Kinetic investigation and wear properties of fe2 b layers on aisi 12l14 steel

1 23
Metallurgical and Materials
Transactions A
ISSN 1073-5623
Volume 49
Number 5
Metall and Mat Trans A (2018)
49:1895-1907
DOI 10.1007/s11661-018-4535-1
Kinetic Investigation and Wear Properties
of Fe2B Layers on AISI 12L14 Steel
M. Keddam, M. Ortiz-Dominguez,
M. Elias-Espinosa, A. Arenas-Flores,
J. Zuno-Silva, D. Zamarripa-Zepeda &
O. A. Gomez-Vargas

1 23
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Kinetic Investigation and Wear Properties of Fe2B
Layers on AISI 12L14 Steel
M. KEDDAM, M. ORTIZ-DOMINGUEZ, M. ELIAS-ESPINOSA,
A. ARENAS-FLORES, J. ZUNO-SILVA, D. ZAMARRIPA-ZEPEDA,
and O.A. GOMEZ-VARGAS
In the current study, the powder-pack boriding was applied to the AISI 12L14 steel in the
temperature range 1123 K to 1273 K for an exposure time between 2 and 8 hours. The
produced boride layer was composed of Fe2B with a sawtooth morphology. A diffusion model
based on the integral method was applied to investigate the growth kinetics of Fe2B layers. As a
main result, the boron diffusion coefficients in Fe2B were estimated by considering the principle
of mass balance at the (Fe2B/substrate) interface with an inclusion of boride incubation times.
The value of activation energy for boron diffusion in AISI 12L14 steel was estimated as
165 kJ molÀ1
and compared with other values of activation energy found in the literature. An
experimental validation of the present model was made by using four different boriding
conditions. Furthermore, the Rockwell-C adhesion test was employed to assess the cohesion of
boride layers to the base metal. The scratch and pin-on-disc tests were also carried out to
analyze the effect of boriding on wear behavior of AISI 12L14 steel.
https://doi.org/10.1007/s11661-018-4535-1
Ó The Minerals, Metals & Materials Society and ASM International 2018
I. INTRODUCTION
BORIDING is a thermochemical process in which
the boron atoms are diffused into the surface of a
workpiece to produce complex borides with the base
metal.[1]
The boriding treatment provides a high hard-
ness corrosion resistance against acids and molten
metals as well as an improvement in the wear resistance
for the treated surfaces. In the case of ferrous alloys, the
boriding process results in the formation of either a
single layer (Fe2B) or double layer (FeB + Fe2B) with
definite composition. By proper control of boron
activity in the boriding agent for powder-pack boriding,
it is possible to avoid the formation of FeB and to
obtain a monolayer configuration (Fe2B). This mono-
layer configuration is desired since FeB is more brittle
than Fe2B and is prone to crack under shock and
impact. In the literature, several approaches have been
developed for studying the kinetics of formation of
boride layers and their properties on steels produced by
different boriding methods (with and without boride
incubation times).
For example, Campos-Silva et al.[2]
investigated the
growth kinetics of FeB and Fe2B layers as well as the
diffusion zone in AISI 316 steel by the pack-boriding
process. They developed a kinetic model for estimating
the values of boron activation energies. They also
proposed a simple approach to estimate the expressions
of weight gain per surface unit associated with the
formation of the bilayer (FeB + Fe2B) and diffusion
zone on the material surface. Kulka et al.[3]
used a
kinetic model for estimating the boron activation
energies for FeB and Fe2B formed on the Armco iron
substrate using the gas boriding process. In their work, a
simple relationship was derived for eliminating the FeB
phase through a diffusion annealing treatment. Cam-
pos-Silva et al.[4]
also investigated the evolution of FeB
and Fe2B layers on AISI 1045 steel by applying a kinetic
model. A validation of their model was made by
comparing the experimental results with the predicted
ones. Relationships were then derived for studying the
reduction of FeB phase at the expense of Fe2B phase
M. KEDDAM is with the Laboratoire de Technologie des Mate´ riaux,
Faculte´ de Ge´ nie Me´ canique et Ge´ nie des Proce´ de´ s, USTHB, El-Alia,
Bab-Ezzouar, 16111 Algiers, Algeria. Contact e-mail: keddam@yahoo.fr
M. ORTIZ-DOMINGUEZ and J. ZUNO-SILVA are with the Escuela
Superior de Ciudad Sahagu´ n-Ingenierıá Meca´ nica, Universidad
Auto´ noma del Estado de Hidalgo, Carretera Cd. Sahagu´ n-O tumba s/n,
Zona Industrial CP 43990, Hidalgo, Mexico. M. ELIAS-ESPINOSA is
with the Instituto Tecnolo´ gico y de Estudios Superiores de Monterrey-
ITESM Campus Santa Fe, Av. Carlos Lazo No. 100, Del. A´ lvaro
Obrego´ n, CP 01389 Mexico City, Mexico. A. ARENAS-FLORES is
with the Centro de Investigaciones en Materiales y Metalurgia,
Universidad Auto´ noma del Estado de Hidalgo, Ciudad Universitaria
Pachuca-Tulancingo, km. 4.5, Pachuca, Hidalgo, Mexico. D.
ZAMARRIPA-ZEPEDA and O.A. GOMEZ-VARGAS are with the
Instituto Tecnolo´ gico de Tlalnepantla-ITTLA, Av., Instituto
Tecnolo´ gico, S/N. Col. La Comunidad, CP 54070 Tlalnepantla de
Baz, Estado de Mexico, Mexico.
Manuscript submitted September 17, 2017.
Article published online March 15, 2018
METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, MAY 2018—1895
Author's personal copy

during the diffusion annealing process. Campos et al.[5]
used a dimensional analysis for analyzing the growth
kinetics of FeB and Fe2B layers on AISI 1045 and AISI
M2 steels obtained by the paste-boriding process. In
their approach, the incubation times were neglected
during the formation of iron borides. An experimental
validation was made by comparing the experimental
results with the predicted values. VillaVela´ zquez-Men-
doza et al.[6]
employed a regression model, using
ANOVA for data analysis, to estimate the boride layer
thickness in the paste-borided AISI 1018 steel in the
temperature range 800 °C to 1000 °C. Iso-thickness
diagrams were proposed to select optimum values of
boride layers’ thicknesses as a function of boriding
parameters (time and temperature). The Anova analysis
indicated that the temperature had a major effect on the
boriding kinetics of AISI 1018 steel.
Campos et al.[7]
used two different approaches (the
neural network and the least-squares models) for
analyzing the kinetics of formation of Fe2B layers on
AISI 1045 steel produced by the paste-boriding treat-
ment. The results of the Fe2B layer thicknesses showed a
mean error of 5.31 pct for the neural network and 3.42
pct for the least-squares method. In another study,
Campos et al.[8]
also used the technique of fuzzy logic
based on two methods (Mamdani and Takagi–Sugeno)
for modeling the growth kinetics of Fe2B layers on AISI
1045 steel produced by the paste-boriding process. A
comparison of experimental results from the technique
of fuzzy logic yielded the corresponding medium errors
of 2.61 pct for the Mamdani method and 3.62 pct for the
Takagi–Sugeno method. Genel et al.[9]
used the artificial
neural network (ANN) to predict the hardness profile
and boride layer thickness with a high accuracy of
approximately 95 pct in the case of the pack-borided
AISI W1 steel in the temperature range 850 °C to
1050 °C for 1 to 8 hours. It was concluded that ANN is
superior to the regression method. A phase-field method
derived from the Ginzburg–Landau free-energy func-
tional was developed by Ramdan et al.[10]
for modeling
the growth kinetics of Fe2B layers on Armco iron taking
into account the boron solubility in the austenite phase.
Elias-Espinosa et al.[11]
proposed a kinetic model for
analyzing the growth kinetics of Fe2B layers on AISI O1
steel. Their model was based on the mass balance
equation at the (Fe2B/substrate) interface by introduc-
ing a nondimensional kinetic parameter with the occur-
rence of a constant boride incubation time independent
of the boriding temperature. Kouba et al.[12]
used a
sharp interface approach to solve the numerical model
describing the growth kinetics of Fe2B layers on Armco
iron with the presence of boride incubation, depending
on the boriding temperature. In this present study, a
diffusion model based on the integral method[13]
has
been proposed to evaluate the boron diffusivity in the
Fe2B layers when pack boriding the AISI 12L14 steel in
the temperature range 1123 K to 1273 K. A nonlinear
boron-diffusion profile through the Fe2B layer that
satisfies the solution of the second Fick’s law was
assumed following the Goodman method. An analytic
solution was then derived to evaluate the boron diffu-
sion coefficients in Fe2B as a function of the parabolic
growth constant for an upper boron concentration of 9
wt pct in Fe2B with the occurrence of boride incubation
times. This kinetic approach was first applied by Leon
Cazares et al.[14]
to model the growth kinetics of e and c’
nitrides formed on the pure iron using the plasma
nitriding treatment. Until now, no kinetics studies were
performed on the boriding of AISI 12L14 steel. For this
reason, an investigation was conducted in order to
simulate the boriding kinetics of AISI 12L14 steel in the
temperature range 1123 K to 1273 K. The present
diffusion model was validated using four additional
boriding conditions. As a main result, the value of
activation energy for boron diffusion in AISI 12L14
steel was estimated and compared with other values of
activation energy found in the literature.
The aim of the current work was to analyze the
kinetics of formation of Fe2B layers on AISI 12L14 steel
by applying a diffusion model, based on the integral
method. The cohesion of Fe2B layers on AISI steel was
also investigated by means of the Rockwell-C cohesion
test. Finally, the scratch and pin-on-disc tests were
employed to carry out a comparative study between the
borided and unborided AISI 12L14 steels in terms of
wear behavior.
II. THE DIFFUSION MODEL
The diffusion model analyzes the growth of a single
boride layer (Fe2B) on a saturated substrate with boron
atoms of AISI 12L14 steel. A schematic representation
of boron concentration profile through the Fe2B layer is
shown in Figure 1.
The f(x,t) function represents the distribution of
boron concentration in the substrate prior to the
nucleation of Fe2B phase. tFe2B
0 ðTÞ is the boride incuba-
tion time necessary to form a compact and continuous
Fe2B layer. CFe2B
up is the upper limit of boron content in
Fe2B (=9 wt pct), while CFe2B
low represents the lower limit
of boron content in Fe2B (= 8.83 wt pct). The point
x(t) = u is the Fe2B layer thickness or the position of
the (Fe2B/substrate) interface. A small homogeneity
range of about 1 at. pct was observed by Brakman
et al.[15]
for the Fe2B layer. The term Cads
B
is the
adsorbed boron concentration in the boride layer during
the boriding treatment.[16]
C0 represents the boron
solubility in the matrix, which is very low
(% 0 wt pct).[17–19]
The following assumptions are taken
into account when formulating the diffusion model.[2]
(1) Growth kinetics is governed by the boron diffu-
sion in the Fe2B layer.
(2) The Fe2B phase nucleates after a specific incuba-
tion time.
(3) The flux of boron atoms is perpendicular to the
sample surface.
(4) Boron concentrations remain constant in the
boride layer during the treatment.
(5) The Fe2B layer is thin in comparison with the
sample thickness.
1896—VOLUME 49A, MAY 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A

(6) A uniform temperature is assumed throughout
the sample.
(7) Planar morphology is assumed for the phase
interface.
The initial and boundary conditions for the diffusion
problem are given by
t ¼ 0; x>0
with
CFe2B½xðtÞ; t ¼ 0Š ¼ C0 % 0 wt pct ½1Š
Boundary conditions:
CFe2B½xðt ¼ tFe2B
0 Þ ¼ 0; t ¼ t0Š ¼ CFe2B
up for CB
ads>8:83 wt pct
½2Š
CFe2B½xðt ¼ tÞ ¼ uðtÞ; t ¼ tŠ ¼ CFe2B
low for CB
ads<8:83 wt pct
½3Š
The second Fick’s law that describes the evolution of
boron concentration in Fe2B as a function of diffusion
distance x(t) and time t is expressed by Eq. [4]:
DFe2B
@2
CFe2B½x; tŠ
@x2
¼
@CFe2B½x; tŠ
@t
; ½4Š
where the boron diffusion coefficient in Fe2B is only
dependent on the boriding temperature. The profile of
boron concentration within the Fe2B layer was taken
from Goodman’s method,[20]
as follows:
CFe2B½x; tŠ ¼ CFe2B
low þ aðtÞðuðtÞ À xÞ þ bðtÞðuðtÞ À xÞ2
for 0 x u
½5Š
The three time-dependent unknowns, a(t), b(t) and
u(t), meet the boundary conditions given by Eqs. [2]
and [3]. By applying the boundary condition on the
surface, Eq. [6] was obtained:
aðtÞuðtÞ þ bðtÞuðtÞ2
¼ ðCFe2B
up À CFe2B
low Þ ½6Š
By integrating Eq. [4] between 0 and u(t) and applying
the Leibniz rule, the ordinary differential equation
given by Eq. [7] was obtained:
uðtÞ2
2
daðtÞ
dt
þ aðtÞuðtÞ
duðtÞ
dt
þ
uðtÞ3
3
dbðtÞ
dt
þ bðtÞuðtÞ2 duðtÞ
dt
¼ 2DFe2BbðtÞuðtÞ
½7Š
The mass balance equation at the (Fe2B/substrate)
interface is given by Eq. [8]:
W
dx
dt

x¼u
¼ ÀDFe2B
@CFe2Bðx; tÞ
@x

x¼u
½8Š
with
W ¼
CFe2B
up À CFe2B
low
2
þ ðCFe2B
low À C0Þ
!
At the (Fe2B/substrate) interface, the boron concen-
tration remains constant and Eq. [8] can be rewritten as
follows:
W À
@CFe2B½x;tŠ
@t

x¼u
@CFe2B½x;tŠ
@x

x¼u
0
B
@
1
C
A ¼ ÀDFe2B
@CFe2B½x; tŠ
@x

x¼u
½9Š
Substituting Eq. [4] into Eq. [9], and after derivation
with respect to the diffusion distance x(t), Eq. [10] was
obtained:
ðCFe2B
up þ CFe2B
low ÞbðtÞ ¼ aðtÞ2
½10Š
Equations [6], [7], and [10] constitute a set of differen-
tial algebraic equations (DAE) in a(t), b(t), and u(t)
subjected to the initial conditions of this diffusion
problem. To obtain the expression of boron diffusion
coefficient in the Fe2B layers, an analytic solution
exists for this diffusion problem by setting
uðtÞ ¼ k½t À tFe2B
0 ðTÞŠ1=2
½11Š
aðtÞ ¼
a
uðtÞ
½12Š
and
bðtÞ ¼
b
uðtÞ2
½13Š
where u(t) is the Fe2B layer thickness and k the corre-
sponding parabolic growth constant at the (Fe2B/sub-
strate) interface. The two unknowns, a and b, have to
be determined for solving this diffusion problem. After
Fig. 1—Schematic representation of the boron-concentration profile
through the Fe2B layer.

substitution of Eqs. [11] through [13] into the DAE
system, and derivation, the expression of the boron
diffusion coefficient was obtained as follows:
DFe2B ¼ gk2
½14Š
with
g ¼
1
16

CFe2B
up þ CFe2B
low
CFe2B
up À CFe2B
low
!
1 þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ 4
CFe2B
up À CFe2B
low
CFe2B
up þ CFe2B
low
!v
u
u
t
0
@
1
A þ
1
12

2
4
3
5
along with the expressions of a(t) and b(t) given by
Eqs. [15] and [16]:
aðtÞ ¼
a
k½t À tFe2B
0 ðTÞŠ1=2
½15Š
bðtÞ ¼
b
k2½t À tFe2B
0 ðTÞŠ
½16Š
with
a ¼
ðCFe2B
up þ CFe2B
low Þ
2
À1 þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ 4
CFe2B
up À CFe2B
low
CFe2B
up þ CFe2B
low
!v
u
u
t
2
4
3
5
and
b ¼
a2
ðCFe2B
up þ CFe2B
up Þ
:
III. EXPERIMENTAL DETAILS
A. The Used Material and the Boriding Process
The AISI 12L14 steel was subjected to powder-pack
boriding in this work. The chemical composition of
AISI 12L14 steel is listed (in wt pct) in Table I. The
samples had a cubic shape with nominal dimensions of
10 mm 9 10 mm 9 10 mm. Before the boriding treat-
ment, the samples were cut and the cross sections were
polished metallographically and then etched by Nital
solution to reveal the microstructure. The powder-pack
boriding was carried out by embedding the samples in a
closed-container containing a mixture of powders com-
posed of 20 pct B4C, 10 pct KBF4, and 70 pct SiC. The
container was placed in a conventional furnace under a
pure argon atmosphere in the temperature range 1123 K
to 1273 K. Four treatment times (2, 4, 6, and 8 hours)
were selected for each temperature. Once the boriding
treatment was finished, the container was removed from
the furnace and slowly cooled to room temperature.
B. Experimental Techniques
The cross sections of formed boride layers were
observed by scanning electron microscopy (SEM, JEOL*
JSM 6300 LV). The boride layer thickness was automat-
ically measured by means of MSQ PLUS software. For
the reproducibility of measurements, 70 tests were
performed from a fixed reference on different sections
of borided samples to estimate the Fe2B layer thickness,
defined as an average value of the long boride teeth.[2,21]
The presence of the iron boride formed at the surface of
the treated sample was verified by use of X-ray diffraction
(XRD) equipment (Equinox 2000) using Co Ka radiation
at kCo = 0.179 nm. The well-known Rockwell-C inden-
tation test was prescribed by the VDI 3198 norm, as a
destructive quality test of coated compounds.[22,23]
In this
method, a conical diamond indenter penetrated into the
surface of an investigated layer, thus inducing massive
plastic deformation to the substrate and fracture of the
boride layer. A load of 1471 N was applied to cause
coating damage adjacent to the boundary of the inden-
tation. Three indentations were made for each borided
sample and SEM was used to evaluate the cohesion test.
The damage to the boride layer was compared with the
adhesion strength quality maps HF1 through HF6. In
general, the adhesion strength quality maps HF1 through
HF4 define sufficient adhesion, whereas HF5 and HF6
represent insufficient adhesion.[22]
The pin-on-disc tests
were performed in dry sliding conditions at ambient
temperature by means of a CSM tribometer, as shown in
Figure 2, with a relative humidity of 40 pct.
Before the tests, the samples were cleaned with
acetone to remove the contaminants from the surface.
The tested samples had a disc shape with a diameter of
25.4 mm and a thickness of 10 mm. All tests were then
made for a total sliding distance of 500 m with a sliding
speed of 0.08 m sÀ1
, and the covered radial distance was
14 mm under a normal load of 5 N. The CSM tribome-
ter was used to determine the magnitude of the friction
coefficient and wear as two surfaces rub together.[24,25]
Before the scratch wear tests, the samples with a
rectangular shape of dimensions 12 mm 9 7 mm 9
7 mm were also cleaned with acetone to remove the
contaminants from the surface. The scratch wear test
consists of scratching the surface of a sample by using an
LG Motion Ltd. (scratch) with a single-pass under
increasing normal load at a rate of 10 N mmÀ1
of
covered distance. Applied loads ranged from 0 to 90 N.
This permitted determination of the critical load (Lc)
corresponding to the apparition of the layer damage.
Table I. Chemical Composition of AISI 12L14 Steel (Weight Percent)
C Pb Mn P S Si Fe
0.13 to 0.15 0.15 to 0.35 0.85 to 1.15 0.04 to 0.09 0.26 to 0.35 0.4 balance
*JEOL is a trademark of Japan Electron Optics Ltd., Tokyo.

The scratch wear tests were carried out in dry sliding
conditions (at ambient conditions without lubrication)
using an LG Motion Ltd. (Figure 3). This technique of
characterization involves generating a controlled scratch
with a sharp tip on a selected area. The tip material
(commonly diamond or hard metal (WC)) is drawn
across the borided surface under constant, incremental,
or progressive load.[24,25]
The roughness profiles were
measured using a Mitutoyo Surftest Profilometer with
the JIS2001 norm.
IV. RESULTS AND DISCUSSION
A. SEM Observations of Boride Layers
Figure 4 shows the cross-sectional views of Fe2B
layers on the surfaces of AISI 12L14 steel borided at
1173 K, for increasing exposure times (2, 4, 6, and
8 hours). The resultant boride layers are continuous and
dense. The morphology of Fe2B layers was sawtoothed,
as shown in Figure 4.
A good mechanical adherence to the base metal is
favored with such morphology.[26]
The sawtooth mor-
phology of boride layers was observed in Armco iron,
low-carbon steels, and low-alloy steels because of the
preferred boron diffusion in certain crystallographic
directions.[27]
Furthermore, Carbucicchio et al.[28]
attrib-
uted the formation of a sawtooth morphology to
enhanced growth at the tips of boride needles. A flat
(boride layer/substrate) interface was observed in the
high-alloy steels due to the effects of alloying elements.
The Fe2B layer thickness increased with the exposure
time at a boriding temperature of 1173 K. The value of
Fe2B layer thickness was between 57.63 ± 10.7 lm (for
2 hours of treatment) and 128.61 ± 21.3 lm for 8 hours
at 1173 K.
B. XRD Analysis
Figure 5 gives the XRD patterns obtained at the
surfaces of borided AISI 12L14 steels at 1123 K for
2 hours and 1273 K for 8 hours, respectively. The XRD
patterns indicate the presence of Fe2B layer at the
surfaces of AISI 12L14 steels.
Figure 5 exhibits a difference in intensities regarding
the diffracted peaks. The formation of such phase
depends on the active boron content available in the
mixture of powders used in this work. In addition, the
growth of Fe2B layer is of a highly anisotropic nature.[29]
The metallic borides were not detected in this borided
steel.
C. Rockwell-C Adhesion Test
Adhesion of the boride layer on the substrate was
verified by using the Rockwell-C adhesion test (per the
VDI 3198 standard). Figure 6 shows the SEM micro-
graphs of the indentation craters generated by VDI
adhesion tests at the surfaces of borided AISI 12L14
steels at 1173 K for 2 and 8 hours. Figure 6(a) revealed
the presence of radial cracks and delamination at the
perimeter of the indentation crater with flaking areas.
The adhesion strength quality of this boride layer is
related to the HF3 standard. Figure 6(b) also showed
little flaking areas at the perimeter of indentation craters
with radial cracking, complying with the HF3 standard.
It is concluded that the Fe2B coating promotes the wear
resistance and presents a good interfacial adhesion.
D. The Pin-on-Disc Test
The pin-on-disc wear test was performed on the
borided and unborided steels through the examination
of change in the friction coefficient vs sliding distance in
dry conditions. Figure 7 describes the change in the
friction coefficient as a function of the sliding distance
when applying a diamond indenter over the surfaces of
tested materials.
The evolution of the tangential force according to the
sliding distance allowed us to distinguish three different
phases from the obtained curves. During the first phase,
the friction coefficient of the unborided substrate is
lower than that of the borided substrate from 0 to 70 m
Fig. 2—Schematic diagram of the typical pin-on-disc test device (1:
elastic arm; 2: weight (1 N, 2 N, 5 N, and 10 N); 3: friction force
sensor; 4: pin, ball holders; 5: wear track; and 6: rotating disc or cap
for liquid testing).
Fig. 3—Schematic diagram of the typical scratch test device (1:
Rockwell-C indenter; 2: weight (1 N, 2 N, 5 N, 10 N, … , 90 N); 3:
trail obtained; 4: tangential force; 5: horizontal displacement of the
borided sample (x(t)); 6: substrate; and 7: borided surface).

of sliding distance. The friction coefficient of the borided
substrate is nearly constant (l = 0.44), and the friction
coefficient of the unborided substrate increases progres-
sively. This phase can be considered as an incubation
period. It corresponds to the indenter slip on the
samples (unborided substrate and borided substrate),
in the absence of all major damage. The difference
between the two friction coefficients in this first phase is
due to the difference that exists in the surface rough-
nesses during this first phase.
The roughness profile (R profile) is the profile
resulting from electronic high-pass filtering of the
primary profile with a cut-off wavelength kc. The
parameter designated is the arithmetical mean rough-
ness value (Ra): The arithmetical mean of the absolute
values of the profile deviations (Zi) from the mean lines
of the roughess profiles, where Ra = 0.04572 lm for
the unborided substrate and Ra = 0.04064 lm for the
borided substrate (Figure 8). A second phase exists
where the friction coefficient of the unborided substrate
increases progressively, until a maximal value of 0.632 is
reached, while the friction coefficient of the borided
substrate decreases until a value of 0.351. This phase is
associated with the apparition of wear particles on the
diamond indenter trails. A third phase occurs where the
friction coefficient of the unborided substrate stabilizes
Fig. 4—SEM micrographs of the cross sections of borided AISI 12L14 steel at 1173 K during different exposure times: (a) 2 h, (b) 4 h, (c) 6 h,
and (d) 8 h.

between 0.61 and 0.67, whereas for the borided sub-
strate, it stabilizes from 0.32 to 0.39. It seems that this
phase is associated with an abrasive action by the wear
particles previously formed. Therefore, the stabilization
of the friction coefficient values of the unborided
substrate and borided substrate is probably due to the
grinding of the removed particles.
It is noted that the unborided sample has a friction
coefficient value higher than that of the borided steel.
The decrease in friction coefficient for the borided
sample at 1223 K for 2 hours was attributed to the
formation of a single hard layer (Fe2B). The average
friction coefficient for the unborided sample was located
between 0.61 and 0.67, whereas the borided sample has a
value of friction coefficient ranging from 0.32 to 0.39.
These results are consistent with those found in the
literature.[24,25]
E. The Scratch Wear Test
The scratch wear test was carried out to study the
wear performance of the borided sample (at 1273 K
during 8 hours) in comparison with the base steel.
Figure 9 gives the SEM micrographs showing the worn
surfaces of the unborided and borided AISI 12L14 steels
after the scratch tests. Figure 9(a) puts into evidence the
presence of cracks and wear debris caused by an intense
plastic deformation when the bare steel was subjected to
the scratch test. Figure 9(b) shows the scratching lines as
well as some areas undergoing a plastic deformation for
the borided sample. Such wear behavior was also seen in
other borided steels after the scratch tests.[24,25]
The
diamond tip also produced a large wear track on the
bare steel, as shown in Figure 9(a). Little wear track on
the borided steel demonstrated the improved wear
resistance during the scratch test (Figure 9(b)). It is
concluded that the presence of a hard single boride layer
(Fe2B) was responsible of improving the wear resistance
of borided AISI 12L14 steel during the scratch test. In
addition, it was demonstrated by studies carried out by
Habig and Chatterjee-Fischer[30]
that the Fe2B layer
exhibited a wear resistance superior to that provided by
the (FeB/Fe2B) bilayer.
Figure 10 displays the SEM images of worn borided
surfaces of AISI 12L14 steels for two boriding condi-
tions (1123 K for 2 hours and 1223 K for 8 hours)
subjected to scratch tests. Cracks with curvilinear and
mosaic forms can be readily observed along the scratch
trails on the worn surfaces of AISI 12L14 steels. This
type of cracks is characteristic of a Hertzian fracture on
brittle solids when a blunted indenter is used. These
cracks propagate in depth in a semiconical shape and
Fig. 5—XRD patterns obtained at the surface of borided AISI 12L14 steels for two boriding conditions: (a) 1123 K for 2 h and (b) 1273 K for
8 h.

start at flaws near the contact surface where high-ten-
sion stresses develop.[24,31,32]
F. Estimation of Activation Energy for Boron Diffusion
The growth kinetics of Fe2B layer is governed by
boron diffusion, which occurs as a consequence of boron
diffusion perpendicular to the sample’s surface. To
analyze the boriding kinetics, it is mandatory to
investigate the time dependence of Fe2B layer thickness
in the considered temperature range 1123 K to 1273 K.
Figure 11 describes the variation of the square of Fe2B
layer thickness vs time at different boriding tempera-
tures. It is seen that the dependence of the Fe2B layer
thickness over the treatment time has a parabolic
character, indicating that the growth of boride layer is
controlled by the diffusion phenomenon of boron
atoms.
Table II lists the experimental values of parabolic
growth constants at the (Fe2B/substrate) interface along
with the corresponding boride incubation times. The
value of boride incubation time at each boriding
temperature was easily deduced from the plot u2
(t) vs t
that corresponds to the null value of boride layer
thickness. Figure 12 describes the evolution of the boron
diffusion coefficients through the Fe2B layers as a
function of boriding temperature according to the
Arrhenius relationship. The temperature dependence
of the boron diffusion coefficient in the Fe2B layer can
be expressed by an Arrhenius-type equation in the
temperature range 1123 K to 1273 K as follows:
DFe2B ¼ 1:84 Â 10À4
exp
À165 kJ molÀ1
RT

½17Š
Fig. 6—SEM micrographs showing indentations of the VDI
adhesion test on surfaces of AISI 12L14 borided at 1173 K for two
exposure times: (a) 2 h and (b) 8 h.
Fig. 7—Variation of the friction coefficient of the diamond indenter
during sliding against the borided surface of AISI 12L14 steel at
1223 K with an exposure time of 8 h and unborided substrate. Fig. 8—Arithmetical mean roughness value Ra.

where R = 8.314 J molÀ1
KÀ1
and T is the absolute
temperature in Kelvin.
Table III gives a comparison between the values of
activation energy for boron diffusion in Armco iron and
some steels and the estimated value of activation energy
for boron diffusion in AISI 12L14 steel.[24,25,33–41]
It is
noted that the found values of boron activation energy
by different authors depended on various factors such as
the method of calculation, the boriding method, the
nature of the boriding agent, and the chemical compo-
sition of the substrate. From a practical point of view,
the growth kinetics of boride layers can be analyzed by
using the empirical relationship relating the square of
boride layer thickness to the treatment time. However,
this empirical approach is not appropriate for a multi-
phase system when the diffusivity of boron in each
boride layer must be known. For instance, Uslu et al.[39]
estimated the activation energy for boron diffusion in
AISI P20 steel by using an empirical approach for a
bilayer configuration (FeB + Fe2B). For this reason,
different mathematical approaches were developed for
estimating the boron diffusion coefficient in each phase
in the case of a multiphase system. The microstructural
nature of boride layers (either Fe2B or (FeB + Fe2B)) is
basically dependent on the quantity of active boron,
supplied by the boron source as a function of the
boriding method. It is beneficial to obtain a single boride
(Fe2B) rather than a bilayer (FeB + Fe2B) since the
Fig. 9—SEM micrographs of the wear scar on surfaces of AISI
12L14 steel: (a) unborided surface and (b) borided surface at 1273 K
for 8 h.
Fig. 10—SEM micrographs of the wear scar on surfaces of AISI
12L14 steel for two boriding conditions: (a) 1123 K with an
exposure time of 2 h and (b) 1223 K with an exposure time of 8 h.

cracks can develop in the vicinity of interphase bound-
aries between FeB and Fe2B. The growth rate of boride
layers is also controlled by the diffusion mechanism of
boron atoms released from the boriding agent in
different media and chemical reactions involved during
the boriding process. The values of activation energy for
boron diffusion in ferrous alloys are affected by the
presence of alloying elements. For steels, the alloying
elements slow the diffusion rate of boron atoms, yielding
a boride layer with reduced thickness and a change in
the morphology of the boride layer/substrate interface.
The value of boron activation energy estimated in this
study (i.e., 165 kJ molÀ1
) was interpreted for the
borided AISI 12L14 steel as the amount of energy
required to activate the diffusion rate of boron atoms in
the easiest path direction [001] along the boride layer
that minimizes the growth stresses.[27]
G. Experimental Validation of the Diffusion Model
The present diffusion model was verified experimen-
tally by making a comparison between the experimental
values of Fe2B layers’ thicknesses and the predicted
values. Figure 13 shows the SEM micrographs of the
cross sections of the samples borided at 1253 K for 1.5
and 4.5 hours and at 1173 K for 2.5 and 3.5 hours,
respectively. The time dependence of the Fe2B layer
thickness at a chosen boriding temperature is given by
Eq. [18]:
uðtÞ ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
DFe2B½t À tFe2B
0 ðTÞŠ
g
s
½18Š
with g = 13.3175.
Equation [18] can be used as a simple tool to predict
the optimum value of Fe2B layer thickness depending on
the boriding parameters (the exposure time and the
boriding temperature), to match the case depth with the
practical use of this kind of borided steel. Table IV
compares the experimental values of Fe2B layers’
thicknesses (obtained at 1223 K for 1.5 and 4.5 hours
and 1173 K for 2.5 and 3.5 hours) and the predicted
values, for an upper boron content in the Fe2B phase
equal to 9 wt pct and a boride incubation time of 1773
seconds.
Fig. 11—Square of boride layer thickness as a function of boriding
time for increasing temperatures.
Table II. Experimental Values of Parabolic Growth
Constants at the (Fe2B/Substrate) Interface Along with the
Corresponding Boride Incubation Times
T
(K)
Experimental Parabolic Growth
Constant k (lm sÀ0.5
)
Incubation Boride
Time tFe2B
0 ðTÞ (s)
1123 0.5394 1773.3
1173 0.7823 1774.2
1223 1.1358 1772.7
1273 1.5133 1772.9
Fig. 12—Temperature dependence of the boron diffusion coefficient
in the Fe2B layer.

Table III. Comparison of Activation Energy for Boron Diﬀusion in AISI 12L14 Steel with Other Borided Materials
Material Boriding Method
Activation Energy for Boron
Diffusion (kJ molÀ1
)
Phases Present in
the Boride Layer References
AISI D2 steel salt-bath 170.0 FeB, Fe2B,CrB and Cr2B 33
Q235 steel plasma electrolytic boriding 186.17 FeB, Fe2B, Ni3B4, NiB, and Ni2B 34
AISI 316 plasma paste boriding 250.0 FeB, Fe2B, CrB, Cr2B, and Ni3B 35
Armco Iron powder 157.5 Fe2B 36
AISI 1025 steel powder 157.5 Fe2B 24
AISI 1026 steel powder 178.4 Fe2B 37
AISI 1018 steel paste 159.3 (Fe2B) Fe2B 38
AISI 9840 steel powder 193.08 (Fe2B) Fe2B 25
AISI P20 steel powder 200 FeB, Fe2B, MnB, and CrB 39
AISI 304 stainless steel powder 244 FeB, Fe2B, Ni2B, and Cr2Ni3B6 40
AISI H10 powder 160.594 FeB, Fe2B, CrB, Cr2B, and MoB 41
AISI 12L14 steel powder 165 (Fe2B) Fe2B this work
Fig. 13—SEM micrographs of the boride layers formed at the surfaces of AISI 12L14 steel at 1253 K for four boriding conditions: (a) 1253 K
for 1.5 h, (b) 1253 K for 4.5 h, (c) 1173 K for 2.5 h, and (d) 1173 K for 3.5 h.

V. CONCLUSIONS
Powder-pack boriding was performed on the AISI
12L14 steel in a mixture of powders constituted of 20
pct B4C, 10 pct KBF4, and 70 pct SiC for an
exposure time ranging from 2 to 8 hours. A single
boride layer (Fe2B) was obtained for the used mixture
of powders with a sawtooth morphology. Its presence
was confirmed by XRD analysis. The Fe2B layer was
dense and compact for all boriding conditions. The
kinetics of Fe2B layers was governed by a parabolic
growth law with a constant boride incubation of 1773
seconds. The boride layer thickness varied from
39.74 ± 8.36 to 248.78 ± 32.1 lm. The Rockwell-C
indentation technique showed a cohesive quality of
boride layers on AISI 12L14 steel consistent with
HF3 per the 3198 VDI norm for two different
boriding conditions (1173 K for 2 and 8 hours). The
average value of the friction coefficient for the
pack-borided steel (at 1223 K for 8 hours of treat-
ment) ranged from 0.32 to 0.39. By contrast, the
average value of the friction coefficient for the
untreated steel was between 0.61 and 0.67. The wear
mechanism, which occurred during the scratch test,
revealed an intense plastic deformation in some areas,
the presence of wear debris, and scratching lines for
the untreated worn surface. For the borided worn
surface, some scratching lines were observed. A
diffusion model, based on the integral method, was
applied to estimate the value of activation energy for
boron diffusion in AISI 12L14 steel
(= 165 kJ molÀ1
). This found value of activation
energy was compared with other values available in
the literature. The present diffusion model was vali-
dated experimentally for four boriding conditions.
The predicted Fe2B layers’ thicknesses were compared
with the experimental values. A satisfactory agree-
ment was observed between these two sets of data.
The present diffusion model can be extended to the
bilayer configuration (FeB + Fe2B) to estimate the
boron diffusion coefficients in FeB and Fe2B for any
borided steel. Similarly, a simple approach based on a
particular solution of a system of DAE, composed of
two differential equations and four algebraic con-
straints, should be provided in order to estimate the
values of boron diffusion coefficients in FeB and
Fe2B, for an upper boron content equal to 16.40 wt
pct in the FeB phase.
ACKNOWLEDGMENTS
The work described in this article was supported by
a grant from PRDEP and CONACyT Me´ xico (Na-
tional Council of Science and Technology) and from
FCS reconoce los fondos del Departamento de Fı´sica
y Matema´ ticas y de la Divisio´ n de Investigacio´ n de la
UIA. The authors thank the Laboratorio de Micro-
scopıá de la UIA.
NOMENCLATURE
u(t) Boride layer thickness (lm)
a(t) and b(t) Time-dependent parameters
k Parabolic growth constant of the Fe2B
layer (lm sÀ0.5
)
t Treatment time (s)
tFe2B
0 ðTÞ Boride incubation time (s)
CFe2B
up Upper limit of boron content in Fe2B
(=9 wt pct)
CFe2B
low Lower limit of boron content in Fe2B
(=8.83 wt pct)
Cads Adsorbed boron concentration in the
boride layer (wt pct)
C0 Boron solubility in the matrix (%0 wt
pct)
CFe2B½x; tŠ Boron concentration profile in the Fe2B
layer (wt pct)
DFe2B Diffusion coefficient of boron in the Fe2B
phase (m2
sÀ1
)
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