Growth kinetics and mechanical properties of fe2 b layers formed on aisi d2 steel

Indian Journal of Engineering & Materials Sciences
Vol. 22, April 2015, pp. 231-243
Growth kinetics and mechanical properties of Fe2B layers formed on AISI D2 steel
M Ortiz-Domíngueza
, M Elias-Espinosab
, M Keddamc
*, O A Gómez-Vargasd
, R Lewise
, E E Vera-Cárdenasf
& J Zuno-Silvaa
a
Universidad Autónoma del Estado de Hidalgo, Campus Sahagún, Carretera Cd. Sahagún-Otumba s/n, Hidalgo, México
b
Instituto Tecnológico y de Estudios Superiores de Monterrey-ITESM Campus Santa Fe, Av. Carlos Lazo No. 100,
Del. Álvaro Obregón, CP. 01389, D. F., México
c
Département de Sciences des Matériaux, Faculté de Génie Mécanique et Génie des Procédés, USTHB, B.P. No. 32, 16111 El-Alia,
Bab-Ezzouar, Algiers, Algeria
d
Instituto Tecnológico de Tlalnepantla-ITTLA. Av., Instituto Tecnológico, S/N. Col. La Comunidad, Tlalnepantla de Baz. CP. 54070. Estado
de México, México
e
Department of Mechanical Engineering, University of Sheffield, Mappin Street, UK. Sheffield S13JD
f
Universidad Politécnica de Pachuca-UPP, Carretera Pachuca-Cd. Sahagún km. 20, Ex Hacienda de Santa Bárbara, CP 43830, Hidalgo, México
Received 15 April 2014; accepted 11 September 2014
In the present study, the growth kinetics and mechanical properties of Fe2B layers formed on the AISI D2 steel are
investigated. A mathematical model for studying the growth kinetics of Fe2B layers on the AISI D2 steel is proposed for the
powder-pack boriding. This process is carried out in the temperature range of 1123-1273 K for treatment time ranging from
2 to 8 h. This kinetic model is based on solving the mass balance equation at the (Fe2B/ substrate) interface to evaluate the
boron diffusion coefficients through the Fe2B layers in the temperature range of 1123-1273 K. The formed boride layers are
characterized by different experimental techniques such as light optical microscopy, scanning electron microscopy, XRD
analysis and the Daimler-Benz Rockwell-C indentation technique. A tribological characterization is also performed using a
Plint TE77 tribometer under dry sliding conditions. The boron activation energy for the AISI D2 steel is estimated as 201.5
kJ mol-1
based on our experimental results. This kinetic model is also validated by comparing the experimental Fe2B layer
thickness with the predicted value at 1243 K for 5 h of treatment. A contour diagram relating the layer boride thickness to
the boriding parameters is suggested to be used in practical applications.
Keywords: Incubation time, Diffusion model, Activation energy, Growth kinetics, Adherence, Tribology
Boriding is a well-known thermochemical surface
hardening extensively used for many decades. It
refers to a process in which the boron atoms are
diffused into a metal substrate to form a hard metallic
boride layer on the metal surface1
. Boriding provides
high wear resistance, corrosion resistance, high
temperature oxidation resistance and 3-10 times
increasing service life2
. Boriding can be achieved with
boron in different states such as solid powder, paste,
liquid and gas. Different methods of boriding exist
such as plasma boriding3
, paste plasma boriding4
,
electrochemical boriding (called PHEB)5
, boriding in
a fluidized bed6
, gas-boriding7,8
, solid boriding
(powder or paste)9,10
. Among the boriding methods,
the pack-boriding has many advantages that make it
potentially the most industrially efficient11,12
. The
boriding of ferrous materials results in the formation
of either a single layer (Fe2B) or double-layer (FeB +
Fe2B) with deﬁnite composition. In a kinetic pint of
view, several approaches concerning the kinetics of
formation of Fe2B layers grown on different
substrates13-23
were developed in the literature. These
models offered the possibility of selecting the
optimum boride layers thicknesses for practical
applications in the industry.
The powder-pack boriding of AISI D2 steel has
been investigated in this study. The growth kinetics of
Fe2B layers formed on the AISI D2 steel has been
studied. The boron diffusion coefficients through the
Fe2B layers are estimated, in the temperature range of
1123-1273 K, using an original diffusion model. In
addition, the obtained boron activation energy for the
AISI D2 steel is compared with the literature data.
The microstructure of boride layers on AISI D2 steel
was investigated by different experimental techniques
such as: optical microscopy (OM), scanning electron
microscopy (SEM) coupled to EDS analysis and XRD
analysis. For the mechanical characterizations, the
interfacial adhesion of boride layer on the AISI D2
steel’s substrate and its tribological behavior under dry
sliding conditions were also investigated.
—————
*Corresponding author (E-mail: keddam@yahoo.fr)

INDIAN J. ENG. MATER. SCI., APRIL 2015232
Diffusion Model
Mass balance equation
The diffusion model considers the growth of Fe2B
layer on a saturated substrate with boron atoms as
displayed in Fig. 1. As boron is added to the surface, it is
used completely to convert the Fe phase to 2Fe B.
The ( ( ))f x t function describes the evolution of
boron concentration inside the matrix before the
nucleation of Fe2B phase. 2Fe B
0t represents the incubation
time necessary to form the Fe2B phase at a maximum
saturation level of the matrix by the boron atoms. 2Fe B
upC
is the upper limit of boron content in the 2Fe B phase
( 3 3
60 10 mol m−
= × ) and 2Fe B
lowC represents the lower
limit of boron content in the 2Fe B phase
( 3 3
59 8 10 mol m. −−−−
= ×= ×= ×= × ). ( ) vx t t= = is the position of
the (Fe2B/substrate) interface. A schematic
representation of the 2Fe B
upC and 2Fe B
lowC values obtained
from the Fe-B phase diagram for a range of temperatures
is given in Fig. 2.
The term B
adsC is the effective adsorbed boron
concentration during the boriding process24
. In Fig. 1,
2 2Fe B Fe B
1 up lowa C C= − defines the homogeneity range of
the 2Fe B layer, 2Fe B
2 low 0a C C= − is the miscibility gap
and C0 is the boron solubility in the matrix considered
as null ( 0 0C ≈ 3
mol m−−−−
)25-27
.
Certain assumptions are considered during the
formulation of the diffusion model:
− The diffusion model is not based on the boron
concentration profile 2Fe B[ ( )]C x t through 2Fe B
layer (Fig. 1).
− The growth kinetics is controlled by the boron
diffusion in the 2Fe B layer.
− The 2Fe B iron boride nucleates after a certain
period of incubation.
− The boride layer grows because of the boron
diffusion perpendicular to the specimen surface.
− Boron concentrations remain constant in the boride
layer during the treatment.
− The boride layer is thin compared to the sample
thickness.
− A uniform temperature is assumed throughout the
sample.
− Planar morphology is assumed for the phase
interface.
With these assumptions, the initial and boundary
conditions can be written as (Fig. 1):
Initial condition:
2Fe B 00, 0, with: [ ( )] 0.t x C x t C= > = ≈ … (1)
Boundary conditions:
Fig. 1—Schematic boron concentration profile through the 2Fe B layer
Fig. 2—Schematic representation of the 2Fe B
upC and 2Fe B
lowC values
obtained from the Fe-B phase diagram for a range of temperatures

ORTIZ-DOMINGUEZ et al.: Fe2B LAYERS FORMED ON AISI D2 STEEL 233
( )2 2
2
Fe B Fe B
Fe B 0 0 up
B 3 3
ads
v
(the upper boron concentration is kept constant),
for 60 10 mol m ,
C x t t C
C −
 = = =  


> × 
… (2)
2
2
Fe B
Fe B low
B 3 3
ads
[ ( ) v]
(the boron concentration at the interface is kept constant),
for 59.8 10 mol m ,
C x t t C
C −
= = =



< × 
… (3)
where ( )2Fe B
v 0t t t= − is the effective growth time of the
2Fe B layer, t is the treatment time, 2Fe B
0t is the boride
incubation time. v0 is a thin layer with a thickness of
5≈ nm that formed during the nucleation stage28
.
However, the value of the 0v ( 0)≈ is small in comparison
with actual measured thickness of Fe2B layer (v). Given
the aforementioned conditions, and taking into account that
the boride layer thickness v is governed by the parabolic
growth law ( )2
2 2
1/2Fe B1/2 1/2 1/2
Fe B Fe B v 0v 2 2D t D t tε ε= = + ,
where ε is the normalized growth parameter of 2Fe B that
will occur by simultaneous consumption of substrate at the
(Fe2B/substrate) interface29
.
2Fe BD denotes the diffusion coefficient of boron in the
Fe2B phase. By applying the principle of mass conservation
at the (Fe2B/substrate) interface30,31
, Eq. (4) is obtained as:
2 2
2
Fe B Fe B
up low 0
Fe B Fe
2
2
( v) ( v)( ) ( v v)( ),
C C C
A d J x A dt J x d A dt
 + −
  
 
⋅ = = ⋅ − = + ⋅
… (4)
where ( 1 1)A = ⋅ is defined as the unit area. The input
and output fluxes of boron atoms in the ( 2Fe B/substrate)
interface during a lapse of time dt are defined as:
( )2 2 2Fe B Fe B Fe B vv { [ ( )] / }xJ x D dC x t dx == = −
, and
( )Fe Fe Fe v vv v { [ ( )] / }x dJ x d D dC x t dx +== + = −
respectively. Thus, Eq. (4) can be rewritten as:
2 2
2
2
Fe B Fe B
up low 0
Fe B
Fe B
( ) v ( ) v
2
2
[ ( )]( )
x t x t
C C C
dC x tdx t
D
dt dx= =
 + −
  
 
= −
… (5)
Using the chain rule on the right term of Eq. (5)
results in:
( )
2 2
2 2
Fe B Fe B
up low 0
2
Fe B Fe B ( ) v( ) v
2
2
( ) / [ ( )] .
x tx t
C C C
dx t dt dt D dC x t
==
 + −
  
 
= −
… (6)
Equation (7) can be obtained by replacing the
derivative of parabolic growth law
( 2
1/2 1/2
Fe Bv ( ) 2x t D tε= = ) with respect to the time t into
Eq. (6).
2 2
2
Fe B Fe B
up low 0 2
Fe B ( ) v
2
[ ( )] .
2 x t
C C C dt
dC x t
t
ε
=
 + −
= −  
 
… (7)
A schematic representation of the square of the
layer thickness as a function of the boriding time is
depicted in Fig. 3.
Now, integrating both sides of Eq. (8) between limits
of 2Fe B
0t to t and 2Fe B
upC to 2Fe B
lowC , respectively on gets:
2 2
Fe B2
low
2
Fe B Fe B2 2
up0
Fe B Fe B
up low 0
2
Fe B ( ) v
2
2
[ ( )] .
Ct
x t
Ct
C C C
dt
dC x t
t
ε =
 + −
  
 
= −∫ ∫
… (8)
Fig. 3—Schematic representation of the square of the layer
thickness as a function of the boriding time

The following solution was derived:
( ) ( )2 2 2 2 2Fe B Fe B Fe B Fe B Fe B2
up low up low 0 02 / 2 / ,/C C C C C ln t tε = − + −
… (9)
where ε is known as the normalized growth parameter
for the ( 2Fe B/substrate) interface, it is a dimensionless
parameter. It is assumed that expressions 2Fe B
upC , 2Fe B
lowC ,
and C0, do not depend significantly on temperature (in
the temperature range applied)28
.
Experimental Procedure
Boriding process
The material to be pack-borided was the AISI D2
steel. It had a nominal chemical composition of 1.40-
1.60% C, 0.30-0.60% Si, 0.30-0.60% Mn, 11.00-
13.00% Cr, 0.70-1.20% Mo, 0.80-1.10% V, 0.030% P
and 0.030% S. The samples were sectioned into cubes
with dimensions of 10 mm × 10 mm × 10 mm Before
boriding, the samples were polished, ultrasonically
cleaned in an alcohol solution and deionized water for
15 min at room temperature. Finally, the samples were
dried and stored under clean-room conditions. The
mean hardness was 287 HV. The samples were
embedded in a closed cylindrical case made of AISI
304L steel containing a fresh Durborid powder
mixture. The powder boriding medium had an average
particle size of 30 µm. This boriding agent was
composed of an active source of boron (boron carbide-
B4C), an inert filler (silicon carbide-SiC), and an
activator (potassium fluoroborate-KBF4). The active
boron is then supplied by the powder quantity placed
over and around the material surface. The powder-pack
boriding process was carried out in a conventional
furnace under a pure argon atmosphere. The boriding
process was carried out in the temperature range of
1123-1273 K for a variable time (2, 4, 6 and 8 h). The
boriding temperatures were selected in accordance with
the position of the solidus line in the Fe-B phase
diagram26
. Once the treatment was finished, the
container was removed from the furnace and slowly
cooled to room temperature.
Microscopical observations of boride layers
The borided samples were sectioned for
metallographic observations using a LECO VC-50
cutting precision machine. The cross-sectional
morphology of the boride layers was viewed with the
Olympus GX51 optical microscope in a clear field.
Figure 4 gives the cross-sections of boride layers
Fig. 4—Optical micrographs of the cross-sections of borided AISI D2 steel at 1173 K for different treatment times: (a) 2 h, (b) 4 h, (c) 6 h
and (d) 8 h

formed on the AISI D2 steel at 1173 K for different
treatment times. The obtained microstructure is
composed of a single phase layer (Fe2B) at the surface
of AISI D2 steel. The formed layers appear to be
compact and homogeneous, exhibiting a flat
morphology. This peculiar morphology is attributed to
the effect of alloying elements present in the AISI D2
steel. These elements tend to concentrate in the tips of
boride layers, reducing the boron flux in this zone. It is
noticed that the boride layer thickness increased with a
change in the boriding time (Fig. 3). The boride layer
thickness was automatically measured with the aid of
MSQ PLUS software. To ensure the reproducibility of
the measured layers, fifty measurements were collected
in different sections of the borided samples to estimate
the 2Fe B layer thickness; defined as an average value
of the long boride teeth32,33
.
All thickness measurements were taken from a fixed
reference on the surface of the borided AISI D2 steel,
as illustrated in Fig. 5. The phases present in the boride
layers were identified by an X-ray diffraction (XRD)
equipment (Equinox 2000) using αCoK radiation of
0.179 nm wavelength. The distribution of elements
within the cross-section of boride layer was determined
by electron dispersive spectroscopy (EDS) equipment
(JEOL JSM 6300 LV) from the surface. The Daimler-
Benz Rocwell-C was made to get a qualitative
information on the adhesive strength of the boride
layers to the substrate. The well-known Rockwell-C
indentation test is prescribed by the VDI 3198 norm, as
a destructive quality test of coated compounds34-36
. The
principle of this method was reported in the reference
work36
. A load of 1471 N was applied to cause coating
damage adjacent to the boundary of the indentation.
Three indentations were conducted for each borided
sample and scanning electron microscopy (SEM) was
used to assess the adhesion test.
The microhardness of the borided surface was
measured at 5 different locations by means of a
Vickers indenter with a load of 50 g and the average
value was taken as representative of the hardness. The
roughness values of borided and unborided samples
were measured using a Mitutoyo Surftest
Profilometer.
The tribological tests were carried out in dry
sliding conditions using a PLINT TE77 high
frequency friction machine (see Fig. 6). This machine
is used to assess the dynamic wear and friction
performance of lubricants, materials and surface
coatings37
. The contact consists of a fixed disc and
reciprocating ball. The ball is mounted on the carrier
head that is mechanically oscillated against the lower
fixed specimen (disc). The normal load is applied via
a spring balance through lever and stirrup mechanism.
The force is transmitted directly onto the carrier head
by means of a needle roller cam follower on the
carrier head and a running plate on the loading stirrup.
The oscillations are produced by a motor with an
eccentric cam, scotch yoke and guide block
arrangement. The fixed specimen is clamped to a
block. The assembly is mounted on flexible supports
that allow free movement in horizontal directions, but
no movement vertically. This is connected to a stiff
force transducer that measures tangential force in both
directions.
AISI 52100 steel balls, commonly employed in the
bearing industry, were used to slide against the
surface of the borided AISI D2 steel. The balls used
had a diameter of 4.75 mm and a microhardness of
850 HV. On the other hand, the stationary samples
Fig. 5—Schematic diagram illustrating the procedure used to
estimate the Fe2B layer thickness
Fig. 6—The PLINT TE77 high frequency wear friction machine
(1: Load meter, 2: Loading stirrup, 3: Force transducer, 4: Heater
block, 5: Oscillation mechanism, 6: Motor)

had a disc shape with a diameter of 18 mm and a
thickness of 3 mm. Before all the tests, the ball and
disc were cleaned from any residue oxide layer or
machining lubricant by washing in ethanol using an
ultrasonic bath (Fisherbrand 11020). The disc and ball
were placed as shown in the simplified schematic
diagram (see Fig. 7)
Then, test parameters such as load, frequency and
stroke were selected and introduced into the computer.
The maximum contact pressure was selected in such a
way that wear would be produced with a low number of
cycles. A Labview program collects the data generated,
which was basically the friction coefficient versus time.
It was possible to control the test parameters and follow
the progression of the friction during every test on the
screen. The tests were run to 36000 cycles. This was
predetermined with several preliminary tests, to know
how many cycles were necessary to cause damage on
the surfaces. Finally, three experiments were carried out
for each test type. Table 1 shows the operating
conditions of the tests conducted.
Results and Discussion
SEM observations and EDS analysis
Figure 8(a) gives the cross-section of boride layer
formed on the AISI D2 steel at 1223 K for 8 h using
SEM. The obtained microstructure exhibited a flat
morphology because of the alloying elements present
in the AISI D2 steel. Figure 8(b) shows the EDS
analysis obtained at the surface of borided AISI D2
steel. It indicates the presence of three substitutional
elements: Cr, V and Mn as well as Fe. In fact,
chromium element can dissolve in the Fe2B phase by
occupying the substitutional sites in the Fe sublattice.
Figure 8(c) provides the EDS analysis obtained at the
(Fe2B/substrate) interface. It reveals that carbon and
silicon are being displaced towards the diffusion zone
by forming together with boron element, solid
solutions like silicoborides (FeSi04B06) and Fe5SiB2)
and boroncementite (Fe3B0.67C0.33)28, 38
.
X-ray diffraction analysis
Figure 9 shows the XRD pattern obtained at the
surface of borided AISI D2 steel at 1273 K for 8 h. It
indicates the presence of Fe2B and interstitials
compounds such as CrB, Cr2B, MoB, Mo4B2 and V2B
because of the affinity of boron for these substitutional
elements. It is known that the growth of Fe2B layer
presents a highly anisotropic nature. The [001] direction
is the easiest path for the boron diffusion through the
Fe2B phase, due to the tendency of boride crystals to
grow along a direction of minimum resistance,
perpendicular to the external surface.
Rockwell-C adhesion test
An indenter hardness tester was used to assess the
Daimler-Benz Rockwell-C adhesion, as a destructive
quality test for examined layers; it was employed for
determination of cohesion. The well-known adhesion
test prescribed by the VDI 3198 norm was used34
. The
principle of this method was presented in Fig. 10. 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.
Table 1—Test operating conditions.
Test atmosphere Hertzian pressure (GPa) Load(N) Frequency (Hz) Amplitude (mm) Cycles
293-296 K and 45% - 50% Relative humidity 2.01 20 10 15 36000
Fig. 7—Simplified schematic diagram of high frequency friction machine (1: Friction force transducer, 2: Ball, 3: Disc, 4: Heater block,
5: Roller, 6: Normal load, 7: Oscillator driver)

The damage to the boride layer was compared with
the adhesion strength quality maps HF1-HF6
(see Fig. 10). In general, the adhesion strength HF1 to
HF4 are defined as sufficient adhesion, whereas HF5
and HF6 represent insufficient adhesion (HF is the
German short form of adhesion strength)34
. SEM image
of the indentation craters for the samples borided at 1273
K for 4 h is shown in Fig. 11. The indentation craters
obtained on the surface of borided AISI D2 steel
revealed that there were radial cracks at the perimeter of
indentation craters. However, a small quantity of spots
with flaking resulting from delamination was visible and
the adhesion strength quality of this boride layer is
related to the HF5 standard.
Tribological characterization
For tribological study, the borided sample at 1273
K for 2 h of treatment was used. The roughness of the
Fig. 8—(a) SEM micrograph of the cross-section of borided AISI
D2 steel at 1223 K for 8 h, (b) EDS spectrum obtained at the
surface of borided sample and (c) EDS spectrum obtained at the
(boride layer/substrate) interface
Fig. 10—Principle of the VDI 3198 indentation test34
Fig. 9—XRD patterns obtained at the surface of borided AISI D2
steel at 1273 K during 8 h of treatment

unborided surface was 0.154 while the borided
surface had a value of 0.154 µm.
The surface hardness of substrate was 287 HV
while the surface microhardness reached a value of
2322 HV. Figure 12 shows the variation in the friction
coefficient of the borided and unborided surfaces
under dry sliding conditions against a steel ball. The
image shows that the borided sample exhibits a
friction coefficient lower than that of the unborided
substrate. The average friction coefficient for the
unborided sample was between 0.292 and 0.363 and
for the borided sample, the average frictton
coefficient ranged from 0.245 to 0.263. These results
are in agreement with those obtained by other
researchers39- 41
.
The tribological tests caused wear scars on the flat
specimens (discs). There were measurable grooves on
the discs. The wear depth of each groove was measured
using a Mitutoyo Surftest Profilometer. Due to the
depth varying along the length of the groove a number
of depth measurements (transverse to the length of the
groove) were taken. The experimental average depth
was taken from these measurements. The volume of a
‘perfect groove’ could be calculated from this
information as done in earlier studies42
. The profiles
shown in Fig. 13(a) and (b) show grooved features,
demonstrating the two-body wear mechanism. Figure
13(a) indicates that the unborided AISI D2 steel’s
surface was more severely worn compared to the
borided surface as shown in Figure 13(b).
Furthermore, the measured wear volumes for the
unborided and borided surfaces on AISI D2 steels
show a remarkable difference, as apparent in Fig. 14.
The specific wear rate of the unborided sample was
1.02×10–5
mm3
/Nm, whereas the value of specific
wear rate for the borided sample at 1273 K during 2 h
Fig. 11—SEM micrograph showing the indentation of VDI adhesion
test on the surface of AISI D2 steel borided at 1273 K for 4 h
Fig. 12—Variation of friction coefficient of steel balls during
sliding against borided surface for 2 h and unborided substrate
Fig. 13—Wear scar depth of the AISI 52100 steel’s ball on: (a)
unborided AISI D2 steel and (b) borided surface at temperature
1273 K during 2 h

was approximately 1.56×10–6
mm3
/Nm. This
difference can be attributed to the low resistance of
the unborided surface against sliding wear.
Figures 15(a) and (b) show the SEM images of the
borided surfaces obtained at 1273 K with exposure
time of 2 h. Figures 15(c) and (d) give the SEM
images of unborided surfaces where wear scars are
produced during sliding contact against a steel ball. In
Figure 15(a) and (b) a defined wear scar is produced,
which has a width of approximately 0.57 mm. Some
pits and spalls are observed and common wear
mechanisms like plastic deformation, cracks and
scratching were formed on the borided surface.
Figures 15(c) and (d) shows the wear scar formed on
the unborided surface, which has a width of
approximately 1.45 mm. Likewise, some pits and
spalls are observed and common wear mechanisms
like plastic deformation, cracks and scratching were
formed on the unborided surface.
Estimation of boron activation energy
The evolution of 2Fe B layers thicknesses as a
function of the boriding time is required for
estimating the boron diffusion coefficients through
the 2Fe B layers by applying the suggested diffusion
model. Figure 16 describes the time dependence of
the squared value of 2Fe B layer thickness for
different temperatures. The slopes of the straight lines
Fig. 14—Variation of wear volume against the boriding condition
Fig. 15—SEM micrographs of wear scar on surfaces of the AISI D2 steel: (a) and (b) borided surface at 1273 K for 2 h; (c) and (d)
unborided surface.

in Fig. 16 provide the values of growth constants
2
2
Fe B( 4 )Dε= . These values can be obtained by a
linear fitting through origin at each boriding
temperature. Table 2 provides the estimated value of
boron diffusion coefficient in 2Fe B at each
temperature along with the squared normalized value
of ε parameter determined from Eq. (9).
The results, which are summarized in Table 2, reflect
a diffusion-controlled growth of the boride layers.
By combining the results (square of normalized
growth parameter ( 2
ε ) and growth constants
( 2
2
Fe B4 Dε )) presented in Table 2, the boron diffusion
coefficient in the 2Fe B layers ( 2Fe BD ) was estimated
for each boriding temperature. So, an Arrhenius
equation relating the boron diffusion coefficient to the
boriding temperature can be assumed. As a result, the
boron activation energy ( 2Fe BQ ) can be determined
from the slope of the straight line shown in coordinate
system: 2Fe BlnD as a function of reciprocal boriding
temperature (see Fig. 17).
The boron diffusion coefficient through 2Fe B
layers was deducted as:
( )2
2 1
Fe B 4.4 10 201.5 kJmol / ,D exp RT− −
= × − … (10)
where 314.8=R Jmol-1
K-1
and T the absolute
temperature in Kelvin. From Eq. (10), the pre-
exponential factor ( 2 2 1
0 4.4 10 m sD − −
= × ) and the
activation energy ( 1
201.5 kJmolQ −
= ) values are
affected by the contact surface between the boriding
medium and the substrate, as well as the chemical
composition of the substrate.
Figure 18 shows the optical micrograph of the
cross-section of the AISI D2 steel’s sample borided at
1243 K for 5 h.
Table 3 compares the value of boron activation energy
for the AISI D2 steel with the values from the literature
data43-47
for some borided steels. The boron activation
energies, found for the powder method are found to be
comparable. The obtained value of boron activation
energy for the AISI D2 steel43
by the electrochemical
method is very low to the value estimated in the present
study. It is concluded that the reported values of boron
activation energy depend on various factors such as: (the
boriding method, the chemical composition of boriding
agent, the chemical composition of base steel and
mechanism of boron diffusion).
The time dependence of Fe2B layer thickness is
given by Eq. (11) as follows:
Table 2—The square of normalized growth parameter and growth
constants as a function of the boriding temperature
Temperature (K) Type of layer ε2
(Dimensionless)
4ε2
DFe2B
(µm2
s-1
)
1123 1.19×10−1
1173 3.79×10−1
1223 7.32×10−1
1273
Fe2B 1.689625×10−3
16.0×−1
Fig. 16—The square of Fe2B layer thickness as a function of the
boriding time
Fig. 17—Arrhenius relationship for the boron diffusion coefficient
through the 2Fe B layer

( )
( )( )
2 2
2
2 2 2 2
Fe B Fe B
Fe B up low1/2 1/2
Fe B Fe B Fe B Fe B
0 up low 0
8
v 2
/ 2
D t C C
D t
ln t t C C C
ε
−
= =
+ −
… (11)
The results obtained by Eq. (11) are in good
agreement with the experimental results given in
Table 4.
An iso-thickness diagram was also plotted as a
function of the boriding temperature and the treatment
time as shown in Figure 19. It can be used as a simple
tool to select the optimum value of Fe2B layer
thickness in relation with the potential applications of
the borided AISI D2 steel in the industry.
As a rule, thin layers (e.g. 15-20 µm) are used to
protect against adhesive wear (such as chipless
shaping and metal stamping dies and tools), whereas
thick layers are recommended to combat abrasive
wear (extrusion tooling for plastics with abrasive
fillers and pressing tools for the ceramic industry). In
the case of low carbon steels and low alloy steels, the
optimum boride layer thicknesses range from 50 to
250 µm, and for high alloy steels, the optimum boride
layer thicknesses are between 25 and 76 µm. In
addition, this model can be extended to predict the
growth kinetics of (FeB+ Fe2B) at the surface of
different ferrous alloys.
Conclusions
In this work, the AISI D2 steel was pack-borided in
the temperature range of 1123-1273 K for a variable
treatment time ranging from 2 to 8 h. The following
conclusions are drawn from this study:
(i) A single Fe2B layers was formed at the
surface of AISI D2 steel for the given
boriding conditions.
(ii) The growth kinetics of Fe2B layers followed
a parabolic growth law.
(iii) A kinetic model was suggested to estimate
the boron diffusion coefficient through the
Fe2B layer.
(iv) The boron activation energy was estimated as
201.5 kJ mol-1
for the AISI D2 steel.
(v) Validation of the diffusion model was made
by comparing the experimental Fe2B layer
thickness with the predicted value for the
Fig. 19—Iso-thickness diagram giving the Fe2B layer thickness as
a function of the boriding parameters
Table 4—Predicted and experimental values of the Fe2B layer
thickness at 1243 K for 5 h of treatment
Temperature
(K)
Type of layer Boride layer
thickness (µm))
estimated by Eq. (11)
Experimental
boride layer
thickness (µm)
1243 Fe2B 128.1 125.97±8.4
Fig. 18—Optical micrograph of the boride layer formed on the
AISI D2 steel at 1243 K for 5 h
Table 3—Comparison of boron activation energy of AISI D2 steel
with other steels using different boriding methods
Material Boriding
method
Boron activation
energy (kJ mol -1
)
References
AISI D2
AISI H13
AISI 316
AISI M2
AISI H13
AISI D2
Electrochemical
Salt-bath
Powder
Powder
Powder
Powder
137.66
244.37
198
207
213.92
201.5
[43]
[ 44]
[ 45]
[ 46]
[47]
Present study

borided AISI D2 at 1243 K for 5 h. A good
concordance was obtained between the
experimental result and the predicted one.
(vi) An iso-thickness diagram relating the boride
layer thickness to the boriding parameters
(time and temperature) was suggested for the
practical use of this kind of steel. This
contour diagram can serve as a simple tool to
the select the optimum value of Fe2B layer
thickness.
(vii) The interfacial adherence of the boride layer
on AISI D2 steel (obtained at 1273 K during
4 h), by the Daimler-Benz Rockwell-C
indentation technique, was found to be
related to HF5 category according to the VDI
3198 norm.
(viii) The average microhardness value of the
unborided surface was approximately 10
times lower than that of the borided surface at
1273 K for 2 h.
(ix) The average friction coefficient value for the
unborided surface was a slightly greater than
that of the borided surface.
(x) Sliding wear resistance for the borided
surface was 7-6 times greater than that of the
unborided surface.
(xi) The wear mechanism for the borided surface
was plastic deformation, cracking and
abrasion scratching lines while cracking and
abrasion scratching lines were observed in
the case of unborided surface.
Acknowledgements
The work described in this paper was supported by
a grant of PROMEP, CONACyT México and The
Tribology Group of The University of Sheffield, UK.
The authors wish to thank Ing. Martín Ortiz Granillo,
Director de la Escuela Superior Campus Ciudad
Sahagún-Universidad Autónoma del Estado de
Hidalgo for his valuable collaboration for this study.
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