Plasma nitridation of aluminized high purity iron

Acta Materialia 53 (2005) 2563–2579

www.actamat-journals.com

Plasma nitridation of aluminized high purity iron

Koji Murakami a,*, Norihide Nishida a, Kozo Osamura b, Yo Tomota c, Tetsuya Suzuki d

a Industrial Technology Center of Okayama Prefecture, Department of Materials Engineering, 5301 Haga, Okayama City Okayama

Prefecture 701-1296, Japanb Department of Materials Science and Engineering, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan

c Institute of Applied Beam Science, Graduate School of Science and Engineering, Ibaraki University, 4-12-1 Nakanarusawa, Hitachi,

Ibaraki 316-8511, Japand Research Center for Superplasticity, Faculty of Engineering, Ibaraki University, 4-12-1 Nakanarusawa, Hitachi, Ibaraki 316-8511, Japan

Received 31 October 2004; received in revised form 3 February 2005; accepted 7 February 2005

Available online 2 April 2005

Abstract

Surface treatment of high-purity iron by powder liquid coating aluminization and plasma nitridation is investigated with respect

to the mechanism of hardening and nitrogen diffusion. Grain boundaries in the aluminized layer are found to be preferentially

nitrided in the early stage of nitridation, accompanied by the formation of c 0-Fe4N platelets in the substrate. Aluminization and

nitridation increase the hardness from HV110–120 for the original a-Fe(Al) to HV1200–1500 for the modified specimen, which con-

sists of an a-Fe(Al) matrix with c 0-Fe4N and rocksalt AlN. Transmission electron microscopy observation reveals the AlN to be

present in the form of platelets of 2–3 nm in thickness with an orientational relationship of (001)a//(001)AlN and [110]a//

[100]AlN (Baker–Nutting relationship). The kinetics of plasma nitridation is formulated, and good agreement with the experimental

results is obtained when first- or second-order reactions are assumed for the formation of AlN under constant N flux at the surface.

� 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Plasma nitridation; Aluminization; Iron; Kinetics

1. Introduction

The powder liquid coating aluminization technique

recently reported by Murakami et al. [1–4], in combina-

tion with plasma nitridation, is expected to be a useful

surface treatment for die casting machines as protectionagainst severe erosion by molten Al or other liquid met-

als. The major benefit of such a treatment technique is

the ability to treat the internal surfaces that are exposed

to these severe environments; in contrast, other protec-

tive coatings such as CrN, TiN, and TiAlN films are

1359-6454/$30.00 � 2005 Acta Materialia Inc. Published by Elsevier Ltd. A

doi:10.1016/j.actamat.2005.02.014

* Corresponding author. Tel.: +81 862 869 600; fax: +81 862 869 630.

E-mail addresses: [email protected] (K. Muraka-

mi), [email protected] (N. Nishida), kozo.osamura@

materials.mbox.media.kyoto-u.ac.jp (K. Osamura), tomota@ mx.ibar-

aki.ac.jp (Y. Tomota), [email protected] (T. Suzuki).

deposited by physical vapor deposition, a technique that

is restricted to external surfaces. The combination of

aluminization and nitridation has already been pro-

posed by Tsuji [5,6] and Bindumadhavan [7] for tool

steel and carbon steel, and hardnesses of HV1000–

1500 have been achieved for the modified layer. Harden-ing by steel nitridation is thought to occur through the

formation of hard nitrides, resulting in higher internal

stress in the matrix, or Guinier–Preston zones. However,

the detailed hardening mechanism has yet to be studied

in detail for this aluminization and nitridation

technique.

In this study, high-purity iron is treated by powder li-

quid coating aluminization and subsequent plasmanitridation, and the hardened layer is characterized. A

diffusion equation for nitrogen is formulated taking

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2564 K. Murakami et al. / Acta Materialia 53 (2005) 2563–2579

the formation of nitrides in the aluminized layer into

consideration.

2. Experimental

High-purity Fe (99.9%) disks were used as substrates.

The substrate was polished with abrasive paper to #600

and washed twice with acetone in an ultrasonic cleaning

bath for 0.3 ks each time. For powder liquid coating

aluminization [4], a slurry was prepared by stirring a

mixture of atomized Al powder (under 3 lm in diame-

ter), crushed Al2O3 (levigated to 1 lm) and ethanol

(12.0 · 103 mm3 for mixed powders of 1.0 · 10�2 kg)with an impeller at 50 revolutions per second for

0.6 ks. The slurry was pasted onto the disks to a cover-

age of 0.50 mg/mm2, and the specimens were heated in

an oven at 333 K for 1.8 ks to remove ethanol. Each

of the prepared disks was then heated in a quartz cylin-

der by infrared radiation in a vacuum of 1.3 · 10�3 Pa.

The temperature was raised at 1.33 K/s, held at

1273 K for 3.6 ks, and then the samples were cooled un-der N2 gas flow at about �2 K/s to room temperature.

Fig. 1. Schematic illustration of (a) plane-polishing and (b) XRD

measurement.

After the residual powder had been removed with

acetone in an ultrasonic cleaning bath, the aluminized

substrates were placed in the plasma nitriding chamber.

The chamber was evacuated to 1.3 Pa and mixture of Ar

and H2 gas (Ar:H2 = 1:1 by volume) was introduced at

an inflow rate controlled by massflow controllers so asto maintain a total chamber pressure of 1.3 · 102 Pa.

The aluminized substrates were heated to 873 K under

direct current (dc) glow discharge to remove the passive

oxide surface layer, which prevents effective nitridation.

After sputtering for 3.6 ks, gas supply was changed to

N2:H2 = 7:3, and the total pressure was maintained at

3.9 · 102 Pa. The nitriding temperature was varied from

773 to 873 K, and nitriding was conducted for 3.6–32.4 ks. The specimens were furnace cooled after nitrid-

ation. The nitriding conditions are hereafter denoted by

TK-tks, and this expression implicitly means that the

Fig. 2. Schematic illustration of specimen preparation for TEM

observation: (a) polished and chemically etched plane showing cross-

sectional microstructure (left) and the FIB configuration (right);

(b) picking of a thin fragment from the molded specimen and

mounting on a grid; (c) final thinning.

(b)

(a)

Fig. 3. Variation in cross-sectional Vickers hardness as a function of

distance from the surface: (a) 773/823/873K-14.4ks; (b) 873K-3.6/14.4/

32.4ks.

(a)

K. Murakami et al. / Acta Materialia 53 (2005) 2563–2579 2565

specimen had also been previously aluminized under the

above conditions.

Cross-sections for testing were polished using a dia-

mond slurry and finished using a colloidal silica suspen-

sion. The hardness profile of the modified layer was then

obtained using a Vickers hardness tester with a load of98 mN, and the microstructure was observed by optical

microscopy and electron probe microanalysis (EPMA).

Concentration profiles for Fe, Al, and N were quantita-

tively measured by EPMA with ZAF matrix correction.

The specimens were subsequently etched with 5% nital

(nitric acid:ethanol = 5:95 by volume) and observed by

field-emission scanning electron microscopy (FE-

SEM). The chemical state of Al was analyzed by field-emission Auger electron spectrometry (FE-AES). For

phase identification of the graded modified layer,

X-ray diffraction (XRD) measurements were taken after

repeated plane-polishing of the modified surface, as

shown in Fig. 1. For this procedure, the modified layer

was polished down by 5–10 lm using 6 lm diamond

slurry, and the Bragg–Brentano geometry was used for

XRD measurement.The detailed microstructure of the aluminized and ni-

trided layer was observed by transmission electron

microscopy (TEM), for which the thin films were pre-

pared using a Ga focused ion beam (FIB) with in-situ

tungsten plucker and tungsten deposition system, as de-

picted in Fig. 2. The acceleration voltage for sputtering

the surrounding (Fig. 2(a)) and rough thinning (Fig.

2(b)) was 40 kV, and that for final thinning was 10 kV.

(b)

(c)

(d)

(e)

Fig. 4. Concentration profiles for Al and N as a function of distance

from the surface: (a) 773K-14.4ks; (b) 823K-14.4ks; (c) 873K-3.6ks;

(d) 873K-14.4ks; (e) 873K-32.4ks.

3. Experimental results

3.1. Cross-sectional properties of modified layer

Fig. 3 shows the cross-sectional Vickers hardness pro-

files of the aluminized and nitrided specimens of 773/823/873K-14.4ks (a) and 873K-3.6/14.4/32.4ks (b). The

hardness of the aluminized and nitrided layer of the

773K-14.4ks specimen is about HV200, which is similar

to that of a-Fe(Al) alloy. However, the hardness of the

823K-14.4ks specimen was much higher, HV1200, dem-

onstrating a remarkable increase at higher nitridation

temperature. Similarly, the thickness of the hardened

layer increased from 10 lm (3.6 ks) to 60 lm (32.4 ks)at 873 K.

Fig. 4 shows concentration profiles of Al and N for

the specimens in Fig. 3, where c 0 corresponds to coarse

platelets of Fe4N, and Fig. 5 shows a compositional im-

age and corresponding area analyses for the modified

layer by EPMA. Condensation of N at the grain bound-

aries of a-Fe(Al) can be observed in Fig. 5, and irregular

platelets of c 0-Fe4N was identified at the interface be-tween the aluminized layer and the substrate. The first

derivatives of the Auger electron spectra and the second-

ary electron image showing the measurement points (fora specimen chemically etched with 5% nital) are shown

in Fig. 6, where the indentations due to Vickers hardness

Fig. 5. Cross-sectional compositional image and X-ray area analysis of 873K-3.6ks specimen after aluminization: (a) compositional image;

(b) Fe-map; (c) Al; (d) N.


measurement and the contamination array of C due toEPMA can be observed. The valley in the Al spectrum

in Fig. 6(b) is shifted from that in Fig. 6(d) by 2 eV,

the former indicating the chemical state of nitride and

the latter metallic state. Fig. 6(c), obtained in the region

of an a-Fe(Al) grain boundary, displays two valleys due

to nitride and metallic Al. A magnified secondary elec-

tron image by FE-SEM of a more deeply etched grain

boundary than that in Fig. 6(a) is shown in Fig. 7,revealing the preferential precipitation of orthogonally

intersecting platelets.

3.2. Phase identification by XRD and TEM

Fig. 8 shows the XRD profiles of the aluminized (a)

and nitrided specimens (773/823/873K-14.4ks, (b)–(f)) be-

fore plane-polishing. In Fig. 8(b)–(f), nitrides of c 0-Fe4Nand e-Fe2-3N can be seen on the surface, and the peaks

due to thea-Fe(Al)matrix appear to become broaderwith

increasing nitriding temperature. In the samples nitrided

at 873 K (Fig. 8(d)–(f)), the peaks of c 0-Fe4N and

e-Fe2-3N became larger with increasing nitriding time,

while those of a-Fe(Al) became weaker and broader.

The series of XRD patterns obtained for the plane-

polished surfaces of the aluminized and nitrided speci-

mens is shown in Fig. 9. Here, the X-ray penetrationdepth was estimated from the relation expð�2lt= sin hÞto be approximately 0.1, suggesting that the depth

ranges from 1 to 3 lm for 2h = 20–60� (Cu Kaline (k = 0.1542 nm), chemical composition of Fe–

10mass%Al–10N). In the specimens nitrided for

14.4 ks (Figs. 9(a), (b), and (d)), polishing revealed a

sudden decrease in e-Fe2-3N and c 0-Fe4N. The diffrac-

tion intensities of c 0-Fe4N increased again at the inter-face between the aluminized layer and the substrate

(Fig. 4(a), (b), and (d)), where the 823K-14.4ks specimen

exhibited the highest intensity for c 0-Fe4N. While the

specimen nitrided at 873 K for 3.6 ks (Fig. 9(c)) did

not exhibit a remarkable increase in the abundance of

c 0-Fe4N at the terminal of the aluminized layer, nitrida-

tion for 32.2 ks at the same temperature (Fig. 9(e)) pro-

duced a large amount of e-Fe2-3N as well as thecharacteristic transition in the c 0-Fe4N content as seen

for specimens nitrided at 873 K for 14.4 ks (Fig. 9(d)).

Transmission electron micrographs of the 873K-

14.4ks specimen are shown in Fig 10, where (a) is a

bright-field image of [001]a-Fe-incident, (b) is the se-

lected-area diffraction for the area in (a), (c) is the in-

dexed patterns for (b), (d) and (e) are the dark-field

images obtained for diffraction spots B and C in (b),

Fig. 6. (a) Cross-sectional secondary electron image and (b) Auger electron spectra of Al obtained at points 1–3 after chemical etching with 5% nital

(873K-3.6ks).


and (f) is a bright-field image obtained at the edge of the

FIB area. The bright-field images (Fig. 10(a) and (f)) re-

veal orthogonally intersecting platelet precipitates of less

than 5 nm in thickness.

4. Discussion

4.1. Precipitation during plasma nitridation of aluminized

high-purity Fe

As shown in Fig. 9, the amount of c 0-Fe4N in thesurface layer was low in the aluminized layer, higher

at the interface between the aluminized layer and the

substrate, and then approached zero in the substrate.

This elevation of c 0-Fe4N abundance at the interface

corresponds to the formation of coarse c 0-Fe4N,and correlates with the plateau in the concentration

profile of N (Fig. 4(b) and (e)) at 20 at.%. Whereas

only platelet c 0-Fe4N is seen in Fig. 6(a), coarse and

irregular platelets of c 0-Fe4N containing Al were

formed at extended nitridation times. This is attribut-

able to the misfit between c 0-(Fe-Al)4N and a-Fe(Al),

where the orientational relationship between a-Feand c 0-Fe4N [8] ðð012Þa==ð112Þc0 Þ is imperfectlysatisfied.

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 8. X-ray diffraction intensity profile of aluminized and nitrided

surface before plane-polishing: (a) aluminized; (b) nitrided under

conditions of 773K-14.4ks; (c) 823K-14.4ks; (d) 873K-3.6ks; (e) 873K-

14.4ks; (f) 873K-32.4ks.

Fig. 7. Cross-sectional secondary electron image observed after

chemical etching with 5% nital (873K-14.4ks).


From Fig. 4(c)–(e), the aluminized layer appears to

have grown during nitridation. The inhomogeneities

in the thickness of the aluminized layer were present

before nitridation, as the substrates were coated by lo-

cally nonuniform adherence of fine liquid particle of Al

during the aluminization process. This spatial inhomo-

geneity resulted in a variation in the thickness of the

aluminized layer from 50 to 70 lm across the specimen.

Although the interdiffusion coefficient of Al in a-Fe at873 K has not yet been reported, extrapolation from

the data of Hirano and Hishinuma [9] and Nishida

et al. [10] gives values of 1.52 · 10�4 and 7.7 ·10�7 lm2/s, respectively. These values indicate that diffu-

sion of Al during nitridation (773–873 K) was essentially

negligible.

From Figs. 3 and 4, the variation in cross-sectional

hardness corresponds well with the N concentrationprofile. Platelets of c 0-Fe4N were observed in the alu-

minized and nitrided layer as well as in the substrate.

As the hardness of c 0-Fe4N is almost the same as that

of high-purity Fe, and the strain introduced by

precipitation is small, the presence of c 0-Fe4N did

not affect the hardness of the surface. Although

e-Fe2-3N is harder than c 0-Fe4N, the former was

only present at the surface and as such did not con-tribute to an increase in the cross-sectional hardness

(Fig. 3).

From the observation that the layer with hardness

of greater than HV500 (layer (i) in Fig. 4) had a nitro-

gen concentration of 15–20 at.% and contained a-Fe(detected by XRD), nitrides containing more than

20 at.% N are considered to be present in the hardened

layer (i). Fig. 5 suggests that fine nitrides precipitatedpreferentially at the grain boundary, then began precip-

itating uniformly in the grains of a-Fe(Al) extending

from the surface. Although part of the aluminized re-

gion was not completely nitrided (layer (ii) in Fig.

6(a) and Fig. 4(c) (873K-3.6ks)), platelet c 0-Fe4N was

present in layer (iii). This suggests that N atoms dif-

fused along the grain boundaries in the aluminized

layer, where preferential precipitation of fine nitridesoccurred, leading to the precipitation of c 0-Fe4N as

platelets in the substrate (a-Fe). The precipitation of

fine nitrides occurred in the grains of a-Fe(Al), and

the effectively hardened layer grew into the substrate,

as shown in Fig. 4.

From Fig. 6, the precipitates that effectively in-

creased the hardness are thought to be aluminum nit-

rides, as previously reported for Fe-Al foils [8,11–16].The orthogonal orientation of coarser nitrides at the

grain boundary (Fig. 7) suggests a certain orientational

relationship between the nitride and the matrix

(a-Fe(Al)). From Fig. 10(b) ([001]a-Fe-incident) and

another pattern for [011]a-Fe-incident, platelet precipi-

tates were identified as rocksalt AlN (space group num-

ber 225(Fm�3m), a = 0.405 nm [17,18]). The

orientational relationship between a-Fe and AlN was(001)a//(001)AlN and [110]a//[100]AlN, which is well

known as the Baker–Nutting orientational relationship.

Fig. 9. X-ray diffraction intensity profile of plane-polished surface: (a) nitrided under conditions of 773K-14.4ks; (b) 823K-14.4ks; (c) 873K-3.6ks;

(d) 873K-14.4ks; (e) 873K-32.4ks.


This semi-coherency is thought to result in the two-

dimensional growth of fine rocksalt AlN. As the con-

centration of N was higher than that of Al as shown

in Fig. 4, the nitride is thought not to be stoichiometricAlN but rather involve some degree of Fe substitution

for Al.

Although the precipitation of wurtzite AlN has been

reported to be chemically more advantageous than that

of rocksalt AlN in terms of the Gibbs� free energy, the

former is accompanied by a large volume misfit with

the matrix, which increases the strain energy [15]. Once

rocksalt AlN forms, it has been reported to resist

transformation to wurtzite AlN due to the large kinetic

barrier hindering the rearrangement of Al and N. It

has also been reported that after wurtzite AlN has

transformed into rocksalt AlN at high pressure(15 GPa), the rocksalt structure is retained even after

the pressure is released [17,18]. Based on these reports,

the Gibbs� free energy change upon nitridation of the

aluminized high-purity Fe is thought to be as shown

in Fig. 11.

As discussed above, the aluminized and nitrided

layer owes its high hardness to the precipitation of fine

platelets of rocksalt (Al,Fe)N. The kinetics dealing with

Fig. 10. Transmission electron micrographs of 873K-14.4ks specimen: (a) bright-field image; (b) selected-area diffraction pattern corresponding to

(a); (c) indices corresponding to (b); (d) dark-field image obtained at spot B in (b); (e) dark-field image obtained at spot C in (b); (f) bright-field image

at the edge of the FIB area.

free

ene

rgy

Fig. 11. Gibbs� free energy diagram for plasma nitridation of a-Fe(Al).


the precipitation of nitrides in this graded Fe–Al

–N system is reduced in this study to a uniform

precipitation process of stoichiometric AlN in a graded

a-Fe(Al) matrix. The model is then calculated numeri-cally in order to investigate the diffusion and precipita-

tion processes.

4.2. Numerical analysis of nitrogen diffusion and phase

precipitation during plasma nitridation of aluminized

high-purity iron

4.2.1. Formulation and calculation procedure

The numerical analysis adopted here is based on the

following assumptions.

(i) Growth of the diffusion layer (a-Fe(Al)) into the

substrate and formation of e-Fe2-3N and c 0-Fe4N

are not considered. Growth of the diffusion layer

was shown in Section 4.1 to be negligible. Super-

saturated N in a-Fe(Al) is treated as interstitial

atoms in the bcc lattice and as such do not cause

a volume change.

(ii) The thin slab is subdivided into two parts; matrix(a-Fe(Al)) and nitride (rocksalt AlN), as shown in

Fig. 12. Nitrogen atoms only pass through the

matrix, and a fraction of the N atoms are trapped

by Al to form stoichiometric AlN. The reaction rate

for this process follows an nth order reaction with

respect to the concentration of N and Al in the

matrix.

x

AlN

J(x,t)

N N

Fig. 12. Schematic illustration of N diffusion and formation of AlN in

a thin slab during plasma nitridation of aluminized high-purity Fe.


(iii) The volume fraction of AlN v(t,x) (x is distance

from the surface, t is nitriding time) is regarded

as the reduction of the section through which N

passes. The size of AlN is not treated explicitly.

(iv) The surface state of the specimen during plasma

nitridation is considered under the following two

conditions:

(a) I ncoming flux is constant (J0).(b) Concentration of N in the matrix is constant

(c0).

(v) The system is semi-infinite.

From assumption (iii), the flux of N in the matrix

J(t,x) is given by

Jðt; xÞ ¼ � 1� vðt; xÞð ÞD ocðt; xÞox

; ð1Þ

where D is the diffusion coefficient of N in a-Fe at 873 K

(in lm2/s) and c(t,x) is the concentration of N in the ma-

trix (in mol/lm3). From assumptions (i) and (ii), the dif-

fusion equation (2) contains two terms in the partial

differentiation with respect to t:

o

ot1� vðt; xÞð Þcðt; xÞ þ qNvðt; xÞð Þ

¼ Do

oxð1� vðt; xÞÞ ocðt; xÞ

ox

� �: ð2Þ

The first term in the partial differentiation on the left-

hand side of Eq. (2) corresponds to the net increase ofN in the matrix (a-Fe(Al)), and the second corresponds

to that in the nitride.

The reaction rate of N with Al in the matrix is pro-

portional to the nth power of the product of the

amounts of Al in the matrix and N, following assump-

tion (ii). The density of N (or Al) in rocksalt AlN,

qN(=qAl) = 1.0 · 10�13 mol/lm3, is used to determine

the reaction rate, as follows.

qN

ovðt; xÞot

¼ K 1� vðt; xÞð Þcðt; xÞ � 1� vðt; xÞð ÞcAlðt; xÞ½ �n;

ð3Þwhere K is a reaction rate constant corresponding to the

reactivity of N towards Al in the matrix, and cAl is the

concentration of Al in the matrix according to the fol-

lowing material balance between the matrix and the

nitride:

cAlðt ¼ 0; xÞ ¼ 1� vðt; xÞð ÞcAlðt; xÞ þ vðt; xÞqAl: ð4ÞEquations (2) and (3) are the fundamental equations for

this system, and the initial and boundary conditions, de-

rived from assumptions (iv) and (v), are as follows.

cðt ¼ 0; xÞ ¼ 0; ð5Þ

Jðt; x ¼ 0Þ ¼ const: ¼ J 0; ð6Þ

cðt; x ¼ 0Þ ¼ const: ¼ c0; ð7Þ

limx!þ1

cðt; xÞ ¼ 0: ð8Þ

As analytical solutions satisfying the above equationsand boundary conditions cannot be obtained, the sys-

tem is converted to difference equations following the

scheme reported previously [1,2]. By Taylor expansion,

the left-hand side of Eq. (2) is converted to a difference

equation with error of O((Dt)2) as follows.

o


¼ 1

Dt1� vðt þ Dt; xÞð Þcðt þ Dt; xÞ þ qNvðt þ Dt; xÞ½ �f

� 1� vðt; xÞð Þcðt; xÞ þ qNvðt; xÞ½ �g

� 1

2

o

oto


� �Dt

þOððDtÞ2Þ: ð9Þ

In the same way, the right-hand side of Eq. (2) is con-verted as follows by averaging the forward and back-

ward difference scheme.

o

oxð1� vðt; xÞÞocðt; xÞ

ox

� �

¼ 1

2ðDxÞ21� vðt;xþDxÞð Þ cðt;xþDxÞ � cðt;xÞð Þ½f

� 1� vðt;xÞð Þ cðt;xÞ � cðt; x�DxÞð Þ�þ 1� vðtþDt;xþDxÞð Þ cðtþDt; xþDxÞð½�cðtþDt;xÞÞ � 1� vðtþDt;xÞð Þ cðtþDt;xÞð

�cðtþDt;x�DxÞÞ�g � 1

2

o

oto

ox1� vðt;xÞð Þoc

ox

� �� Dt

þ 1

2

o

oxovðt;xÞox

ocðt;xÞox

� �DxþOðDtDxÞ: ð10Þ

By substituting Eqs. (9) and (10) into Eq. (2), the diffu-sion equation to be solved is expressed as


ð1� viþ1;jÞciþ1;j þ qNviþ1;j

� �� ð1� vi;jÞci;j þ qNvi;j� �

¼ a ð1� vi;jþ1Þðci;jþ1 � ci;jÞ � ð1� vi;jÞðci;j � ci;j�1Þ� ��

þ ð1� viþ1;jþ1Þðciþ1;jþ1 � ciþ1;jÞ�

�ð1� viþ1;jÞðciþ1;j � ciþ1;j�1Þ��; ð11Þ

a � DDt

2ðDxÞ2; ð12Þ

where t = iDt (0 6 i 6M) and x = jDx (0 6 j 6 N). The

local round-off error for this system is of the order of

DtDx.The numerical solution for the evolution of v(t,x)

(Eq. (3)) can be obtained by the Runge–Kutta method

as follows.

viþ1;j ¼ vi;j þ1

6Dv1 þ 2Dv2 þ 2Dv3 þ Dv4ð Þ; ð13Þ

where

ovðt; xÞot

¼ f ðvðt; xÞÞ; ð14Þ

(a)

(c)

(e)

Fig. 13. Profiles of (a,b) concentration of N in a-Fe(Al), (c,d) total concentra

from the surface calculated assuming boundary condition (6): MDt = 3.6 ks,

Dv1 ¼ f ðvi;jÞDt;Dv2 ¼ f ðvi;j þ Dv1

2ÞDt;

Dv3 ¼ f ðvi;j þ Dv22ÞDt;

Dv4 ¼ f ðvi;j þ Dv3ÞDt:

9>>=>>;: ð15Þ

The boundary condition Eq. (6) is converted to the dif-

ference form by the Savitzki–Golay method, where a cu-

bic curve is fitted to the first four data points from the

surface (ci,0,ci,1,ci,2,ci,3) and the first differentiation at

j = 0 is calculated as follows.

Jðt; x ¼ 0Þ ¼ J 0

¼ � 1� vðt; xÞð ÞD ocðt; xÞox

� ��x¼0

’ �ð1� vi;0ÞD � 11ci;0 � 18ci;1 þ 9ci;2 � 2ci;36Dx

� �:

ð16Þ

Here, as D for the Fe–Al system has not yet been re-

ported, the value for a-Fe (13 lm2/s [19–21]) was used

for the calculation. The incoming flux at the surfaceJ0 = 7.7 · 10�17 mol N/lm2/s was determined from the

(b)

(d)

(f)

tion of N, and (e,f) volume fraction of nitride as a function of distance

Dx = 0.5 lm, N = 400 (N = 200 for Dt = 0.01 s).


mass gain of the nitrided specimens, which is expected to

include error due to the sputtering of Fe.

The full calculation procedure is summarized as

follows.

(I) Set the time increment Dt and the spatial resolu-tion Dx.

(II) Load the initial condition cAl(t = 0,x) and set

v0,j = 0 for any j.

(III) Calculate {vi + 1,j} from {vi,j} (calculate Eq. (15),

then (13)).

(IV) Calculate {ci + 1,j} from {ci,j}, {vi + 1,j}, and {vi,j}

(solve Eqs. (11) and (16)).

(V) Repeat from step (III).

4.2.2. Calculation results for boundary condition (6)

Fig. 13 shows the calculated N concentration and

volume fraction of AlN (v · 100) at t = 3.6 ks for the

first- and second-order reactions (n = 1, 2). Here, for

(a)

(c)

(e)

Fig. 14. Profiles of (a,b) concentration of N in a-Fe(Al), (c,d) total concentra

from the surface calculated assuming boundary condition (6): MDt = 7.2 ks,

convenience, the N concentration in at.% was calculated

by

xNðt; xÞ ¼ð1� vÞcþ vqN

cAlðt ¼ 0; xÞ þ cFeðt ¼ 0; xÞ þ ð1� vÞcþ vqN

� 100: ð17Þ

To shorten the calculation time, the temporal resolu-

tion for Dt for each condition was set as coarse as pos-

sible while avoid divergence in c and v.As shown in Figs. 13(a) and (b), the near-linear de-

crease in c was broken at the basal terminal of the ni-

trided layer with increasing K (arrows in Figs. 13(a)

and (b)). A similar tendency was observed for xN and v

in both cases (n = 1,2), where a gradual decrease occurred

at smallerK and sharper decrease was seen at largerK. At

smaller K (�1.0 · 1010 lm3/mol/s, n = 1), the profiles of c

and xN suggest that N atoms pass through the aluminizedlayer (a-Fe(Al)) to form c 0-Fe4N in the substrate (a-Fe)before the aluminized layer is thoroughly nitrided.

However, at larger K (�1.0 · 1016 lm3/mol/s, n = 1),

(b)

(d)

(f)

tion of N, and (e,f) volume fraction of nitride as a function of distance

Dx = 0.5 lm, N = 400 (N = 200 for Dt = 0.01 s).


representing higher reactivity of N towards Al in the ma-

trix (a-Fe(Al)), N atoms cannot pass through the alumi-

nized layer and the concentration profiles of N and v

exhibit steep gradients where Al is present in the matrix.

As diffusion of N in the matrix occurs rapidly (ffiffiffiffiffiDt

p¼ 3:6

lm/s), the nitrided region of thematrix is considered to bein a steady state with respect to N. The actual cross-sec-

tional N concentration profiles (Figs. 4(c) and (d)) agree

well with the calculated results for larger K. Therefore,

the actual reactivity of N towards Al in the matrix

(a-Fe(Al)) is suggested to be high in this system.

Fig. 14 shows the calculation results for

MDt = 7.2 ks. As the aluminized layer becomes ni-

trided, the shapes of the xN and v profiles approachthat of the initial Al distribution. A slight increase

in xN is observed in the substrate (a-Fe), which was

not observed in Fig. 13 for larger K. Fig. 15 shows

the change of each quantity at x = 10, 30, and

50 lm as a function of nitriding time. Here, a tempo-

rary decrease in J (circled region in Fig. 15) occurs at

around 6 ks, corresponding to the time at which the

aluminized layer becomes completely nitrided. FromFig. 15(c), the decrease is apparently brought about

by a decrease in oc/ox attributable to the rapid diffu-

sion of N and the resultant plateau of c in the alumi-

nized layer.

(a)

(c)

Fig. 15. Evolution of (a) volume fraction of nitride; (b) concentration of N i

the surface; and (d) flux of N at x = 10, 30, and 50 lm assuming boundary con

N = 200.

Although the above numerical solutions explain the

experimental results well in terms of the N concentration

profile, particularly for larger K (�1.0 · 1014–1.0 · 1016

lm3/mol/s, n = 1), the precipitation of c 0-Fe4N in the

substrate (a-Fe) before complete nitridation of the alu-

minized layer, as shown in Fig. 6(a), is inconsistent withthe calculation results. This is discussed in Section 4.2.4

in more detail.

4.2.3. Calculation results for boundary condition (7)

Figs. 16(a), (c), and (e) show the results calculated

using the boundary condition (7), that is, assuming that

the matrix is saturated with N (c0 = 6.0 · 10�16 mol N/

lm3) at the surface. The saturation concentration was

derived from the Fe–N binary phase diagram [22] with

other parameters of n = 1, K = 1.0 · 1016 lm3/mol N/s,

Dt = 0.01 s, Dx = 0.5 lm, and N = 200. The calculated

profiles for xN and v for the N-saturated surface (Figs.16(a), (c), and (e)) are almost the same, with a sharp de-

crease before complete nitridation of the aluminized

layer similar to the results obtained assuming constant

J0 (Figs. 13 and 14). However, the time required for

complete nitridation of the aluminized layer under this

calculation condition was less than one quarter of that

required under constant J0 (Fig. 15).

(b)

(d)

n a-Fe(Al); (c) partial differentiation of c with respect to distance from

dition (6): n = 1, K = 1.0 · 1016 lm3/mol N/s, Dt = 0.01 s, Dx = 0.5 lm,

(a) (b)

(c) (d)

(e) (f)

Fig. 16. Variation in (a,b) concentration of N in a-Fe(Al), (c,d) total concentration of N, and (e,f) volume fraction of nitride as a function of distance

from the surface calculated assuming boundary condition (7): n = 1, K = 1.0 · 1016 lm3/mol N/s, Dt = 0.01 s, Dx = 0.5 lm, N = 200.


From Figs. 16(b), (d), and (f), halving c0 (3.0 ·10�16 mol N/lm3) reduces the diffusion rate by about

half. As shown in Figs. 17 and 18, the time required

for saturation of v after the initiation of nitridation be-

comes exactly twofold under this assumption, where c

and J are halved by halving c0. This relationship arisesbecause c varies almost linearly from the surface to the

advancing front of the nitrided layer (Figs. 16(a) and

(b)), and J is given by its gradient. The linearity in c is

thought to originate from the rapid diffusion of N

through the matrix, extracting Al for the formation of

AlN at large K. The break in the c profile is thought to

cause a sudden increase in J at that point, with J decreas-

ing thereafter accompanying the development of the ni-trided layer.

4.2.4. Comparison of boundary conditions

The results for J0 and c0 obtained using the two

boundary conditions (6) and (7) were compared with

the experimental results to determine which model is

the most accurate. As mentioned in Section 4.1,

(Al,Fe)N is thought to be the precipitate in this sys-

tem based on the observed concentration of N. To

satisfy assumption (ii), the increase in nitride abun-

dance was obtained by modifying the initial concen-

tration of Al in the matrix on the basis of the

observed N concentration profile (Fig. 4(e)). Fig. 19

shows the calculated total N concentration for eachboundary condition using values of J0 and c0 that

gave the best agreement with the experimental data

for 873K-14.4ks (4.0 · 10�17 mol N/lm2/s and 4.0 ·10�17 mol N/lm3, respectively). In Fig. 19(b), the

depth of the nitrided region appears to increase para-

bolically with nitriding time (d /ffiffit

p). Here, c0

(4.0 · 10�17 mol N/lm3) is less than one-tenth of the

saturation value (6.0 · 10�16 mol N/lm3). On the otherhand, the profile in Fig. 19(a) is close to the observed

data (Fig. 4(c)–(e)), indicating accelerated growth of

the nitrided layer compared to the case of constant

c0 (Fig. 19(b)). This acceleration is thought to be

due to the gradual increase in c at the surface, as

shown in Fig. 20(b). The temporary decrease in oc/

ox and J corresponds to the time at which nitridation

of the aluminized layer became complete, as discussed

(a) (b)

(c) (d)

Fig. 17. Evolution of (a) volume fraction of nitride; (b) concentration of N in a-Fe(Al); (c) partial differentiation of c with respect to distance from

the surface; and (d) flux of N at x = 10, 30, and 50 lm assuming boundary condition (7): c0 = 6.0 · 10�16 mol N/lm3, n = 1, K = 1.0 · 1016 lm3/mol

N/s, Dt = 0.01 s, Dx = 0.5 lm, N = 200.

(a) (b)

(c) (d)

Fig. 18. Evolution of (a) volume fraction of nitride; (b) concentration of N in a-Fe(Al); (c) partial differentiation of c with respect to distance from

the surface; and (d) flux of N at x = 10, 30, and 50 lm assuming boundary condition (7): c0 = 3.0 · 10�16 mol N/lm3, n = 1, K = 1.0 · 1016 lm3/mol

N/s, Dt = 0.01 s, Dx = 0.5 lm, N = 200.


(a)

(b)

Fig. 19. Calculated total concentration profile for N as a function of distance from the surface fitted to the experimental data for 873K-14.4ks (n = 1,

K = 5.0 · 1014 lm3/mol N/s,Dt = 0.1 s, Dx = 0.5 lm): (a) J0 = 4.0 · 10�17 mol N/lm2/s, (b) c0 = 4.0 · 10�17 mol N/lm3.

(a) (b)

(c) (d)

Fig. 20. Evolution of (a) volume fraction of nitride; (b) concentration of N in a-Fe(Al); (c) partial differentiation of (b) with respect to distance from

the surface; and (d) flux of N at x = 1, 30, and 60 lm assuming boundarycondition(6):J0 = 4.0 · 10�17 mol N/lm3,n = 1,K = 5.0 · 1014lm3/mol N/s,

Dt = 0.1 s, Dx = 0.5 lm, N = 400.


Fig. 21. Schematic cross-sectional illustration of nitridation process

for aluminized high-purity iron: (a) aluminized; (b) partial nitridation

of aluminized layer; (c) complete nitridation.


in Section 4.2.2 (Fig. 15). The experimental results also

support the validity of boundary condition (6), as fol-

lows. Since the temperature of the specimen was main-

tained constant by tuning the discharge power, the heat

balance of the specimen was established by the heat input

due to sputtering of the surface and output due to heatconduction and radiation. Sputtered Fe atoms are con-

sidered to combine with N in the plasma and return to

the surface where N is released upon decomposition.

Thus, N atoms are considered to be steadily supplied

from the surface into the specimen under this condition.

Then, assuming boundary condition (6) to be valid,

the precipitation of c 0-Fe4N in the substrate (a-Fe) be-fore nitridation of the aluminized layer is complete, asshown in Fig. 6(a), can be explained as follows. From

Fig. 5(d), the grain boundaries in the aluminized layer

are preferentially nitrided in the early stage of nitrida-

tion as channels guiding the N atoms into the substrate.

The grain boundaries and immediate vicinity in the alu-

minized layer are completely nitrided within a short time

in the nitridation process. The width of the nitridation

paths is suggested to be �0.5 lm (the N-rich region inFig. 5(d) or the region of high nitride concentration in

Fig. 7). Based on this evidence, the N flux reaching the

substrate is considered to be �J0 · 3600 · 0.016 =

2.3 · 10�15 mol N/lm2/3.6 ks. Here, the factor 0.016 rep-

resents the averaged cross-sectional grain boundary area

(channel cross-section) derived from the number of grain

boundaries in the cross-sectional optical micrographs

and the assumed grain boundary width of 0.5 lm.From Fig. 9(c), the ratio of the XRD peak of

(110)a to that of ð111Þc0 is 22000/55 at the interface

between the aluminized layer and the substrate. Con-

sidering that the substrate (a-Fe) did not exhibit a

characteristic texture, and based on the crude approx-

imation that XRD intensity is proportional to the

product of a form factor of a phase, the multiplicity

factor, Lorentz-polarization factor, and volume frac-tion, the volume fraction of c 0-Fe4N is considered to

be 1.2 · 10�3. The lower magnification image for

Fig. 6(a) shows that the region in which platelets of

c 0-Fe4N are present is �50 lm in thickness. The vol-

ume of c 0-Fe4N in the substrate (1 · 50 lm3) is there-

fore 50 · 1.2 · 10�3 = 0.06 lm3. This indicates that

1.8 · 10�15 mol N was supplied per 1 lm2-3.6 ks,

which agrees well with the value derived from the as-sumed flux and the area fraction of the channel region

(2.3 · 10�15 mol N/lm2/3.6 ks).

The dependence of K on temperature is expressed

as K � exp(�Q/RT), as the formation of nitride is

based on a thermal activation process as shown in

Fig. 11. This means that the formation of AlN and

c 0-Fe4N, and the diffusion of N in a-Fe, are sup-

pressed at lower nitridation temperatures. However,the difference between the temperature dependences

of each rate may result in an increase in c 0-Fe4N with

respect to AlN at lower nitridation temperature. From

this point of view, it is reasonable that the 823K-

14.4ks specimen (Figs. 4(b) and 9(b)) exhibited a com-

parable amount of c 0-Fe4N at the interface betweenthe aluminized layer and the substrate to that dis-

played by the 873K-14.4ks specimen (Figs. 4(d) and

9(d)). The nitridation process derived on this basis is

illustrated schematically in Fig. 21.

5. Conclusions

From a detailed analysis of the composition and

structure of aluminized and nitrided high-purity iron,


it was found that e-Fe2-3N, c 0-Fe4N, and rocksalt AlN

are formed as nitrides during plasma nitridation. The

rocksalt AlN was shown to be likely to contain substitu-

tional Fe, and represents the major contributor to the

hardening of the aluminized layer (�HV1000). The

rocksalt AlN precipitated as platelets satisfying the Ba-ker–Nutting orientational relationship with the matrix

(a-Fe(Al)).

Numerical solutions for a diffusion equation taking

the precipitation of nitrides into account revealed that

Al in the matrix is highly reactive towards N, forbidding

the passage of N into the substrate (a-Fe) before com-

plete nitridation of the aluminized layer. Meanwhile,

the grain boundaries in the aluminized layer are prefer-entially nitrided in the early stage of nitridation and are

thought to represent channels through which N diffuses

to the substrate, promoting the formation of platelet

c 0-Fe4N in the high-purity iron.

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Documents

Plasma nitridation of aluminized high purity iron