- Email: [email protected]
Simulation of the growth kinetics of boride layers formed on Fe during gas boriding in H2-BCl3 atmosphere
Journal of Solid State Chemistry 199 (2013) 196–203
Contents lists available at SciVerse ScienceDirect
Journal of Solid State Chemistry journal homepage: www.elsevier.com/locate/jssc
Simulation of the growth kinetics of boride layers formed on Fe during gas boriding in H2-BCl3 atmosphere M. Kulka a,n, N. Makuch a, A. Pertek a, L. Ma"dzin´ski b a b
Poznan University of Technology, Institute of Materials Science and Engineering, Pl. M.Sklodowskiej-Curie 5, Poznan 60-965, Poland Poznan University of Technology, Institute of Machines and Motor Vehicles, Piotrowo Street 3, Poznan 60-965, Poland
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 October 2012 Received in revised form 24 December 2012 Accepted 24 December 2012 Available online 7 January 2013
The modeling of the boriding kinetics is considered as a necessary tool to select the suitable process parameters for obtaining boride layer of an adequate thickness. Therefore, the simulation of the growth kinetics of boride layers has gained much attention for last years. The majority of the published works described the kinetics of the pack-boriding or paste-boriding. In this study, the model of growth kinetics of two-phase boride layer (FeB þ Fe2B) on pure Fe was proposed for gas boriding. Displacements of the two interfaces (FeB/Fe2B and Fe2B/substrate) resulted from a difference of the arrival flux of interstitial boron atoms to one phase and the departure flux of the boron atoms from this phase to the second phase. The mass balance equations were formulated. The measurements of thickness of both zones (FeB and Fe2B), for different temperature of boriding, were used for calculations. Based on the experimental data, the parabolic growth constants AFeB and BFe2 B versus the temperature of boriding were determined. The linear relationships were accepted. As a consequence, the activation energies (QFeB and Q Fe2 B ) were calculated. The calculated values were comparable to other data derived from gas boriding. The presented model can predict the thicknesses of the FeB and Fe2B zones (XFeB and Y Fe2 B , respectively) formed on pure Fe during gas boriding. Additionally, the diffusion annealing after boriding was analyzed. This process was carried out in order to obtain a single-phase boride layer (Fe2B). The relationship between the reduction in FeB zone (dXFeB) and the growth in Fe2B phase (dY Fe2 B ) was determined. The time tXFeB ¼ 0, needed for the total elimination of FeB phase in the boride layer was calculated and compared to the experimental data. & 2013 Elsevier Inc. All rights reserved.
Keywords: Gas boriding Boride layers Growth kinetics Parabolic growth constants Activation energy Diffusion annealing
1. Introduction The diffusion boriding is a surface hardening of ferrous and nonferrous alloys to improve their surface properties. In this process, the boron atoms are introduced into the material surface to form a hard layer consisting of borides. Generally, the growth kinetics of solid phases (or zones) in single, two- and multi-phase systems, is controlled by diffusion of elements occurring in these phases. A speed of the displacement of interfaces is being analyzed depending on diffusion fluxes of elements to these interfaces and from them. It is being assumed that balance of diffusion fluxes of diffusing elements (penetrating into individual phase and leaving this phase) is determining the growth (or reduction) of phases, that is after all—their thickness after the process. If only one element participates in the diffusion or diffusion of the second element is negligible small in relation to the first element, then balance of diffusion fluxes is reduced to an
n
Corresponding author. E-mail address: [email protected] (M. Kulka).
0022-4596/$ - see front matter & 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jssc.2012.12.029
arrival flux providing the element to the phase (or phases) at the interface and a departure flux taking away this element from this phase. Mathematical model of the single-phase growth (of the single zone on the saturated substrate) for the first time was drawn up by Wagner [1] in order to determine the diffusion coefficient. In the later period, a significant number of models of the growth turned up at literature. These models concerned twoor more phases, assuming diffusion of one element of the system, as well as several elements [2–10]. The modeling of the boriding kinetics is considered as a necessary tool to select the suitable process parameters for obtaining boride layer of adequate thickness. It is very important for the practical applications of boriding. Therefore, the modeling of the growth kinetics of boride layers has gained much attention to simulate the boriding kinetics for last years. For this reason, many different models [11–27] were reported in the literature. The majority of these papers described the kinetics of pack-boriding [11,23,27] or pasteboriding [12,18,21,22,24,25]. However, during these processes, the composition of the produced atmosphere is not constant. Therefore, the diffusion flux from the boriding medium can be changeable for a time of boriding. It is very difficult to assess to
M. Kulka et al. / Journal of Solid State Chemistry 199 (2013) 196–203
what extent it affects diffusion model. During the gas boriding, the composition of boriding medium can be controlled [28–36]. There is a possibility of keeping this composition on the constant level. It provides the stability of the diffusion flux from the boriding medium. The results of many papers indicate that gradient of boron concentration does not occur along the needles of iron borides [37,38] and the boron diffuses along the grain boundaries. In this case, the presented model could not be applied. However, according to other opinions [2,11–27], a small gradient of boron concentration in the iron borides (about 1 at% B) is possible. Therefore, in this study, the kinetic model of twophase growth on saturated and non-saturated substrate was used in order to simulate the growth kinetics of boride layers. The thermodynamics and kinetics of gas boriding influenced the microstructure obtained. The possibilities of boride layer producing resulted from these conditions [28,39]. The process of boriding with the use of H2-BCl3 atmosphere was studied in the paper [28]. Based on the thermodynamic analysis, there was a possibility of controlling the activity of boron during boronizing in H2-BCl3 atmosphere. When the content of BCl3 in the atmosphere increased or the temperature decreased, the boron activity diminished [28]. Then, the decrease of boron potential was obtained. Theoretically, the use of lower boron potential of atmosphere could produce a singlephase boride layer. It required the relatively high BCl3 content in the atmosphere. However, within the temperature range usually used during gas boronizing 800–1000 1C (1073–1273 K), BCl3 content higher than 5 vol% provided the boride layers with a larger porosity. The considerable quantity of ferrous and ferric chlorides in atmosphere was the reason for this porosity and brittleness. Therefore, the content of BCl3 below 5 vol% in H2-BCl3 atmosphere was the most advisable. The highest acceptable BCl3 content, taking the porosity into account, was equal to about 10 vol%. In these conditions, the activity of boron was equal to 1, within the analyzed temperature range. Such a situation, in result of continuous gas boriding, always caused the formation of two-phase boride layer of good quality (without porosity). The diffusion annealing after boriding was the only method, which could produce the singlephase boride layer in case of gas boriding. In this process, the reduction of FeB borides was possible. As a consequence, a singlephase (Fe2B) boride layer could be produced. Some problems concerning the thermodynamics and kinetics of gas boriding in N2-H2-BCl3 atmosphere were also examined [39]. The gas boriding was carried out at the temperature of 800 1C (1073 K). The conclusions were similar. Too high BCl3 content also provided the boride layer with large porosity due to the considerable quantity of FeCl2 in atmosphere. The single-phase boride layer was also formed as a consequence of diffusion annealing, carried out after boriding. In this paper, the two-stage process (boriding þdiffusion annealing) was analyzed. The growth kinetics of two-phase boride layer on the ferrous substrate was studied during the gas boriding in H2-BCl3 atmosphere. The parabolic growth constants of FeB and Fe2B zones were determined. The activation energies regarding the both iron borides were calculated and compared to literature data. The presented model was formulated to predict the thickness of the FeB and Fe2B borides formed on pure Fe. Simultaneously, the kinetics of the second stage (diffusion annealing) was also presented. This step provided the boride layer with single-phase structure (Fe2B).
2. The diffusion model 2.1. Formation of two-phase boride layer (FeB þFe2B) The process consists in diffusion boriding in H2-BCl3 atmosphere for a time. The growth of two phases (FeB and Fe2B) with
197
one diffusing element (boron) is observed. Therefore, for analysis, the kinetic model of two-phase growth on saturated and nonsaturated substrate will be used [2] (modified model described by Fromm [3]). This model will be discussed regarding the boride layer that consists of phases (borides) FeB and Fe2B, formed on pure Fe. The model is imposing the following restrictions:
the growth of boride layer is being controlled exclusively by boron diffusion in FeB and Fe2B zones;
the participation of diffusion of Fe-atoms is negligible small; the growth of boride layer is a consequence of the boron diffusion perpendicular to the sample surface;
the solubility of boron in the substrate is equal to zero or the substrate is saturated with boron;
a linear concentration-profile of boron is assumed through the FeB and Fe2B zones;
the surface boron concentration, cB,s/FeB and boron concentra-
tions at the interfaces: FeB/Fe2B/Fe, relatively: cB,FeB=Fe2 B , cB,Fe2 B=FeB and cB,Fe2 B=Fe , are independent of temperature (are constant) and equal to: cB,s/FeB ¼100.5 103 mol m 3, cB,Fe2 B=FeB ¼59.8 103 mol m 3; the range of homogeneity of both zones is small and is equal to about 1 at% B; a local equilibrium is attained at the moving interfaces; the planar morphology is assumed for the phase interfaces; the volume change during the phase transformation is not considered; the diffusion coefficient of boron in each iron boride is independent of concentration and follows an Arrhenius relationship; a uniform temperature is assumed throughout the sample; the presence of porosity is neglected during the boron diffusion; the effect of the boride incubation time on the kinetics of the boriding is not taking into account.
The layer growth kinetics during a diffusion-controlled phase transformation in the Fe–B system can be analyzed by considering the displacement of the two interfaces (FeB/Fe2B and Fe2B/substrate) between the adjacent phases, due to a difference of the arrival flux of interstitial boron atoms to one phase and the departure flux of the boron atoms from this phase to the next phase. The mass balance equations should be then described. The considered model will be discussed with the help of Fig. 1. The growth of the surface-FeB zone (towards the core), caused by the infinitesimal dXFeB-segment during dt, is accompanied by an accumulation of B atoms what is marked as gray area in Fig. 1. This accumulation is being determined by the difference of boron diffusion fluxes: from the boriding medium, to the FeB zone, JFeB B 2B and from the FeB zone to Fe2B, JFe . By analogy, the growth of the B Fe2B zone during the same dt, for the infinitesimal dY Fe2 B -segment, is accompanied by an accumulation of B atoms, also marked with gray color in Fig. 1. This accumulation is a result of diffusion flux 2B from FeB zone to Fe2B, JFe . In case of the diffusion of B atoms from B the Fe2B zone into base material (Fe), the increase in the Fe2B zone is being additionally determined by diffusion flux from the Fe2B zone to this substrate (Fe), JFe B . However, the model considers the (FeB/Fe2B) bilayer growth on the substrate saturated with boron atoms. In this case, the diffusion flux JFe B is equal to zero. Therefore, according to the law of mass conservation, the growth of considered zones (FeB and Fe2B) on Fe can be described by the set of two differential equations, mutually dependent [3]. Based on Fig. 1 it is possible to write these equations into the following way: 1 cB,FeB=Fe2 B cB,Fe2 B=FeB þ cB,s=FeB cB,FeB=Fe2 B U 2
198
M. Kulka et al. / Journal of Solid State Chemistry 199 (2013) 196–203
Fig. 1. Diagram of growth of boride layer (FeB/Fe2B/Fe zones) during gas boriding.
cB,s=FeB cB,FeB=Fe2 B Fe2 B c B,Fe2 B=FeB c B,Fe2 B=Fe dX FeB ¼ DFeB D Udt B B X FeB Y Fe2 B ð1aÞ
1 cB,Fe2 B=FeB cB,Fe2 B=Fe U cB,Fe2 B=Fe cB,Fe=Fe2 B þ 2 Fe2 B cB,Fe2 B=FeB c B,Fe2 B=Fe Udt dY Fe2 B ¼ DB Y Fe2 B cB,Fe2 B=Fe cB,Fe=Fe2 B þ cB,Fe2 B=FeB cB,Fe2 B=Fe ÞUdX FeB DFeB B ,
ð1bÞ
Fe2 B
DB —effective diffusion coefficients of boron in FeB where: and Fe2B zones, cB,s/FeB—surface boron content in FeB zone at the interface: gas phase/solid phase, cB,FeB=Fe2 B —boron content in FeB zone at the interface: FeB/Fe2B, cB,Fe2 B=FeB —boron content in Fe2B zone at the interface: Fe2B/FeB, cB,Fe2 B=Fe —boron content in Fe2B zone at the interface: Fe2B/Fe, cB,Fe=Fe2 B —boron content in the substrate (Fe) at the interface: Fe/Fe2B. Relationships which are solving the above set of differential equations are as follows X FeB ¼ 2UAFeB Ut 1=2
ð2aÞ
Y Fe2 B ¼ 2UBFe2 B Ut 1=2
ð2bÞ
where: XFeB, Y Fe2 B —thickness of FeB and Fe2B zones, respectively, AFeB, BFe2 B —parabolic growth constants, dependent only on the chemical composition (concentrations of boron) at the surface and at the interfaces and on diffusion coefficients, t—time of boriding. Solution (2a and 2b) is imposing the following conditions:
the growth in both phases (FeB and Fe2B) have to start
simultaneously since the time of the t ¼0, that is from the moment of commencing the process; the boron concentration in FeB phase at the surface (also at interfaces) at the time of t ¼0 has a maximum value; diffusion flux of boron to the substrate (Fe) is equal to zero.
At fulfilling above relations, according to relations (2a) and (2b), straight lines of the growth of zones FeB and Fe2B in the coordinate systems: X2FeB–t and Y 2Fe2 B –t (after the extrapolation until the t¼ 0) should intersect point with coordinates (0,0). In real conditions above relations are not fulfilled. Before the considered phases will appear on the surface, their nucleation and coagulation occur till the surface will be completely covered with borides. The maximum concentration of boron on the surface
(in the FeB phase) will be obtained after a still longer time. In such a situation, instead of analytical, the numerical methods are necessary in order to solve the Eqs. (1a) and (1b). The effect of the boride incubation time on the kinetics of the process was presented in paper [27]. It was assumed that incubation time of FeB phase was longer than incubation time of Fe2B borides. However, basing on the paper [40], in case of gas boriding, FeB boride was the first phase appearing in boride layer. The nucleation of FeB boride occurred promptly on the surface of the iron or steel after a short time of boriding (about 4 s). After 8 s of boriding, both phases (FeBþFe2B) coexisted, and the entire surface of the sample was full of the crystal nuclei of borides. Next, the growth of the crystal nuclei in two directions was observed: perpendicular to the surface (privileged direction) and parallel to the surface. Within a few minutes, the growth of crystal nuclei caused the formation of a continuous boride layer [40]. Therefore, the effect of the boride incubation time on the kinetics of the boriding was omitted in the presented model. 2.2. Diffusion annealing in order to form single-phase boride layer (Fe2B) The diffusion annealing of previously produced borided layer should be performed in order to form the single-phase boride layer. During this process, carried out in H2 atmosphere, the providing of BCl3 is stopped and so the diffusion flux JFeB from the B boriding medium to the FeB zone is equal to zero. It is being assumed that a process of deboriding is not appearing, that is, the diffusion flux from the solid phase up to the gaseous phase does not exist. Therefore, the growth in the Fe2B phase is possible exclusively as a result of the reduction in the FeB phase. The reduction of this phase by the infinitesimal dXFeB-segment during dt was emphasized with gray color in Fig. 2. The growth in the Fe2B zone is being determined by diffusion flux of B atoms from the FeB zone to Fe2B, J BFe2 B . And so the growth of the Fe2B zone, caused by the infinitesimal segment dY Fe2 B during the same dt, is accompanied by an accumulation of B atoms, also marked with gray color in Fig. 2. Equations of mass balance are as follows: 1 cB,s=FeB cB,FeB=Fe2 B U cB,FeB=Fe2 B cB,Fe2 B=FeB þ 2 Fe2 B cB,Fe2 B=FeB cB,Fe2 B=Fe Udt ð3aÞ dX FeB ¼ DB Y Fe2 B 1 cB,Fe2 B=FeB cB,Fe2 B=Fe U cB,Fe2 B=Fe cB,Fe=Fe2 B þ 2
M. Kulka et al. / Journal of Solid State Chemistry 199 (2013) 196–203
199
Fig. 2. Reduction in FeB phase and growth of Fe2B phase during diffusion annealing.
cB,Fe2 B=FeB cB,Fe2 B=Fe Udt Y Fe2 B þ cB,Fe2 B=Fe cB,Fe=Fe2 B þ cB,Fe2 B=FeB cB,Fe2 B=Fe ÞUdX FeB
Table 1 Chemical composition of material used [wt%].
dY Fe2 ¼ DBFe2 B
ð3bÞ
From the Eq. (3a), knowing the concentration of boron at the interfaces (that is gradient of boron concentration), thickness of zones after the stage of saturating with boron (XFeB and Y Fe2 B ) and effective diffusion coefficient in Fe2B zone (DB Fe2 B ), it is possible to calculate the time tXFeB ¼ 0, needed for the total elimination of FeB phase in the boride layer (accepting dXFeB ¼XFeB). Integrating Eq. (3a): Z X FeB 1 cB,s=FeB cB,FeB=Fe2 B U cB,FeB=Fe2 B cB,Fe2 B=FeB þ 2 0 Z tXFeB ¼ 0 cB,Fe2 B=FeB cB,Fe2 B=Fe DBFe2 B Udt ð4Þ dX FeB ¼ Y Fe2 B 0 The following solution was received: 1 1 2 c B,FeB=Fe2 B c B,Fe2 B=FeB þ 2 cB,s=FeB UX FeB UY Fe2 B t XFeB ¼ 0 ¼ DBFe2 B U cB,Fe2 B=FeB cB,Fe2 B=Fe
ð5Þ
Assuming that the entire reduced FeB zone will result in the accumulation of boron in the Fe2B zone, it was possible to write (Fig. 2): cB,Fe2 B=Fe cB,Fe=Fe2 B þ 12 cB,Fe2 B=FeB cB,Fe2 B=Fe U dY Fe2 B ¼ cB,FeB=Fe2 B cB,Fe2 B=FeB þ 12 cB,s=FeB cB,FeB=Fe2 B UdX FeB þ cB,Fe2 B=Fe cB,Fe=Fe2 B þ cB,Fe2 B=FeB cB,Fe2 B=Fe ÞUdX FeB ð6Þ From Eq. (6) it was possible to determine the relationship between the size of the reduction in the FeB zone (dXFeB) and size of the growth of the Fe2B phase (dY Fe2 B ): 1 cB,FeB=Fe2 B þ 12cB,s=FeB cB,Fe=Fe2 B ð7Þ UdX FeB dY Fe2 B ¼ 21 1 2 cB,Fe2 B=Fe 2cB,Fe2 B=FeB cB,Fe=Fe2 B In real conditions above relations are not fulfilled. If the diffusion flux from the boriding medium up to the FeB phase (JFeB B ) is equal to zero, a gradient of the boron concentration in this phase is being reduced gradually during the process what is difficult to estimate. It is known that gradient of the concentration is disappearing after the certain time. The surface boron concentration (cB,s/FeB), at the interface: gas phase/solid phase, is decreasing gradually until the value corresponding to the cB,FeB=Fe2 B .
Material
C
Mn
Si
Cr
P
S
Ni
Cu
Fe (Armco iron)
0.035
0.20
0.22
0.10
0.025
0.025
0.12
0.10
3. Material and methods 3.1. Material Pure iron (Armco iron) was used for investigation. Its chemical composition was presented in Table 1. 3.2. Formation of two-phase boride layers (FeB þFe2B) Gas boriding was carried out in H2-BCl3 atmosphere [28] with the usage of devices presented in Fig. 3. The specimens were put into the quartz tube. Prior to heating, the system was checked by vacuum meter, in order to ensure that the air had been removed by the vacuum pump. Then, the flow of nitrogen was activated and the heating process was started. After the furnace had reached the temperature of boriding 800 1C (1073 K), 900 1C (1173 K), or 1000 1C (1273 K), H2 was fed through the quartz tube at a flow rate of 50 l/h. The gases of high purity were used (nitrogen 6.0 and hydrogen 6.0). Then, the addition of BCl3 was realized during the process of boronizing. The relatively high ratio of BCl3 to the hydrogen was used (about 1:10). The amount of BCl3 resulted from its temperature, which was measured by thermometer resistor PT100 located on the gas cylinder. BCl3 was added to H2 atmosphere for 80, 120, 160 or 240 min. After boriding the specimens were slowly cooled in a nitrogen atmosphere. 3.3. Formation of single-phase boride layers (Fe2B) In order to form single-phase boride layers, the two-stage process was carried out. The first step consisted in gas boriding in H2-BCl3 atmosphere. The ratio of BCl3 to the hydrogen amounted to 1:10. The process was continued at 900 1C (1173 K) for 2 h. Then the boriding finished and the second step, diffusion annealing in H2 atmosphere, commenced. During this stage, carried out at 900 1C (1173 K), the delivery of boron was stopped. The addition of BCl3 was switched off. This stage lasted 2, 4, 6, 8 or 10 h. Then, the specimens were cooled in a nitrogen atmosphere.
200
M. Kulka et al. / Journal of Solid State Chemistry 199 (2013) 196–203
Fig. 3. Devices used for gas boriding.
Fig. 4. Principle of measurements of borides’ thickness; OM microstructure of borided layer formed on Fe in result of gas boriding in H2-BCl3 atmosphere at 1273 K for 2 h.
3.4. Measurements of boride layer thickness The microstructures of polished and etched cross-sections of the specimens were observed by an optical microscope (OM). The thickness of boride layer obtained was analyzed. Of about 100 measurements were performed for parameters of boriding used [28]. The needle-like microstructure of borides was the main problem during measuring. The results of the measurements were averaged. The principle of measurements was shown in Fig. 4.
4. Results and discussion 4.1. Formation of two-phase boride layers (FeB þFe2B) The microstructure of boride layer, formed on Fe as a consequence of gas boriding, consisted of two phases: FeB at the
surface and Fe2B below. In detail, the influence of boriding temperature and time of boriding on the microstructure was reported in the paper [28]. The microstructure of borided layers formed during gas boriding for the time of 2 h was shown in Fig. 5, at the respective temperatures: 1073, 1173 and 1273 K. The growth of FeB and Fe2B phases was observed with the increasing of boriding temperature. The results of measurements of boride zones’ thickness [28], XFeB and Y Fe2 B , were used for determination of parabolic growth constants AFeB and BFe2 B in presented study. It was assumed that straight lines of the growth of zones FeB and Fe2B in the coordinate systems: X2FeB t and Y 2Fe2 B 2t intersect the coordinate axes in the zero point (0,0). The values of parabolic growth constants, AFeB and BFe2 B , were determined for each temperature used. The linear dependence of parabolic growth constants on temperature was accepted and presented in Fig. 6. The equations are as follows (with the
M. Kulka et al. / Journal of Solid State Chemistry 199 (2013) 196–203
201
Fig. 6. Parabolic growth constants AFeB and BFe2 B vs. temperature.
Fig. 5. OM microstructure of boride layers formed on Fe during gas boriding for 2 h, at the respective temperatures: 1073, 1173 and 1273 K. Fig. 7. Averaged squares of boride zones thickness XFeB (a) and Y Fe2 B (b) vs. boriding time at different temperature.
correlation factors 0.9834 and 0.9951, respectively): AFeB ¼ 0:9175 103 UT0:79269
ð8aÞ
BFe2B ¼ 2:0793 103 UT2:0325
ð8bÞ
where: T—absolute temperature [K]. The averaged squares of thickness of boride zones versus the boriding time were presented in Fig. 7. Better compatibility with the model was obtained for the thickness of the FeB phase (Fig. 7a). The results for Fe2B zone (Fig. 7b) indicated the need of taking the incubation time into account in the future. According to the paper [2], using the Eqs. (1a) and (1b) and accepting cB,Fe=Fe2 B 0 and cB,Fe2 B=FeB cB,Fe2 B=Fe 0, there is the possibility of notation: C FeB ¼ DFeB B U c B,s=FeB cB,FeB=Fe2 B ¼ 2UAFeB U AFeB UcB,FeB=Fe2 B þBFe2 B UcB,Fe2 B=Fe 2B U cB,Fe2 B=FeB cB,Fe2 B=Fe C Fe2 B ¼ DFe B ¼ 2UBFe2 B U AFeB þ BFe2 B UcB,Fe2 B=Fe
The concentrations cB,s=FeB cB,FeB=Fe2 B and cB,Fe2 B=FeB cB,Fe2 B=Fe can be calculated for boriding of pure Fe from lattice parameter data. According to the paper [2], these values are as follows: cB,s/FeB ¼ 100.5 103 mol m 3, cB,Fe2B/FeB ¼59.8 103 mol m 3. It is assumed that expressions: cB,s=FeB cB,FeB=Fe2 B and cB,Fe2 B=FeB cB,Fe2 B=Fe , do not depend significantly on temperature (in the temperature range applied) [2]. Therefore, the diffusion coefficients, DFeB and DB Fe2 B , play the most important role, conB sidering the dependence of CFeB and C Fe2 B on temperature. So, Arrhenius-type temperature relationships for the diffusion coefficients can be adopted [2]: C FeB ¼ kFeB Uexp Q FeB =RT ð10aÞ
ð9aÞ
C Fe2 B ¼ kFe2 B Uexp Q Fe2 B =RT
ð9bÞ
where: kFeB, kFe2 B —pre-exponential constants, QFeB, Q Fe2 B — the activations energies [J/mol], R¼8.3144621—gas constant [J/(mol K)], T—absolute temperature [K].
ð10bÞ
202
M. Kulka et al. / Journal of Solid State Chemistry 199 (2013) 196–203
As a consequence, the activation energies (QFeB and QFe2B) and preexponential factors (kFeB and kFe2B) can be calculated from the slopes and intercepts of the straight lines shown in coordinate systems: ln CFeB–1/T and ln C Fe2 B –1/T. The values of CFeB and C Fe2 B derived from Eqs. (9a) and (9b) can be taken into account. The values of ln CFeB and ln C Fe2 B , as a function of reciprocal boriding temperature, are presented in Fig. 8. The linear relationships are assumed (with the correlation factors 0.9963 and 0.9913, respectively). The determined activation energies are as follows: QFeB ¼87,867 J/mol and Q Fe2 B ¼117,508 J/mol. The values of kFeB and kFe2 B were equal to 23.2 10 5 mol m 1 s 1 and 512.51 10 5 mol m 1 s 1, respectively. Therefore, the following relationships can be accepted: C FeB ¼ 23:2 105 Uexp 87,867=RT ð10cÞ C Fe2 B ¼ 512:51 105 Uexp 117,508=RT
ð10dÞ
The values of activation energy obtained are lower than thosepresented in the paper [2] (175 and 156 kJ/mol, respectively) as a consequence of powder boriding. However, in comparison with other data derived from gas boriding (QFeB ¼82.5 kJ/mol and Q Fe2 B ¼105.5 kJ/mol) [41], a large compatibility was observed. 4.2. Formation of single-phase boride layers (Fe2B) The experimental results of boride layer thickness obtained after gas boriding followed by diffusion annealing [28] were shown in Fig. 9. The initial averaged thicknesses of FeB and Fe2B zones were 44.12 and 58.82 mm, respectively. It resulted from the parameters of gas boriding used. The increase in duration of diffusion annealing caused the reduction of FeB borides and
Fig. 10. Calculated and measured thickness of boride zones (XFeB, Y Fe2 B and XFeB þY Fe2 B ) vs. the reduction in FeB phase.
growth of Fe2B thickness. After 2 h of annealing the thickness of FeB phase reduced to 10 mm. Simultaneously, increasing the thickness of Fe2B boride (up to 124 mm) was observed. Therefore, the overall thickness of borides (FeBþFe2B) increased up to 134 mm. The increase in the duration of annealing caused the total elimination of the FeB phase. Then the overall thickness of borides decreased to about 120 mm. Assuming that: cB,FeB=Fe2 B cB,s=FeB ,cB,Fe2 B=Fe cB,Fe2 B=FeB and cB,Fe=Fe2 B 0, Eq. (7) can be rewritten: dY Fe2 B ¼
cB,s=FeB UdX FeB cB,Fe2 B=FeB
ð11aÞ
Substituting cB,s/FeB ¼100.5 103 mol m 3 and cB,Fe2 B=FeB ¼ 59.8 103 mol m 3 [2], the relationship between the size of the reduction in the FeB zone (dXFeB) and size of the growth of the Fe2B phase (dY Fe2 B ) is as follows dY Fe2 B ¼ 1:68UdX FeB
ð11bÞ
The calculated and measured thickness of boride layer (XFeB, Y Fe2 B and XFeB þY Fe2 B ) as a function of reduction in FeB phase (dXFeB) was presented in Fig. 10. The experimental data were comparable to these calculated values. The calculated thickness of FeB phase (XFeB) was obvious and depended on the assumed reduction in this phase (DXFeB) and the initial thickness of FeB zone (44.12 mm): Fig. 8. Values of ln CFeB and ln C Fe2 B vs. 1/T.
X FeB ¼ DX FeB þ 44:12
ð12Þ
The calculated thickness of Fe2B phase (Y Fe2 B ) took the Eq. (11b) and initial thickness of Fe2B phase (58.82 mm) into account: Y Fe2 B ¼ 1:68UDX FeB þ 58:82
ð13Þ
The calculated overall thickness (XFeB þY Fe2 B ) corresponded to the sum of the thickness of both borides: X FeB þY Fe2 B ¼ DX FeB þ 44:12 þ 1:68UDX FeB þ 58:82 ¼ 0:68UDX FeB þ102:94
ð14Þ
Making the same assumptions (cB,Fe=Fe2 B 0,cB,FeB=Fe2 B cB,s=FeB , and cB,Fe2 B=Fe cB,Fe2 B=FeB ) and using the Eqs. (9b) and (10b), the formula (5) can be modified as follows: cB,s=FeB cB,Fe2 B=FeB UX FeB UY Fe2 B ð15Þ t XFeB ¼ 0 ¼ kFe2 B Uexp Q Fe2 B =RT
Fig. 9. Thickness of boride layer as a consequence of diffusion annealing [28].
Substituting the values previously calculated, assumed and obtained (Q Fe2 B ¼117,508 J/mol, kFe2 B ¼512.51 10 5 mol m 1 s 1, cB,s/FeB ¼100.5 103 mol m 3, cB,Fe2B/FeB ¼59.8 103 mol m 3, XFeB ¼ 44.12 mm and Y Fe2 B ¼58.82 mm), the time needed for the total
M. Kulka et al. / Journal of Solid State Chemistry 199 (2013) 196–203
elimination of FeB phase was about 1 h. The detailed calculation was shown below: tXFeB ¼ 0 ¼
ð100:559:8Þ 103 ½mol m3 44:12 106 ½m 58:82 106 ½m 117,508½Jmol1 512:51 105 mol m1 s1 exp 1 1 8:314462½Jmol
K
1173½K
ð15aÞ t XFeB ¼ 0 ¼
10562:2 108 ½mol m1 2:99963 108 ½mol m1 s1
¼ 3521:172½s ¼ 0:9781 h
ð15bÞ The experimental data, obtained in the paper [28], indicated that this duration was longer (above 2 h). Perhaps, a time was needed in order to commence the reduction in FeB phase during diffusion annealing. It could also indicate the need to take the incubation time into account in the model of boronizing. Then, calculated values of the activation energy would be different and would influence the time tXFeB ¼ 0 obtained. Not taking the gradient of boron concentration in borides into account could also be significant. The proposed model of diffusion annealing assumed a simplification. The gradual reduction in gradient of boron concentration in FeB phase (until the concentration of boron was equalized in the entire phase) did not take into account during this process. The decrease in this gradient could impede the reduction of the FeB borides during the initial stage of annealing.
5. Summary and conclusions The model of growth kinetics of two-phase boride layer (FeB þFe2B) on pure Fe was proposed for gas boriding. The main assumptions were adopted based on work [2], which reported this model for the powder boronizing. The gas boriding provided a constant composition of the atmosphere, and thus a constant diffusion flux from the boriding medium. Assuming that incubation time of borides was negligible small, an analytical solution of the set of differential Eqs. (1a) and (1b) was found. Basing on the experimental data [28], the parabolic growth constants AFeB and BFe2 B were determined for each temperature of boriding used. The linear profiles of parabolic growth constants versus temperature were accepted within the range of temperature 1073–1273 K. As a consequence, the activation energies (QFeB and Q Fe2 B ) were also calculated. The values obtained were lower than those-presented in the paper [2] for powder boriding. However, the calculated activation energies were comparable with other data derived from gas boriding [41]. The presented model can be applied to predict the thicknesses of the FeB and Fe2B zones (XFeB and Y Fe2 B ) formed on pure Fe during gas boriding. However, in the future, the incubation time should be taken into account. The parabolic growth constant, obtained for Fe2B phase (BFe2 B ), did not correspond well to experimental data, especially for temperature 1273 K. The model of diffusion annealing, carried out after gas boriding in order to form the single-phase boride layer (Fe2B), was also presented. During this process, the reduction in FeB phase was
203
observed. Simultaneously, the thickness of Fe2B borides increased. The interdependence between these phenomena was determined. The calculated time, needed for the total reduction in FeB phase, was equal to about 1 h. The experimental data shown that duration of diffusion annealing in order to eliminate the entire FeB zone was longer (above 2 h). The obtained divergences necessitate developing the model of growth kinetics of boride layers during gas boriding. The incubation time and the gradient of the boron concentration in borides should be taken into consideration. References [1] C. Wagner, in: W. Jost (Ed.), Diffusion in Solids, Liquids and Gases, Academic Press Inc., New York, 1960, pp. 71–72. [2] G. Brakman, A.W.J. Gommers, E.J. Mittemeijer, J. Mater. Res. 4 (6) (1989) 1354–1370. [3] E. Fromm, Z. Metallkd. 57 (1966) 60–65. [4] M. Hillert, M. Waldenstroem, Scand. J. Metall. 6 (1977) 211–218. [5] G.V. Kidson, J. Nucl. Mater. 3 (1961) 21–29. [6] U. Roy, Acta Metall. 16 (1968) 243–253. [7] A.K. Sarkhel, L.L. Seigle, Metall. Trans. A 7A (1976) 899–902. [8] S.R. Shatynski, J.P. Hirth, R.A. Rapp, Acta Metall. 24 (1976) 1071–1078. [9] C. Wagner, Acta Metall. 17 (1969) 99–107. [10] D.S. Wiliams, R.A. Rapp, J.P. Hirth, Metall. Trans. A 12 (1981) 639–652. [11] M. Keddam, S.M. Chentouf, Appl. Surf. Sci. 252 (2005) 393–399. [12] M. Keddam, Int. J. Mater. Res. 100 (2009) 901–905. [13] O. Kayacan, S. Sahin, F. Tastan, Math. Comput. Appl. 15 (2010) 14–24. [14] R.D. Ramdan, T. Takaki, K. Yashiro, Y. Tomita, Mater. Trans. 51 (2010) 62–67. [15] R.D. Ramdan, T. Takaki, Y. Tomita, Mater. Trans. 49 (2008) 2625–2631. [16] M. Keddam, Defect Diffus. Forum 273–276 (2008) 318–322. [17] I. Campos, M. Islas, G. Ramirez, L. Zuniga, C. VillaVelazquez, C. Mota, Appl. Surf. Sci. 253 (2007) 6226–6231. [18] I. Campos, G. Ramirez, U. Figueroa, C.V. Velazquez, Surf. Eng. 23 (2007) 216–222. [19] I. Campos, G. Ramirez, U. Figueroa, J. Martinez, O. Morales, Appl. Surf. Sci. 253 (2007) 3469–3475. [20] I. Campos-Silva, M. Ortiz-Dominguez, M. Keddam, N. Lopez-Perrusquia, A. Carmona-Vargas, M. Elias-Espinosa, Appl. Surf. Sci. 255 (2009) 9290–9295. [21] M. Keddam, Appl. Surf. Sci. 253 (2006) 757–761. [22] I. Campos, O. Bautista, G. Ramirez, M. Islas, J. de La Parra, L. Zuniga, Appl. Surf. Sci. 243 (2005) 429–436. [23] L.G. Yu, X.J. Chen, K.A. Khor, Acta Mater. 53 (2005) 2361–2368. [24] M. Keddam, Appl. Surf. Sci. 236 (2004) 451–455. [25] I. Campos, J. Oseguera, U. Figueroa, J.A. Garcia, O. Bautista, G. Keleminis, Mater. Sci. Eng. A 352 (2003) 261–265. [26] D.S. Kukharev, S.P. Fizenko, S.I. Shabunya, J. Eng, Phys. Thermophys. 69 (1996) 187–193. [27] M. Keddam, Appl. Surf. Sci. 257 (2011) 2004–2010. [28] A. Pertek, The Structure Formation and the Properties of Boronized Layers Obtained in Gaseous Boriding Process, Dissertation no. 365, Publishing House of Poznan University of Technology, Poznan, 2001. [29] A. Pertek, M. Kulka, Appl. Surf. Sci. 102 (2002) 252–260. [30] A. Pertek, M. Kulka, J. Mater. Sci. 38 (2003) 27–269. [31] A. Pertek, M. Kulka, Surf. Coat. Technol. 173 (2003) 309–314. [32] M. Kulka, A. Pertek, Appl. Surf. Sci. 214 (2003) 161–171. [33] M. Kulka, A. Pertek, L. Klimek, Mater. Charact. 56 (3) (2006) 232–240. [34] M. Kulka, A. Pertek, Appl. Surf. Sci. 218 (2003) 113–122. [35] M. Kulka, A. Pertek, Appl. Surf. Sci. 254 (2008) 5281–5290. [36] M. Kulka, A. Pertek, N. Makuch, Mater. Sci. Eng. A 528 (2011) 8641–8650. [37] B. Kastner, K. Przyby"owicz, I. Grygoruk, Haerterei-Tech. Mitt. 34 (4) (1979) 173–179. [38] H. Kunst, O. Schaaber, Haerterei-Tech. Mitt. 22 (1) (1967) 1–25. [39] F. Hegewaldt, L. Singheiser, M. Tuerk, Haerterei-Tech. Mitt. 39 (1984) 7–15. [40] A. Pertek, Mater. Sci. Forum 163–165 (1994) 323–328. ¨ ¨ ¨ [41] H. Planitz, G. Treffer, H. Konig, G. Marx, Neue Hutte 27 (1982) 228–230.
Contents lists available at SciVerse ScienceDirect
Journal of Solid State Chemistry journal homepage: www.elsevier.com/locate/jssc
Simulation of the growth kinetics of boride layers formed on Fe during gas boriding in H2-BCl3 atmosphere M. Kulka a,n, N. Makuch a, A. Pertek a, L. Ma"dzin´ski b a b
Poznan University of Technology, Institute of Materials Science and Engineering, Pl. M.Sklodowskiej-Curie 5, Poznan 60-965, Poland Poznan University of Technology, Institute of Machines and Motor Vehicles, Piotrowo Street 3, Poznan 60-965, Poland
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 October 2012 Received in revised form 24 December 2012 Accepted 24 December 2012 Available online 7 January 2013
The modeling of the boriding kinetics is considered as a necessary tool to select the suitable process parameters for obtaining boride layer of an adequate thickness. Therefore, the simulation of the growth kinetics of boride layers has gained much attention for last years. The majority of the published works described the kinetics of the pack-boriding or paste-boriding. In this study, the model of growth kinetics of two-phase boride layer (FeB þ Fe2B) on pure Fe was proposed for gas boriding. Displacements of the two interfaces (FeB/Fe2B and Fe2B/substrate) resulted from a difference of the arrival flux of interstitial boron atoms to one phase and the departure flux of the boron atoms from this phase to the second phase. The mass balance equations were formulated. The measurements of thickness of both zones (FeB and Fe2B), for different temperature of boriding, were used for calculations. Based on the experimental data, the parabolic growth constants AFeB and BFe2 B versus the temperature of boriding were determined. The linear relationships were accepted. As a consequence, the activation energies (QFeB and Q Fe2 B ) were calculated. The calculated values were comparable to other data derived from gas boriding. The presented model can predict the thicknesses of the FeB and Fe2B zones (XFeB and Y Fe2 B , respectively) formed on pure Fe during gas boriding. Additionally, the diffusion annealing after boriding was analyzed. This process was carried out in order to obtain a single-phase boride layer (Fe2B). The relationship between the reduction in FeB zone (dXFeB) and the growth in Fe2B phase (dY Fe2 B ) was determined. The time tXFeB ¼ 0, needed for the total elimination of FeB phase in the boride layer was calculated and compared to the experimental data. & 2013 Elsevier Inc. All rights reserved.
Keywords: Gas boriding Boride layers Growth kinetics Parabolic growth constants Activation energy Diffusion annealing
1. Introduction The diffusion boriding is a surface hardening of ferrous and nonferrous alloys to improve their surface properties. In this process, the boron atoms are introduced into the material surface to form a hard layer consisting of borides. Generally, the growth kinetics of solid phases (or zones) in single, two- and multi-phase systems, is controlled by diffusion of elements occurring in these phases. A speed of the displacement of interfaces is being analyzed depending on diffusion fluxes of elements to these interfaces and from them. It is being assumed that balance of diffusion fluxes of diffusing elements (penetrating into individual phase and leaving this phase) is determining the growth (or reduction) of phases, that is after all—their thickness after the process. If only one element participates in the diffusion or diffusion of the second element is negligible small in relation to the first element, then balance of diffusion fluxes is reduced to an
n
Corresponding author. E-mail address: [email protected] (M. Kulka).
0022-4596/$ - see front matter & 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jssc.2012.12.029
arrival flux providing the element to the phase (or phases) at the interface and a departure flux taking away this element from this phase. Mathematical model of the single-phase growth (of the single zone on the saturated substrate) for the first time was drawn up by Wagner [1] in order to determine the diffusion coefficient. In the later period, a significant number of models of the growth turned up at literature. These models concerned twoor more phases, assuming diffusion of one element of the system, as well as several elements [2–10]. The modeling of the boriding kinetics is considered as a necessary tool to select the suitable process parameters for obtaining boride layer of adequate thickness. It is very important for the practical applications of boriding. Therefore, the modeling of the growth kinetics of boride layers has gained much attention to simulate the boriding kinetics for last years. For this reason, many different models [11–27] were reported in the literature. The majority of these papers described the kinetics of pack-boriding [11,23,27] or pasteboriding [12,18,21,22,24,25]. However, during these processes, the composition of the produced atmosphere is not constant. Therefore, the diffusion flux from the boriding medium can be changeable for a time of boriding. It is very difficult to assess to
M. Kulka et al. / Journal of Solid State Chemistry 199 (2013) 196–203
what extent it affects diffusion model. During the gas boriding, the composition of boriding medium can be controlled [28–36]. There is a possibility of keeping this composition on the constant level. It provides the stability of the diffusion flux from the boriding medium. The results of many papers indicate that gradient of boron concentration does not occur along the needles of iron borides [37,38] and the boron diffuses along the grain boundaries. In this case, the presented model could not be applied. However, according to other opinions [2,11–27], a small gradient of boron concentration in the iron borides (about 1 at% B) is possible. Therefore, in this study, the kinetic model of twophase growth on saturated and non-saturated substrate was used in order to simulate the growth kinetics of boride layers. The thermodynamics and kinetics of gas boriding influenced the microstructure obtained. The possibilities of boride layer producing resulted from these conditions [28,39]. The process of boriding with the use of H2-BCl3 atmosphere was studied in the paper [28]. Based on the thermodynamic analysis, there was a possibility of controlling the activity of boron during boronizing in H2-BCl3 atmosphere. When the content of BCl3 in the atmosphere increased or the temperature decreased, the boron activity diminished [28]. Then, the decrease of boron potential was obtained. Theoretically, the use of lower boron potential of atmosphere could produce a singlephase boride layer. It required the relatively high BCl3 content in the atmosphere. However, within the temperature range usually used during gas boronizing 800–1000 1C (1073–1273 K), BCl3 content higher than 5 vol% provided the boride layers with a larger porosity. The considerable quantity of ferrous and ferric chlorides in atmosphere was the reason for this porosity and brittleness. Therefore, the content of BCl3 below 5 vol% in H2-BCl3 atmosphere was the most advisable. The highest acceptable BCl3 content, taking the porosity into account, was equal to about 10 vol%. In these conditions, the activity of boron was equal to 1, within the analyzed temperature range. Such a situation, in result of continuous gas boriding, always caused the formation of two-phase boride layer of good quality (without porosity). The diffusion annealing after boriding was the only method, which could produce the singlephase boride layer in case of gas boriding. In this process, the reduction of FeB borides was possible. As a consequence, a singlephase (Fe2B) boride layer could be produced. Some problems concerning the thermodynamics and kinetics of gas boriding in N2-H2-BCl3 atmosphere were also examined [39]. The gas boriding was carried out at the temperature of 800 1C (1073 K). The conclusions were similar. Too high BCl3 content also provided the boride layer with large porosity due to the considerable quantity of FeCl2 in atmosphere. The single-phase boride layer was also formed as a consequence of diffusion annealing, carried out after boriding. In this paper, the two-stage process (boriding þdiffusion annealing) was analyzed. The growth kinetics of two-phase boride layer on the ferrous substrate was studied during the gas boriding in H2-BCl3 atmosphere. The parabolic growth constants of FeB and Fe2B zones were determined. The activation energies regarding the both iron borides were calculated and compared to literature data. The presented model was formulated to predict the thickness of the FeB and Fe2B borides formed on pure Fe. Simultaneously, the kinetics of the second stage (diffusion annealing) was also presented. This step provided the boride layer with single-phase structure (Fe2B).
2. The diffusion model 2.1. Formation of two-phase boride layer (FeB þFe2B) The process consists in diffusion boriding in H2-BCl3 atmosphere for a time. The growth of two phases (FeB and Fe2B) with
197
one diffusing element (boron) is observed. Therefore, for analysis, the kinetic model of two-phase growth on saturated and nonsaturated substrate will be used [2] (modified model described by Fromm [3]). This model will be discussed regarding the boride layer that consists of phases (borides) FeB and Fe2B, formed on pure Fe. The model is imposing the following restrictions:
the growth of boride layer is being controlled exclusively by boron diffusion in FeB and Fe2B zones;
the participation of diffusion of Fe-atoms is negligible small; the growth of boride layer is a consequence of the boron diffusion perpendicular to the sample surface;
the solubility of boron in the substrate is equal to zero or the substrate is saturated with boron;
a linear concentration-profile of boron is assumed through the FeB and Fe2B zones;
the surface boron concentration, cB,s/FeB and boron concentra-
tions at the interfaces: FeB/Fe2B/Fe, relatively: cB,FeB=Fe2 B , cB,Fe2 B=FeB and cB,Fe2 B=Fe , are independent of temperature (are constant) and equal to: cB,s/FeB ¼100.5 103 mol m 3, cB,Fe2 B=FeB ¼59.8 103 mol m 3; the range of homogeneity of both zones is small and is equal to about 1 at% B; a local equilibrium is attained at the moving interfaces; the planar morphology is assumed for the phase interfaces; the volume change during the phase transformation is not considered; the diffusion coefficient of boron in each iron boride is independent of concentration and follows an Arrhenius relationship; a uniform temperature is assumed throughout the sample; the presence of porosity is neglected during the boron diffusion; the effect of the boride incubation time on the kinetics of the boriding is not taking into account.
The layer growth kinetics during a diffusion-controlled phase transformation in the Fe–B system can be analyzed by considering the displacement of the two interfaces (FeB/Fe2B and Fe2B/substrate) between the adjacent phases, due to a difference of the arrival flux of interstitial boron atoms to one phase and the departure flux of the boron atoms from this phase to the next phase. The mass balance equations should be then described. The considered model will be discussed with the help of Fig. 1. The growth of the surface-FeB zone (towards the core), caused by the infinitesimal dXFeB-segment during dt, is accompanied by an accumulation of B atoms what is marked as gray area in Fig. 1. This accumulation is being determined by the difference of boron diffusion fluxes: from the boriding medium, to the FeB zone, JFeB B 2B and from the FeB zone to Fe2B, JFe . By analogy, the growth of the B Fe2B zone during the same dt, for the infinitesimal dY Fe2 B -segment, is accompanied by an accumulation of B atoms, also marked with gray color in Fig. 1. This accumulation is a result of diffusion flux 2B from FeB zone to Fe2B, JFe . In case of the diffusion of B atoms from B the Fe2B zone into base material (Fe), the increase in the Fe2B zone is being additionally determined by diffusion flux from the Fe2B zone to this substrate (Fe), JFe B . However, the model considers the (FeB/Fe2B) bilayer growth on the substrate saturated with boron atoms. In this case, the diffusion flux JFe B is equal to zero. Therefore, according to the law of mass conservation, the growth of considered zones (FeB and Fe2B) on Fe can be described by the set of two differential equations, mutually dependent [3]. Based on Fig. 1 it is possible to write these equations into the following way: 1 cB,FeB=Fe2 B cB,Fe2 B=FeB þ cB,s=FeB cB,FeB=Fe2 B U 2
198
M. Kulka et al. / Journal of Solid State Chemistry 199 (2013) 196–203
Fig. 1. Diagram of growth of boride layer (FeB/Fe2B/Fe zones) during gas boriding.
cB,s=FeB cB,FeB=Fe2 B Fe2 B c B,Fe2 B=FeB c B,Fe2 B=Fe dX FeB ¼ DFeB D Udt B B X FeB Y Fe2 B ð1aÞ
1 cB,Fe2 B=FeB cB,Fe2 B=Fe U cB,Fe2 B=Fe cB,Fe=Fe2 B þ 2 Fe2 B cB,Fe2 B=FeB c B,Fe2 B=Fe Udt dY Fe2 B ¼ DB Y Fe2 B cB,Fe2 B=Fe cB,Fe=Fe2 B þ cB,Fe2 B=FeB cB,Fe2 B=Fe ÞUdX FeB DFeB B ,
ð1bÞ
Fe2 B
DB —effective diffusion coefficients of boron in FeB where: and Fe2B zones, cB,s/FeB—surface boron content in FeB zone at the interface: gas phase/solid phase, cB,FeB=Fe2 B —boron content in FeB zone at the interface: FeB/Fe2B, cB,Fe2 B=FeB —boron content in Fe2B zone at the interface: Fe2B/FeB, cB,Fe2 B=Fe —boron content in Fe2B zone at the interface: Fe2B/Fe, cB,Fe=Fe2 B —boron content in the substrate (Fe) at the interface: Fe/Fe2B. Relationships which are solving the above set of differential equations are as follows X FeB ¼ 2UAFeB Ut 1=2
ð2aÞ
Y Fe2 B ¼ 2UBFe2 B Ut 1=2
ð2bÞ
where: XFeB, Y Fe2 B —thickness of FeB and Fe2B zones, respectively, AFeB, BFe2 B —parabolic growth constants, dependent only on the chemical composition (concentrations of boron) at the surface and at the interfaces and on diffusion coefficients, t—time of boriding. Solution (2a and 2b) is imposing the following conditions:
the growth in both phases (FeB and Fe2B) have to start
simultaneously since the time of the t ¼0, that is from the moment of commencing the process; the boron concentration in FeB phase at the surface (also at interfaces) at the time of t ¼0 has a maximum value; diffusion flux of boron to the substrate (Fe) is equal to zero.
At fulfilling above relations, according to relations (2a) and (2b), straight lines of the growth of zones FeB and Fe2B in the coordinate systems: X2FeB–t and Y 2Fe2 B –t (after the extrapolation until the t¼ 0) should intersect point with coordinates (0,0). In real conditions above relations are not fulfilled. Before the considered phases will appear on the surface, their nucleation and coagulation occur till the surface will be completely covered with borides. The maximum concentration of boron on the surface
(in the FeB phase) will be obtained after a still longer time. In such a situation, instead of analytical, the numerical methods are necessary in order to solve the Eqs. (1a) and (1b). The effect of the boride incubation time on the kinetics of the process was presented in paper [27]. It was assumed that incubation time of FeB phase was longer than incubation time of Fe2B borides. However, basing on the paper [40], in case of gas boriding, FeB boride was the first phase appearing in boride layer. The nucleation of FeB boride occurred promptly on the surface of the iron or steel after a short time of boriding (about 4 s). After 8 s of boriding, both phases (FeBþFe2B) coexisted, and the entire surface of the sample was full of the crystal nuclei of borides. Next, the growth of the crystal nuclei in two directions was observed: perpendicular to the surface (privileged direction) and parallel to the surface. Within a few minutes, the growth of crystal nuclei caused the formation of a continuous boride layer [40]. Therefore, the effect of the boride incubation time on the kinetics of the boriding was omitted in the presented model. 2.2. Diffusion annealing in order to form single-phase boride layer (Fe2B) The diffusion annealing of previously produced borided layer should be performed in order to form the single-phase boride layer. During this process, carried out in H2 atmosphere, the providing of BCl3 is stopped and so the diffusion flux JFeB from the B boriding medium to the FeB zone is equal to zero. It is being assumed that a process of deboriding is not appearing, that is, the diffusion flux from the solid phase up to the gaseous phase does not exist. Therefore, the growth in the Fe2B phase is possible exclusively as a result of the reduction in the FeB phase. The reduction of this phase by the infinitesimal dXFeB-segment during dt was emphasized with gray color in Fig. 2. The growth in the Fe2B zone is being determined by diffusion flux of B atoms from the FeB zone to Fe2B, J BFe2 B . And so the growth of the Fe2B zone, caused by the infinitesimal segment dY Fe2 B during the same dt, is accompanied by an accumulation of B atoms, also marked with gray color in Fig. 2. Equations of mass balance are as follows: 1 cB,s=FeB cB,FeB=Fe2 B U cB,FeB=Fe2 B cB,Fe2 B=FeB þ 2 Fe2 B cB,Fe2 B=FeB cB,Fe2 B=Fe Udt ð3aÞ dX FeB ¼ DB Y Fe2 B 1 cB,Fe2 B=FeB cB,Fe2 B=Fe U cB,Fe2 B=Fe cB,Fe=Fe2 B þ 2
M. Kulka et al. / Journal of Solid State Chemistry 199 (2013) 196–203
199
Fig. 2. Reduction in FeB phase and growth of Fe2B phase during diffusion annealing.
cB,Fe2 B=FeB cB,Fe2 B=Fe Udt Y Fe2 B þ cB,Fe2 B=Fe cB,Fe=Fe2 B þ cB,Fe2 B=FeB cB,Fe2 B=Fe ÞUdX FeB
Table 1 Chemical composition of material used [wt%].
dY Fe2 ¼ DBFe2 B
ð3bÞ
From the Eq. (3a), knowing the concentration of boron at the interfaces (that is gradient of boron concentration), thickness of zones after the stage of saturating with boron (XFeB and Y Fe2 B ) and effective diffusion coefficient in Fe2B zone (DB Fe2 B ), it is possible to calculate the time tXFeB ¼ 0, needed for the total elimination of FeB phase in the boride layer (accepting dXFeB ¼XFeB). Integrating Eq. (3a): Z X FeB 1 cB,s=FeB cB,FeB=Fe2 B U cB,FeB=Fe2 B cB,Fe2 B=FeB þ 2 0 Z tXFeB ¼ 0 cB,Fe2 B=FeB cB,Fe2 B=Fe DBFe2 B Udt ð4Þ dX FeB ¼ Y Fe2 B 0 The following solution was received: 1 1 2 c B,FeB=Fe2 B c B,Fe2 B=FeB þ 2 cB,s=FeB UX FeB UY Fe2 B t XFeB ¼ 0 ¼ DBFe2 B U cB,Fe2 B=FeB cB,Fe2 B=Fe
ð5Þ
Assuming that the entire reduced FeB zone will result in the accumulation of boron in the Fe2B zone, it was possible to write (Fig. 2): cB,Fe2 B=Fe cB,Fe=Fe2 B þ 12 cB,Fe2 B=FeB cB,Fe2 B=Fe U dY Fe2 B ¼ cB,FeB=Fe2 B cB,Fe2 B=FeB þ 12 cB,s=FeB cB,FeB=Fe2 B UdX FeB þ cB,Fe2 B=Fe cB,Fe=Fe2 B þ cB,Fe2 B=FeB cB,Fe2 B=Fe ÞUdX FeB ð6Þ From Eq. (6) it was possible to determine the relationship between the size of the reduction in the FeB zone (dXFeB) and size of the growth of the Fe2B phase (dY Fe2 B ): 1 cB,FeB=Fe2 B þ 12cB,s=FeB cB,Fe=Fe2 B ð7Þ UdX FeB dY Fe2 B ¼ 21 1 2 cB,Fe2 B=Fe 2cB,Fe2 B=FeB cB,Fe=Fe2 B In real conditions above relations are not fulfilled. If the diffusion flux from the boriding medium up to the FeB phase (JFeB B ) is equal to zero, a gradient of the boron concentration in this phase is being reduced gradually during the process what is difficult to estimate. It is known that gradient of the concentration is disappearing after the certain time. The surface boron concentration (cB,s/FeB), at the interface: gas phase/solid phase, is decreasing gradually until the value corresponding to the cB,FeB=Fe2 B .
Material
C
Mn
Si
Cr
P
S
Ni
Cu
Fe (Armco iron)
0.035
0.20
0.22
0.10
0.025
0.025
0.12
0.10
3. Material and methods 3.1. Material Pure iron (Armco iron) was used for investigation. Its chemical composition was presented in Table 1. 3.2. Formation of two-phase boride layers (FeB þFe2B) Gas boriding was carried out in H2-BCl3 atmosphere [28] with the usage of devices presented in Fig. 3. The specimens were put into the quartz tube. Prior to heating, the system was checked by vacuum meter, in order to ensure that the air had been removed by the vacuum pump. Then, the flow of nitrogen was activated and the heating process was started. After the furnace had reached the temperature of boriding 800 1C (1073 K), 900 1C (1173 K), or 1000 1C (1273 K), H2 was fed through the quartz tube at a flow rate of 50 l/h. The gases of high purity were used (nitrogen 6.0 and hydrogen 6.0). Then, the addition of BCl3 was realized during the process of boronizing. The relatively high ratio of BCl3 to the hydrogen was used (about 1:10). The amount of BCl3 resulted from its temperature, which was measured by thermometer resistor PT100 located on the gas cylinder. BCl3 was added to H2 atmosphere for 80, 120, 160 or 240 min. After boriding the specimens were slowly cooled in a nitrogen atmosphere. 3.3. Formation of single-phase boride layers (Fe2B) In order to form single-phase boride layers, the two-stage process was carried out. The first step consisted in gas boriding in H2-BCl3 atmosphere. The ratio of BCl3 to the hydrogen amounted to 1:10. The process was continued at 900 1C (1173 K) for 2 h. Then the boriding finished and the second step, diffusion annealing in H2 atmosphere, commenced. During this stage, carried out at 900 1C (1173 K), the delivery of boron was stopped. The addition of BCl3 was switched off. This stage lasted 2, 4, 6, 8 or 10 h. Then, the specimens were cooled in a nitrogen atmosphere.
200
M. Kulka et al. / Journal of Solid State Chemistry 199 (2013) 196–203
Fig. 3. Devices used for gas boriding.
Fig. 4. Principle of measurements of borides’ thickness; OM microstructure of borided layer formed on Fe in result of gas boriding in H2-BCl3 atmosphere at 1273 K for 2 h.
3.4. Measurements of boride layer thickness The microstructures of polished and etched cross-sections of the specimens were observed by an optical microscope (OM). The thickness of boride layer obtained was analyzed. Of about 100 measurements were performed for parameters of boriding used [28]. The needle-like microstructure of borides was the main problem during measuring. The results of the measurements were averaged. The principle of measurements was shown in Fig. 4.
4. Results and discussion 4.1. Formation of two-phase boride layers (FeB þFe2B) The microstructure of boride layer, formed on Fe as a consequence of gas boriding, consisted of two phases: FeB at the
surface and Fe2B below. In detail, the influence of boriding temperature and time of boriding on the microstructure was reported in the paper [28]. The microstructure of borided layers formed during gas boriding for the time of 2 h was shown in Fig. 5, at the respective temperatures: 1073, 1173 and 1273 K. The growth of FeB and Fe2B phases was observed with the increasing of boriding temperature. The results of measurements of boride zones’ thickness [28], XFeB and Y Fe2 B , were used for determination of parabolic growth constants AFeB and BFe2 B in presented study. It was assumed that straight lines of the growth of zones FeB and Fe2B in the coordinate systems: X2FeB t and Y 2Fe2 B 2t intersect the coordinate axes in the zero point (0,0). The values of parabolic growth constants, AFeB and BFe2 B , were determined for each temperature used. The linear dependence of parabolic growth constants on temperature was accepted and presented in Fig. 6. The equations are as follows (with the
M. Kulka et al. / Journal of Solid State Chemistry 199 (2013) 196–203
201
Fig. 6. Parabolic growth constants AFeB and BFe2 B vs. temperature.
Fig. 5. OM microstructure of boride layers formed on Fe during gas boriding for 2 h, at the respective temperatures: 1073, 1173 and 1273 K. Fig. 7. Averaged squares of boride zones thickness XFeB (a) and Y Fe2 B (b) vs. boriding time at different temperature.
correlation factors 0.9834 and 0.9951, respectively): AFeB ¼ 0:9175 103 UT0:79269
ð8aÞ
BFe2B ¼ 2:0793 103 UT2:0325
ð8bÞ
where: T—absolute temperature [K]. The averaged squares of thickness of boride zones versus the boriding time were presented in Fig. 7. Better compatibility with the model was obtained for the thickness of the FeB phase (Fig. 7a). The results for Fe2B zone (Fig. 7b) indicated the need of taking the incubation time into account in the future. According to the paper [2], using the Eqs. (1a) and (1b) and accepting cB,Fe=Fe2 B 0 and cB,Fe2 B=FeB cB,Fe2 B=Fe 0, there is the possibility of notation: C FeB ¼ DFeB B U c B,s=FeB cB,FeB=Fe2 B ¼ 2UAFeB U AFeB UcB,FeB=Fe2 B þBFe2 B UcB,Fe2 B=Fe 2B U cB,Fe2 B=FeB cB,Fe2 B=Fe C Fe2 B ¼ DFe B ¼ 2UBFe2 B U AFeB þ BFe2 B UcB,Fe2 B=Fe
The concentrations cB,s=FeB cB,FeB=Fe2 B and cB,Fe2 B=FeB cB,Fe2 B=Fe can be calculated for boriding of pure Fe from lattice parameter data. According to the paper [2], these values are as follows: cB,s/FeB ¼ 100.5 103 mol m 3, cB,Fe2B/FeB ¼59.8 103 mol m 3. It is assumed that expressions: cB,s=FeB cB,FeB=Fe2 B and cB,Fe2 B=FeB cB,Fe2 B=Fe , do not depend significantly on temperature (in the temperature range applied) [2]. Therefore, the diffusion coefficients, DFeB and DB Fe2 B , play the most important role, conB sidering the dependence of CFeB and C Fe2 B on temperature. So, Arrhenius-type temperature relationships for the diffusion coefficients can be adopted [2]: C FeB ¼ kFeB Uexp Q FeB =RT ð10aÞ
ð9aÞ
C Fe2 B ¼ kFe2 B Uexp Q Fe2 B =RT
ð9bÞ
where: kFeB, kFe2 B —pre-exponential constants, QFeB, Q Fe2 B — the activations energies [J/mol], R¼8.3144621—gas constant [J/(mol K)], T—absolute temperature [K].
ð10bÞ
202
M. Kulka et al. / Journal of Solid State Chemistry 199 (2013) 196–203
As a consequence, the activation energies (QFeB and QFe2B) and preexponential factors (kFeB and kFe2B) can be calculated from the slopes and intercepts of the straight lines shown in coordinate systems: ln CFeB–1/T and ln C Fe2 B –1/T. The values of CFeB and C Fe2 B derived from Eqs. (9a) and (9b) can be taken into account. The values of ln CFeB and ln C Fe2 B , as a function of reciprocal boriding temperature, are presented in Fig. 8. The linear relationships are assumed (with the correlation factors 0.9963 and 0.9913, respectively). The determined activation energies are as follows: QFeB ¼87,867 J/mol and Q Fe2 B ¼117,508 J/mol. The values of kFeB and kFe2 B were equal to 23.2 10 5 mol m 1 s 1 and 512.51 10 5 mol m 1 s 1, respectively. Therefore, the following relationships can be accepted: C FeB ¼ 23:2 105 Uexp 87,867=RT ð10cÞ C Fe2 B ¼ 512:51 105 Uexp 117,508=RT
ð10dÞ
The values of activation energy obtained are lower than thosepresented in the paper [2] (175 and 156 kJ/mol, respectively) as a consequence of powder boriding. However, in comparison with other data derived from gas boriding (QFeB ¼82.5 kJ/mol and Q Fe2 B ¼105.5 kJ/mol) [41], a large compatibility was observed. 4.2. Formation of single-phase boride layers (Fe2B) The experimental results of boride layer thickness obtained after gas boriding followed by diffusion annealing [28] were shown in Fig. 9. The initial averaged thicknesses of FeB and Fe2B zones were 44.12 and 58.82 mm, respectively. It resulted from the parameters of gas boriding used. The increase in duration of diffusion annealing caused the reduction of FeB borides and
Fig. 10. Calculated and measured thickness of boride zones (XFeB, Y Fe2 B and XFeB þY Fe2 B ) vs. the reduction in FeB phase.
growth of Fe2B thickness. After 2 h of annealing the thickness of FeB phase reduced to 10 mm. Simultaneously, increasing the thickness of Fe2B boride (up to 124 mm) was observed. Therefore, the overall thickness of borides (FeBþFe2B) increased up to 134 mm. The increase in the duration of annealing caused the total elimination of the FeB phase. Then the overall thickness of borides decreased to about 120 mm. Assuming that: cB,FeB=Fe2 B cB,s=FeB ,cB,Fe2 B=Fe cB,Fe2 B=FeB and cB,Fe=Fe2 B 0, Eq. (7) can be rewritten: dY Fe2 B ¼
cB,s=FeB UdX FeB cB,Fe2 B=FeB
ð11aÞ
Substituting cB,s/FeB ¼100.5 103 mol m 3 and cB,Fe2 B=FeB ¼ 59.8 103 mol m 3 [2], the relationship between the size of the reduction in the FeB zone (dXFeB) and size of the growth of the Fe2B phase (dY Fe2 B ) is as follows dY Fe2 B ¼ 1:68UdX FeB
ð11bÞ
The calculated and measured thickness of boride layer (XFeB, Y Fe2 B and XFeB þY Fe2 B ) as a function of reduction in FeB phase (dXFeB) was presented in Fig. 10. The experimental data were comparable to these calculated values. The calculated thickness of FeB phase (XFeB) was obvious and depended on the assumed reduction in this phase (DXFeB) and the initial thickness of FeB zone (44.12 mm): Fig. 8. Values of ln CFeB and ln C Fe2 B vs. 1/T.
X FeB ¼ DX FeB þ 44:12
ð12Þ
The calculated thickness of Fe2B phase (Y Fe2 B ) took the Eq. (11b) and initial thickness of Fe2B phase (58.82 mm) into account: Y Fe2 B ¼ 1:68UDX FeB þ 58:82
ð13Þ
The calculated overall thickness (XFeB þY Fe2 B ) corresponded to the sum of the thickness of both borides: X FeB þY Fe2 B ¼ DX FeB þ 44:12 þ 1:68UDX FeB þ 58:82 ¼ 0:68UDX FeB þ102:94
ð14Þ
Making the same assumptions (cB,Fe=Fe2 B 0,cB,FeB=Fe2 B cB,s=FeB , and cB,Fe2 B=Fe cB,Fe2 B=FeB ) and using the Eqs. (9b) and (10b), the formula (5) can be modified as follows: cB,s=FeB cB,Fe2 B=FeB UX FeB UY Fe2 B ð15Þ t XFeB ¼ 0 ¼ kFe2 B Uexp Q Fe2 B =RT
Fig. 9. Thickness of boride layer as a consequence of diffusion annealing [28].
Substituting the values previously calculated, assumed and obtained (Q Fe2 B ¼117,508 J/mol, kFe2 B ¼512.51 10 5 mol m 1 s 1, cB,s/FeB ¼100.5 103 mol m 3, cB,Fe2B/FeB ¼59.8 103 mol m 3, XFeB ¼ 44.12 mm and Y Fe2 B ¼58.82 mm), the time needed for the total
M. Kulka et al. / Journal of Solid State Chemistry 199 (2013) 196–203
elimination of FeB phase was about 1 h. The detailed calculation was shown below: tXFeB ¼ 0 ¼
ð100:559:8Þ 103 ½mol m3 44:12 106 ½m 58:82 106 ½m 117,508½Jmol1 512:51 105 mol m1 s1 exp 1 1 8:314462½Jmol
K
1173½K
ð15aÞ t XFeB ¼ 0 ¼
10562:2 108 ½mol m1 2:99963 108 ½mol m1 s1
¼ 3521:172½s ¼ 0:9781 h
ð15bÞ The experimental data, obtained in the paper [28], indicated that this duration was longer (above 2 h). Perhaps, a time was needed in order to commence the reduction in FeB phase during diffusion annealing. It could also indicate the need to take the incubation time into account in the model of boronizing. Then, calculated values of the activation energy would be different and would influence the time tXFeB ¼ 0 obtained. Not taking the gradient of boron concentration in borides into account could also be significant. The proposed model of diffusion annealing assumed a simplification. The gradual reduction in gradient of boron concentration in FeB phase (until the concentration of boron was equalized in the entire phase) did not take into account during this process. The decrease in this gradient could impede the reduction of the FeB borides during the initial stage of annealing.
5. Summary and conclusions The model of growth kinetics of two-phase boride layer (FeB þFe2B) on pure Fe was proposed for gas boriding. The main assumptions were adopted based on work [2], which reported this model for the powder boronizing. The gas boriding provided a constant composition of the atmosphere, and thus a constant diffusion flux from the boriding medium. Assuming that incubation time of borides was negligible small, an analytical solution of the set of differential Eqs. (1a) and (1b) was found. Basing on the experimental data [28], the parabolic growth constants AFeB and BFe2 B were determined for each temperature of boriding used. The linear profiles of parabolic growth constants versus temperature were accepted within the range of temperature 1073–1273 K. As a consequence, the activation energies (QFeB and Q Fe2 B ) were also calculated. The values obtained were lower than those-presented in the paper [2] for powder boriding. However, the calculated activation energies were comparable with other data derived from gas boriding [41]. The presented model can be applied to predict the thicknesses of the FeB and Fe2B zones (XFeB and Y Fe2 B ) formed on pure Fe during gas boriding. However, in the future, the incubation time should be taken into account. The parabolic growth constant, obtained for Fe2B phase (BFe2 B ), did not correspond well to experimental data, especially for temperature 1273 K. The model of diffusion annealing, carried out after gas boriding in order to form the single-phase boride layer (Fe2B), was also presented. During this process, the reduction in FeB phase was
203
observed. Simultaneously, the thickness of Fe2B borides increased. The interdependence between these phenomena was determined. The calculated time, needed for the total reduction in FeB phase, was equal to about 1 h. The experimental data shown that duration of diffusion annealing in order to eliminate the entire FeB zone was longer (above 2 h). The obtained divergences necessitate developing the model of growth kinetics of boride layers during gas boriding. The incubation time and the gradient of the boron concentration in borides should be taken into consideration. References [1] C. Wagner, in: W. Jost (Ed.), Diffusion in Solids, Liquids and Gases, Academic Press Inc., New York, 1960, pp. 71–72. [2] G. Brakman, A.W.J. Gommers, E.J. Mittemeijer, J. Mater. Res. 4 (6) (1989) 1354–1370. [3] E. Fromm, Z. Metallkd. 57 (1966) 60–65. [4] M. Hillert, M. Waldenstroem, Scand. J. Metall. 6 (1977) 211–218. [5] G.V. Kidson, J. Nucl. Mater. 3 (1961) 21–29. [6] U. Roy, Acta Metall. 16 (1968) 243–253. [7] A.K. Sarkhel, L.L. Seigle, Metall. Trans. A 7A (1976) 899–902. [8] S.R. Shatynski, J.P. Hirth, R.A. Rapp, Acta Metall. 24 (1976) 1071–1078. [9] C. Wagner, Acta Metall. 17 (1969) 99–107. [10] D.S. Wiliams, R.A. Rapp, J.P. Hirth, Metall. Trans. A 12 (1981) 639–652. [11] M. Keddam, S.M. Chentouf, Appl. Surf. Sci. 252 (2005) 393–399. [12] M. Keddam, Int. J. Mater. Res. 100 (2009) 901–905. [13] O. Kayacan, S. Sahin, F. Tastan, Math. Comput. Appl. 15 (2010) 14–24. [14] R.D. Ramdan, T. Takaki, K. Yashiro, Y. Tomita, Mater. Trans. 51 (2010) 62–67. [15] R.D. Ramdan, T. Takaki, Y. Tomita, Mater. Trans. 49 (2008) 2625–2631. [16] M. Keddam, Defect Diffus. Forum 273–276 (2008) 318–322. [17] I. Campos, M. Islas, G. Ramirez, L. Zuniga, C. VillaVelazquez, C. Mota, Appl. Surf. Sci. 253 (2007) 6226–6231. [18] I. Campos, G. Ramirez, U. Figueroa, C.V. Velazquez, Surf. Eng. 23 (2007) 216–222. [19] I. Campos, G. Ramirez, U. Figueroa, J. Martinez, O. Morales, Appl. Surf. Sci. 253 (2007) 3469–3475. [20] I. Campos-Silva, M. Ortiz-Dominguez, M. Keddam, N. Lopez-Perrusquia, A. Carmona-Vargas, M. Elias-Espinosa, Appl. Surf. Sci. 255 (2009) 9290–9295. [21] M. Keddam, Appl. Surf. Sci. 253 (2006) 757–761. [22] I. Campos, O. Bautista, G. Ramirez, M. Islas, J. de La Parra, L. Zuniga, Appl. Surf. Sci. 243 (2005) 429–436. [23] L.G. Yu, X.J. Chen, K.A. Khor, Acta Mater. 53 (2005) 2361–2368. [24] M. Keddam, Appl. Surf. Sci. 236 (2004) 451–455. [25] I. Campos, J. Oseguera, U. Figueroa, J.A. Garcia, O. Bautista, G. Keleminis, Mater. Sci. Eng. A 352 (2003) 261–265. [26] D.S. Kukharev, S.P. Fizenko, S.I. Shabunya, J. Eng, Phys. Thermophys. 69 (1996) 187–193. [27] M. Keddam, Appl. Surf. Sci. 257 (2011) 2004–2010. [28] A. Pertek, The Structure Formation and the Properties of Boronized Layers Obtained in Gaseous Boriding Process, Dissertation no. 365, Publishing House of Poznan University of Technology, Poznan, 2001. [29] A. Pertek, M. Kulka, Appl. Surf. Sci. 102 (2002) 252–260. [30] A. Pertek, M. Kulka, J. Mater. Sci. 38 (2003) 27–269. [31] A. Pertek, M. Kulka, Surf. Coat. Technol. 173 (2003) 309–314. [32] M. Kulka, A. Pertek, Appl. Surf. Sci. 214 (2003) 161–171. [33] M. Kulka, A. Pertek, L. Klimek, Mater. Charact. 56 (3) (2006) 232–240. [34] M. Kulka, A. Pertek, Appl. Surf. Sci. 218 (2003) 113–122. [35] M. Kulka, A. Pertek, Appl. Surf. Sci. 254 (2008) 5281–5290. [36] M. Kulka, A. Pertek, N. Makuch, Mater. Sci. Eng. A 528 (2011) 8641–8650. [37] B. Kastner, K. Przyby"owicz, I. Grygoruk, Haerterei-Tech. Mitt. 34 (4) (1979) 173–179. [38] H. Kunst, O. Schaaber, Haerterei-Tech. Mitt. 22 (1) (1967) 1–25. [39] F. Hegewaldt, L. Singheiser, M. Tuerk, Haerterei-Tech. Mitt. 39 (1984) 7–15. [40] A. Pertek, Mater. Sci. Forum 163–165 (1994) 323–328. ¨ ¨ ¨ [41] H. Planitz, G. Treffer, H. Konig, G. Marx, Neue Hutte 27 (1982) 228–230.