Acta Materialia 52 (2004) 2173–2184

www.actamat-journals.com

Aluminization of high purity iron and stainless steelby powder liquid coating

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

a Department of Materials Engineering, Industrial Technology Center of Okayama Prefecture, 5301, Haga, Okayama 701-1296, Japanb Department of Materials Science and Engineering, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan

c Department of Materials Science, Faculty of Engineering, Ibaraki University, 4-12-1 Nakanarusawa, Hitachi, Ibaraki 316-8511, Japan

Received 1 December 2003; received in revised form 1 December 2003; accepted 8 January 2004

Abstract

Powder liquid coating is investigated metallographically as an aluminization technique for high-purity iron [Acta Mater., in

press] and stainless steel. In this process, Fe2Al5 forms initially during heat treatment, with c axis preferentially aligned with the

sample normal. In Fe–18mass%Cr alloy, Cr exhibits almost the same concentration profile as Fe except for the temporary formation

of a Cr5Al8 network in the early stage of heat treatment. Fe–25Cr–18Ni alloy forms a thinner aluminized layer compared to the

other substrates, and contains an Al–Ni-rich layer and spherical precipitates (ordered B2). The diffusion of Al and Ni in the system

(B2/bcc/fcc) is simulated using a new formulation of the diffusion equation for the ternary Fe–Al–Ni system taking the concen-

tration-dependent interdiffusion coefficient into account. The bcc layer is found to be predominantly in a steady state due to the

large interdiffusion coefficients, and characteristic uphill diffusion of Al in the B2 layer is attributed to the existence of Ni.

� 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Powder processing; Aluminization; Steels; Texture; Kinetics

1. Introduction

The present authors recently presented a new methodfor aluminizing the surface of iron and steel [1], utilizing

a slurry of mixed Al and Ti (or Al and Al2O3) powder.

The method involves simply pasting the slurry onto the

substrate and a heating at close to the quenching or

solution temperature of the steels. The thickness and Al

concentration of the modified layer can be readily varied

at low cost by tuning the mixing ratio in the slurry

composition and/or heat treatment conditions. Theprocess can be applied to harden steel surfaces, as the

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

630.

E-mail addresses: kouji_murakami@pref.okayama.jp (K. Mura-

kami), norihide_nishida@pref.okayama.jp (N. Nishida), osamura@

hightc.mtl.kyoto-u.ac.jp (K. Osamura), tomota@mx.ibaraki.ac.jp

(Y. Tomota), tetsuya@mx.ibaraki.ac.jp (T. Suzuki).

1359-6454/$30.00 � 2004 Acta Materialia Inc. Published by Elsevier Ltd. A

doi:10.1016/j.actamat.2004.01.009

subsequent nitridation creates hard nitrides and induces

internal stress in the modified layer [2,3]. The aluminized

and subsequently nitrided surfaces have high hardnessesof about HV1500, and also exhibit excellent resistivity

against erosion by molten Al. These properties make

long-run casting operations possible, where severe me-

chanical erosion and metallurgical reaction of steels with

molten Al cause deterioration in dies, pins, or other

construction materials in injection molding machines.

The corrosion resistance of stainless steels is also im-

proved by aluminization [4], with potential applicationsin environments involving of molten salt corrosion [5,6]

or vanadium attack. In this study, the process applied to

high-purity Fe was reexamined crystallographically,

followed by similar investigations of the aluminized

layers in ferritic and austenitic stainless steels. The dif-

fusion equation for the multi-component system is

treated numerically here using a new formulation that

takes the concentration-dependent interdiffusion coeffi-cient into consideration.

ll rights reserved.

2174 K. Murakami et al. / Acta Materialia 52 (2004) 2173–2184

2. Experimental

Disks of high-purity Fe (99.9%), Fe–Cr alloy (com-

mercial ferritic stainless steel, Fe–18mass%Cr), and Fe–

Cr–Ni alloy (austenitic, Fe–25Cr–18Ni) were used assubstrates. The surface of 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. A slurry was prepared by stirring a mixture of

atomized Al powder (under 3 lm in diameter), crushed

Ti (under 38 lm) and ethylene glycol (5.0� 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 pastedonto the disks at 0.65 mg/mm2, and the specimens were

heated in an oven at 473 K for 3.6 ks to remove ethylene

glycol. Each of the prepared disks was then heated in a

quartz cylinder by infrared radiation in a vacuum of

1.3� 10�3 Pa. In order to investigate the evolution of

the aluminized layer of the substrates, the heat treat-

ment conditions were varied as shown in Fig. 1. For

final heating, the temperature was raised at 1.33 K/s,after which the samples were cooled under N2 gas flow

(about )2 K/s) to room temperature. As shown in

Fig. 1, the heat treatment conditions are denoted here-

after in the form T 0 K–cooled or T K–t ks.X-ray diffraction (XRD) patterns of the aluminized

sample surface were measured in order to identify pha-

ses and textures. The microstructure of the modified

layer was observed by optical microscopy, electronprobe microanalysis (EPMA), and Auger electron

spectrometry (AES) with micro ion etching equipment.

Fe (Cr,Ni) and Al concentration profiles were quanti-

tatively measured by EPMA with ZAF matrix correc-

Fig. 1. Heat treatment pattern.

Fig. 2. Sample coordinates used in XRD and EBSD.

tion. Electron backscattering diffraction (EBSD) was

employed to collect local crystal orientations on sample

cross sections and to analyze the growth of the alumi-

nized region. Sample coordinates for XRD and EBSD

are depicted in Fig. 2.

3. Experimental results

3.1. Aluminized layer in high-purity Fe

As reported previously [1], the aluminized layer was

formed by heat treatment under conditions of 1173 K–cooled. Fig. 3(a) shows an XRD pattern obtained by 2h–h scan. According to reported diffraction data [7] for the

isotropic powder of Fe2Al5 (space group number 63,

orthorhombic, a ¼ 0:76559, b ¼ 0:64154, c ¼ 0:42184nm), the (2 2 1) diffraction intensity is largest and about

three times that of (0 0 2). Comparing the data with the

present diffraction pattern, it is apparent that the Fe2Al5layer is highly textured, and the pole figure of the Fe2Al5(0 0 2) plane (Fig. 3(b)) actually reveals a fibrous texture

with a sharp peak at the center and a second peak at 60�around the z axis. Fig. 4(a) shows a cross-sectional

Fig. 3. XRD patterns of surface of aluminized high-purity Fe: (a) 2h–hscan, (b) Fe2Al5 (0 0 2) pole figure.

Fig. 4. Cross-sectional microstructure of high-purity Fe aluminized

under conditions of 1173 K–cooled: (a) secondary electron image after

Ar ion etching, (c) histogram of crystal direction b in (b), (d) grain

boundary map of a-Fe.

Fig. 5. Ternary phase diagram for the Fe–Al–Cr system at 1273 K

(calculated using Thermo-Calc) and diffusion path (1273 K–3.6 ks).

Fig. 6. Cross-sectional microstructure of aluminized high-purity Fe:

(a) 1273 K–0.3 ks, (b) 1273 K–3.6 ks.

K. Murakami et al. / Acta Materialia 52 (2004) 2173–2184 2175

secondary electron image obtained by AES after Ar ion

etching. The image reveals Fe2Al5, the substrate (a-Fe),and columnar a-Fe at the interface. The orientation of

the c axis of Fe2Al5 grains is shown in Fig. 4(b). The

majority of grains are aligned with c axes subparallel

with the z axis. However, 90% of the oriented Fe2Al5grains had misorientation by more than 10� with eachother, and no characteristic orientational relationship

could be identified. The Fe2Al5 layer overlies the co-

lumnar a-Fe, as shown in Fig. 4(d), where misalignment

of adjacent grains is mostly within 10�. No clear FeAl2layer formed in the 1173 K–cooled sample, whereas a 10

lm-thick layer of FeAl2 was observed by EPMA in the

sample treated under conditions of 1273 K–cooled. This

1273 K–cooled sample exhibited a relatively smoothFe2Al5/FeAl2/a-Fe interface with textured Fe2Al5 (ckz).

In the 1273 K–0.3 ks sample, the Fe2Al5 and FeAl2compound layers were no longer apparent, and the en-

tire aluminized layer consisted of a-Fe. As shown in

Fig. 5, the solid solubility of Al in a-Fe is so broad that

all Al at the surface can be involved in the a-Fe phase.

The orientational relationship of a-Fe grains was ob-

served by EBSD analysis for samples treated underconditions of 1273 K–0.3/0.9/1.8/3.6/7.2 ks. Selected

grain boundary maps are shown in Fig. 6. The bound-

aries between the substrate and the diffusion layer were

preserved during the growth of the diffusion layer (a-Fe), and the misalignment is less than 1�. At treatment

above 1185 K, the substrate was c-Fe. Misalignment

between the additive and diffusion layers was observed

to become smaller as heat treatment was prolonged, asexpressed quantitatively in Fig. 7. Here, the misalign-

ment histograms were calculated from 1000 pairs of

adjacent points across the additive/diffusion layer in-

terface in 1 lm steps.

3.2. Aluminized layer in Fe–Cr alloy

Fig. 8(a) shows a cross-sectional compositional imageof the aluminized Fe–Cr alloy (1173 K–cooled). Two

intermetallic compound layers; Fe2Al5, and FeAl2 and

Fig. 8. Cross-sectional compositional image of aluminized Fe–Cr alloy:

(a) 1173 K–cooled, (b) 1273 K–cooled.

(a)

(c)

(b)

Fig. 9. Concentration profiles of: (a) Al, (b) Fe, and (c) Cr in Fe–Cr

alloy aluminized at 1273 K for 3.6 ks.

Fig. 10. Cross-sectional grain boundary maps of aluminized Fe–Cr

alloy: (a) 1273 K–3.6 ks (vertical arrow denotes the diffusion path in

Fig. 5), (b) 1173 K–3.6 ks.

Fig. 7. Histogram of misalignment between additive layer and diffusion

layer in high-purity Fe (1 lm step, 1000 points for each specimen).

2176 K. Murakami et al. / Acta Materialia 52 (2004) 2173–2184

a-Fe, formed on the substrate (a-Fe). In the FeAl2 layer,

a second phase Cr5Al8 is observed as a bright network in

the image. The Fe2Al5 layer has a fibrous texture (ckz),as determined by XRD (2h–h scan) and EBSD. The a-Feregion does not have a columnar structure in this case,

instead forming a flat a/FeAl2 interface. In the sample

prepared under conditions of 1273 K–cooled (Fig. 8(b)),

an intermetallic compound of FeAl2 and a-Fe phaseswere observed.

The concentration profiles of Al, Fe, and Cr in the a-Fe layer of the samples 1273 K–0.3, 0.9, 1.8, 3.6 ks are

shown in Fig. 9. Spikes in the profiles correspond to

AlN particles formed due to N originally present in the

substrate. The Al profiles weakened gradually and fi-

nally disappeared in the a-Fe(Cr) region, whereas there

was a concentration gap in high-purity Fe at the inter-

face between the diffusion layer and the substrate, con-

sistent with the previous report [1]. Cr coexistedpreferentially with Al at 1173 K as shown in Fig. 8(a),

but did not form intermetallic compounds at 1273 K–0.3

ks or above, and the Cr content decreased gradually

toward the surface.

Fig. 10(a) shows a grain boundary map of the alu-

minized Fe–Cr alloy (1273 K–3.6 ks). Misalignment

between adjacent grains across the additive/diffusion

layer interface was mostly within 5�, and the grain size inthe vicinity of the surface was similar to that in the

substrate. However, a diffusion layer began to grow in

the coarse columnar structure toward the substrate. In

the Fe–Cr alloy aluminized at 1173 K–3.6 ks, shown

in Fig. 10(b), grains close to the additive/diffusion layer

interface appear similar to those in the 1273 K–3.6 ks

case with almost the same orientation, differing only

in that the grain boundaries of the substrate werepreserved throughout the diffusion layer.

K. Murakami et al. / Acta Materialia 52 (2004) 2173–2184 2177

3.3. Aluminized layer in Fe–Cr–Ni alloy

In the aluminization of Fe–Cr–Ni alloy, unlike the

cases for high-purity Fe and Fe–Cr alloy, an FeAl3 layer

with no characteristic texture was detected by XRD forthe 1073 K–cooled sample. However, the sample had a

flat interface similar to that obtained in the case of Fe–

Cr alloy. The Fe2Al5 layer, confirmed by EPMA anal-

ysis in the 1173 K–cooled sample, was not present in the

1273 K–cooled sample.

Fig. 11. Cross-sectional microstructures in Fe–Cr–Ni alloy aluminized under c

map, (e) grain boundary map.

Fig. 12. Cross-sectional microstructures in Fe–Cr–Ni alloy aluminized under c

map.

In Fig. 11, three characteristic boundaries parallel to

the surface can be observed. Boundary (ii) corresponds

to the additive/diffusion interface, (iii) is the interface

between the diffusion layer and the substrate, and

boundary (i) in the additive layer separates two regionsof different grain size. The coarse-grain region in the

additive layer, between (i) and (ii) in Fig. 11(e), corre-

sponds to the Ni-rich layer in Fig. 11(b). The Ni con-

centration in the coarse-grain region was 10–20 at.%,

whereas that in the fine-grain region was 3–9 at.%.

onditions of 1273 K–cooled: (a) Al map, (b) Ni map, (c) Fe map, (d) Cr

onditions of 1273 K–3.6 ks: (a) Al map, (b) Ni map, (c) grain boundary

umnar,wav.:wavy,net.:network,fin.:fine,

coa.:coarse,

sph.:spherical,(a;c):phase

ofsubstrate

atroom

temperature)

Fe–Cr

Fe–Cr–Ni

3.6

ks

1173K–cooled

1273K–cooled

1173K–3.6

ks

1273K–0.3–3.6

ks

1073K–cooled

1273K–cooled

1273K–0.3–3.6

ks

Fe 2Al 5FeA

l 2Cr 5Al 8(net.)

FeA

l 2a-Fe

a-Fe

a-Fe

FeA

l 3B2(fin.)B2

(coa.)

B2(A

l–Ni-poor)

B2(A

l–Ni-rich)

–a-Fe

a-Fe

a-Fe

–a-Fe

a-FeB2(sph.)

aðaÞ

cðcÞ

Fig. 13. Concentration profiles for Al, Ni, Fe, and Cr in Fe–Cr–Ni

alloy aluminized under conditions of 1273 K–3.6 ks.

2178 K. Murakami et al. / Acta Materialia 52 (2004) 2173–2184

An Al–Ni-rich layer formed in the additive layer for

sample treated under heating conditions of 1273 K–

cooled or higher, and spherical Al–Ni-rich regionsbecame distributed separately in the diffusion layer in the

samples treated at above 1273 K–0.3 ks. These Al–Ni

regions evolved into the structure shown in Fig. 12(a)

and (b), where Al and Ni coexist preferetially in the same

area. In Fig. 12(c), there is no grain morphology by

which the Al–Ni-rich layer can be distinguished in the

additive layer, and the orientation of Al–Ni-rich particles

is consistent with that of the surrounding diffusion layermatrix. The Al, Ni, Fe, and Cr concentration profiles of

the 1273 K–3.6 ks sample are plotted in Fig. 13. Al and

Ni both exhibit similar a variation, whereas Fe and Cr

vary complementarily. The concentration varied gradu-

ally in the Al–Ni-poor layer of the additive layer and also

in the diffusion layer, whereas a concentration gap oc-

curred at the interface between the diffusion layer and the

substrate. Phase formation in the aluminized layers andthe substrate in high-purity Fe, Fe–Cr, and Fe–Cr–Ni

alloy is summarized in Table 1.

Table

1

Phase

form

ationin

aluminized

layer

andsubstrate.(col.:col

Substrate

Fe

Heat

treatm

ent

1173K–cooled

1273K–cooled

1273K–0.3–

Additive

layer

Fe 2Al 5

a-Fe(col.)

Fe 2Al 5FeA

l 2a-Fe(w

av.)

a-Fe

Diffusion

layer

–a-Fe

a-Fe

Substrate

aðaÞ

cðaÞ

4. Discussion

4.1. Phase transformation and grain growth during

aluminization of high-purity Fe

From the thermochemical data [8], the free energy of

FeAl3 formation is the lowest among the solid phases.

However, Fe2Al5 has been reported to be the first phase

that appears in hot dipping processes [9,10]. The growth

rate of reaction layer when an Fe substrate is dipped

into molten Al is given by

d2 ¼ kt; ð1Þwhere d is the thickness of the reaction layer, t is the

holding time, and k is a constant. The reported value of

k is 2.2� 102 lm2/s for Fe2Al5 at 988 K [11], and

Fig. 14. Schematic illustration of decomposition of intermetallic compounds and growth of a-Fe on high-purity Fe substrate: (a) immediately after

contact with molten Al, (b) 1173 K–cooled, (c) 1273 K–cooled, (d) held at 1273 K.

K. Murakami et al. / Acta Materialia 52 (2004) 2173–2184 2179

2.1� 101 lm2/s for FeAl3 [12]. This large difference isrelated to the differing diffusion properties of Fe2Al5and FeAl3, which have interdiffusion coefficients at

1273 K of 4.74� 102 [13] and 1.00� 101 [14] lm2/s,

respectively. The unit cell of Fe2Al5 is characteristic in

having densely packed Al columns along the c axis,

which is the shortest of its axes. Therefore, movement

of vacancies has been suggested to fastest along the caxis in Fe2Al5, in comparison to other directions [11].From these reports, it can be said that the phase

transformation in the early stage of this process is al-

most the same as that for hot dipping. The development

of a strong fibrous texture by Fe2Al5 with c axis alignedparallel with the z direction is explained as due to the

minimization of surface energy between molten Al and

Fe2Al5, the (0 0 l) planes of which are thought to be the

most densely packed and smooth, giving the lowestsurface energy.

When the a-Fe phase nucleates at the interface be-

tween Fe2Al5 and a-Fe (Fig. 14(a)), the excess Al atoms

may diffuse into the substrate or the Fe2Al5 layer. As no

meaningful amount of Al was detected in the 1173 K–

cooled sample [1], the excess Al is thought to diffuse into

the Fe2Al5 layer initially due to the large interdiffusion

coefficient for the Fe2Al5 phase. The interface frontwould then proceed toward the Fe2Al5 phase, producing

the columnar a-Fe phase structure as shown in

Fig. 14(b). Growth of the a-Fe region is accelerated with

increasing temperature, accompanied by increased Al

diffusion into the substrate and the formation of FeAl2between Fe2Al5 and a-Fe (Fig. 14(c)). As columnar

grains of a-Fe phase are observed in high-purity Fesamples aluminized under conditions of 973 K–3.6 ks

[1], the nucleation sites of a-Fe are suggested to be

sparsely dispersed. The increase in nucleation frequency

and active diffusion lead to the less wavy Fe2Al5/FeAl2/

a-Fe interface with increasing temperature, and the

small a-Fe grains in the additive layer are gradually

grown over by the large adjacent grains in the diffusion

layer (Fig. 14(d)).

4.2. Effect of Cr and Ni in the aluminization of Fe–Cr and

Fe–Cr–Ni alloy

In the aluminized Fe–Cr alloy, the concentration gap

in the Al, Fe, and Cr profiles for the other substrates was

not observed (Fig. 9). This is because the substrate

composition falls outside of the c-loop at 1273 K asshown in Fig. 5, that is, the substrate remained as a-Fethroughout heat treatment. The diffusion path in the

1273 K–3.6 ks sample lies on the isothermal section of

the Fe–Al–Cr phase diagram (Fig. 5), however, the in-

terdiffusion coefficients for this system have not yet been

reported. In Fig. 10(a), the grain boundaries in the

substrate appear to have been preserved in the vicinity

of the additive/diffusion layer interface, as can also beobserved in the map in Fig. 10(b). The preservation of

grain boundaries is thought to be determined by the

aluminizing temperature; the diffusion layer forming in

the early stages of heating preserves the grain bound-

aries in the substrate, while subsequent heating above a

certain temperature (between 1173 and 1273 K) results

Fig. 15. Ternary phase diagram for the Fe–Al–Ni system at 1273 K [25]

and diffusion path in sample 1273 K–3.6 ks (Fe concentration is the

sum of the observed values of Fe and Cr).

2180 K. Murakami et al. / Acta Materialia 52 (2004) 2173–2184

in the formation of the columnar structure, overwriting

the original features.

In the aluminized Fe–Cr–Ni alloy (Fig. 11, 1273 K–

cooled), the diffusion layer (a-Fe) developed to a

thickness of about 3 lm into the substrate, seemingly

due to a lack of c-form Ni in the substrate rather than

due to the existence of a-form Al. The Al and Ni con-centration profiles were characteristic, indicating an

enriched layer in these two elements around the additive/

diffusion layer interface as well as precipitates in the

diffusion layer. According to the ternary phase diagram

for the Fe–Al–Ni system (Fig. 15), these spherical pre-

cipitates are thought to represent ordered B2 phase,

presumably formed during cooling through the en-

largement of the B2+bcc region with decreasing tem-perature as reported by [15,16].

The concentration gap in the elements at the interface

between the diffusion layer and the substrate, as shown

in Fig. 13, is observed for both aluminized high-purity

Fe [1] and aluminized Fe–Cr–Ni alloy. It should be

noted that the Al concentration gradient is very low in

the diffusion layer (Fig. 13) compared with the result for

the high-purity Fe [1]. This fact may explain the signif-icant difference in thickness of the aluminized layer for

these two substrates; about 110 lm for 1273 K–3.6 ks

high-purity Fe, and 30 lm for Fe–Cr–Ni alloy. As the

quaternary phase diagram for the Fe–Cr–Ni–Al system

has yet to be reported, the ternary Fe–Al–Ni phase di-

agram will be considered in the present discussion as-

suming that the diffusion of Cr is similar to that of Fe in

the a-Fe phase because Cr is a ferritic element with largebcc region in the Fe–Cr binary system. Although the

presence of Cr is expected to result in enlargement of the

a region and shrinkage of the c region in the phase di-

agram, this assumption of diffusion is also supported by

the very similar intrinsic diffusion coefficients of Fe and

Cr at 1273 K in an Fe-based bcc alloy (3.2� 10�3 and

2.7� 10�3 lm2/s, respectively [17]). Qualitatively, the

Al–Ni-rich layer, corresponding to the B2 phase in

Fig. 15, is thought to lower the diffusion rate, as the

diffusion of Al and Ni reduces the degree of order of the

B2 alloy. Fe has been reported to substitute into both Aland Ni sites [18]. Therefore, Al supply from the additive

layer into the diffusion layer is supported by the sub-

stitution of Fe from the substrate, avoiding a reduction

in the degree of order. However, Ni supply into the

additive layer leads to disorder in the B2 phase. The

numerical analyses below will provide a quantitative

description of this ternary diffusion system.

4.3. Numerical analysis of diffusion in the aluminization of

Fe–Cr–Ni alloy

4.3.1. Formulation and calculation procedure

The numerical analysis reported previously [1] is ex-

tended here to deal with a ternary system. Flux in the

system is expressed in terms of the concentration of two

solute elements as follows [19–21]:

~Jijðt; xÞ ¼ �~D3ij

ocjðt; xÞox

; ð2Þ

~Jiðt; xÞ ¼ ~Ji1ðt; xÞ þ ~Ji2ðt; xÞ: ð3Þ

Here i ¼ 1 (Al), 2 (Ni), and the superscript 3 to the right

of ~D indicates an dependent element (Fe). The conser-

vation of each solute element leads to the followingdiffusion equations for the ternary system.

ociðt; xÞot

¼ o

ox~D3i1ðxÞ

oc1ðt; xÞox

�þ ~D3

i2ðxÞoc2ðt; xÞ

ox

�06 x < 1;

06 t < 1:

�ð4Þ

The value of ci (in mol/mm3) is calculated using the

following equation:

ci ¼xi

xAlvAl þ xNivNi þ ð100� xAl � xNiÞvFe: ð5Þ

This equation takes the atomic percent xi and the

molar volume of each element vi (vAl ¼ 10:0� 103,

vNi ¼ 6:60� 103, vFe ¼ 7:10� 103 mm3/mol) for sim-

plicity. Each side of Eq. (4) is rewritten as follows:

l:h:s of ð4Þ ¼ ciðtþDt; xÞ � ciðt; xÞDt

� 1

2

o2ciot2

DtþOððDtÞ2Þ;

ð6Þ

r:h:s of ð4Þ

¼ 1

2ðDxÞ2~D3i1ðx

n�þ DxÞ½c1ðt; xþ DxÞ � c1ðt; xÞ�

þ ~D3i2ðxþ DxÞ½c2ðt; xþ DxÞ � c2ðt; xÞ�

� ~D3i1ðxÞ½c1ðt; xÞ � c1ðt; x� DxÞ�

oK. Murakami et al. / Acta Materialia 52 (2004) 2173–2184 2181

� ~D3i2ðxÞ½c2ðt;xÞ�c2ðt;x�DxÞ�

þ ~D3i1ðx

nþDxÞ½c1ðtþDt;xþDxÞ�c1ðtþDt;xÞ�

þ ~D3i2ðxþDxÞ½c2ðtþDt;xþDxÞ�c2ðtþDt;xÞ�

� ~D3i1ðxÞ½c1ðtþDt;xÞ�c1ðtþDt;x�DxÞ�

� ~D3i2ðxÞ½c2ðtþDt;xÞ�c2ðtþDt;x�DxÞ�

o��1

2

o

oxo~D3

i1

oxoc1ox

þo~D3

i2

oxoc2ox

!Dx

�1

2

o2ciot2

DtþOðDtDxÞ: ð7Þ

Substituting Eq. (6) and (7) into Eq. (4) gives the dif-

ference equation with a round-off error of OðDtDxÞ. InEq. (7), m and n represent time and position, respec-

tively, that is, t ¼ mDt (m ¼ 0; 1; . . . ;M � 1) and x ¼ nDx(n ¼ 0; 1; . . . ;N � 1). Using m and n, the difference

equation is given by

ci;mþ1;n � ci;m;n

¼ a2½~D3

i;1;nþ1ðc1;m;nþ1 � c1;m;nÞ þ ~D3i;2;nþ1ðc2;m;nþ1 � c2;m;nÞ

� ~D3i;1;nðc1;m;n � c1;m;n�1Þ � ~D3

i;2;nðc2;m;n � c2;m;n�1Þþ ~D3

i;1;nþ1ðc1;mþ1;nþ1 � c1;mþ1;nÞþ ~D3

i;2;nþ1ðc2;mþ1;nþ1 � c2;mþ1;nÞ� ~D3

i;1;nðc1;mþ1;n � c1;mþ1;n�1Þ� ~D3

i;2;nðc2;mþ1;n � c2;mþ1;n�1Þ�; ð8Þ

where

a ¼ Dt

ðDxÞ2: ð9Þ

Although there are 2N unknown values (ci;mþ1;0;ci;mþ1;1; . . . ; ci;mþ1;N�1 ði ¼ 1; 2Þ), the number of inde-

pendent equations generated from Eq. (8) is 2N � 4

(i ¼ 1; 2 and n ¼ 1; 2; . . . ;N � 2). Four additional

equations are derived from the following boundary

conditions as described in [1].

ci;mþ1;0 � ci;m;0

¼ a2

~D3i;1;0ðc1;m;2

hn� 2c1;m;1 þ c1;m;0Þ

þ ~D3i;2;0ðc2;m;2 � 2c2;m;1 þ c2;m;0Þ

iþ ~D3

i;1;0ðc1;mþ1;2

h� 2c1;mþ1;1 þ c1;mþ1;0Þ

þ ~D3i;2;0ðc2;mþ1;2 � 2c2;mþ1;1 þ c2;mþ1;0Þ

io; ð10Þ

ci;m;N�1 ¼ 0: ð11ÞTreatment of the B2/bcc and bcc/fcc interface is

handled in the same as in [1], i.e.,

DX ¼~J1;m;k � ~J1;m;kþ1

c1;m;k � c1;m;kþ1

Dt: ð12Þ

Here X is the position of the interface (kDx6X 6

ðk þ 1ÞDx), and DX is the movement of the interface in

Dt.The observed concentration profile (1273 K–0.3 ks)

was used for the initial condition. The values of the

observed concentration profile, which corresponds to

the bcc structure (circled area in Fig. 18(a)), were shifted

to the bcc region of the Fe–Al–Ni phase diagram (cir-

cled area in Fig. 18(b)). The time increment and spatialresolution were set at Dt ¼ 0:05 s and Dx ¼ 0:2 lm. In-

terdiffusion coefficients were taken from [22–25], as

plotted in Fig. 16. These interdiffusion coefficients indi-

cate that diffusion in the bcc region is much faster than

that in the B2 or fcc regions, that is, the Al–Ni-rich layer

(B2) at the additive/diffusion interface acts as a barrier

to the supply of Al from the additive layer into the

diffusion layer. Thus, it is qualitatively recognizedthat almost flat concentration profiles at the surface of

the additive layer and in the diffusion layer result

from the highly concentration-dependent interdiffusion

coefficients.

4.3.2. Calculation results

Figs. 17 and 18 show the observed and calculated

concentration profiles and diffusion paths for the alu-

minized Fe–Cr–Ni alloy. The calculated results repro-

duce the concentration profiles in the Al–Ni-poor and

Al–Ni-rich regions well, particularly in terms of the

gentle slope of the profile in the Al–Ni-poor layer. Theconcentration gap at the bcc/fcc interface was also

properly represented. These results are in qualitative

agreement with the observed data, except for the

thickness of the aluminized layer, which is overestimated

by a factor of two or more. In the Al–Ni-poor region of

the additive layer, the Al concentration decreased

monotonically with time, even though the partial de-

rivative of Al concentration with respect to x is positive(oc1=ox > 0).

This uphill diffusion phenomenon indicates that the

total flux of Al (Eq. (3)) is positive (~J1 > 0). This can be

explained based on the present calculations as follows.

The partial derivative of ci with respect to x was calcu-

lated by considering a cubic and its derivative at each

point by the Savitzky–Golay method (5-point-smooth-

ing). As a consequence of the sum of partial flux (~J11 < 0and ~J12 > 0), the total flux of Al (~J1 ¼ ~J11 þ ~J12) be-

comes positive in the Al–Ni-poor region (Fig. 19(a) and

(c)). The derivative of flux for the diffusion of Ni ~J2 withrespect to x changes sign at the Ni concentration peak.

This means that the Ni concentration increases in the

Al–Ni-poor region of the additive layer and decreases in

the region between the peak and the additive/diffusion

layer interface, leading to shrinkage of the B2 layer as

(a)

(c) (d)

(b)

Fig. 16. Interdiffusion coefficients for the Fe–Al–Ni system at 1273 K reported by [22–25]: (a) ~Dð3Þ1;1, (b)

~Dð3Þ1;2, (c)

~Dð3Þ2;1, (d)

~Dð3Þ2;2.

(a) (b)

(d)(c)

Fig. 17. Observed and calculated concentration profiles of the sample aluminized at 1273 K: (a) observed Al concentration, (b) calculated Al

concentration, (c) observed Ni concentration, (d) calculated Ni concentration.

2182 K. Murakami et al. / Acta Materialia 52 (2004) 2173–2184

(a) (b)

Fig. 18. Observed and calculated diffusion paths of the sample

aluminized at 1273 K: (a) observed, (b) calculated.

K. Murakami et al. / Acta Materialia 52 (2004) 2173–2184 2183

shown in Fig. 17(b). The entire aluminized layer is then

thought to consist solely of bcc phase.

The diffusion rate of Al and Ni was qualitatively

discussed in Section 4.2, which can be discussed basedon the difference observed in Fig. 19. Around the peak

position in the Al and Ni concentration profile, j~J1j islarger than j~J2j. This flux imbalance suggests that the

decrease in Al concentration is compensated not only by

the incoming Ni flux toward the surface, but also by the

flux of Fe, which can substitute into both Al and Ni sites

without decreasing the degree of order in B2 NiAl alloy

[18].In the diffusion layer, the variation in the concen-

tration profile is almost linear between the B2/bcc and

bcc/fcc interfaces. This can be explained in terms of the

(a) (b

(c)

Fig. 19. Calculated flux profiles: (a) J1 and J1j (ini.+0.6 ks), (b) J2 and J2j

interdiffusion coefficients in the bcc region, which are

much larger than those in other phases. In contrast to

the B2 and fcc regions, the bcc region is in a steady state

(oci=ot ’ 0), resulting in a linear compositional varia-

tion regardless of the changes in the position of the B2/bcc and bcc/fcc interfaces. The dominant term in the

numerator of Eq. (12) is ~J1;m;k at the bcc/fcc interface, asshown in Fig. 19. Therefore, the velocity of bcc/fcc

boundary movement DX=Dt can be discussed directly

based on the gradient of the Al concentration profile in

the bcc layer. As the calculated gradient of the Al con-

centration in the bcc layer is much larger than in the

observed data (Fig. 17(a) and (b)), a higher gradient isthought to result in the thicker aluminized layer. In

other words, the large discrepancy between the observed

and the calculated thickness of the aluminized layer is

attributable to the differences in B2/bcc and bcc/fcc in-

terface concentration.

As discussed above, the thickness of the diffusion

layer is suggested to be governed by the difference in

interdiffusion coefficients between phases and the dif-ference in the equilibrium concentration between the

two extremes of the bcc region in the phase diagram. It

is thought that the change in Al and Ni concentration

along the diffusion path in the bcc layer is limited by the

existence of Cr, which modifies the phase diagram of the

Fe–Al–Ni ternary system, shifting the B2/bcc phase

boundary toward the origin in Fig. 18. From this

viewpoint, an appropriate amount of Cr in the substrateis effective for suppressing any deterioration in oxidation

resistivity as a result of secondary diffusion in high-

temperature service.

)

(d)

(ini.+0.6 ks), (c) J1 and J1j (ini.+3.3 ks), (d) J2 and J2j (ini.+3.3 ks).

2184 K. Murakami et al. / Acta Materialia 52 (2004) 2173–2184

5. Conclusions

The main results obtained in this study can be sum-

marized as follows:

1. In the aluminization of high-purity Fe, Fe2Al5formed first, aligned with [0 0 1] direction parallel

with the z axis of the sample, followed by the decom-

position of the intermetallic compound layer to form

a-Fe. After complete conversion of the aluminized

layer to a-Fe, grains in the additive layer became

aligned with the diffusion layer.

2. The formation and decomposition process for the in-

termetallic compound layer in the aluminization ofFe–Cr alloy proceeded in almost the same as for

high-purity Fe. Both the aluminized layer and the

substrate formed a bcc structure during heat treat-

ment due to the presence of a-form Cr. In this case,

there was no clear interface between the diffusion

layer and the substrate in the concentration profile.

However, characteristic columnar grains correspond-

ing to the diffusion layer formed during heat treat-ment at 1273 K. At lower temperature, 1173 K,

the original grain boundaries in the substrate were

preserved.

3. In the aluminization of Fe–Cr–Ni alloy, an Al–Ni-

rich layer (ordered B2 phase) formed in the additive

layer in the early stage of heat treatment. Each ele-

ment diffused through the ordered layer, resulting in

the growth of the diffusion layer (bcc) as a columnarstructure with spherical Al–Ni-rich precipitates and a

flat interface with the substrate. The thickness of the

diffusion layer was 20 lm, in contrast to 70 and 100

lm for high-purity Fe and Fe–Cr alloy, respectively.

4. Numerical analysis of the Fe–Al–Ni ternary system

satisfactorily explained the uphill diffusion of Al in

the Al–Ni-poor region of the additive layer, where

oc1=ox > 0. This occurs because the flux of Al is de-fined not only by the concentration profile of Al,

but also by that of Ni, which contributes to makeeJ1 positive, resulting in the supply of Al from the ad-

ditive layer to the diffusion layer. The equilibrium

concentration at the B2/bcc and bcc/fcc interfaces

derived from the phase diagram and the diffusion

path is an important factor determining the growth

rate of the diffusion layer, as well as the interdiffusion

coefficients for each phase.

References

[1] Murakami K, Nishida N, Osamura K, Tomota Y. Acta Mater.

2003, doi:10.1016/j.actamat.2003.11.011, in press.

[2] Tsuji S, Furusawa T, Saitou T, Kamata M. J Jpn Inst Met

1995;59:726.

[3] Tsuji S. J Jpn Inst Met 1999;63:145.

[4] Ueda S, Tominaga H, Mitsuda S. J Met Finish Soc Jpn

1973;24:681.

[5] Tortorelli PF, Bishop PS. US Department of Energy Reports,

ORNL-TM-11598, 1991.

[6] Oka K. Graduate thesis, Department of Mechanical Engineering,

Faculty of Engineering, Okayama university, 2002.

[7] Burkhardt U, Grin Y, Ellner M, Peters K. Acta Crystall

1994;50:313.

[8] Ivanov EG. Metal Sci Heat Treat 1979;21(5/6):449.

[9] Richards RW, Jones RD, Clements PD, Clarke H. Int Mat Rev

1994;39(5):191.

[10] Bindumadhavan PN, Makesh S, Gowrishankar N, Wah HK,

Prabhakar O. Surf Coat Technol 2000;127:252.

[11] Heumann T, Dittrich S. Z Metall 1959;50:617.

[12] Eremenko VN, Nantanzon VY, Dybkrov VI. Russ Metall

1973;5:66.

[13] Neverov VE, Pimenov VN. Fiz N Chim Obrab Meter 1980;5:104.

[14] Bamola PK, Seigle LL. Metall Trans A 1989;20A:2561.

[15] Bradley AJ. J Iron Steel Inst 1949;163:19.

[16] Bradley AJ. J Iron Steel Inst 1951;165:233.

[17] Sugihara M, Yamazaki Y, Takaki S, Abiko K, Iijima Y. Mater

Trans JIM 2000;41:87.

[18] Minamino Y, Koizumi Y, Takaki S. Mater Jpn 2000;39(6):493.

[19] Onsager L. Phys Rev 1931;37:405.

[20] Onsager L. Ann NY Acad Sci 1945-46;46:241.

[21] Bakker H et al. Landolt–B€ornstein, Numerical data and func-

tional relationships in science and technology, new series, group

III. In: Diffusion in solid metals and alloys, vol. 26. Berlin:

Springer-Verlag; 1990.

[22] Moyer TD, Dayananda MA. Metall Trans A 1976;7A:1035.

[23] Cheng GH, Dayananda MA. Metall Trans A 1979;10A:1407.

[24] Moyer TD, Dayananda MA. Metall Trans A 1979;10A:1415.

[25] Sohn YH, Dayananda MA. Metall Mater Trans A

2002;33A:3375.