), is found again here between the two studied alloys. This remains true when the results previously obtained for the Ni-30%Cr alloy are added. Indeed, the parabolic constant is the lowest when there are no carbides in grain boundaries. The parabolic constant almost follows an Arrhenius law (Fig. 5 b) but the calculated activation energies are sensibly lower for the carbides-containing alloys than for the Ni-30%Cr alloy. Table III also displays the values of the constant K v . The volatilization of chromia already exists for 1000°C but logically with the lowest values of K v . The volatilization constant appears to be of the same order of magnitude between the two carbides-containing alloys and the binary alloy (except for 1000°C for which K v is negligible for the binary alloy). Although these values cannot be clearly ordered with regards to the carbon content of the alloy, it seems that carbon or carbides tend to increase chromia volatilization. Like for the K p constant, the K v constant seems to obey an Arrhenius law (Fig. 5 c) and the activation energy seems to increase with the carbide density. This can explain why there is not a clear dependence of K v on the carbon content for all temperatures.

Knowing the values of the initial mass gain before parabolic oxidation, of K p and of K v , it is now possible to plot the mathematical mass gain curves, for comparison with the corresponding experimental thermogravimetry curves. This was done in Fig. 6 for 1100 and 1200°C in which the successive points were determined using the equation ( 6) where 1 n m + is the mass gain at t = t o + (n+1).dt and 0 m is the mass gain at the end of the isothermal transient oxidation:

1 n m + = n m + dt . K dt . m K v n p - (6)
with m n and m n+1 expressed in g cm -2 , K p in g 2 cm -4 s -1 , and K v in g cm -2 s -1 .

The mathematical curves are more or less close to the experimental mass gain curves. The fit is particularly good for the Ni-30Cr-0.2C alloy at 1000°C and 1100°C (Fig. 6 b), but it is also very good for the other curves as shown by the perfect parallelism of the last parts of the mathematical curves and the experimental curves. In the case of a Ni-30%Cr alloy the fit was also very good (Ref. 11).

Metallographic results

After the thermogravimetry tests, all samples were prepared for metallography and observed. Their surface and sub-surface states are shown in Fig. 7 for 1000°C and 1200°C. All samples present an external oxide scale which was unfortunately partly lost during cooling after test. The high carbon alloy is also affected by internal oxidation and by appearance of voids at all temperatures, because of the disappearance of the coarse carbides that existed here for this alloy. External and internal oxides were identified by EDS and are all clearly Cr 2 O 3 . The two alloys also present a carbide-free zone between the external surface and the bulk, in which, for the Ni-30Cr-0.8C alloy, internal oxides and voids exist together. Between the carbide-free zone and the zone not affected by oxidation, a third zone exists in the Ni-30Cr-0.2C alloy oxidized at 1000°C. This zone is characterized by the precipitation of small acicular new carbides in matrix. As demonstrated and quantified in a previous work (Ref. 12), this is due to an inwards diffusion of the carbon released by the dissolving carbides which promotes the intergranular solid state formation of new carbides involving chromium present in solid solution in matrix. Other phenomena can be a growth or a change of stoichiometry of the interdendritic carbides which already existed here.

The thicknesses of the external chromia layer and the depth of the carbide-free zone for all samples are shown in Table IV. The thickness of the external chromia layer logically increases with temperature for the two alloys. For the two lowest temperatures the chromia scale is sensibly thicker for the high carbon alloy than for the low carbon alloy while the two scales have almost the same thicknesses for 1200°C. Except for 1000°C, the carbide-free zone of the Ni-30Cr-0.2C alloy tends to be deeper than the one of the Ni-30Cr-0.8C alloy, as is to say they are inversely ordered compared to the bulk carbides density. Two WDS Cr content profiles were performed per sample through the zone affected by oxidation. They are shown in Fig. 8 for 1000°C and 1200°C. First, the chromium content of the matrix in the bulk is of course higher in the case of Ni-30Cr-0.2C for which almost all the chromium is contained in the matrix, than for Ni-30Cr-0.8C for which a significant part of the 30wt.%Cr is included in the intergranular carbides that are more present. Second, the chromium content gradient becomes lower for the two alloys when temperature rises while the Cr-depletion depth increases. At each temperature the Cr-gradient appears to be higher and the Crdepletion depth seems to be less extended for the Ni-30Cr-0.2C alloy than for the Ni-30Cr-0.8C.

Assessment of the Chromium involved in Oxidation and Comparison between Thermogravimetry and Metallography Results

The chromium mass per unit area that diffused towards the oxidation front can be estimated from the Cr-profiles by the sum of two terms. The first one is (equation 7):

m 1 = ∑ = - ∆ N 1 i Cr bulk Cr alloy )] i ( W W [ . d . ρ (7)
where m 1 is expressed in g cm -2 , ρ alloy is the density of the alloy (about 8.2 g cm -3 for the two alloys), ∆d is the profile step (e.g. 5µm = 5× 10 -4 cm for samples oxidized at 1100°C), W Cr bulk is the chromium weight content of the matrix in the bulk (e.g. 24.2% = 0.242 for Ni-30Cr-0.8C at 1100°C, content measured by WDS microanalysis), W Cr (i) is the chromium weight content of the matrix at the depth i × ∆d from the extreme surface, and N is the entire value of the ratio of the profile length divided by the step ∆d. The second one is (equation 8): m 2 = ρ alloy . d cfz . f w (Cr 7 C 3 ) . W Cr carb (8) where m 2 is expressed in g cm -2 , d cfz is the depth of the carbide-free zone (e.g. 60µm = 60 × 10 -4 cm for Ni-30Cr-0.8C oxidized at 1100°C), f w (Cr 7 C 3 ) is the weight fraction of the Cr 7 C 3 carbide in the alloy bulk at the considered temperature (e.g. 8.51% = 0.0851 for Ni-30Cr-0.8C at 1100°C, calculated using the Thermo-Calc TCW software and its SSOL database), and W Cr carb the weight content of chromium in the Cr 7 C 3 carbides (e.g. 91% = 0.91). The chromium quantity per unit area present on the external surface with the form Cr 2 O 3 (m 3 expressed in g cm -2 ), can be estimated from the average chromia thicknesses d oxide (expressed in cm here and in µm in Table IV), its density ρ oxide (5.2 g cm -3 ) and the molar weights of Cr (M Cr = 52 g mol -1 ) and of Cr 2 O 3 (M Cr2O3 = 152 g mol -1 ) by (equation 9):

m 3 = oxide 3 O 2 Cr Cr oxide d . ) M M . 2 ( . ρ (9)
The chromium lost by volatilization of chromia can be determined by equation [START_REF] Diliberto | [END_REF]:

m 4 = t . K . M M . 2 v 3 O 2 Cr Cr ∆ = t . K . 684 . 0 v ∆ (10)
where m 4 is expressed in g cm -2 , K v is the volatilization constant (e.g. 85.1 × 10 -10 g cm -2 s -1 for Ni-30Cr-0.8C at 1100°C) and t ∆ is the test duration (180,000 s).

If the K v determination was correct the following equation ( 11) must be verified:

m 1 + m 2 = m 3 + m 4 ( 11
)
The values of the four chromium quantities for the two alloys and the three temperatures are presented in Table V. For the Ni-30Cr-0.2C alloy there is, for the three temperatures, a good correspondence between on the one hand the mass of chromium that left the alloy, and on the other hand the sum of chromium present in the Cr 2 O 3 layer and of chromium that disappeared as gaseous CrO 3 . On the contrary, for the Ni-30Cr-0.8C alloy, the mass of chromium lost by the alloy is always higher than the total mass of oxidized chromium, although the two quantities have the same order of magnitude. This can probably be explained by the presence of internal chromium oxides in the case of this alloy, which was not taken into account in the chromium balance sheet.

Diffusion of Chromium during Oxidation

It was remarked in the previous section that the chromium gradient was higher for Ni-30Cr-0.2C than for Ni-30Cr-0.8C. In addition most of the Cr profiles appear to often contain an extended part of linear variation of the chromium content versus the distance from the extreme surface (Fig. 8). Knowing now the kinetics of oxidation of chromium on the external surface it is possible to better know how the density of intergranular carbides can influence the diffusion of chromium.

Here the first Fick's law was simply considered. It can be written as follows (equation 12):

dt dn Cr = - Cr Cr C grad . D ( 12
)
where Cr dn is the number of Cr moles per unit area (expressed in mol cm -2 ) that reached the oxidation front during dt (expressed in s) at the end of experiment to be oxidised first into Cr 2 O 3 , D Cr is the average diffusion coefficient of chromium through the alloy (expressed in cm 2 s -1 ), and Cr C grad (expressed in mol cm -4 ) is the value of the gradient of concentration of chromium C Cr (expressed in mol cm -3 ).

The second term of this equation is equal to When volatilization of chromia can be neglected, e.g. when T is not higher than 1000°C, where D Cr is in cm 2 s -1 , end dt dm in g cm -2 s -1 , K v in g cm -2 s -1 , ρ alloy = 8.2 g cm -3 and x

      ∆ ∆         x W . M
W Cr ∆ ∆ in cm -1 .
The knowledge of both the Cr gradient and the final mass gain kinetics leads to the assessment of the chromium diffusion coefficient. The values obtained for the two alloys and the three temperatures are presented in Table VI, together with the corresponding values calculated from the results for the Ni-30wt.%Cr alloy (Ref. 11). Several observations can be done. First the chromium gradient, which decreases with temperature, also depends on the alloy. Indeed the gradient across the carbide-free zone appears to be lower when the density of carbides is higher, for all temperatures. In addition a second gradient is visible, at all temperatures, deeper in the Ni-30Cr-0.8C alloy where carbides still exist, while such a gradient is visible only for 1000°C for the Ni-30Cr-0.2C alloy. The Cr gradients measured for the Ni-30%Cr alloy (Ref. 11) are close to the Cr gradients for the Ni-30Cr-0.2C alloy which differs from the latter alloy only by a small quantity of carbides. The Cr diffusion coefficient, calculated as described above, logically increases with temperature for all alloys and it seems to be, for all temperatures, higher for Ni-30Cr-0.8C than for Ni-30Cr-0.2C, and higher for Ni-30Cr-0.2C than for Ni-30%Cr.

DISCUSSION

First, the values obtained for K p appear to be consistent with the results observed earlier on similar alloys based on Ni-30wt.%Cr and oxidized in air, e.g. about 60 × 10 -12 g 2 cm -4 s -1 at 1200°C (Ref. 13), or logically lower than other parabolic constants obtained for P O2 =1 atm, e.g. about 20 × 10 -12 g 2 cm -4 s -1 at 1000°C (Ref. [START_REF] Wright | Oxidation of iron, nickel and cobalt base alloys[END_REF], and 90 × 10 -12 (1100°C) and 220× 10 -12 g 2 cm -4 s -1 (1200°C) (Ref. [START_REF] Moulin | [END_REF]. Second, the values obtained for K v are of the same order of magnitude as volatilization constants previously measured by other techniques directly on Cr 2 O 3 , 37× 10 -10 g cm -2 s -1 (1100°C) and 124× 10 -10 g cm -2 s -1 (1200°C) (Ref. 16), and 83× 10 -10 g cm -2 s -1 (1100°C) and 280× 10 -10 g cm -2 s -1 (1200°C) (Ref. 17). The density of carbides seems to have a real effect on the global oxidation rate of these simple cast alloys. It was already seen on more complex alloys (Ref. 6), but only for the parabolic constant. With the measurement of the transient oxidation rate and the double determination of the parabolic and volatilization constants allowed by the { dt dm . m = K p -K v . m} -type treatment of the thermogravimetry results, it appeared here that a higher carbide density leads to higher linear K l constants, to higher parabolic constants K p again, and seemingly to higher volatilization constants K v too. This influence is obvious for the K l and K p constants between the two carbides-containing alloys, and can be explained, for the Ni-30Cr-0.8C alloy, by an easier nucleation of chromia on its external surface which can be supposed because of the higher density of emerging chromium carbides for this alloy. This could first act by a more dense nucleation of oxide, and thereafter to a more rapid mass gain by growth of chromia perpendicular to the extreme surface until the scale becomes continuous. Thereafter, the higher grain boundaries density obtained in the structure of this external oxide (due to the initial more dense nucleation) could promote an easier diffusion of the species involved in the oxidation phenomena, then a higher mass gain rate characterized by the higher K p values which were seen here. This is also true when K p and K v constants previously measured on the Ni-30wt.%Cr alloy with the same method of (K p , K v ) determination, are also considered. Indeed they are lower than for the Ni-30Cr-0.2C alloy and for the Ni-30Cr-0.8C alloy. The presence of carbides and a higher density of these ones can help the diffusion of chromium towards the oxidation front. When the mass gain rates and chromium profiles are analysed together, the coefficients of chromium diffusion can be assessed. Their values clearly show that the chromium carbides have effectively a real influence on the diffusion easiness of chromium. When present with a higher density, they lead to higher diffusion coefficients. Since they contain a part of chromium in the carbides the grain boundaries act as good diffusion paths for chromium and this contribution is added to the volume diffusion of chromium. When the intergranular carbides have disappeared, grain boundaries in the carbide-free zone are probably more disordered if the intergranular carbides were initially more present. Then chromium certainly diffuses easier through the grain boundaries of the carbide-free zone for the Ni-30Cr-0.8C alloy than for the other alloys. Concerning the kinetic of chromia volatilization, some differences were also seen between the K v values obtained for the carbides-richest alloy and the two others. One can think that the finer structure of the Ni-30Cr-0.8C external oxide, due to its more dense initial nucleation, allowed a faster new oxidation of chromia.

During oxidation, the chromium carbides disappear from the oxidation front on a depth which increases with time, and also with temperature. The depth of the carbide-free zone also depends of the density of the initial carbides since it is deeper for the Ni-30Cr-0.2C alloy than for the Ni-30Cr-0.8C one (except for 1000°C where a part of the carbon obviously remained in the first alloy between the carbide-free zone and the bulk), a phenomena which was already encountered in previous works (Ref. 12). Even if the contribution of the chromium carbides to the Cr quantity supplied on the oxidation front is lower for the Ni-30Cr-0.2C alloy than for the Ni-30Cr-0.8C alloy (Table V), the carbides of the first alloy necessarily dissolve deeper than for the second alloy, because of its less dense initial carbides network. To finish, one can remark than the method used here to know both the K p and K v constants, which allowed this double determination for a particularly simple chromia-forming alloy (Ni-30wt.%Cr) in a previous work (Ref. 11), was successfully used here for alloys that contain chromium carbides, although the more complex microstructures lead to thermogravimetry curves that are less parabolic then not so easy to exploit according to this method. But the chromia volatilization constants, then also the parabolic constants, were correctly assessed. Indeed, on the one hand the mathematical curves are close to the experimental thermogravimetry ones, and on the other hand the chromium balance sheet which was dressed up between the metallography measurements and the quantified chromium loss by chromia volatilization is well respected (or the differences can be explained by the internal oxidation).

CONCLUSION

The thermogravimetry runs and their treatment in order to extract all the different oxidation constants allowed to clearly show that the presence and the density of the interdendritic carbides network of cast nickel alloys are of a great importance on their high temperature oxidation behavior. The oxidation kinetics (transient, parabolic and re-oxidation of chromia) increase when the carbides density of the alloy increases. Moreover, the determination of the K v constants allowed to know more precisely the whole chromium quantity that arrives on the oxidation front, then to obtain the Cr diffusion coefficients. This led to clearly see that the interdendritic chromium carbides facilitate the Cr diffusion towards the oxidation front. In addition this appears to be a possible method to measure the diffusion coefficients of chromium at high temperature, which can also be used for the determination of high temperature diffusion coefficients of other elements that can be easily oxidised: Al, Si, Ti, Ta, ... It appears also that the treatment based on the dt dm . m = K p -K v . m differential equation, which already gave good results for a binary alloy, is also efficient for alloys containing chromium carbides and it allows the determination of the volatilization constant and a more precise parabolic constant. This method remains to be tried on other more complex chromia-forming alloys, e.g. containing other types of carbides.

Table III.

Values of the parabolic oxidation constant K p and of the chromia volatilization constant K v for the two alloys with assessment of the corresponding activation energies K p (× 10 -12 g 2 cm -4 s -1 ) K v (× 10 -10 g cm -0,0016 -0,0014 -0,0012 -0,001 -0,0008 -0,0006 -0,0004 -0,0002 0 -m (g.cm -2 ) m.(dm/dt) (

) a (very high temperature): the volatilization of chromia occurs -> tilted straight line b (lower temperature): the volatilization of chromia is not significant -> horizontal straight line

  ): R C (t) = ρ alloy . S . W C alloy . d cfz .

  . to D Cr multiplied by the product of, on the one hand the alloy density divided by the molar weight of Cr, and on the other hand the value of the Cr weight content gradient.The first term is equal to the final value (i.e. at t = 180,000s) area of oxygen moles involved first by the growth of chromia,

  the final value (i.e. at t = 180,000s) of the derived function of the measured surface mass gain end dt dm . When the volatilization of chromia must be taken into account, the measured mass gain dm is equal at each time to dm O -K v .

Fig. 1 Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .Fig. 7 .Fig. 8 .

 12345678 Fig. 1.Two examples of synthetic curves built with data calculated from { } dt . K dt . ) m / K ( dm v n p 1 n -= +

  is the mass gain per surface unit area (Ref. 7). It is also possible to use another technique based on the differential equation derived from the Wagner's theory (Ref. 8) in which the term (

	equation where m dt . K v	) is
	subtracted from the mass gain dm (i.e.	dm	=	(	K	p	/	m	)	.	dt	-	K	v	.	dt	) and m is replaced by a function
	m +	k	'	.	t	.	B
																		m	=	K . 2	p	.	t	-	K	v	.	t	}-type

Table I .

 I Chemical compositions of the two obtained alloys (average and standard deviation values from three EDS measurements on each alloy)

	Chemical		Ni-30Cr-0.2C			Ni-30Cr-0.8C
	composition (wt.%)	Ni	Cr	C	Ni	Cr	C
	average contents	70.46	29.54	≅ 0.2	70.76	29.24	≅ 0.8
	standard deviation	0.21	0.21	/	0.71	0.71	/

Table II .

 II Values of the transient linear oxidation constant K l for the two alloys and with assessment of the corresponding activation energies

	K l (× 10 -8 g cm -2 s -1 )	1000°C	1100°C	1200°C	Activation energy (kJ mol -1 )
	Ni-30Cr-0.8C	18.3	30.5	44.2	69
	Ni-30Cr-0.2C	7.1	23.3	60.0	166
	Ni-30%Cr *	5.1	17.7	29.7	167
	* (alloy previously studied in Ref. 11)

Table IV .

 IV Average values and standard deviation for the thickness of the external chromia layer e Cr2O3 and for the depth of the carbide-free zone d cfz (about 20 measures per sample in each case)

			1000°C	1100°C	1200°C	Activation
	-2 s -1 )						energies
							(kJ mol -1 )
	Ni-30Cr-0.8C	K p	8.7	54.5		177		204
		K v	15.1	85.1		142		177
	Ni-30Cr-0.2C	K p	5.9	29.4		77		201
		K v	19.2	60.4		125		147
	Ni-30%Cr *	K p	2.8	18.1		64		239
		K v	0.72**	64.7		134		122**
	* (alloy previously studied in Ref. 11);
	** (value for 1000°C not precise and not taken into account for the determination of the activation energy)
	External Cr 2 O 3 thickness (µm)	1000°C	1100°C	1200°C
	Carbide-free zone depth (µm)	e Cr2O3	d cfz	e Cr2O3	d cfz	e Cr2O3	d cfz
	Ni-30Cr-0.8C		8.7 ± 1.4	27.0 ± 2.2	14.3 ± 1.6	60.1 ± 6.0	26.5 ± 1.1	105 ± 6
	Ni-30Cr-0.2C		3.7 ± 0.7	18.4 ± 2.8	11.4 ± 2.1	90.7 ± 10.7	25.1 ± 1.5	197 ± 12

Table V .

 V Chromium balance sheets for the two alloys and the three temperatures

	Ni-30Cr-0.8C (mg cm -2 )	Cr lost by the alloy matrix carbides	Total Alloy	Oxidized Cr Cr 2 O 3 volat. CrO 3	Total Oxides
		m 1	m 2		m 3	m 4
	1200°C	9.82	6.29	16.11	9.42	1.75	11.17
	1100°C	6.48	3.72	10.20	5.09	1.05	6.14
	1000°C	2.07	1.71	3.79	3.08	0.19	3.27
	Ni-30Cr-0.2C (mg cm -2 )	Cr lost by the alloy matrix carbides	Total Alloy	Oxidized Cr Cr 2 O 3 volat. CrO 3	Total Oxides
		m 1	m 2		m 3	m 4
	1200°C	7.48	2.60	10.07	8.94	1.54	10.48
	1100°C	5.10	1.30	6.39	4.07	0.74	4.81
	1000°C	2.01	0.28	2.29	1.31	0.24	1.54

Table VI .

 VI Weight content gradients and diffusion coefficients of chromium through the zone affected by oxidation

		K p = 70.10 -12 g 2 .cm -4 .s	-1 K v = 125.10 -10 g.cm -2 .s -1
			(e.g. alloy oxidized at 1200°C)	1,6E-10
							1,4E-10
	-1 )						1,2E-10
	.cm -4 .s						1E-10
	m.(dm/dt) (g	regression equation: y = 126 .10	-10 x + 70,2 .10	-12	4E-11 6E-11 8E-11
							2E-11
							0
		-0,004 -0,0035 -0,003 -0,0025 -0,002 -0,0015 -0,001 -0,0005	0
			-m (g.cm -2 )
	a
			K p = 5.10 -12 g	2 .cm -4 .s -1 K v = 0 g.cm -2 .s	-1
			(e.g. alloy oxidized at 1000°C)	1,2E-11
							1E-11
	Cr-profiles	Weight content chromium gradients x W Cr ∆ ∆ (wt.% × µm -1 ) regression equation: y = 0,344 .10 -10 x + 5,04 .10 -12	6E-12 D Cr (× 10 -10 cm 2 s -1 ) Cr diffusion coefficient 8E-12
		carbide-free		deeper	carbide-free	deeper
		zone	not negligible)		zone	4E-12	(if not negligible)
	Ni-30Cr-0.8C
	1200°C (50 hours)	0.014		0.011		44.5	2E-12	56.6
	1100°C	0.040		0.033		10.1	12.3
	(50 hours)						0
	1000°C	0.203		0.061		0.69	2.30
	(50 hours) Ni-30Cr-0.2C b
	1200°C	0.029		/			17.5	/
	(50 hours)
	1100°C	0.104		/			2.89	/
	(50 hours)
	1000°C	0.274		0.173		0.46	0.73
	(50 hours)
	Ni-30%Cr *
	1200°C	0.031		/			15.8	/
	(50 hours)
	1100°C	0.094		/			2.81	/
	(50 hours)
	1000°C	0.349		/			0.17	/
	(50 hours)
		* (alloy previously studied in Ref. 11)

ACKNOWLEDGEMENTS

The author thanks Lionel Aranda (thermogravimetry runs) and the Microanalysis Common Service of the Faculty of Science of Nancy, especially Sophie Adeline (WDS measurements and concentrations profiles).