Nitriding of Nanocrystalline Iron in the Atmospheres with Variable

Article pubs.acs.org/JPCC

Nitriding of Nanocrystalline Iron in the Atmospheres with Variable Nitriding Potential Dariusz Moszyński* West Pomeranian University of Technology, Szczecin, Institute of Inorganic Chemical Technology and Environment Engineering, Pułaskiego 10, 70-322 Szczecin, Poland S Supporting Information *

ABSTRACT: The properties of nanostructured materials differ significantly from chemically identical bulk materials. The phase transitions in these materials are of a complex nature since the size of the particles is a crucial parameter. In this paper, the series of phase transitions occurring during the gaseous nitriding of nanocrystalline iron is studied, and a detailed analysis of the phase composition and the structure of the material is given. An evolution of the mean crystallite size along the whole process is examined. The influence of variable nitriding potential on the lattice parameters of α-Fe, γ′-Fe4N, and ε-FexN phases is shown. Unexpectedly high mean crystallite size of the products is observed at the initial stage of each phase transition. The observed concentration of nitrogen in the sample volume is much higher than the one predicted by the classical thermodynamic description of the Fe−N system. This discrepancy is explained in the light of a phase transition mechanism regarding the Gibbs− Thomson effect. ε-Fe3N1+x at values of thermodynamic nitriding parameters for which pure γ′-Fe4N1+x was predicted to form according to bulk thermodynamics. Tong et al.8 observed formation of the εFe3−2N phase when nitriding potential was much smaller than the critical value for ε-Fe3−2N phase formation. Similar deviations have been reported in the studies performed on highly porous iron samples of nanocrystalline structure.13−15 A characteristic hysteresis effect was revealed; i.e., phase composition of a material obtained at a given nitriding potential was different when formed by direct gaseous nitriding and different when the saturated ε phase was reduced while ammonia concentration was decreased. In the case of nanostructured material the particle size has an important influence on its properties. The conditions of phase transitions are shifted with change of particles’ size.16 Cusenza et al.17 studied the influence of particle size on the phase transitions in iron substrates. They observed the change of thermodynamic parameters of the phase transition α-Fe → γ-Fe with the evolution of grain sizes. Another report18 has shown that the course of nitriding of nanocrystalline iron differs significantly with the change of mean crystallite size. With increased size of particles, the behavior of the Fe−N system is closer to the predictions based on classical observations reported for the coarse-grained samples. Recently the phase transformation α → γ′ in the nanocrystalline Fe−N system was studied.19 An unusual character of the evolution of mean

1. INTRODUCTION Nitriding is a thermochemical process widely used for iron and iron-based alloys to supply nitrogen into the bulk of solid. Usually it is applied as a surface treatment to produce a layer composed of iron nitrides ε and/or γ′ at the surface of the workpiece.1−3 Aside from beneficial mechanical properties iron nitrides have good magnetic properties,4−6 and recently there is a growing interest in application of nanocrystalline iron nitrides.5−9 The control of the nitriding process depends significantly on the accuracy of thermodynamic models describing the formation of γ′ and ε phases in the Fe−N system. Although the thermodynamics of this system is relatively well known most of the data pertain to bulk or coarse-grained samples.2,3,10 Gaseous nitriding is the most often used technique applied to produce iron nitrides. It can be carried out either under atmosphere with constant ammonia concentration or under atmosphere containing NH 3/H2 mixtures with variable nitriding potential.2 The latter process was first studied by Lehrer11 on iron powder. As a result the so-called Lehrer diagram was constructed. It relates the stability of Fe−N phases, temperature, and nitriding potential rN in the form of rN = f(T) dependence. This diagram is used to predict the composition of nitrided material under chosen nitriding conditions. Recent reports show that the application of nanocrystalline iron samples results in significant deviations from predictions based on classical thermodynamic studies. Wohlschlögel et al.12 studied the nitriding process of small iron grains deposited on α-Al2O3 by molecular beam epitaxy and observed formation of © 2014 American Chemical Society

Received: January 12, 2014 Revised: May 28, 2014 Published: June 24, 2014 15440

dx.doi.org/10.1021/jp500349d | J. Phys. Chem. C 2014, 118, 15440−15447

The Journal of Physical Chemistry C

Article

recorded in two diffraction angle ranges: 43° ≤ 2θ ≤ 58° and 65° ≤ 2θ ≤ 85°. Data evaluation by the Rietveld method was performed using HighScore Plus software by PANalytical B.V. iteratively utilizing the Semiautomatic Mode of the HighScore Plus program. At first a polynomial background was fitted to the diffractogram, and then the refinement procedure was initialized for identified crystallographic phases. The initial parameters of refinement pertaining to the crystallographic phases identified in the studied system were taken from the ICDD PDF 4+ database. The data given in reference patterns No. 04-007-9753, No. 01-086-0231, and No. 04-007-3379 were used to analyze structural parameters of phases α-Fe, γ′-Fe4N, and ε-FexN, respectively. Next scale factor and unit cell parameters were fitted. Finally, the shape of the model profile was refined by fitting of profile variables. As a result of this procedure unit cell parameters, crystallite size, as well as weight fractions of identified phases were calculated.

crystallite size was observed indicating that the biggest iron crystallites are transformed into the γ′ phase at the lowest nitriding potential. This unusual behavior of the nanocrystalline iron and its nitrides under NH3/H2 atmosphere is explained as a result of the Gibbs−Thomson effect.12,17,18 In the present paper, a whole sequence of phase transitions α → γ′ → ε occurring during iron nitriding is studied. The thermogravimetric studies complemented by a comprehensive analysis of in situ XRD observations demonstrate the structural changes and phase transformations occurring in the nanocrystalline iron sample in the course of the nitriding process carried out at 400 °C. The experimental results are compared with theoretical considerations, and an explanation is given in light of the Gibbs−Thomson effect.

2. EXPERIMENTAL METHODS 2.1. Sample Preparation and Characterization. Sintered iron oxide doped with aluminum, calcium, and potassium oxides was used as a starting material. The nitriding process was preceded by the reduction of the sample under pure hydrogen carried out for an hour at 500 °C. As a result, a highly porous material consisting mainly of elemental iron of nanocrystalline structure was formed. The mean size of iron crystallites estimated by the XRD line broadening method was 17 nm. Chemical analysis revealed that apart from elemental iron the material contained 3.3 wt % of Al2O3, 2.8 wt % of CaO, and 0.65 wt % of K2O. The nitrided sample was checked by XRD analysis, and no phase coming from the reaction of ammonia with aluminum, calcium, and potassium compounds was detected. Therefore, it is assumed that the mass change observed during the nitriding process reflects exclusively the incorporation of nitrogen atoms into iron bulk. 2.2. Thermogravimetric Analysis. The thermogravimetric observations of iron nitriding were performed in a tubular glass reactor equipped with the thermogravimetric measurement. An inlet gas composition was controlled by means of a set of mass flow controllers. High purity gases, hydrogen (99.999% vol.), ammonia (99.97% vol.), and nitrogen (99.999% vol.) purchased by Messer Polska, were used. The hydrogen concentration in the outlet gas stream was analyzed on the basis of thermal conductivity of gas, and partial pressures of all gas components were calculated from the measured concentration of hydrogen assuming stoichiometric decomposition of ammonia. Gas composition is expressed as nitriding potential rN = −1/2 3 ((pNH3)/(p3/2 ]. Since the values of nitriding potential H2 )) [Pa extend over several orders of magnitude, the logarithm of this quantity, denoted as ln rN, was used to simplify its numerical representation throughout the text. The nitriding process was carried out isothermally at 400 °C. All experiments were performed under atmospheric pressure. The mixtures of hydrogen and ammonia were introduced into the reactor, increasing the ratio NH3:H2 stepwise, starting from pure hydrogen. A total flow was kept constant (200 sccm). 2.3. In Situ X-ray Diffraction. Structural evolution of the material during nitriding was investigated by in situ X-ray diffraction (XRD). An iron sample identical with the one used during thermogravimetric experiment was placed in the sample holder inside the reactor chamber XRK 900 (Anton Paar) attached to a Philips X’pert MPD powder diffractometer. All diffraction spectra were acquired with use of Co Kα radiation (λα1 = 0.178901 nm, λα2 = 0.179290 nm). Diffraction data were

3. RESULTS AND DISCUSSION 3. 1. Phase Transitions and Evolution of Mean Crystallite Size. The iron samples used in the present study have a nanocrystalline structure. Former X-ray diffraction studies as well as microscopic observations of identical material have proven that the substrate is a mixture of small highly crystalline iron platelets of nonuniform size between 10 and 50 nm combined in slightly bigger blocks.20,21 The typical mean crystallite size of this sort of material is in the range 17−19 nm. The mean crystallite size of the present sample at room temperature was 17 nm. Oxidic additives present in the substrate are necessary to restrain the sintering of iron nanocrystallites at elevated temperatures, and they form bridges between iron platelets. As a result the material has nanometric structure and is highly porous, facilitating a very good diffusion of gas atmosphere into its bulk. Due to this the reaction rate of the nitriding process is relatively high. A 1 g sample of this material exposed at 400 °C to NH3/H2 mixtures reaches stable mass in less than an hour regardless of ammonia concentration in gas.14 During iron nitriding under ammonia atmosphere nitrogen atoms originating from the ammonia decomposition diffuse into iron bulk. Depending on nitriding potential the solution of nitrogen atoms in α-Fe or the formation of γ′ and ε iron nitrides is expected.11,22 On the basis of the Lehrer diagram, the course of the phase transition sequence α → γ′ → ε can be predicted. The course expected at 400 °C is shown as a dashed line in Figure 1. This figure depicts a process of nanocrystalline iron nitriding as a relation between nitriding potential rN and nitriding level, defined as mN/mFe [gN/gFe]. In Figure 1 the experimental points coming from the thermogravimetric studies are shown as red dots. Each experimental point corresponds to a stable nitriding level obtained at a constant nitriding potential. Hence, the experimental points are considered to display the equilibrium states. The thermogravimetric analysis is complemented with the phase analysis by in situ XRD. A sequence of X-ray diffractograms was acquired at variable nitriding potential. After each rise of ammonia concentration nitriding potential was kept stable for 1 h to attain an equilibrium state. The sequence of diffractograms is shown as a contour plot in Figure 2. A set of diffraction reflections indicating the presence of three crystallographic phases, α-Fe, γ′-Fe4N, and ε-FexN, are 15441



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Figure 1. Thermogravimetric analysis of the nitriding process of nanocrystalline iron at 400 °C under variable nitriding potential. The stability regions of α, γ′, and ε phases according to the Lehrer diagram11 are given as differently shaded fields. The dashed line depicts the course of the reaction predicted by the Lehrer diagram.

Figure 3. Quantitative phase analysis using the Rietveld method for the sample nitrided at variable nitriding potentials.

rN = −6.3 the nitriding level is very low and corresponds well to the solubility of nitrogen in α-iron.23 The diffraction data confirm that the starting material contains only the α-Fe phase. However, the behavior of the system at higher nitriding potential diverges substantially from expectations. The increase of nitriding potential above ln rN = −6.3 results in a gradual increase of nitriding level. XRD analysis shows that with the advancement of the process the γ′-Fe4N phase appears. According to XRD data the total conversion of iron into γ′Fe4N is observed at ln rN = −4.8, and below the latter value a mixture of α and γ′ phases is present. Within the range between ln rN = −4.8 and ln rN = −3.9 only the γ′ phase occurs in the sample. Starting from ln rN = −3.9 the nitriding level increases substantially again. A mixture of γ′ and ε phases is observed at ln rN = −3.7. Above ln rN = −3.2, ε-FexN is the only constituent of the material even though a mass gain is still recorded. Additionally a characteristic shift of diffraction reflections to lower diffraction angles 2θ is observed in this region of nitriding potential. The diffraction reflection shift indicates that the interplanar spacings in the ε phase increase with the advancement of nitriding process and together with the mass gain prove that the saturation of the ε-FexN phase with nitrogen atoms takes place. Finally the nitriding level settles at mN/mFe = 0.113, and no further mass gain is observed notwithstanding the pure ammonia is admitted into the reactor. Due to the partial decomposition of ammonia the real nitriding potential in the vicinity of the sample reaches only 0.368 Pa−1/2 (ln rN = −1.0). Kooi et al.23 proposed a theoretical dependence between the nitriding potential and nitrogen concentration in the ε phase at equilibrium. At 400 °C the nitriding level corresponding to the nitriding potential ln rN = −1.0 calculated according to this dependence is equal to mN/mFe = 0.1125 and is in excellent agreement with the experimental observations. It indicates that the system reached equilibrium, and no further increase of nitrogen concentration in the bulk is possible without change of the experimental conditions. The XRD data provide additional information about the structure of the material, i.e., mean crystallite size (MCS) of the particular phase. As mentioned before the starting material is a mixture of iron crystallites, nonuniform in size. Therefore, the analysis of mean crystallite size during nitriding of nanocrystalline iron gives a supplementary insight into this process.

Figure 2. Contour plot of the in situ XRD analysis sequence of the nitriding process of nanocrystalline iron at 400 °C. The advancement of the nitriding process follows from bottom to top. The regions of α, γ′, and ε phase occurrence are depicted by thick bars at the left-hand side of the plot.

observed. Additionally, utilizing the Rietveld refinement of the recorded X-ray diffraction data, the weight fractions of crystallographic phases identified in the sample were determined and are shown in Figure 3. According to the Lehrer diagram below ln rN = −6.3 the presence of only α-Fe is expected with the number of dissolved nitrogen atoms limited by nitrogen solubility in this phase. At ln rN = −6.3 the α → γ′ phase transition is expected to occur, and the corresponding nitriding level, i.e., mN/mFe = 0.062, should be reached. The stability region of the γ′ phase is located between ln rN = −6.3 and ln rN = −3.9; therefore, no further mass gain is expected as long as ln rN = −3.9 is reached. Once nitriding potential reaches the latter value the γ′ → ε phase transition is predicted based on the Lehrer diagram. An increase of nitriding level to mN/mFe = 0.083 is expected to obtain Fe3N stoichiometry. Since the homogeneity region of the ε phase is wide, a gradual increase of the nitrogen concentration is expected as long as Fe2N stoichiometry is reached. The nitriding level calculated for stoichiometry Fe2N is mN/mFe = 0.125. The present experimental results are consistent with the theoretical expectations in the region of α-Fe stability. Below ln 15442



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nitriding.24 The model supposes that iron particles of different size transform in their whole volume as soon as a critical concentration of nitrogen in the solid is reached. Provided the above assumption is valid, the appearance of big γ′ crystallites and big ε crystallites at the beginning of the α → γ′ and γ′ → ε stages, respectively, implies that only a fraction of crystallites composed of the biggest particles in the whole population transform initially. The decrease of MCS of the product with increasing conversion is due to the transformation of smaller and smaller crystallites of the substrate as suggested in the recent report.19 3.2. Evolution of Lattice Parameters under Variable Nitriding Potential. In the interstitial solution the incorporation of atoms introduces additional stress to the lattice which results in the change of lattice parameters. Since during the studied process nitrogen atoms are introduced into the iron lattice the diffraction data were used to determine the lattice parameters of α, γ′, and ε phases on each nitriding stage. The values of lattice parameters calculated by Rietveld refinement are presented in Figure 5. The parameter aα for the bcc lattice of α-Fe (Figure 5a), parameter aγ′ for the fcc lattice of γ′-Fe4N phase (Figure 5b), and parameters aε and cε for the hcp lattice of ε-FexN (Figure 5c) are related to ln rN. In situ XRD analysis was started at room temperature. Under these conditions, parameter aα = 0.28667 nm. This value is in excellent agreement with the one reported for the pure α phase elsewhere.10,25 All other XRD observations were performed at 400 °C. The parameter aα increases at this temperature and under the nitriding atmosphere containing less than 10 vol % of NH3 (ln rN = −8.5) is equal to 0.28814 nm. The dependence of the bcc lattice parameter aα on temperature is described by eq 110

In Figure 4 the values of MCS for each phase identified in the material are related to nitriding potential. The first experimental

Figure 4. Evolution of mean crystallite size for α, γ′, and ε phases during the nitriding process carried out at variable nitriding potential at 400 °C. The phase concentration profiles described in Figure 2 are given as thin lines for comparison. The data obtained at room temperature are depicted by a RT symbol. Experimental data of limited reliability due to the low intensity of respective diffraction reflections are shown as empty symbols.

point corresponds to the sample reduced under hydrogen flow and examined at room temperature (the box ascribed as RT). The obtained value for α-Fe is 17 nm and is in agreement with the observations performed for this material earlier.18,24 After heating of the sample up to 400 °C MCS of the α phase increases to about 21 nm due to the thermal expansion of the iron lattice. Below ln rN = −6.3, MCS of the α phase is stable. As the α phase starts to convert into the γ′ phase, its MCS begins to decrease and at ln rN = −5.1 drops to 9 nm. The reliability of the latter experimental point is limited due to a small intensity of the diffraction lines of α-Fe; however, the trend is held. The first crystallites of the γ′ phase emerge at ln rN = −6.3. At this stage MCS of the γ′ phase exceeds 40 nm and is the highest from the whole set of data pertaining to that phase. As the conversion α → γ′ proceeds MCS of γ′ decreases to stabilize once the γ′ phase becomes the only component of the sample. Then the value of MCS for the γ′ phase (product) is practically identical with the one observed initially for α-Fe (substrate). The number of experimental points corresponding to the subsequent phase transformation γ′ → ε is limited; however, the general trends are similar to those observed for the α → γ′ transition. At nitriding potential where the γ′ + ε mixture is observed, the MCS of the substrate, γ′ phase now, is reduced to 16 nm, while the product, ε phase, emerges with high MCS of 40 nm. At the final stage of nitriding the MCS of the ε phase settles at about 28 nm. The final MSC of the ε phase is expanded in comparison to that of the γ′ phase likely due to higher molar volume of the ε phase. Regarding the evolution of MCS during the whole process of nitriding, it is assumed that each crystallite passes by two subsequent phase transformations as an undivided entity. Any crackling of the crystallites during the reaction would be reflected as a decreased MCS of the product, which is not observed. This assumption was already proposed for the nanocrystalline iron in the adsorption range model of iron

aα(T ) = 0.285449 + 3.973 × 10−6T [nm]

(1)

where T is temperature in kelvin. It gives at 400 °C aα = 0.28813 nm, the value very close to the experimental one. With the rise of nitriding potential the parameter aα slightly increases. The rise is more noticeable above ln rN = −6.3. The parameter aα reaches the maximal value aα = 0.28931 nm at ln rN = −5.1; however, the reliability of this experimental point is limited due to a very small intensity of diffraction lines coming from α-Fe in the respective diffraction pattern. The results indicate a very distinctive dependence of the lattice parameter aα on nitriding potential. The expansion of the α iron lattice is due to the increasing amount of nitrogen atoms dissolved in iron volume causing internal stress and leading to the shift of iron atoms from their initial sites. The dependence of the structural parameter aγ′ of the γ′Fe4N phase on nitriding potential is given in Figure 5b. It was observed only at 400 °C. A direct comparison with previously reported values is impossible since most of the data provided in the literature are given for room temperature. However, Somers et al.26 determined the linear thermal expansion coefficient for the lattice parameter aγ′. Its value is α = (7.62 ± 0.75) × 10−6 K−1 for the sample obtained at 570 °C. Considering this, the value for 400 °C is aγ′(400 °C) = 0.38115 nm, and it is shown in Figure 5b as a horizontal dotted line. Most of the determined values of parameter aγ′ are slightly bigger than the one estimated according to the linear thermal expansion coefficient. The set of data acquired within the range of nitriding potential between ln rN = −5.6 and ln rN = −3.9 is scattered around the average value aγ′ = 0.38124 ± 0.00004 nm. Therefore, it is supposed that within this range of nitriding potential the lattice 15443



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The shift of the position of diffraction reflections originating from the ε phase shown in Figure 2 suggests that the lattice parameters of this phase change considerably. In Figure 5c the parameters aε and cε characteristic of the hcp lattice of the ε phase are related to nitriding potential. Within the whole range of nitriding potential where the ε phase is observed, parameters aε and cε increase with increasing nitriding potential. Similarly to the case of the γ′ phase the obtained values of lattice parameters cannot be directly compared with the data reported in the literature since the present data have been acquired at elevated temperature. The gradual rise of aε and cε parameters corresponds to a wide homogeneity region of the ε phase and reflects increasing concentration of nitrogen atoms in the εFexN phase. Previous reports indicate that lattice parameters for each crystallographic phase occurring in the Fe−N system can be directly related to the concentration of nitrogen in the lattice.10,26−28 However, the dependencies have been derived based on the data acquired at room temperature. The diffraction experiments in the present studies were carried out at 400 °C, and direct calculation of nitrogen concentration upon determined lattice parameters is not possible. Therefore, a special procedure was proposed to estimate the dependence of the lattice parameters at 400 °C, and it is described in detail in the Supporting Information. Applying this procedure the concentration of nitrogen atoms in each crystallographic phase was calculated for each experimental stage. Since in the previous reports concentration units were different for a particular phase they were herein unified, and nitrogen concentration is expressed as the fraction of interstitial octahedral sites occupied by nitrogen atoms, denoted as yN. The fraction of interstitial sites occupied by nitrogen atoms calculated for the α phase in the equilibrium states is plotted as ln yN = f(ln rN) in Figure 6. Below ln rN = −6.3 only the α phase exists in the material, while between ln rN = −6.3 and ln rN = −5.1 a mixture of α and γ′ phases is observed. Therefore, these regions were highlighted by a different background color. Kooi et al.23 derived the temperature dependence of the

Figure 5. Lattice parameters calculated by Rietveld refinement of obtained in situ X-ray diffractograms for crystallographic phases: (a) αFe, (b) γ′-Fe4N, and (c) ε-FexN. Experimental data of limited reliability due to low intensity of respective reflections are shown as empty symbols.

parameter aγ′ is stable and only 0.02% higher than estimated for the thermal expansion. Three other values located at the borders of nitriding potential range where the γ′ phase is observed deviate noticeably from the average. At low nitriding potential, ln rN = −6.3 and ln rN = −6.1, parameter aγ′ is smaller than average, 0.38083 and 0.38098 nm, respectively. These values suggest a deficiency of nitrogen atoms in the lattice of the γ′ phase. On the other hand, at ln rN = −3.7 which is the highest nitriding potential where γ′ is observed, the parameter a γ′ is bigger than average and equals 0.38144 nm. Correspondingly, it can be explained by an excess of nitrogen atoms dissolved in the γ′ phase in comparison to the stoichiometric compound.

Figure 6. Fraction of interstitial sites occupied by nitrogen atoms, yN, in the α-Fe phase for the nanocrystalline iron sample nitrided at variable nitriding potential. Black squares represent experimental data. Solid line extended by a dashed line depicts the equilibrium nitrogen concentration calculated for the process at 400 °C according to eq 2. A dotted line is a linear estimation of experimental data and is given to guide an eye only. The experimentally observed regions of α and α + γ′ occurrence are shown as shaded areas. 15444



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nitrogen absorption isotherms of α-Fe valid in the temperature range 300 °C < t < 690 °C given as ⎡ 1⎤ 9096 −ln⎢yN, α · ⎥ = −11.56 + rN ⎦ T ⎣

structure of the studied material the increased nitrogen concentration can be explained in analogy to the reasoning applied above in the case of the nitrogen solubility in α-Fe. Considering the Gibbs−Thomson effect, it is assumed that for the particles of small size the nitrogen concentration in the γ′ phase can be higher than in bulk material. At the lower boundary of the nitriding potential region where the γ′ phase is observed, two experimental points were recorded with yN values noticeably lower than the average given above. At ln rN = −6.3 and ln rN = −6.3, the fraction of nitrogen atoms occupying interstitial sites is yN = 0.217 and yN = 0.233, respectively. Due to the low intensity of diffraction reflections the experimental point at ln rN = −6.3 is of a limited reliability. Regarding this limitation the results suggest that at the lowest nitriding potentials a hypostoichiometric γ′ phase exists. According to the analysis of MCS of the γ′ phase, these data correspond to the particle sets of the biggest size in the whole population. It means that the biggest γ′ crystallites are stable at low nitriding potential even though the nitrogen concentration in their volume is much below stoichiometric. Hypostoichiometry of the γ′ phase is observed, especially at elevated temperature. However, according to the Fe−N phase diagram the minimal concentration of nitrogen in the γ′ phase observed at 650 °C is yN = 0.236.32 At 400 °C it is not lower than yN = 0.248.33 The origin of the observed significant hypostoichiometry is unclear. In contrast, at the highest value of nitriding potential where the γ′ phase is observed, namely, at ln rN = −3.1, the nitrogen concentration reaches yN = 0.281, indicating substantial excess of nitrogen atoms in the lattice. The evaluation of MCS of the γ′ phase suggests that at that nitriding potential the γ′ phase still present in the sample consists of small crystallites only. In this case the influence of the Gibbs−Thomson effect is supposed to lead to the increase of γ′ phase stability at an excess of nitrogen atoms in the bulk. In Figure 7 the data corresponding to the ε phase are also shown. In accordance with a broad homogeneity region of the ε phase yN values change from 0.376 to 0.424 for ln rN = −3.7 and ln rN = −1.7, respectively. The theoretical dependence between nitriding potential rN and the fraction of nitrogen atoms occupying interstitial sites in the ε phase, denoted as yN,ε, is described by eq 323

(2)

−1/2

where rN is given in Pa and T is given in kelvin. Applying eq 2, a dependence ln yN = f(ln rN) was calculated for 400 °C, and it is depicted in Figure 6 as a solid line. Since herein α-Fe was observed at the nitriding potential higher than ln rN = −6.3, this dependence was extrapolated by a linear function. All experimental points are placed above the theoretical line indicating that the concentration of nitrogen atoms in the iron lattice is above expected values determined by the nitrogen absorption isotherm. Equation 2 describing the nitrogen absorption isotherm of α-Fe was derived based on the literature data acquired for bulk and coarse-grained iron samples.23 However, the studied material is a set of iron nanocrystallites. Earlier it was proposed that the critical concentration of nitrogen in iron crystallites is changed for small particles due to the Gibbs−Thomson effect.18 Considering this effect the solubility limit of nitrogen in iron is higher for smaller particles. Therefore, the increased values of nitrogen concentration in iron nanoparticles are expected as observed experimentally. At nitriding potential above ln rN = −6.3 a slight increase of the difference between the theoretical values and observed concentration of nitrogen can be noticed. Earlier it was shown that with the reaction advancement MCS of iron decreases. Since the size of nanocrystallites is smaller than in the starting material, the solubility limit of nitrogen in iron due to the Gibbs−Thomson effect is higher. In Figure 7 the dependence yN = f(ln rN) is shown for phases γ′ and ε. The data corresponding to the γ′ phase gather around

⎛ r ⎞ ln⎜⎜ oN ⎟⎟ = −3.84 − 30.76·yN, ε + 82.87· (yN, ε )2 ⎝ rN, ε ⎠

(3)

roN,ε

where can be interpreted as the nitriding potential in equilibrium with the ε phase having a hypothetical composition Fe2N. roN,ε is dependent on temperature according to eq 4 Figure 7. Fraction of interstitial sites occupied by nitrogen atoms, yN, in γ′-Fe4N and ε-FexN phases for the nanocrystalline iron sample nitrided at variable nitriding potential. The solid line depicts the equilibrium nitrogen concentration calculated for the ε phase at 400 °C according to eq 3 and eq 4.

o ln(rN, ε) = − 4.92 +

roN,ε

3.59 × 103 T

(4)

−1/2

where is given in Pa and T in kelvin. The dependence corresponding to the equilibrium was calculated for 400 °C, and it is shown in Figure 7 as a solid line. The experimental data correspond well to that dependence, indicating that the Fe−N system reached the equilibrium at the considered range of nitriding potential. In analogy to α and γ′ phases the yN values observed experimentally for the ε phase due to the nanometric structure of the present sample are slightly higher than those predicted for bulk materials. The analyses given above provide the weight fractions of α, γ′, and ε phases in the material as well as nitrogen

yN = 0.25 which represents the stoichiometric Fe4N compound. The experimental points acquired between ln rN = −5.6 and ln rN = −3.9 are averaged to yN = 0.259 ± 0.005. This value corresponds to Fe4N1+0.036 stoichiometry indicating a hyperstoichiometric γ′ phase. The excess of nitrogen above yN = 0.25 has been previously observed in the samples identified as the γ′ phase;11,29,30 however, the reliability of those data has been recently questioned.31 Regarding the specific, nanometric 15445



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are nonuniform in size the observed effects are complex. Considering both the Gibbs−Thomson effect and nonuniformity of grain size distribution the phase transition mechanism for the present material is described below. At the lowest nitriding potentials nitrogen atoms dissolve in α-Fe to form a solid solution with limited nitrogen concentration. Due to the Gibbs−Thomson effect the Gibbs’ free energy of iron particles is changed for the small particles. As a result the solubility of nitrogen in the α phase is increased as shown in Figure 5. At the beginning of the α → γ′ transition the biggest iron crystallites are converted into the γ′ phase since the solubility limit of nitrogen in iron is first reached in the biggest iron crystallites. The solubility limit of nitrogen for the remaining, small iron crystallites is higher, and therefore the difference between experimentally observed nitrogen concentration and theoretical predictions rises with increasing nitriding potential. The γ′ phase is first formed from the biggest iron crystallites. With increasing nitriding potential the smaller and smaller iron particles transform into the γ′ phase. As a result the mixtures of the α + γ′ phases are observed at the nitriding potential between ln rN = −6.3 and ln rN = −5.1. Once the α phase is completely converted into the γ′ phase, the latter is stable despite increasing nitriding potential. The ε phase emerges at ln rN = −3.7, and the biggest crystallites occur first. Since the critical concentration of nitrogen required for the γ′ → ε transition is the lowest for the biggest γ′ crystallites, they will be converted first. As soon as all crystallites are converted into the ε phase only the saturation with nitrogen atoms occurs. The description given above appropriately explains the transformations in the nanometric iron substrate during its nitriding process. On the basis of this mechanism, some general behavior of the nanocrystalline Fe−N system can be predicted. In a hypothetical nanocrystalline iron sample with the grains of a single size all particles transform at identical nitriding potential. The smaller the size of the grains, the higher the nitriding potential required to initiate the phase transformation. Considering a nonuniform grain size distribution in the sample and the wider size distribution, the occurrence of phase mixtures is expected in the broader range of nitriding potential. Similar effects as predicted above have been already reported for the nanocrystalline iron samples elsewhere.18 The iron samples with a different grain size distribution were compared. The range of nitriding potential where the mixtures of α + γ′ phases were observed was narrower for the sample with smaller grain size distribution of iron. Moreover, the onset of γ′ presence was shifted to the higher nitriding potentials for the samples with a smaller mean crystallite size.

concentration in each particular phase for each stage of nitriding. Therefore, based exclusively on XRD data analysis the total concentration of nitrogen in the sample can be calculated applying eq 5 rN rN rN rN rN Nat. % = cαrN·x N, α + cγ ′ · x N, γ + cε · x N, ε

(5)

where Nat.% is the atomic percent of nitrogen in the sample, N and cri N and xrN,i denote the weight fraction of a given phase and the molar fraction of nitrogen in this phase, respectively. The molar fractions are calculated from yN according to eq 610 given below

xN =

1

c y a N c + a yN

(6)

In fcc and hcp lattices the number of octahedral sites, c, is equal to the number of sites in the substitutional sublattice, a, and therefore c/a = 1 for γ′ and ε phases. It is c/a = 3 for the bcc lattice (α phase). The respective values of total nitrogen concentration are shown in Figure 8 as stars, and they are

Figure 8. Comparison of the variation of nitrogen concentration during the nitriding process at variable nitriding potential rN, observed thermogravimetrically and calculated upon data obtained by in situ XRD analysis. The nitrogen concentration is expressed as atomic percent.

compared with the thermogravimetric data (black dots). A good agreement is found between the nitrogen concentrations evaluated by two different analytical methods. The data obtained from XRD analysis complement the thermogravimetric data giving a more complete view of the nitriding process. 3.3. General Discussion. Hitherto, it is shown that the behavior of the nanocrystalline Fe−N system deviates significantly from the predictions based on classical studies of bulk and coarse-grained iron samples, to name the most prominent: (a) extended stability of α and γ′ phases, (b) the occurrence of stable α + γ′ and γ′ + ε mixtures in ranges of nitriding potential, (c) surprisingly high values of MCS of γ′ and ε phases at the lowest nitriding potential they occur, and (d) higher concentration of nitrogen in all phases than predicted by calculations pertaining to bulk iron. It was previously mentioned that due to the specific nanometric structure of the studied material a good explanation for these observations can be given on the basis of the Gibbs− Thomson effect. Since iron crystallites observed in the sample

4. CONCLUSIONS The present results show that the behavior of the nanocrystalline Fe−N system deviates significantly from the predictions based on the thermodynamic data collected for coarse-grained samples. In comparison to classical thermodynamic parameters given for that system, the prominent shift of the stability region of α and γ′ phases has been observed. The extended solubility of nitrogen in the iron lattice was observed at particular stages of the nitriding process. Additionally, the behavior of the system is dependent on the size distribution of crystallites constituting the material. The influence of the Gibbs− Thomson effect explains the observed anomalies. 15446



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(18) Moszyński, D.; Kiełbasa, K.; Arabczyk, W. Influence of Crystallites’ Size on Iron Nitriding and Reduction of Iron Nitrides in Nanocrystalline Fe-N System. Mater. Chem. Phys. 2013, 141, 674− 679. (19) Moszyński, D.; Moszyńska, I.; Arabczyk, W. The Transformation of α-Fe into γ′-Fe4N in Nanocrystalline Fe-N System: Influence of Gibbs-Thomson Effect. Appl. Phys. Lett. 2013, 103 (25), 253108. (20) Mahdi, W.; Schütze, J.; Weinberg, G.; Schoonmaker, R.; Schlögl, R.; Ertl, G. Microstructure of the Activated Industrial Ammonia Synthesis Catalyst. Catal. Lett. 1991, 11, 19−32. (21) Schütze, J.; Mahdi, W.; Herzog, B.; Schlögl, R. On the Structure of the Activated Iron Catalyst for Ammonia Synthesis. Top. Catal. 1994, 1, 195−214. (22) Du, H. A Reevaluation of Fe-N and Fe-C-N Systems. J. Phase Equilib. 1993, 14 (6), 682−693. (23) Kooi, B. J.; Somers, A. J.; Mittemeijer, E. J. An Evaluation of the Fe-N Phase Diagram Considering Long-Range Order of N Atoms in γ′-Fe4N1‑x and ε-Fe2N1‑z. Metall. Mater. Trans. A 1996, 27A, 1063− 1071. (24) Wróbel, R.; Arabczyk, W. Solid - Gas Reaction with Adsorption as the Rate Limiting Step. J. Phys. Chem. A 2006, 110, 9219−9224. (25) Wriedt, H. A.; Gokcen, N. A.; Nafziger, R. H., The Fe-N (IronNitrogen) System. Bull. Alloy Phase Diagrams 1987, 8 (4). (26) Somers, M. A. J.; van der Pers, N. M.; Schalkoord, D.; Mittemeijer, E. J. Dependence of the Lattice-Parameter of γ′ Iron Nitride, Fe4N1‑x, on Nitrogen-Content - Accuracy of the Nitrogen Absorption Data. Metall. Trans. A 1989, 20 (8), 1533−1539. (27) Somers, M. A. J.; Kooi, B. J.; Maldzinski, L.; Mittemeijer, E. J.; van der Horst, A. A.; van der Kraan, A. M.; van der Pers, N. M. Thermodynamics and Long-Range Order of the Interstitials in an h.c.p Lattice: Nitrogen in ε-Fe2N1‑z. Acta Mater. 1997, 45 (5), 2013−2025. (28) Liapina, T.; Leineweber, A.; Mittemeijer, E. J.; Kockelmann, W. The Lattice Parameters of ε-Iron Nitrides: Lattice Strains Due to a Varying Degree of Nitrogen Ordering. Acta Mater. 2004, 52, 173−180. (29) Brunauer, S.; Jefferson, M. E.; Emmett, P. H.; Hendricks, S. B. Equilibrium in the Iron-Nitrogen System. J. Am. Chem. Soc. 1931, 53, 1778−1786. (30) Eisenhut, O.; Kaupp, E. The System Iron-Nitrogen from X-ray Diffraction Investigations. Z. Elektrochem. 1930, 36 (6), 392−404. (31) Woehrle, T.; Leineweber, A.; Mittemeijer, E. J. The Shape of Nitrogen Concentration-Depth Profiles in γ′-Fe4N1‑z Layers Growing on α-Fe Substrates; the Thermodynamics of γ′-Fe4N1‑z. Metall. Mater. Trans. A 2012, 43A (2), 610−618. (32) Kardonina, N. I.; Yurovskikh, A. S.; Kolpakov, A. S. Transformations in the Fe-N System. Met. Sci. Heat Treat. 2010, 52 (9−10), 457−467. (33) Somers, M. A. J.; Mittemeijer, E. J. Phase-Transformations and Stress-Relaxation in γ′-Fe4N1‑x Surface-Layers During Oxidation. Metall. Trans A 1990, 21 (4), 901−912.

ASSOCIATED CONTENT

S Supporting Information *

The procedure for calculation of the nitrogen concentration in the iron bulk utilizing the lattice parameters of respective phases evaluated upon Rietveld refinement of XRD data is described in detail. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The author would like to acknowledge the fruitful discussions with Prof. Walerian Arabczyk and help from Mrs. Izabela Moszyńska.

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REFERENCES

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Nitriding of Nanocrystalline Iron in the Atmospheres with Variable

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