Surface & Coatings Technology 225 (2013) 1–10

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Surface & Coatings Technology

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Chromium carbonitride coating produced on DIN 1.2210 steel by thermo-reactivedeposition technique: Thermodynamics, kinetics and modeling

Gholamreza Khalaj a, Ali Nazari b,⁎, Seyyed Mohammad Mousavi Khoie c,Mohammad Javad Khalaj a, Hesam Pouraliakbar d,e

a Department of Engineering, Saveh Branch, Islamic Azad University, Saveh, Iranb Modeling and Simulation Department, WorldTech Scientific Research Center (WT-SRC), Tehran, Iranc Mining and Metallurgical Department, Amirkabir University of Technology, P.O. Box 15875 4413, Tehran, Irand Advanced Materials Department, WorldTech Scientific Research Center (WT-SRC), Tehran, Irane Department of Materials Science and Engineering, Sharif University of Technology, Azadi Ave., Tehran, Iran

⁎ Corresponding author. Tel.: +98 912 2208049.E-mail address: anazari@worldtech-src.com (A. Naz

0257-8972/$ – see front matter © 2013 Elsevier B.V. Allhttp://dx.doi.org/10.1016/j.surfcoat.2013.02.030

a b s t r a c t

a r t i c l e i n f o

Article history:Received 19 August 2012Accepted in revised form 16 February 2013Available online 28 February 2013

Keywords:Duplex surface treatmentDiffusion coatingsTRDGene expression programming

A duplex surface treatment on DIN 1.2210 steel has been developed involving nitriding and followed by chro-mium thermo-reactive deposition (TRD) techniques. The TRD process was performed in molten salt bath at550, 625 and 700 °C for 1–14 h. The process formed a thickness up to 9.5 μm of chromium carbonitride coat-ings on a hardened diffusion zone. Characterization of the coatings by means of scanning electron microscopy(SEM) and X-ray diffraction analysis (XRD) indicates that the compact and dense coatings mainly consist ofCr(C,N) and Cr2(C,N) phase. All the growth processes of the chromium carbonitride obtained by TRD tech-nique followed a parabolic kinetics. Activation energy (Q) for the process was estimated to be 185.6 kJ/molof chromium carbonitride coating. A model based on genetic programming for predicting the layer thicknessof duplex coating of the specimens has been presented. To construct the model, training and testing wasconducted by using experimental results from 82 specimens. The data used as inputs in genetic programmingmodels were five independent parameters consisting of the pre-nitriding time, ferro-chromium particle size,ferro-chromium weight percent, salt bath temperature and coating time. The training and testing results ingenetic programming models illustrated a strong capability for predicting the layer thickness of duplexcoating.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Chromizing, a technology employed to build up corrosion andwear-resistant layer on metal or alloy substrates [1–3] was firstreviewed by Samuel and Lockington [4] and after that, such chromiz-ing processes have been developed as solid method [5], liquid method[6], and gas method [7]. Limited by the relatively slow diffusion rateof Cr atoms, however, the entire conventional chromizing processesare generally conducted at temperatures above 1000 °C for 6–10 h[8]. Treating at such temperatures produces substrates simplysubjected to serious deteriorating and coarsening. Therefore, devel-opment of a lower temperature chromizing process is of interest toavoid the negative impacts of the conventional chromizing processesand extending the applications of chromizing.

There are many reports on the duplex processes where nitriding,nitrocarburizing or carburizing is utilized for chemical or physical vapordeposition (CVD/PVD) pre-treatment [9–14], or thermo-reaction deposi-tion and diffusion (TRD) [15,16] to achieve a hard surface layer. Some in-dications reveal the formation of chromium nitride or carbonitride hard

ari).

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coatings at low temperatures (below 600 °C) through a duplex processinvolving a prior nitriding or nitrocarburizing following by a subsequentTRD chromizing. Arai et al. [17] claimed the achievement of about 8 μmCrN layers on nitrided substrates by means a TRD treatment at 570 °Cfor 5 h in a fluidized bed reactor.

King et al. [18,19] conducted nitrocarburizing and a fluidized bedTRD process on AISI H13 and plain carbon steels at 570 °C. They con-cluded that both porosity and the formation of an iron nitride ‘coverlayer’ during nitrocarburizing may influence the microstructure ofthe Cr(N,C) coating. In fact, they suggested higher temperature orextending longer treatments for attaining a thicker Cr deposition.Fabijanic et al. [20] developed a duplex process compromising of apre-nitrocarburized AISI H13 and a fluidized bed TRD treatment ofthe nitrocarburized surface at 575 °C. They concluded that the rela-tively lower processing temperature allowed the properties of thecore substrate to be retained. Wu et al. [21] studied the phase trans-formations in 0.2 wt.% C plain steel duplex chromized at 580–800 °Cin a salt bath, and reported [22] a higher surface microhardness onAISI H13 nitrided prior to salt bath TRD chromizing at 590 °C. Cao etal. [23,24] claimed the formation of 40–80 nm nanosized CrN grainsby a 24 h salt bath chromizing of a plasma-nitrided tool steel at773 K. Fan et al. [25] derived a mathematical model evaluating the

Table 1Chemical composition of the 1.2210 steel investigated in this study.

Steel Chemical compositions (wt.%)

C Mn Si S P Cr Ni Mo V W

DIN 1.2210 (AISI L2) 1.16 0.2 0.26 0.006 0.025 0.6 0 0 0.058 0

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influence of the treating temperature, the immersing time and espe-cially the substrate composition on the growth of vanadium carbidecoatings in the TRD process.

Genetic programming (GP), used for the explicit formulation ofthe properties and the performances of engineering materials recent-ly [26,27], offers many advantages as compared to classical regressiontechniques where no predefined function is considered. GP is be-lieved to be superior with respect to regression techniques and neuralnetworks and has proven to be an effective tool to model and obtainexplicit formulations of experimental studies including multivariateparameters where there are no existing analytical models [26,27].

Proposed byKoza [28], GP is an extension toGenetic Algorithms (GA).GP is defined by Koza [28] as a domain independent problem-solving ap-proach where computer programs solve, partially or completely, prob-lems based on the Darwinian principle of reproduction and survival ofthe fittest and analogs of such naturally occurring genetic operations ascrossover and mutation [29]. GenXProTools4, the gene expression pro-gramming (GEP) software used in this study, is an extension to GEPthat incorporates computer programs of different sizes and shapesencoded in linear chromosomes of fixed lengths. The chromosomesare comprised of multiple genes where each encoding a smallersub-program. Moreover, the structural and functional organizations ofthe linear chromosomes consent to the unconstrained operation ofsuch important genetic operators as mutation, transposition and recom-bination [29]. The two main parameters of GEP are the chromosomesand expression trees (ETs) with two utilized languages: the languageof the genes and the language of ETs [29]. A significant advantage ofGEP, called Karva language, is its capability to infer exactly the phenotypegiven the sequence of a gene, and vice versa [30].

The type of linking function as well as the number of genes andthe length of each gene is a priori preferred for each problem. Tosolve a problem, a single-gene chromosome could be selected andthen the modeling may proceed by increasing the length of thehead. However, the number of genes could be increased and a func-tion to link the sub-ETs could be chosen when it becomes verylarge. The program may be initiated with addition for algebraic ex-pressions or for Boolean expressions, but in some cases, utilizing ofanother linking function is of interest (like multiplication or IF, for

Fig. 1.Microstructure and element concentration profiles, for chromium, carbon and nitroge10 h, 20% Fe-Cr, 500 mesh; nitriding: 3 h, 570 °C).

instance). The idea, of course, is to find a high efficiency solutionwhich could be acquired appropriately by GEP [28,30].

Genetic programming offers many advantages as compared toclassical regression techniques. Regression techniques are oftenbased on predefined functions where regression analyses of thesefunctions are later performed. On the other hand, in the case of GP ap-proach, there is no predefined function to be considered. In this sense,GP can be accepted to be superior to regression techniques and neuralnetworks. GP has proven to be an effective tool tomodel and obtainexplicit formulations of experimental studies including multivariateparameters where there are no existing analytical models [31–33].

As authors' knowledge, the conducted works on utilizing a chro-mium carbonitride coating produced by thermo-reactive depositionand diffusion is limited. In addition, since the concept of duplex sur-face treatment and evaluating its properties are relatively novel, ap-plication of such rarely reported computer programs in this area asGEP to predict their properties is of interest. The aim of this study isto investigate the layer thickness of chromium carbonitride coatingproduced by thermo-reactive deposition and diffusion experimental-ly and presenting suitable GEP-based models to predict the layerthickness of coating. Both nitriding and chromising have been donein molten salt bath at temperatures below 700 °C.

Chromising with different ferro-chromium amounts and particlesizes have been used with different treatment time and temperatureto produce chromium carbonitride coatings. Layer thickness of thecoated specimens has been investigated after specific times oftreating. Totally 82 data of layer thickness in different conditionswere collected, trained and tested by means of GEP. The obtained re-sults have been compared by experimental ones to evaluate the soft-ware power for predicting the layer thickness of chromiumcarbonitride of the coated specimens [26,27].

2. Experimental procedure

Cubic specimen with 10 mm edge were polished and cleaned, andthen nitrided at 570 °C for 1.5 and 3 h. The nitriding salt bath mixtureused was 30% NaCN, 25% Na2CO3, 45% KCl and aged for 12 h [34]. Sub-sequently, for chromizing, the specimens were immersed in saltbaths, comprising mainly of NaCl (33 mass%) and CaCl2 (67 mass%).Carbonitride forming element was introduced to the bath in theform of ferro-chromium powder with particle size ranges: 230, 270,325, 400 and 500 meshes and in weight percents: 10, 15 and 20. Re-ducing agent as aluminum flake was added 3 wt.% [35]. TRD processwas performed at 550, 625 and 700 °C for 1 to 14 h with 1 hour inter-vals [36].

n across the thickness of the chromium-carbonitride coating.(1.2210 steel, TRD: 700 °C,

Fig. 2. XRD analysis of nitrided and chromium-carbonitride coating (1.2210 steel, TRD: 700 °C, 10 h, 20% Fe-Cr, 500 mesh; nitriding: 3 h, 570 °C).

3G. Khalaj et al. / Surface & Coatings Technology 225 (2013) 1–10

The nominal composition (wt.%) 115CrV3 (1.2210; ASTMA681(L2))steel specimens used in this experiment is shown in Table 1. Coatingprocedure was carried out in titanium crucible by an internally heatedelectric resistant furnace. The treated test pieces were thoroughlycooled in air and washed in hot water to a bright surface finish andthen lightly polishedwith 3 μmdiamondpaste.Metallographic sectionswere prepared from the treated test pieces in the usual manner and,after etching in 4% nital, coating thicknesseswere determined as the av-erage of at least 10 measurements at 500 magnification.

The coatings and the adjacent substrate regions were examined byoptical microscopy (OM) and by scanning electron microscopy (SEM).As well, SEM with energy dispersive X-ray spectrometry (EDS) andX-ray diffraction (XRD)were utilized to characterize the surface regions.Wavelength dispersive X-ray spectrometry (WDS)was employed to de-termine the concentration of themain elements present in the coatings.This analysis was undertaken to study chemical variations through the

Fig. 3. Relationship between pre-nitriding time (h) and Fe-Cr content (wt.%) on layerthickness of chromium carbonitride at various coating temperatures. Fe-Cr 500 meshand coating time 10 h.

coating thickness. It was chosen over energy dispersive X-ray spectros-copy (EDX) because of its better accuracy, precision and detection limit.It was employed to record the C-Kα, N-Kα, Cr-Kα and Fe-Kα, intensitiessimultaneously. A W/Si X-ray reflective multilayer with a 2d-spacing of9.80 nm was used for selecting the C-Kα and N-Kα radiation, A(200)-LiF crystal was used for selecting Cr-Kα and Fe-Kα radiation.The peak intensity for a single spot on the specimen was determinedfrommeasuring thenumber of counts during 4 min. The background in-tensities for C-Kα, N-Kα, Cr-Kα and Fe-Kαwere determined similarly atthe same location. The background intensity of C-Kα and N-Kα weremeasured separately on a pure α-Fe reference.

The diffraction patterns were obtained by PHILIPS PW1140/90with Sol-X detector using Cu Kα radiation of 0.1542 nm with an op-eration voltage of 40 kV and current of 30 mA. The pattern rangewas from 2θ of 35° to 85°, in the step size of 0.05° and 1 s dwelltime for each step for microstructure analysis samples.

Fig. 4. Effect of wt.% and mesh Fe-Cr on layer thickness at different coating tempera-tures. (Coating time 10 h).

Fig. 5. Chromium carbonitride layers thickness as a function of treatment time at dif-ferent temperatures, Fe–Cr 500 mesh and 20 wt.%.

Fig. 7. Variation of the microhardness versus distance from the surface of the specimennitride for 3 h at 570 °C and coated(after pre-nitriding) at 700 °C and 10 h in salt bathcontaining 20 wt.% and 500 mesh Fe–Cr.

4 G. Khalaj et al. / Surface & Coatings Technology 225 (2013) 1–10

3. Results and discussion

3.1. Formed layer

Fig. 1 exemplifies the coating which is formed on the specimen(9-μm-thick εFe2–3N and γ′ Fe4N layers were formed) nitride in a saltbath at 700 °C for 10 h.WDS line analysis reveals that chromium is con-centrated up to about 70% in the outer layer of 4.5 μm (c2) and 60% theinner layer of 3 μm thick (c1). Nitrogen is enriched in both layers, andthe peak intensity is observed in the inner layer (c1). Carbon is slightlyenriched in both layers (c1, c2), too. Chromium, nitrogen and carbon aredetected in the 4-μm-deeper regionwhere the dark area adjacent to theinner white layer is observed in the microstructures (b).

Coating similar in microstructure and in the enrichment of Cr, Nand C were formed on all kinds of substrates at the temperatures test-ed regardless of the nitriding method, although there are some differ-ences in the thickness and distribution of Cr, N and C therein.

CrN and Cr2N are detected by XRD (Fig. 2), demonstrating that thelayers enriched in Cr and N, as exemplified in Fig. 1, consists of Cr2N(maybe for the outer layer (c2)) and CrN (for the inner layer (c1)).Since the chromium and nitrogen enriched layers contain carbon asshown in Fig. 1, the layers should be expressed as Cr(C,N) andCr2(C,N).

6.0

5.0

4.0

3.0

2.5

2.0

1.5

1.0

Time (h)

1412108642

700

675

650

625

600

575

550

Fig. 6. Contour diagram of chromium carbonitride layer thickness of coated DIN 1.2210steel.

3.2. Effect of ferro-chromium content on coating layer

During the TRD process, the chromium spread from the surface tothe diffusion zone, while nitrogen and carbon spread from the diffu-sion zone to the surface. Finally, they together formed chromiumcarbonitride compound layer. It can be observed from Fig. 3 thatpre-nitriding time have a notable effect on the growth of layers at700 °C.

The relationship between ferro-chromium content in wt.% and thethickness of coating layer at various coating temperatures was shownin Fig. 3. Bath temperature did not have a remarkable effect on the

Fig. 8. (a) relationship between square root of coating time and temperature on layerthickness of chromium carbonitride in salt bath containing 20 wt.% and 500 mesh Fe–Cr. (b). A plot of lnK versus 1/T for chromium carbonitride coated steel.

Fig. 9. Expression tree with 3 gens for predicting layer thickness of duplex coating in GEP-I model. Sub-ET 1(C0 = 9.833283; C1 = −1.087249), sub-ET 2 (C0 = 5.489441;C1 = −0.369263), sub-ET 3(C0 = 5.706177; C1 = 9.155609).

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growth of layers between 550 and 625 °C. Above700 °C, a thin chro-mium carbide layer was formed on the chromium carbonitride layeras in the case of the vanadium-carbonitride [15]. Thickness of coatinglayer increased linearly with the increase in ferro-chromium content.

Fig. 4 showed the effect of ferro-chromium size on the thicknesslayer at coating time 10 h. Layer thickness increased with the increasingferro-chromium content from 10 to 20 wt.% and from 230 to 500meshes. Increasing in coating thickness is noticeable in high temperature(700 °C) rather than 625 and 550 °C. It is thought that salt bath was sat-urated with chromium oxide by this amount of ferro-chromium.Ferro-chromium should be supplied enough to dissolve in the salt bathso that chromium nitride was effectively formed and the optimumferro-chromium was 20 wt.% and 500 mesh for the tested salt bath.

3.3. Effect of coating temperature on thickness and hardness of coatinglayer

Fig. 5 showed the effect of coating temperature on the layer thick-ness in the salt bath using 20 wt.% of ferro-chromium. Layer thicknessincreased with increasing coating temperature from 550 to 700 °C atall coating time from 1 to 14 h. The relationship between layer thick-ness of 550 and 625 is in parabolic line as well as that of 700 °C. The

Fig. 10. Expression tree with 4 gens for predicting layer thickness of duplex coating in GEsub-ET 3(C1 = 1.91565).

diffusion of nitrogen and carbon from matrix to surface and diffusionof chromium form surface to matrix are believed to control the growthof layer thickness since the thickness was in direct proportion to thesquare root of time in hour and nitrogen, carbon and chromium diffusemore quickly at high temperature of 700 °C than at lower temperatures.

A contour diagram (Fig. 6) derived from Fig. 5 shows the processparameters (treatment time and temperature) for predeterminedlayer thickness for industrial applications. It is possible to predictthe chromium carbonitride layer thickness depending on the processtime and temperature from Fig. 5. Fig. 5 can be used for two purposes:(a) to predict the coating layer thickness with respect to the processparameters, namely time and temperature; (b) to determine thevalue of process time and temperature for obtaining a predeterminedcoating layer thickness [37].

Depending on different coating conditions, hardness of surfacevaries between 1300 and 1600 HV. Increasing nitriding time, resultin a thicker layer with decreased surface hardness. However increas-ing ferrochromium content in the bath along with the use of finerferrochromium powder and increasing time in conjunction with thehigher temperature results in increased surface hardness. Hardnessdistribution from surface to substrate produces a good compatibilitybetween coating and substrate (Fig. 7).

P-II model. Sub-ET 1(C0 = 4.763001; C1 = −2.70755), sub-ET 2(C0 = −0.061523),

Fig. 10 (continued).

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3.4. Thermodynamic calculations of coatings

Oxidation of chromium atoms coming from the added ferro-chromium powders to salt bath is the first step for layer formation.The oxidation state depends on the oxygen content, temperature ofbath, crucible type and treatment time [38]. Carbide formation wasfirst proposed as a result of reaction between carbon atoms andsolid ferro-alloy of carbide forming elements oxidize and these oxidescause the formation of carbide layers [39,40]. Therefore the relation-ship between temperature and standard energy values of oxides ofcarbide forming elements have to be investigated.

The oxide which causes chromium carbonitride formation wasCr2O3. Aluminum flakes played a role as reducing agent in reducingchromium oxide in case of adding 3 wt.% Al. aluminum may reducemore stable chromium oxide to less stable chromium oxide or tofree chromium prior to forming chromium nitrocarbide. Without alu-minum content, no layer was observed.

In the TRD process the deposition of chromiummainly react in thefollowing ways:

Cr2O3 þ Al→Al2O3 þ Cr½ � ð1Þ

The nitrogen resources needed to form chromium nitridesresulted from the decomposition of iron nitrides [41]:

2ε−Fe2N→γ’−Fe4Nþ 2 N½ � ð2Þ

γ0−Fe4N→4α−Feþ N½ � ð3Þ

And, the chromium nitrides were formed via the following reac-tions [42]:

Crþ N;C½ �→Cr N;C½ � ð4Þ

Table 2Parameters of GEP approach models.

Parameter definition GEP-I GEP-II

P1 Function set +, −, *, /, sqrt, x2,Ln, Exp, Inv, Sin, Cos

+, −, *, /, sqrt, x2,Ln, Exp, Inv, Sin, Cos

P2 Chromosomes 30 40P3 Head size 12 14P4 Number of genes 3 4P5 Linking function Addition MultiplicationP6 Mutation rate 0.044 0.044P7 Inversion rate 0.1 0.1P8 One-point recombination rate 0.3 0.3P9 Two-point recombination rate 0.3 0.3P10 Gene recombination rate 0.1 0.1P11 Gene transposition rate 0.1 0.1

8 G. Khalaj et al. / Surface & Coatings Technology 225 (2013) 1–10

2Crþ N;C½ �→Cr2 N;C½ � ð5Þ

the thermodynamic driving force for the decomposition of ε-Fe2N(reaction 2) is greater than that for the decomposition of γ′-Fe4N (re-action 3), thus suggesting that there would be un-decomposedγ′-Fe4N remaining in the nitrided compound layer [43,44]. Mean-while, since Cr2N is more stable than CrN, the former may becomethe major phase in the coating layer, if there are adequate quantitiesof [Cr] and [N] atoms supplied to forming the chromium carbonitride.Furthermore, the calculated negative ΔGT° for reaction (1) indicatesthat the reaction can proceed from left to right spontaneously in thetemperature range of 550–700 °C, to form the active species [Cr].

Fig. 11. The correlation of the measured and predicted layer thickness values of duplexcoatings in a) training and b) testing phase for GEP models.

3.5. Growth kinetics of coatings

The activation energy value for chromium carbonitride formationwas found as 185.6 kJ/mol. This is much higher value than the freeenergies for CrN and Cr2N formation at 1000 K which are 39.5 and51.3 kJ/mol, respectively [43]. So it is apparent that the process is dif-fusion controlled. By assuming that the diffusion of nitrogen, carbonand chromium in the coatings is the dominant factor affecting thecoatings layer thickness, the growth of chromium carbonitride coat-ings can be modeled. Fig. 5 indicates the variations of the thicknessof chromium carbonitride layers with the increase of the treatmenttime and temperature. On the basis of the classical kinetic theory,the thickness of chromium carbonitride layer varies with time as aparabolic law as follows (see Fig. 5):

d2 ¼ Kt ð6Þ

where d is the coating thickness (m), K is the diffusion coefficient (orgrowth rate constant) (m2/s), and t is the treating time (s). Eq. (6)can be transformed into:

K ¼ d2

tð7Þ

Fig. 8(a) shows the square of the layer thickness versus treating timeat different temperatures. It is clear that the square of the layer thick-ness changes linearly with the treating time. In Fig. 8(a), the experi-mental results are found in good agreement with the relationshipsshown in Eq. (7) although the lines do not pass through the origin.This could be caused by the incubation time needed for the formationof carbide layer. The fitted three straight lines in Fig. 8(a) correlationcoefficients R2 are higher than 0.98, indicating that it is credible thatthe growth rate constant K at the same temperature conditions is aconstant. In addition, the relationship between the growth rate, con-stant K, activation energy Q, and the process temperature in Kelvin T,can be expressed as an Arrhenius equation [37,45,46]:

K ¼ Ko exp−QRT

� �ð8Þ

where K0 is the pre-exponential constant and R is the gas constant(8.314 J/mol K). Eq. (9) was expressed from the natural logarithmof Eq. (8) as follows:

ln K ¼ ln Koð Þ− QRT

ð9Þ

Q and K0 can be calculated from a plot of lnK versus 1/T. The activa-tion energy, Q, is the slope of line in Fig. 8(b). In this experimentalcondition, the value of activation energy Q for chromium carbonitridecoating is 185.6 kJ/mol and the pre-exponential constant K0 is0.0759 m2/s.

Table 3Statistical parameters of the proposed GEP models.

GEP-Itrainingset

GEP-Itestingset

GEP-IItrainingset

GEP-IItestingset

Correlation coefficient (R2) 0.9778 0.9723 0.9600 0.9546Root mean squared error (RMSE) 0.6821 0.8774 0.9596 1.3770Relative absolute error (RAE) 0.2085 0.2251 0.2960 0.3376Mean absolute error (MAE) 0.5663 0.6997 0.8042 1.0495Root relative squared error (RRSE) 0.2214 0.2587 0.3114 0.4061

9G. Khalaj et al. / Surface & Coatings Technology 225 (2013) 1–10

Inserting the calculated values of Q and K0 in Eq. (8), Eq. (10) isobtained:

KCr N;Cð Þ ¼ 0:0759exp −203151:31T

� �ð10Þ

The relationship among chromium carbonitride coating thickness,treating time and temperature can be obtained, combining Eqs. (6)and (10):

dCr N;Cð Þ ¼ 0:275

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffit exp −203151:31

T

� �sð11Þ

Eq. (11) can be used for predicting the chromium carbonitride coat-ing thickness at different treating time and temperatures. Comparingwith direct chromizing steels by TRD [38,42], the pre-nitrocarburizingcan improve the growth rate constant K, increase the carbonitridecoatings thickness and accelerate the formation of carbonitride coat-ings. The mechanism is that the pre-nitrocarburizing provides morefree nitrogen and carbon atoms at the surface, and also chromiumare strong carbonitride forming elements.

Actually activation energy Q is not a constant, but changes withtemperature. However, Q can be still considered as a constant if thetemperature change ΔT is small [47,48]. Line fitting correlation coef-ficient R2 in Fig. 8(b) is higher than 0.98. It indicates that the toler-ance of Q is very small, which can be used to estimate and predictthe thickness of chromium carbonitride.

3.6. Results of GEP models

Figs. 9 and 10 show the expression trees of two different GEP ap-proach models called GEP-I and GEP-II which were constructed forprediction layer thickness values of duplex coating. d0, d1, d2, d3and d4 in Figs. 9 and 10 represent the values for input layers includingthe pre-nitriding time (Nt), the ferrochromium particle size (FCp),the ferrochromium weight percent (FCw), the temperature of coating(T) and the time of coating (t), respectively. In GEP-I and GEP-IImodels, the number of genes was 3 and 4, and the linking functionwas addition and multiplication, respectively. Among 82 experimen-tal sets, 58 sets were randomly selected for training set of GEP-I andGEP-II models and the remaining 24 sets were used for testing theconstructed models [26,27].

“For this problem, firstly, the fitness, fi, of an individual program, i,is measured by:

fi ¼ ∑Ct

j¼1M− C ijð Þ−Tj

��� ���� �ð12Þ

where M is the range of selection, C(i,j) is the value returned by theindividual chromosome i for fitness case j (out of Ct fitness cases)and Tj is the target value for fitness case j. If |C(ij) − Tj| (the preci-sion) is less than or equal to 0.01, then the precision is equal to zero,and fi = fmax = CtM. In this case, M = 100 was used, therefore,fmax = 1000. The advantage of this kind of fitness functions isthat the system can find the optimal solution by itself” [35,36].

Afterward, the set of terminals and functions, T and F, to create thechromosomes are preferred, where T = {Nt, FCp, FCw, T, t} and Fconsisted of four basic arithmetic operators (+, −, ×, /) and somebasic mathematical functions such as Square root (Sqrt), Exponential(Exp), Natural logarithm (Ln), x to the power of 2 (X2), Sine (Sin), Cosine(Cos), Inverse (Inv) were used [35,36].

Another major step is choosing the chromosomal tree, or in theother words, the length of the head and the number of genes [26,27].In both GEP-I and GEP-II approaches, initially a single gene and two

lengths of heads were used. Then, these numbers were increased oneafter another during each run and the training and testing set perfor-mances of each model were monitored. In this study, for GEP-I andGEP-II models, respectively 3 and 4 genes 12 and 14 lengths of headswere observed to gain the best performance [26,27].

The entire genetic operators compromising of mutation, transpo-sition and crossover were utilized as a set of genetic operators. Pa-rameters for training the proposed GEP models are given in Table 2.For GEP-I and GEP-II models, 30 and 40 chromosomes were observedto be the best of generation individuals predicting layer thickness ofduplex coating [26,27,35,36]. Explicit formulations based on GEP-Iand GEP-II models for LT were obtained by:

LT ¼ f Nt; FCp; FCw; T; tð Þ ð13Þ

The related equations to GEP-I and GEP-II models obtained fromFigs. 9 and 10 are in accordance to Eqs. (14) and (15), respectively[26,27,35,36];

LT ¼ ½ ffiffiffiffiffiffiNt

p � cos ln

ffiffiffiffiffiffiNt

p

T� FCpð Þ−FCw−5:977þ t

! #

þ sin1

FCwþFCw2 þ t

1:3432þ 0:2951− Nt

5:7874

� ��

þ sin tð Þ � ffiffiffiT

p � sin tð Þ þ 4:9838ð Þ � FCpt

" # ð14Þ

LT ¼ sin t− −8:4975� texp Ntð Þ− 3:3265þ t−FCpð Þ2� �2� ��

� cos FCwð Þ− ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi9:4732=FCw

p0:89471� Tþ Nt−2:4466ð Þ þ 0:89471

" #

� sin t− FCwFCp� Ntð Þ= FCp� tð Þð Þ− FCpþ 3:4115ð Þ=ln FCpð Þð Þ

� 2� ��

� T−2� t−FCwð Þ= −9:4216� FCpð Þð Þ þ Tþ 2þ Nt

� ð15Þ

In this study, the error that arose during the training and testing inGEP-I and GEP-II models can be expressed as absolute fraction of var-iance (R2), mean absolute error (MAE), root mean squared error(RMSE), relative absolute error (RAE) and root relative squarederror (RRSE) which are calculated by Eqs. (16)–(20), respectively[49]:

R2 ¼ 1− ∑i ti−oið Þ2∑i oið Þ2

!ð16Þ

MAPE ¼ 1n∑i

ti−oij j � 100 ð17Þ

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1n∑i

ti−oið Þ2s

ð18Þ

RAE ¼ ∑i ti−oij j∑i ti− 1

n∑iti�� �� ð19Þ

RRSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

∑i ti−oið Þ2∑i ti− 1

n∑iti �2

vuut ð20Þ

where t is the target value, o is the output value and n is the numberof data sets in each of training and testing phases.

The entire obtained results from the experimental studies andthose predicted by using the training and testing results of GEP-Iand GEP-II models are given in Fig. 11a and b, respectively [26,27].

10 G. Khalaj et al. / Surface & Coatings Technology 225 (2013) 1–10

The linear least square fit line, its equation and R2 values are shown inthese figures for both training and testing data and the complete sta-tistical parameters of training and testing sets of the GEP models arepresented in Table 3. The predicted values obtained from the trainingand testing in both GEP-I and GEP-II models are very close to the ex-perimental ones as Fig. 11 illustrates. This indicates the capability ofthe proposed GEP-I and GEP-II of generalizing between input and out-put variables with rationally superior predictions [26,27].

The performance of GEP-I andGEP-IImodels is shown in Table 3. Thebest values of R2, RMSE, RAE, MAE and RRSE are 0.9878, 0.6821, 0.2085,0.5663 and 0.2214, respectively all for the training set in GEP-II model.The minimum value of R2 and the maximum values of RMSE, RAE,MAE and RRSE are 0.9546, 1.3370, 0.3376, 1.0495 and 0.4061, respec-tively all for testing set in GEP-I model. This shows that GEP-I model isbetter trained than GEP-II where the entire statistical evaluators ofeven testing phase of GEP-I model has higher performance than thoseof GEP-II training and testing sets. However, both of the models exhibitvaluable results and the entire statistical values show that the proposedGEP-I and GEP-II models are suitably trained and can predict the layerthickness values very close to the experimental ones.

4. Conclusions

From the experimental procedure, the following results wereobtained:

1. Chromiumcarbonitride coating can be formed on pre-nitrocarburized115CrV3 steel by TRD process. The chromized layer formed at the ini-tial stages of the duplex chromizing process consisted of threesub-layers, namely the outer Cr2N layer, the CrN intermediate diffu-sional layer and the inner nitrided compound layer. The Cr(C,N) andCr2(C,N) layers were formed at the expense of the decomposition ofthe prior nitrided compound layer.

2. Aluminum flakes played a role as reducing agent in reducing chro-mium oxide in case of adding 3 wt.% Al. aluminum may reducemore stable chromium oxide to less stable chromium oxide or tofree chromium prior to forming chromium nitrocarbide.

3. Layer thickness increasedwith the increasing ferro-chromiumcontentfrom 10 to 20 wt.% and from 230 to 500meshes. Increasing in coatingthickness is noticeable in high temperature (700 °C) rather than 625and 550 °C. It is thought that salt bath was saturated with chromiumoxide by this amount of ferro-chromium. Ferro-chromium should besupplied enough to dissolve in the salt bath so that chromium nitridewas effectively formed and the optimum ferro-chromiumwas 20 wt.%and 500 mesh for the tested salt bath.

4. The thickness of chromium carbonitride layer varies with time as aparabolic law. The growth rate constants and activation energy ofthe chromium carbonitride formation in the salt bath method werecalculated and were 0.0759 m2/s and 185.6 kJ/mol, respectively.

5. GEP may be considered as a suitable approach for the evaluation ofthe effect of nitriding and chromizing conditions on the layerthickness values of duplex coatings. Comparison between GEPmodels in terms of their R2, RMSE, RAE, MAE and RRSE values re-vealed their capability for predicting appropriate results for layerthickness values of duplex coatings.

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