Interdiffusion in the Al-V System in the 800-1000 °C Temperature Range

Abstract

Vanadium and its alloys have potential for application as fuel cladding in new fast breeder reactors cooled by sodium. Diffusion aluminide coatings could be a solution of choice in providing protection against high-temperature corrosion by liquid sodium or residual oxygen for these materials. In this work, multilayered coatings were formed on V and V-44Al substrates by halide activated pack cementation, using CrCl₃ as transport agent and pure aluminum (high activity) as master alloy. Two types of diffusion couples, V/Al and V-44Al/Al, were investigated in order to determine the growth kinetics of the aluminide compounds in the 800-1000 °C temperature range. The growth of the saturated V_ss as well as of the VAl₃ and V₅Al₈ layers was controlled exclusively by solid state diffusion following a parabolic law, allowing the determination of the parabolic growth constants. Wagner’s analysis was adopted to calculate the integrated interdiffusion coefficients, resulting in values ranging approximately from 10⁻¹⁰ to 10⁻¹² cm²/s for temperatures between 800 and 1000 °C. In general, VAl₃ has the highest ${\tilde{\text{D}}}_{\text{int}}$ values in relation to those of the other two layers, considering the nominal temperatures (except for 1000 °C).

Introduction

Vanadium alloys intended for use in future nuclear fission/fusion reactors have been investigated regarding their behavior in harsh and high-temperature environments. Unfortunately, like all refractory elements, such as Nb and Mo, vanadium alloys exhibit low oxidation resistance, even in atmospheres with low oxygen content.^[1,2] Consequently, external protection is required for vanadium and its alloys in order to avoid premature degradation at high temperatures. Diffusion coatings based either on aluminum or silicon, produced by the halide activated pack cementation technique, seem to be very promising to protect V-based substrates.^[3,4] These coatings provide high resistance against oxidation by forming a protective oxide scale such as Al₂O₃ and SiO₂, by selective oxidation of Al and Si, respectively. However, the main drawback of diffusion coatings is their thermal instability induced by the existence of chemical potential gradients through the coating/substrate system as a consequence of activity changes across the interfaces. Under these gradients, elements from the coating tend to migrate into the substrate and vice-versa, which modify its initial morphology and chemical composition. In multilayered coatings, Wagner’s model can be used to predict their lifespan by simulating the changes in the layer’s thicknesses over time.^[5] Using a diffusion-based approach, this model directly correlates the interdiffusion coefficients for phases with narrow homogeneity range (also designated by integrated interdiffusion coefficients) to the thickness of the phases and their molar volumes.

The halide activated pack cementation technique has already been widely used to study the growth kinetics of coating layers in multilayered systems.^{[6, 7, 8, 9, 10, 11, 12-13]} In the present work, this technique is applied in such a way that a negative gradient of chemical activity (driving force) exists between the cement and the substrate, allowing aluminum to migrate to the vanadium alloy being coated. Therefore, diffusion couples produced by the pack cementation technique can be analyzed using Wagner’s model.^[5] Hence, the aim of the present work is to determine the interdiffusion coefficients in the Al-V system that can be further used, inter alia, to predict microstructural change in aluminide-based coatings for vanadium-based alloys.

Previous works on the growth kinetics of phases in the Al-V system focused, in general, on different properties, or analyzed only composition and morphology of the formed phases. Murarka et al.^[14] have used the residual activity method to calculate the impurity diffusion coefficient of V in Al, in the 400-630 °C temperature range. Nakamura et al. ^[15] calculated the formation rate of the VAl₃ phase between 450 and 500 °C as part of a study of V as a barrier to the interaction of Al films with polycrystalline Si. Fomin et al. ^[16] used V/Al thin films to analyze the composition, quantity, and growth kinetics of the VAl₃ and V₅Al₈ phases at temperatures ranging from 350 to 500 °C. Eizenberg et al. ^[17] reported interdiffusion between Al and V as part of a study of V as diffusion barrier between Al and GdSi₂. Finstad et al. ^[18] analyzed interdiffusion in V/Al thin films between 400 and 700 °C, paying special attention to the influence of oxygen content on the inhibition of phase growth. Lappalainen ^[19] used ionic implantation of Al in polycrystalline V in the range of 600 to 1000 °C, calculating impurity diffusion coefficients of Al in V. Maslov et al. ^[20] studied the diffusion of Al in V using x-ray diffraction within the range 1000-1500 °C, calculating the same parameters as. ^[19]

The novelty of this work lies in the determination of interdiffusion coefficients in the Al-V system using the pack cementation technique at temperatures above the melting point of Al. Thus, the obtained kinetic data may significantly contribute to the development of mobility databases for systems containing both Al and V.

Brief Description of the Al-V Phase Diagram

The Al-V system presents seven solid phases, five of them being intermetallic compounds (V₂Al₂₁, V₇Al₄₅, V₄Al₂₃, VAl₃ and V₅Al₈) formed by peritectic reactions. Murray ^[21] summarized all the experimental results available before 1989. In a more recent experimental study, Richter and Ipser ^[22] proposed modifications of the temperatures of the peritectic formation for VAl₃ and V₅Al₈ from 1360 and 1670 °C^[21] to 1270 and 1408 °C, respectively. Gong et al. ^[23] proposed a thermodynamic description for the entire binary system, which is presented in Fig. 1.

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Fig. 1

Calculated Al-V phase diagram using data from Gong et al. ^[23]

Materials and Methods

Substrates with dimensions 10 × 10 × 2 mm were cut from a high-purity vanadium plate (>99.9%) and an arc-melted and annealed (1000 °C/4 h) ingot of V-44Al (at.%) alloy. The composition of the alloy V-44Al (at.%) as a substrate was adopted because it is approximately the solubility limit of Al in V_ss at the temperature range used in the present work ^[21,23,24]. The assessment of the interdiffusion coefficients in the Al-V system was carried out via results from experiments involving the halide activated pack cementation technique. Details on the experimental configuration for the deposition of elements on vanadium and its alloys is available elsewhere ^[25], and the schematic of the experimental setup is illustrated in Fig. 2. The cement (total mass of approximately 10 g) was composed of pure Al powder (40 wt.%) as master alloy, Al₂O₃ (60 wt.%) as inert filler, and CrCl₃ (10-15 mg) as activator. In this process, the gas phase containing aluminum halides, that is generated from the cement, and the substrates can be considered as the terminal phases of classical semi-infinite diffusion couples,^{[26, 27-28]} i.e., V/Al and V-44Al/Al. Prior to the aluminization process, the substrates were prepared by grinding the surface with SiC papers down to 2400 grits, rounding the corners, ultrasonically cleaning in ethanol, and drying in hot air. Prior to the sealing step, the cement and the substrates were introduced in alumina crucibles to avoid any contact with the silica tube walls and the consequent formation of gaseous species such as Si_xCl_y and a subsequent co-deposition of Al and Si. The aluminization process was performed in silica vessels sealed under primary vacuum (10⁻² mbar). The deposition process was performed during 4-, 9-, 16-, and 25-hours using muffle furnaces heated to 800, 850, 900, 950, and 1000 °C with a heating rate of 20 °C/min. The capsules containing the samples were furnace cooled to room temperature prior to removal of the resulting coated samples. They were subsequently ultrasonically cleaned in ethanol, cold mounted in epoxy resin, ground with SiC papers down to 2400 grits and polished with 0.05 µm colloidal silica. Micrographs from the cross sections were obtained in a table-top scanning electron microscope (SEM), HITACHI-TM3000 model, using the backscattered electrons (BSE) mode. Elementary concentration profile and chemical identification of the phases were obtained by energy dispersive x-ray spectroscopy (EDS) using a Swift ED3000 system from Oxford instruments. X-ray diffractometry (XRD) characterization of the outer layers on the sample’s surfaces was performed in a Panalytical Empyrean diffractometer using Cu-K_α radiation, angular range 2θ of 20-90° with a step size of 0.02° and 50 s counting time. The thicknesses of the layers were measured on SEM micrographs and the average values were obtained from 15 points for each layer. The standard deviations were insignificant (1-2%) mainly because of the elevated thickness uniformity of the layers.

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Fig. 2

Schematics of the experimental setup adopted in the present work

Results and Discussion

Characterization of the Interdiffusion Regions

Figure 3 presents typical microstructures of the coatings formed on V and on V-44Al substrates and the associated EDS composition profiles. Aluminum deposition treatments carried out at a given temperature for different durations resulted in the formation of the same phases, differing only in thicknesses. The coating layers were uniform and crack-free along the substrates surfaces. The layers were identified by XRD analyses as well as by correlating their expected compositions to those determined by EDS. The phases formed on both coated substrates are in accordance with the Al-V phase diagram. The layer compositions (VAl₃, V₅Al₈, and V_ss) are very close to their expected values, except for significant deviations when measured in thin layers, which is influenced by electron interactions coming from neighbor layers. XRD patterns obtained from the surface analysis of the coatings at 950 °C for different durations are shown in Fig. 4. They show the presence of the same phases identified by the concentration profiles, except for V_ss due to the thicknesses of the outer layers. The combined results of SEM, EDS and XRD indicated that, for both substrates, VAl₃ formed as the outermost layer, followed by V₅Al₈ and V_ss as the innermost layer only for V substrate.

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Fig. 3

SEM images of the cross sections of (a) V and (b) V-44Al aluminized at 950 °C for 9 hours and (c) and (d) associated composition profiles measured by EDS

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Fig. 4

XRD patterns from the surface of the V and V-44Al substrates at 950 °C for different durations

For pure V substrates, the V₅Al₈ layer is not continuous at 800 and 850 °C, due to the limited growth kinetics of this phase. Since kinetic calculations are only feasible for phases exhibiting continuous and uniform growth across the entire substrate, it becomes impracticable to determine the parabolic growth constant, ${\text{K}}_p$, and consequently the interdiffusion coefficient, ${\tilde{D}}_{\mathit{int}}$, for the V₅Al₈ phase at 800 and 850 °C on pure V substrate. This negligible growth of the V₅Al₈ phase at lower temperatures is in line with observations made by other authors.^[4,17,18] The outermost layer of the coatings (VAl₃) is thicker than the other two layers, except for the V_ss layer formed on the V substrate at 1000 °C. It is worth mentioning that the VAl₃ thickness does not change considerably with temperature. The V₅Al₈ layer is thinner on the pure V substrate compared to the V-44Al substrate, as expected, because when the difference in end-member compositions decreases, the thicknesses of the phase layers increase.

The Growth Kinetics

At first glance, the growth kinetic constants of the coatings were treated without any explicit assumption on the nature of the kinetic order $n$. A double logarithmic treatment was applied on the curves of global thickness change ($\mathrm{\Delta }x$) versus time ($t$) taking into consideration a general equation for the growth expressed as:^[29]

1

$$\mathrm{\Delta }{x}^n=\text{K}·t$$where $K$ corresponds to the rate constant. The values of $n$ presented in Table 1 are very close to 2, verifying a parabolic behavior for the global growth of the coatings. Also, the coefficients of determination (R²) are very close to 1, confirming the good linear fitting with the experimental data. The small deviations of these values from a pure parabolic regime can be associated with: (i) the limited number of points used for such treatment; (ii) kinetic limitations associated with the diffusion of aluminum halides species in the gas phase; (iii) and/or interface reactions during the growth of the coatings.

Table 1. Kinetics order (n) determined from the double logarithmic plot at different temperatures together with coefficients of determination R² for aluminized V and V-44Al

Diffusion couple	Temperature, °C	Slope, n−1	n	R2
V/Al	800	0.67 ± 0.14	1.5	0.917
	850	0.49 ± 0.05	2.1	0.988
	900	0.50 ± 0.03	2.0	0.993
	950	0.46 ± 0.01	2.2	0.999
	1000	0.43 ± 0.02	2.3	0.995
V-44Al/Al	800	0.57 ± 0.10	1.8	0.944
	850	0.55 ± 0.06	1.8	0.976
	900	0.41 ± 0.02	2.4	0.995
	950	0.43 ± 0.02	2.3	0.997
	1000	0.46 ± 0.03	2.2	0.992

Assuming now that the coatings growth is only governed by solid state diffusion, the thickness variation of each layer ($\mathrm{\Delta }{x}_i$) should follow a parabolic law that may be expressed by the following equation:

2

$$\mathrm{\Delta }{x}_i^2={\text{K}}_p·t$$

${\text{K}}_p$ is the parabolic growth constant of the layer (also called the apparent growth constant ^[30,31]). The parabolic growth constants for each temperature were determined from the plots of the thickness versus √t, as shown illustratively in Fig. 5. These values were obtained through a linear fitting based on four points, each one representing an arithmetic mean of 15 thickness measurements. The parabolic growth constants are presented in Table 2 and varied approximately between 10⁻¹³ and 10⁻¹⁰ cm²/s within the 800-1000 °C temperature range. The V₅Al₈ phase presented the lowest ${\text{K}}_p$ at all temperatures for both substrates. On pure V substrates, VAl₃ presented the highest ${\text{K}}_p$ up to a temperature of 950 °C above which V_ss presented the highest ${\text{K}}_p$. The growth rate of VAl₃ was not significantly affected by temperature variations, unlike the other layers whose ${\text{K}}_p$ varied by two orders of magnitude. The data obtained for each phase for both substrates indicated that the growth rates of VAl₃ were practically not influenced by the change in the terminal phases. For V₅Al₈, the values were approximately four times smaller for the pure V substrate. This can be related to the slow growth kinetics of V₅Al₈, thus being more sensitive to changes of the terminal phase’s nature.

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Fig. 5

Growth kinetics of the aluminide coatings at 950 °C, on the (a) V substrate and (b) V-44Al substrate

Table 2. Parabolic growth constants in 10⁻¹² cm²/s at different temperatures determined from the plots of Δx versus t^0.5 for aluminized V and V-44Al

Diffusion couple	Layer	Temperature, °C
		800	850	900	950	1000
V/Al	VAl3	221.2	257.9	275.9	268.1	252.4
	V5Al8	…	…	0.5	2.1	9.5
	Vss	2.4	9.3	42.8	164.3	488.2
V-44Al/Al	VAl3	270.3	260.6	313.9	364.4	383.3
	V5Al8	0.1	0.3	2.1	8.4	39.8

Considering that the growth of the layers is thermally activated and there is no change in kinetic regime, the dependence of ${\text{K}}_p$ with temperature can be described by an Arrhenius equation,

${\text{K}}_p={\text{K}}_0{e}^{-\frac{\text{Q}}{\text{RT}}}$, in which ${\text{K}}_0$ is a pre-exponential factor, $\text{Q}$ the activation energy, $\text{T}$ the absolute temperature and $\text{R}$ the gas constant. Their values are represented in an Arrhenius plot $\left(ln{\text{K}}_p=f\left(\frac{1}{\text{T}}\right)\right)$ as shown in Fig. 6, together with results from Refs. ^[15,18]. The activation energies for the growth of each phase were determined from the Arrhenius plots and are presented in Table 3.

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Fig. 6

Arrhenius plot of the parabolic growth constants for the VAl₃, V₅Al₈ and V_ss compounds in different diffusion couples

Table 3. Activation energies in kJ/mol determined from the parabolic growth constants for aluminized V and V-44Al

Diffusion couple	Layer	Activation energy from Kp, kJ/mol
V/Al	VAl3	7.4
	V5Al8	369.4
	Vss	307.6
V-44Al/Al	VAl3	23.3
	V5Al8	359.2

As expected, the activation energy determined for VAl₃ is the lowest among the phases, since its growth rate is only slightly influenced by the increase in temperature. The activation energy for the growth of V_ss is approximately 40 times greater than that of VAl₃ on the pure V substrate, and V₅Al₈ presented the highest $\text{Q}$ values for both substrates, with an average value of 364 kJ/mol. Considering the phases growing on V and V-44Al substrates, the $\text{Q}$ values for a given phase are similar for both diffusion couples, suggesting that these values are independent of the compositions of the terminal phases.

Finstad et al. ^[18] and Nakamura et al. ^[15] analyzed the growth of VAl₃ as an interdiffusion product in thin films formed via electron beam evaporation. Finstad et al. ^[18] performed Al deposition experiments on V between 400 and 700 °C, while Nakamura et al. ^[15] deposited V on Al between 450 and 500 °C. Both authors also found the growth of VAl₃ to be parabolic. The average activation energy found in the present work for VAl₃ (15 kJ/mol) is much lower than those reported by Finstad et al. ^[18], 164 kJ/mol, and by Nakamura et al. ^[15], 260 kJ/mol. The difference in ${\text{K}}_p$ data found in the present work and by the other works may be due to the experiments carried out at lower temperatures by the aforementioned authors,^[15,18] for which the kinetic mechanisms that enable the growth of VAl₃ are different, as well as to the nature of diffusion couples (semi-infinite and finite) and their preparation processes (pack cementation versus electron beam evaporation). Within this context, the difference between activation energies may indicate different transport mechanisms.

As there is limited data in the literature about parabolic growth constants or interdiffusion coefficients for the phases present in the Al-V system, comparison of the growth behavior from chemically close systems seems to be suitable. NbAl₃ and TiAl₃ have the same stoichiometry and the same prototype as VAl₃. Among the studies on Nb aluminization, Oğurtani ^[32] and Tunca and Smith ^[33] used hot dipping to investigate growth kinetics of NbAl₃ at temperatures between 700 and 1300 °C and reported ${\text{K}}_p$ values between 10⁻¹¹ and 10⁻⁷ cm²/s and activation energies between 150 and 200 kJ/mol. Chaia et al. ^[7] compared their own results with those from the literature regarding the growth kinetics of TiAl₃ determined using different techniques in the 375-760 °C temperature range, reporting ${\text{K}}_p$ between 10⁻¹⁵ and 10⁻⁹ cm²/s and $\text{Q}$ between 33 and 296 kJ/mol. These values were determined by different groups considering parabolic and non-parabolic growth regimes. For example, Xu et al. ^[34] reported $\text{Q}$ values of 66.4 and 295.8 kJ/mol for kinetic orders 1 and 2, respectively. In general, the scarcity of experimental studies makes it difficult to correctly interpret and compare activation energies for these compounds.

Finally, it is important to point out that the parabolic growth constant is not an intrinsic property of each phase, since the thickness of a layer is influenced by the changes in composition of the terminal phases, e.g., Al and V_ss in the V-44Al/Al diffusion couple against Al and pure V in the V/Al diffusion couple. Therefore, it is not suitable to study growth kinetics in multilayered systems based only on ${\text{K}}_p$ values. The determination of intrinsic properties is instead highly recommended, such as the interdiffusion coefficients, which remain constant for each phase of a specified composition, whatever the compositions of the terminal phases.

Interdiffusion Coefficients

Wagner’s model allows to calculate interdiffusion coefficients for phases with a narrow homogeneity range in multilayered binary systems.^[5] Its conceptual efficiency has already been successfully proven for the description of multilayer growth in various systems involving metals combined with silicon or aluminum.^{[8,9,33,35, 36, 37-38]} According to this model, and assuming negligible solubilities of the elements in the terminal phases, it is possible to calculate the interdiffusion coefficients for the phases growing in the interdiffusion region. For the sake of simplification, we have considered that the apparent layer of V_ss at its solubility limit in the V/Al couple could be treated as a phase in the interdiffusion region, denoted here as V_ss, rather than a terminal phase. As shown in Fig. 3 for the V/Al couple, the aluminum composition at this apparent layer did not exhibit an important variation, i.e., it is almost constant in this layer.

Since the phases in the present work have a very narrow homogeneity range, with a virtually constant composition, their composition profiles exhibit gradients that are too small to be accurately measured. Therefore, it is not possible to apply the traditional methods of Boltzmann-Matano ^[39,40] or Sauer and Freise ^[41] for determining the interdiffusion coefficients, since they need the use of the composition profile derivatives, being suitable only for phases with a wide homogeneity range. In fact, the Wagner’s analysis ^[5] is an extension of the analysis of Boltzmann-Matano ^[39,40] and Sauer and Freise ^[41]. Wagner ^[5] introduced the concept of integrated interdiffusion coefficient, ${\tilde{D}}_{\text{int}}$, to describe the interdiffusion coefficient of a phase, $\tilde{D}$, integrated over an unknown composition range, expressed by Eq 3.

3

$${\tilde{D}}_{\text{int}}\left({\text{N}}_{\text{Al}}^i\right)=\underset{{\text{N}}_{\text{Al}}^{i^{\prime }}}{\overset{{\text{N}}_{\text{Al}}^{i^{″}}}{\int }}\tilde{D}d{N}_{\text{Al}}^i$$where ${\text{N}}_{\text{Al}}^i$ is the molar fraction of Al in the phase $i$ and ${\text{N}}_{\text{Al}}^{i\prime }$ and ${\text{N}}_{\text{Al}}^{i^{\prime \prime }}$ are the molar fractions of Al in the phase boundaries. Details regarding the mathematical considerations that lead to the dispense of the ${\partial \text{N}}_i/\partial x$ calculus are available in Wagner’s paper.^[5]

Taking into consideration a hypothetical multilayered diffusion couple constituted by the elements Al and V, the integrated interdiffusion coefficient is expressed by Eq. (4).

4

$${\tilde{D}}_{\text{int}}\left({\text{N}}_{\text{Al}}^i\right)=\frac{\mathrm{\Delta }{x}_i}{2t}{\text{N}}_V^i\sum _{\nu =2}^{\nu =i-1}\frac{{\text{V}}_m^i}{{\text{V}}_m^{\nu }}{\text{N}}_{\mathit{Al}}^{\upsilon }\mathrm{\Delta }{x}_{\nu }+{\text{N}}_V^i{\text{N}}_{\mathit{Al}}^i\frac{{\left(\mathrm{\Delta }{x}_i\right)}^2}{2t}+\frac{\mathrm{\Delta }{x}_i}{2t}{\text{N}}_{\mathit{Al}}^i\sum _{\nu =i+1}^{\nu =n-1}\frac{{\text{V}}_m^i}{{\text{V}}_m^{\nu }}{\text{N}}_V^{\nu }\mathrm{\Delta }{x}_{\nu }$$where $t$ is time, ${\text{N}}_{\text{Al}}^i$ and ${\text{N}}_V^i$ are, respectively, the molar fractions of Al and V in the phase $i$, ${\text{V}}_m^i$ is the molar volume of phase $i$, and $\nu$ is the serial number of a phase in the interdiffusion zone. The molar fractions of Al and V in the V-BCC phase, which has a wide homogeneity range, were taken at the solubility limits at each temperature for which the kinetic calculations were carried out, according to the Al-V system proposed by Murray ^[21]. The molar volume of each phase was calculated according to Paul et al. ^[42]. The parabolic growth constants (${\text{K}}_p$) were used rather than the individual thickness data in order to minimize errors.

The calculated interdiffusion coefficients are presented in Table 4. For both types of diffusion couples, the values varied approximately between 10⁻¹² and 10⁻¹¹ cm²/s, which is narrower than the ${\text{K}}_p$ values that are in the 10⁻¹³-10⁻¹⁰ cm²/s range. It is worth noting that the nature of the terminal phases (V or V-44Al) has a small influence on the interdiffusion of the elements in each phase present in the diffusion couples. The most significant differences in the interdiffusion coefficients for the same phase at the same temperature, but in different diffusion couples, were observed for V₅Al₈. This shows that, even without fulfilling the consideration of Wagner’s model that the solubilities of the elements in the terminal phases must be negligible,^[5] the intrinsic kinetic parameters are determined with good accuracy in both cases.

Table 4. Interdiffusion coefficients in 10⁻¹² cm²/s at different temperatures using the Wagner’s model ^[5] for aluminized V and V-44Al

Diffusion couple	Layer	Temperature, °C
		800	850	900	950	1000
V/Al	VAl3	43.9	53.7	65.5	77.2	94.5
	V5Al8	…	…	2.7	7.4	22.0
	Vss	2.9	7.3	22.6	65.3	168.9
V-44Al/Al	VAl3	51.4	50.2	62.7	76.7	90.5
	V5Al8	0.7	1.5	4.5	10.6	28.8

Figure 7 presents the interdiffusion coefficients for the three layers as a function of their homologous temperatures, T/T_m, showing that the interdiffusion coefficients for V_ss are the highest, followed by VAl₃ and V₅Al₈, respectively. Considering only the intermetallic phases, VAl₃ has higher interdiffusion coefficients compared to those of V₅Al₈, which is expected considering that the diffusion of the species is faster closer to the solidus temperature of a given phase. Taking this line of thought further, diffusion mechanism in the bulk might be considered to be predominant in the investigated layers since T/T_m ratios vary from 0.70 to 0.83 for VAl₃, 0.64 to 0.76 for V₅Al₈ and 0.54 to 0.65 for V_ss in the 800-1000 °C temperature range, taking the values reported by Richter and Ipser ^[22] for the peritectic formation of VAl₃ (1270 °C) and V₅Al₈ (1408 °C) and those of Gong et al. ^[23] for the solidus temperature of the V_ss (1700 °C for V-44Al). Diffusive flux in the bulk is considered much higher than that at the grain boundaries for temperatures greater than half the solidus temperature of the compounds (i.e., T/T_m> 0.5) ^[43].

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Fig. 7

Interdiffusion coefficients for the VAl₃, V₅Al₈ and V_ss compounds as a function of their homologous temperatures in the V and V-44Al substrates

From an atomistic point of view, the diffusion rate strongly depends on the type of crystalline network where the elements diffuse, according to Paul et al. ^[42]. It is reasonable to think that the interdiffusion coefficients in disordered phases, in which all atoms can change position freely, are higher than in intermetallic phases, which have ordered structures. For the V_ss, the interdiffusion coefficients may be dependent on the creation of thermal vacancies as this is the principal transport mechanism in disordered substitutional solid solutions.^[44,45] The dependence of the interdiffusion coefficients with the homologous temperature is less pronounced for VAl₃ than for V_ss, which should be reflected in the activation energies for the diffusion of elements in these phases. The crystal structure of VAl₃ is presented in Fig. 8(a). VAl₃ crystallizes in the D0₂₂ tetragonal type structure, with I4/mmm space group, where Al atoms have 8 Al and 4 V atoms as nearest neighbors, while V atoms are surrounded by 12 Al atoms, forming a cuboctahedron environment in both cases ^[46]. This means that Al atoms are completely interconnected on their sublattice while it is not the case for V atoms. This configuration implies that Al can change position by vacancy motion in its sublattice without breaking the symmetry of the structure. On the other hand, the movement of V atoms would impose a breaking of this symmetry, jump lengths larger that nearest neighbor distance, and/or creation of anti-site defects which require high activation energies. Thus, it is likely that the growth of VAl₃ is dominated by a high diffusive flux associated with the Al atoms through dense atomic plane (003) at ¼ $\overrightarrow{c}$ and ¾ $\overrightarrow{c}$ in the VAl₃ crystal structure. Fig. 8(b) illustrates the V₅Al₈ structure, which has the lowest values of interdiffusion coefficients among the three phases for all produced diffusion couples. V₅Al₈ crystallizes in D8₂ type γ-brass structure with the $I\overline{4}3m$ space group, in a cubic cell containing 52 atoms. According to the crystallographic description performed by Brandon et al. ^[47], there are four inequivalent sites with the following Wyckoff positions: 24g (Al), 12e (1/3Al+2/3V), 8c (1/2Al+1/2V) and 8c (V). In the first 24g position, Al is bonded in a pentacapped trigonal prism to 6 V and 5 Al atoms. In the 12e position, Al/V atoms are bonded in pseudo Frank-Kasper (13) polyhedron to 3 V and 10 Al atoms. Both atoms in the 8c positions are surrounded by an icosahedral environment. Atoms in the 8c (1/2Al+1/2V) position are bonded to 6 Al and 6 V atoms while in the other 8c V is bonded to 9 Al and 3 V atoms. In this case, it is likely that diffusion of Al and V atoms on their different sublattices of this structure may occur with equivalent order of magnitude through complex sequences of jumps. However, in order to build a more comprehensive vision of the diffusion process in these phases, further investigations of self-diffusion and defects in these structures are fundamental.

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Fig. 8

Crystal structures of the (a) VAl₃ and (b) V₅Al₈ compounds

In the same way as ${\text{K}}_p$, considering that the change in interdiffusion coefficients obeys an Arrhenius law, their values are presented in the Arrhenius plot in Fig. 9 and the activation energies for each phase are calculated and presented in Table 5. For both diffusion couples, VAl₃ has interdiffusion coefficients of the same order of magnitude as a function of temperature for the five temperatures, which indicates that the growth of this phase is only slightly dependent on the temperature. Thus, the activation energies for VAl₃ are the lowest compared to those of the other phases, presenting an average value of 39 ± 6 kJ/mol. V₅Al₈ and V_ss have very close $\text{Q}$ values, with 235 ± 34 kJ/mol being the average activation energy for V₅Al₈ against 234 kJ/mol for V_ss. According to Chaia et al. ^[8], $\text{Q}$ values reflect several mechanisms that operate simultaneously: self-diffusion of elements in their own sublattices, diffusion at grain boundaries and diffusion in bulk. Therefore, these values must be considered very carefully. The three mechanisms act independently, and thus each one has its own activation energy. The low activation energy values determined for VAl₃ in both diffusion couples may also be associated with other factors than those related to diffusion, possibly including an unknown effect of the pack cementation process itself.

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Fig. 9

Arrhenius plot of the interdiffusion coefficients for the VAl₃, V₅Al₈ and V_ss compounds in the V and V-44Al substrates

Table 5. Activation energies in kJ/mol determined from the interdiffusion coefficients for aluminized V and V-44Al

Diffusion couple	Layer	Activation energy from ${\tilde{D}}_{\mathit{int}}$, kJ/mol
V/Al	VAl3	42.9
	V5Al8	259.5
	Vss	233.8
V-44Al/Al	VAl3	34.9
	V5Al8	211.3

The kinetic parameters obtained in the present work are compared with those of NbAl₃. Tunca and Smith ^[33] determined interdiffusion coefficients for this phase between 700 and 900 °C, also using the Wagner’s model,^[5] which are an order of magnitude higher than those of VAl₃. They also reported an activation energy of approximately 197 kJ/mol, almost five times higher than that of VAl₃. These differences may be due to different growth mechanisms (diffusion across grain boundaries, in the bulk, etc.) and coating methods (hot dipping versus pack cementation). Furthermore, Tunca and Smith ^[33] mentioned a difference between the upper and lower sides of the Nb sample immersed in liquid Al bath, probably associated with the increase in atomic transport in the lower part of the sample due to greater convection of the liquid, causing variations in their kinetic parameters.

Conclusions

The pack cementation technique was effectively used to produce aluminide coatings on vanadium and on V-44Al substrates in the 800-1000 °C temperature range, resulting in coatings with uniform layers in terms of thickness, absence of cracks and high adhesion to the substrate. The coatings produced by HAPC were composed of two layers (VAl₃ and V₅Al₈) for V-44Al substrate and three layers (VAl₃, V₅Al₈ and V_ss) for pure V substrate. The growth of all layers was controlled by solid state diffusion, following a parabolic law, allowing the determination of the parabolic growth constants, the integrated interdiffusion coefficients through Wagner’s model and the activation energies.^[5]

In general, VAl₃ presented the highest ${\tilde{D}}_{\mathit{int}}$ values in relation to those of the other two layers, considering the nominal temperatures (except for 1000 °C). The order of the interdiffusion coefficients changes when the comparison is made as a function of the homologous temperature, resulting in the highest values for the V_ss layer and the lowest for V₅Al₈. This behavior would not be explained straightforwardly since there are no available data on the concentration and the structure of defects as well as the intrinsic diffusion coefficients of the elements in the solid solution and intermetallic compounds of the Al-V system.

Acknowledgments

The authors gratefully acknowledge the financial support from FAPESP (project numbers 2022/06285–6 and 2021/11363–3). This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)—Brazil—Finance Code 001.

Data availability

Data will be made available on request.

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Publisher's Note

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