Boriding is a thermochemical treatment in which boron atoms are diffused into the surface of a workpiece and form borides with the base metal. Apart from constructional materials, which meet these high demands, processes have been developed which have a positive effect on the tribological applications including abrasive, adhesive, fatigue and corrosion wear of the component surface.

1. UNCORRECTEDPROOF
1 REGULAR ARTICLE
2 Characterization and boriding kinQ1
etics of AISI T1 steel
3 Martin Ortiz-Domínguez1
, Mourad Keddam2,*
, Milton Elias-Espinosa3
, Marius Ramírez-Cardona4
,
4 Alberto Arenas-Flores4
, Juno Zuno-Silva1
, F. Cervantes-Sodi5
, and E. Cardoso-Legorreta4
5
1
Universidad Autónoma del Estado de Hidalgo, Escuela Superior de Ciudad Sahagun-Ingeniería Mecánica, Carretera Cd.
6 Sahagun-O tumba s/n, Zona Industrial, CP. 43990, Hidalgo, México
7 2
Laboratoire de Technologie des Matériaux, Faculté de Génie Mécanique et Génie des Procédés, USTHB, B.P. No. 32, El-Alia,
8 16111, Bab-Ezzouar, Algiers, Algeria
9 3
Tecnológico de Monterrey-Campus Santa Fe, Av. Carlos Lazo No. 100, Del. Álvaro Obregón, CP. 01389, México City, México
10 4
Centro de Investigaciones en Materiales y Metalurgia, Universidad Autónoma del Estado de Hidalgo, Ciudad Universitaria
11 Pachuca-Tulancingo km. 4.5, Pachuca, Hidalgo, México
12
5
Universidad Iberoamericana Ciudad de México, Departamento de Física y Matemáticas, Prolongación Paseo de la Reforma
13 880, Lomas de Santa Fe, CP. 01219, México City, México
14
15 Received: 11 October 2017 / Accepted: 9 August 2018
16
17 Abstract. The AISI T1 steel was hardened by the solid boriding process in the temperature range 1123–1273 K
18 for a time duration of 2 to 8 h. A kinetic model, based on the integral method, was applied to the growth of a
19 single boride layer (Fe2B) at the surface of AISI T1 steel. This diffusion model has been validated experimentally
20 by considering two additional boriding conditions. A numerical solution was then obtained after solving the set
21 of differential algebraic equations in order to compare the experimental thicknesses of Fe2B layers with the
22 predicted values. The activation energy for boron diffusion in AISI T1 steel was estimated as 212.76 kJ molÀ1
and
23 a comparison was made with other values available in the literature. The formed boride layers with a saw-tooth
24 morphology were examined by scanning electron microscopy (SEM). X-ray diffraction confirmed that the
25 borided layer was composed of only Fe2B. The Daimler-Benz Rockwell-C indentation technique was employed
26 to assess the cohesion of Fe2B layers on AISI T1 steel. In addition, the pin-on-disc and wear scratch tests were
27 carried out for investigating the wear behaviour of borided AISI T1 steel.
28 Keywords: boriding / kinetics / diffusion / Fick’s laws / integral method / iron boride / activation energy /
29 tribology / adherence / wear
30 1 Introduction
31 The boriding process is a thermo-chemical surface
32 hardening treatment used to harden the surfaces of
33 metallic parts. This thermochemical process can be applied
34 to both ferrous and nonferrous alloys in the temperature
35 range 700–1000 °C for a time duration of 0.5 to 10 h. As a
36 consequence of this treatment, a boride layer is formed by
37 thermodiffusion [1].
38 The resulting metallic boride layer yields a high surface
39 hardness, good tribological properties and moderate
40 oxidation resistance at high temperature. Particularly,
41 the morphology of boride layers in the ferrous alloys
42 depends upon the alloying elements present in the matrix.
43Amongst boriding techniques, the powder-pack borid-
44ing is the most widely used one because of its simplicity and
45cost-effectiveness.
46The boriding process is widely employed in various
47industrial sectors, such as chemical industry, textile
48industry, agriculture, mechanical industry and railway
49transport [2]. Dimensional changes induced by boriding are
50about one third of the layer thickness in tool steels because
51of the increase in volume of boride layer [3].
52In general, obtaining Q2of a single boride layer (Fe2B) is
53more desirable for industrial applications than FeB [4]. So,
54an adequate choice of the chemical composition of powder
55mixture results in the formation of a boride layer with only
56Fe2B phase.
57Kinetically, some diffusion models devoted to the
58modeling of the growth kinetics of Fe2B layers on various
59ferrous alloys and Armco iron were published in the
60literature [5–34]. These models considered the principle of
61mass equation at the (Fe2B/substrate) interface subjected* e-mail: keddam@yahoo.fr
Metall. Res. Technol. Vol, No (2018)
© EDP Sciences, 2018
https://doi.org/10.1051/metal/2018081
Metallurgical Research
Technology
Available online at:
www.metallurgical-research.org

2. UNCORRECTEDPROOF
62 to initial and boundary conditions. The influence of boride
63 incubation time during the formation of Fe2B layer was
64 taken into account in most models except for a few
65 reference works [9,31–34]. In particular, these kinetic
66 approaches can be employed as a simple tool in order to
67 choose the optimum boride layers’ thicknesses for the given
68 boriding conditions. In the present study, a recent kinetic
69 approach called the integral method [5] was successfully
70 applied to the boriding kinetics of AISI T1 steel. This model
71 allowed to estimate the value of activation energy for boron
72 diffusion in AISI T1 steel. An experimental validation of
73 the present model was also made by considering two
74 additional boriding conditions. For this purpose, a
75 numerical solution for this diffusion problem was developed
76 by solving the set of differential Algebraic equations
77 resulting from the integral method.
78 The objective of this study was to analyze the boriding
79 kinetics of AISI T1 steel and to study the wear properties of
80 Fe2B layers. Till now, no kinetics studies were reported in
81 the literature about the boriding of AISI T1 steel.
82 For tribological characterization, the Daimler-Benz
83 Rockwell-C indentation technique was used to qualitative-
84 ly assess the cohesion of boride layers on AISI T1 steel.
85 Furthermore, the pin-on-disc and wear scratch tests were
86 employed in order to study the effect of the boriding
87 treatment on wear behaviour of this steel.
88 2 Diffusion model
89 The kinetic model based on the integral method was
90 successfully applied to analyze the kinetics of formation of
91 Fe2B layer on the AISI T1 in a matrix saturated with boron
92 atoms. Schematic boron-concentration profile along the
93 Fe2B layer is illustrated in Figure 1. The f(x, t) function
94 gives the distribution of boron concentration in the
95 substrate before the nucleation of Fe2B phase. tFe2B
0 ðTÞ
96 represents the boride incubation time required to form a
97 continuous and compact layer of Fe2B. CFe2B
up is the upper
98 limit of boron content in Fe2B (= 9 wt.%), while CFe2B
low
99 represents the lower limit of boron content in Fe2B
100 (= 8.83 wt.%) and the point x(t) = u is the Fe2B layer
101 thickness. A small homogeneity range of about 1 at.%
102 exists in Fe2B as reported by Brakman et al. [35].
Theterm CB
ads denotestheadsorbedboronconcentration
103 in the boride layer during the boriding treatment as
104 explained by Yu et al [36]. C0 represents the boron solubility
105 in the matrix which is very low (≈ 0 wt.%) [37,38].
The following assumptions were taken into account
106 during the mathematical formulation of the diffusion model:
107 The initial and boundary conditions for this diffusion
108 problem are set as follows:
t ¼ 0; x 0; with CFe2B½xðtÞ; t ¼ 0Š
¼ C0 ≈ 0 wt:%: ð1Þ
109110
111 Boundary conditions:
CFe2B½xðt ¼ t
Fe2B
0 Þ ¼ 0; t ¼ t0Š ¼ CFe2B
up for112113
CB
ads 8:83 wt:% ; ð2Þ114115
CFe2B½xðt ¼ tÞ ¼ uðtÞ; t ¼ tŠ ¼ C
Fe2B
low for
116117
CB
ads 8:83 wt:%: ð3Þ
118119
120The second Fick’s law describing the change in
121boron concentration within the Fe2B layer as a function
122of time t and diffusion distance x(t) is given by equation (4):
DFe2B
∂2
CFe2B½x; tŠ
∂x2
¼
∂CFe2B½x; tŠ
∂t
; ð4Þ
123124
125where the boron diffusion coefficient is only dependent on
126the boriding temperature. It is possible to obtain the
127expression of boron-concentration profile through the Fe2B
128layer using the Goodman’s method [39].
CFe2B½x; tŠ ¼ C
Fe2B
low þ aðtÞðuðtÞ À xÞ
þ bðtÞðuðtÞ À xÞ2
for 0 x u: ð5Þ
129130
The three time-dependent unknowns a(t), b(t) and
131u(t) must satisfy the boundary conditions given by
132equations (2) and (3). It is noticed that the two
133parameters a(t) and b(t) must be positive because of a
134decreasing nature of the boron-concentration profile. By
135applying the boundary condition on the surface, equation
136(6) was obtained:
aðtÞuðtÞ þ bðtÞuðtÞ2
¼ ðCFe2B
up À C
Fe2B
low Þ: ð6Þ
137138
Fig. 1. Schematic boron-concentration profile in the Fe2B layer.
Fig 1. Profil schématique de la concentration du bore dans la
couche Fe2B.
2 M. Ortiz-Domínguez et al.: Metall. Res. Technol. Vol, No (2018)

3. UNCORRECTEDPROOF
139 By integrating equation (4) between 0 and u(t) and
140 applying the Leibniz rule, the ordinary differential
141 equation (ODE) given by equation (7) was obtained:
uðtÞ2
2
daðtÞ
dt
þ aðtÞuðtÞ
duðtÞ
dt
þ
uðtÞ3
3
dbðtÞ
dt
þbðtÞuðtÞ2 duðtÞ
dt
¼ 2DFe2BbðtÞuðtÞ: ð7Þ
142143
144 The mass balance equation at the (Fe2B/substrate)
145 interface is given by equation (8):
W
dx
dt
jx¼u ¼ ÀDFe2B
∂CFe2B½x; tŠ
∂x
jx¼u ; ð8Þ
146147
148
with W ¼ ½
ðCFe2B
up À C
Fe2B
low Þ
2
þ ðC
Fe2B
low À C0ÞŠ:
149150
151 At the (Fe2B/substrate) interface, the boron concen-
152 tration remains constant and equation (8) can be rewritten
153 as follows:
WðÀ
∂CFe2B½x;tŠ
∂t jx¼u
∂CFe2B½x;tŠ
∂x jx¼u
Þ ¼ ÀDFe2B
∂CFe2B½x; tŠ
∂x
jx¼u: ð9Þ
154155
156 Substituting equation (4) into equation (9) and after
157 derivation with respect to the diffusion distance x(t),
158 equation (10) was obtained:
ðCFe2B
up þ C
Fe2B
low ÞbðtÞ ¼ aðtÞ2
: ð10Þ
159160
161 Equations (6), (7) and (10) represent a set of differential
162 algebraic equations (DAE) in a(t), b(t) and u(t) subjected
163 to the initial conditions of this diffusion problem. This
164 resulting DAE system can be solved numerically [40] if the
165 diffusion coefficient of boron in Fe2B is known. An analytic
166 treatment of this diffusion model was made in the reference
167 work [5] where the expression of boron diffusion coefficient
168 in Fe2B was given by equation (11):
DFe2B ¼ hk2
; ð11Þ
169170
171 with h = 13.3175where k is the parabolic growth constant
172 of the Fe2B layer for a given boriding temperature. For
173 solving numerically this set of differential algebraic
174 equations (DAE), it is necessary to have the initial values
175 of a(t), b(t) and u(t) for a time equal to the boride
176 incubation time tFe2B
0 ðTÞ.
177 3 Experimental details
178 3.1 The material and the boriding process
179 The AISI T 1 tool steel was selected for boriding process. It
180 had a nominal chemical composition of 0.65–0.80% C,
181 0.10–0.40% Mn, 0.20–0.40% Si, 3.75–4.00% Cr, 17.25–
182 18.75% W, 0.90–1.30% V, 0.3% Ni, 0.25% Cu, 0.03% P and
1830.03% S. This kind of steel is usually used in the
184manufacture of all kinds of cutting tools, such as turning
185tool, milling cutter, cutter, reamer, drill bit, saw blade, tap,
186etc. It can also be used for high temperature wear resistance
187parts and cold work tool steel. The samples had a cubic
188shape with dimensions of 10 mm  10 mm  10 mm. Before
189boriding, the samples were prepared metallographically
190and cleaned. The samples were embedded in a closed,
191cylindrical case in contact with a mixture of powders
192consisting of 20% B4C as the donor, 10% KBF4 as an
193activator, and 70% SiC as the diluent. The boriding
194treatment was realized in a conventional furnace under a
195pure argon atmosphere in the temperature range of 1123–
1961223 K. Four treatment times (2, 4, 6 and 8 h) were selected
197for each temperature. The container was removed from the
198furnace and slowly cooled to room temperature after
199finishing the boriding treatment.
2003.2 Experimental techniques
201The cross-sections of borided samples were prepared
202metallographically and etched by Nital to be examined
203by SEM (JEOL JSM 6300 LV). Afterwards, the boride
204layer thickness was automatically measured by means of
205MSQ PLUS software. To ensure the reproducibility of the
206measured layers, fifty measurements were taken from
207different sections of the borided samples to estimate the
208Fe2B layer thickness; defined as an average value of the
209long boride teeth [41,42]. The boride formed at the surface
210of the treated sample was identified by using X-Ray
211Diffraction (XRD) equipment (Equinox 2000) with a Co-
212Ka radiation at l = 0.179 nm. The Daimler-Benz Rockwell-
213C technique was performed to obtain a qualitative
214information on the cohesion of boride layers to the
215substrate. The well-known Rockwell-C indentation test
216is prescribed by the VDI 3198 norm, as a destructive
217quality test of coated compounds [43,44].
218The principle of this method was reported in the
219reference work [44]. A load of 1471 N was applied to cause
220coating damage adjacent to the boundary of the indenta-
221tion. Three indentations were made for each borided
222sample to assess the cohesion test. The indentation craters
223were examined by SEM. During the cohesion test, a conical
224diamond indenter penetrated into the surface of an
225investigated layer, thus inducing massive plastic deforma-
226tion to the substrate and fracture of the boride layer. The
227damage of the boride layer was compared with the cohesion
228strength quality maps HF1-HF6 displayed in Figure 2.
229In general, the cohesion strength HF1-HF4 is defined as
230sufficient cohesion, whereas HF5 and HF6 represent
231insufficient cohesion [43,44]. The pin-on-disc tests were
232carried out in dry sliding conditions at ambient tempera-
233ture using a CSM tribometer shown in Figure 3 with a
234relative humidity of 40% [6]. Before the tests, the samples
235were cleaned with acetone in order to remove contaminants
236from the surface. The tested samples had a disc shape with
237a diameter of 25.4 mm and a thickness of 10 mm. All tests
238were then conducted for a total sliding distance of 500 m
239with a sliding speed of 0.08 m/s and the covered radial
240distance was of 14 mm under a normal load 5 N. The CSM
M. Ortiz-Domínguez et al.: Metall. Res. Technol. Vol, No (2018) 3

4. UNCORRECTEDPROOF
241 tribometer was used to determine the magnitude of friction
242 coefficient and wear as two surfaces rub together. In one
243 measurement method, a pin or a sphere is loaded onto the
244 test sample with a precisely known force. The pin is
245 mounted on a stiff lever, designed as a frictionless force
246 transducer. The friction coefficient is determined during
247 the test by measuring the deflection of the elastic arm.
248 Diamond-made indenter with a 10 mm-diameter hemi-
249 spheric, commonly employed, was used to slide against the
250 surface of the pack-borided AISI T1 steel. Before the
251 scratch wear tests, the samples with a rectangular shape of
252 dimensions: 12 mm  7 mm  7 mm were cleaned with
253 acetone in order to remove the contaminants from the
254 surface. The scratch wear test consists in scratching the
255 sample surface by using a LG Motion Ltd (scratch) with a
256 single-pass under increasing normal load at a rate of
257 10 N mmÀ1
of covered distance. Applied loads were
258 between 0 and 90 N. This permitted determination of
259 the critical load (Lc) corresponding to the apparition of the
260 layer damage. The scratch wear tests were carried out in
261 dry sliding conditions (at ambient conditions without
262 lubrication) using a LG Motion Ltd (see Fig. 4) [6].
2634 Results and discussions
2644.1 SEM observations of boride layers
265Figure 5 shows the cross-sections of boride layers on AISI
266T1 steel treated at 1173 K for 2, 4, 6 and 8 h. The
267morphology of produced hard layers was saw-toothed for
268all boriding conditions.
269Such observed peculiar morphology favoured the
270adhesion of boride layers on borided steels [45].
In addition, the occurrence of more or less pronounced
271saw-tooth morphology depends mainly on the concentra-
272tion of alloying elements present in the matrix as observed
273in different ferrous alloys [46]. A strong textured growth of
274boride needles along the preferred crystallographic
275direction [001] is observed when boriding Armco iron
276due to the absence of alloying elements [47]. The boride
277layer thickness is affected by the time duration of process
278at 1173 K because a large amount of boron atoms was
279supplied with time at the surface of borided AISI T1 steel.
280Thus, the boride layers become thicker with prolonged
281boriding time.
2824.2 X-Ray diffraction analysis
283Figure 6 shows the XRD pattern obtained at the surface of
284borided AISI T1 steel at a temperature of 1273 K for 8 h.
285The diffracting peaks of Fe2B with different intensities are
286visible in the XRD pattern confirming its presence in the
287boride layer.
288In the present study, the metallic borides were not
289probably identified by XRD analysis due to their low
290fraction volumes inside the boride layer. In a study by
Fig. 3. Schematic diagram of 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; 6: Rotating disc.
Fig 3. Diagramme schématique du dispositif pour le test pion-sur-
disque. 1 : Bras élastique ; 2 : Poids (1 N, 2 N, 5 N et 10 N) ; 3 :
Capteur de la force de frottement ; 4 : Pion, Porte billes ; 5 : Trace
d’usure; 6 : Disque rotatif.
Fig. 2. Principle of the VDI 3198 indentation test [44].
Fig 2. Principe du test d’indentation VDI 3198 [44].
Fig. 4. Schematic diagram of typical scratch test device. 1:
Rockwell-C indenter; 2: Weight (1 N, 2 N, 5 N, 10 N…, 90 N); 3:
Trail obtained; 4: Tangent force; 5: Horizontal displacement of
the borided sample (x(t)); 6: Substrate; 7: Borided surface.
Fig 4. Diagramme schématique du dispositif pour le test
d’arrachement. 1 : Indenteur Rockwell-C ; 2 : Poids (1 N, 2 N,
5 N, 10 N…, 90 N) ; 3 : Trace obtenue ; 4 : Force tangentielle ; 5 :
Déplacement horizontal de l’échantillon boruré (x(t)) ; 6 :
Substrat; 7 : Surface borurée.
4 M. Ortiz-Domínguez et al.: Metall. Res. Technol. Vol, No (2018)

5. UNCORRECTEDPROOF
291Ozbek and Bindal [48], the following metallic borides (CrB,
292MoB and Mo2B) besides FeB and Fe2B were identi Q3fied in
293the pack-borided AISI steel M2 steel using Ekabor I. In an
294other investigation, Campos et al. [49] paste borided the
295AISI M2 steel at 1273 K during 4 h. They found by XRD
296analysis that the boride layer was composed of FeB and
297Fe2B along with chromium boride CrB. The same AISI M2
298steel was also paste borided by Campos et al [48] at 1273 K
299for 6 h, however the chromium borides inside the boride
300layer were not identified in this case by XRD analysis. It is
301seen that the reported XRD results on these borided tool
302steels are not always consistent with the literature data
303[48–50].
3044.3 Tribological characterization
3054.3.1 Cohe Q4sion test
306The cohesion of boride layers on AISI T1 steel was
307investigated by using the Daimler-Benz Rockwell-C
308indentation technique. Two borided samples treated (at
3091173 K for 2 h and 8 h) were then subjected to the cohesion
Fig. 5. SEM micrographs of the cross-sections of borided AISI T1 steels at 1173 K for different treatment times: (a) 2 h, (b) 4 h, (c) 6 h,
and (d) 8 h.
Fig 5. Micrographies MEB des sections droites des aciers AISI T1 borurés à 1173 K pour différents temps de traitement : (a) 2 h, (b)
4 h, (c) 6 h, et (d) 8 h.
Fig. 6. XRD patterns obtained at the surface of borided AISI T1
steel at 1273 K for 8 h.
Fig 6. Spectre DRX obtenu à la surface de l’acier AISI T1 boruré
à 1273 K pendant 8 h.
M. Ortiz-Domínguez et al.: Metall. Res. Technol. Vol, No (2018) 5

6. UNCORRECTEDPROOF
310 tests. The damage around the indentation can be viewed by
311 SEM and compared with a defined pattern of adhesion
312 strength according to the VDI 3198 norm.
313 Figure 7 shows the SEM micrographs of the craters of
314 indentation caused by applying a conical diamond indenter
315 on the surfaces of tested samples.
316 Radial cracks are generated at the perimeter of
317 indentation as shown in Figure 7a. The adhesion quality
318 was found to be acceptable foQ5 r the sample borided at
319 1173 K for 2 h according to H4 category. Figure 7b puts into
320 evidence the presence of a small quantity of spots with
321 flaking due to extended delamination at the vicinity of the
322 indentation. The adhesion quality was also acceptable for
323 the borided sample at 1173 K for 8 h, following HF3
324 category. Compressive stresses are immediately induced
325 under the indent after the cohesion test with generation of
326 tensile stresses at the indentation perimeter [51].
Taktak [51] studied the adhesive quality of boride layers
327 produced on AISI 304 and AISI H3 steels using a slurry salt
328 bath. He found that the adherence by Rockwell C
329 indentation test decreased with increasing boriding temper-
330 ature and treatment time. Rodriguez-Castro et al. [52] have
331 pack-boridedtheAISI304steelandtheyusedtheRockwellC
332 adhesion test to assess qualitatively the cohesive strength of
333 boride layers (FeB and Fe2B). In their study, the tested
334 samples were treated at 1223 K during 2, 6 and 10 h.
335 Rodriguez-Castro et al. [52] showed that the adhesion of the
336 boride layers on AISI 304 steel was affected by the treatment
337 timeInparticular,theadhesion ofboridelayerobtainedwith
338 10 h of treatment wasrelatedtoH5category. Vera-Cardenas
339 et al. [53] borided the two tool steels (AISI H13 and AISI D2)
340 at 1273 K for 8 h. They showed that the interfacial adherence
341 of the boride layer on AISI H13 and D2 steels was related to
342 HF5 and HF3 maps, respectively. This behaviour could be
343 explainedbytheeffectofchemicalcompositionontheresults
344 of cohesion tests made on both borided steels.
3454.3.2 Pin-on-disc test
346The wear behaviour of boride layers was investigated by
347performing the pin-on-disc test on both borided sample
348(at 1223 K for 8 h) and untreated sample. Figure 8
349describes the evolution of friction coefficient as a function
350of sliding distance by comparing the frictional behaviour
351between borided and untreated samples. This pin-on-disc
352test was carried out by using a diamond indenter during
353sliding under dry conditions. It is noted that the borided
354sample has a friction coefficient lower than that of the
355unborided sample. The average friction coefficient for the
356untreated sample ranged from 0.475 to 0.551 while for
357the borided sample, it possesses a value of friction
358coefficient located between 0.244 and 0.251. The
359obtained results regarding the values of friction coeffi-
360cient are consistent with the data reported in the
361literature [6–8].
3624.3.3 Wear scratch test
363For a comparison of tribological performance between the
364borided sample (at 1223 K for 8 h) and the untreated
365sample, the wear scratch test was performed.
366Figure 9 shows the SEM micrographs of the worn
367surfaces of unborided and borided samples after applying
368the wear scratch test. Figure 9a shows the existence of
369cracks and wear debris resulting from an intense plastic
370deformation produced on the worn surface of unborided
371sample.
372Figure 9b puts into evidence the occurrence of
373scratching lines and some areas undergoing a plastic
374deformation on the worn surface of unborided sample. The
375wear scar, produced on the worn borided surface, has a
376small width compared to that of unborided surface. Such
377wear behaviour was also observed in other findings for the
Fig. 7. SEM micrographs showing indentation marks of VDI adhesion tests on the surfaces of borided AISI T1 steels at 1173 K for two
treatment times: (a) 2 h and (b) 8 h.
Fig 7. Micrographies MEB montrant les marques d’indentation des tests d’adhérence VDI sur les surfaces des aciers borurés AISI T1 :
(a) 2 h et (b) 8 h.
6 M. Ortiz-Domínguez et al.: Metall. Res. Technol. Vol, No (2018)

7. UNCORRECTEDPROOF
378 borided steels [6–8]. The formation of Fe2B layer on the
379 surface of AISI T1 steel allowed to improve its tribological
380 performance.
381 4.4 Estimation of activation energy for boron diffusion
382 To determine the value of activation energy for boron
383 diffusion in AISI T1 steel, it is necessary to have the kinetic
384 data concerning the time evolution of Fe2B layer thickness
385 in the temperature range 1123–1273 K. An analytic
386solution of the integral method has been developed to
387obtain the expression of diffusion coefficient of boron in
388Fe2B given by equation (11) for an upper born content in
389Fe2B equal to 9 wt.% depending on the parabolic growth
390constants at the (Fe2B/ substrate) interface. Figure 10
391gives the variation of the square of Fe2B layer thickness as a
392function of times at increasing boriding temperatures.
393The slopes of the straight lines plotted in Figure 10
394represent the value of experimental parabolic growth
395constants at the considered interface. The value of boride
Fig. 8. Variation of friction coefficient versus the sliding distance using a diamond indenter against the borided surface of AISI T1 steel
at 1223 K for 8 h and the unborided substrate.
Fig 8. Variation du coefficient de frottement en fonction de la distance de glissement en utilisant un indenteur en diamant contre la
surface borurée de l’acier AISI T1 à 1223 K pendant 8 h et le substrat non boruré.
Fig. 9. SEM micrographs of wear scar on the surfaces of AISI T1 steels: (a) borided surface at 1223 K during 8 h and (b) unborided
surface.
Fig 9. Micrographies MEB de la trace d’usure sur les surfaces des aciers AISI T1 : (a) surface borurée à 1223 K durant 8 h et (b) Surface
non borurée.
M. Ortiz-Domínguez et al.: Metall. Res. Technol. Vol, No (2018) 7

8. UNCORRECTEDPROOF
396 incubation time, required to form a compact and continuous
397 Fe2B layer, can be deduced from the intercept of the abscissa
398 which gives an additional point as shown in Figure 10.
399 Table 1 gives the experimental values of parabolic growth
400 constants at the (Fe2B/substrate) interface along with the
401 corresponding boride incubation times. From Table 1, it is
402 seenthattheborideincubationtimeisnearlyindependenton
403 the boriding temperature (= 1996 s).
404 Figure 11 describes the evolution of boron diffusion
405 coefficients in Fe2B according to the Arrhenius equation.
406 The expression of boron diffusion coefficients in the
407 Fe2B layers can be readily obtained using a linear fitting in
408 the temperature range 1123–1273 K:
DFe2B ¼ 1:09 Â 10À2
expð
À212:76 kJmolÀ1
RT
Þ;
409410
411 where R = 8.314 J molÀ1
KÀ1
and T the absolute tempera-
412 ture in Kelvin.
413Table 2 lists the values of activation energy for boron
414diffusion in different ferrous alloys and Armco iron along
415with the estimated value of boron activation energy in AISI
416T1 steel [11,13,14,19,50,54–61]. It is noticed from Table 2
417that the reported values of activation energy for boron
418diffusion in different borided materials depended on
419various factors such as: (the temperature range, the
420boriding method, the chemical composition of the
421substrate, the method of calculation and mechanism of
422boron diffusion). The estimated value of activation energy
423for boron diffusion in AISI T1 steel was interpreted as the
424necessary amount of energy to stimulate the diffusion of
425boron atoms in the preferred crystallographic direction
426[001] [11,14,47]. The estimated value of activation energy
427for boron diffusion in AISI T1 steel is very close to that
428found by Campos et al. [50] for paste-boriding of AISI M2
429steel.
4304.5 Experimental validation of the diffusion model
431The validity of the present model was checked experimen-
432tally by comparing the experimental values of Fe2B layers’
433thicknesses with the numerical results.
434Figure 12 shows the SEM micrographs of the cross-
435sections of borided AISI T1 steels at 1253 K for 1.5 and
4362.5 h, respectively.
437Table 3 compares between the experimental values of
438Fe2B layers’ thicknesses and the predicted values for an
439upper boron content equal to 9 wt.%. A good agreement
440was observed between these two set of data. The numerical
441solutions of differential algebraic equations were obtained
442for the initial values of u(t =1996 s) =0.10 mm, a(t =1996s)
443=0.0157 and b(t =1996s)= 0.00138.
Fig. 10. Square of Fe2B layer thickness as a function of time for
different temperatures.
Fig 10. Le carré de l’épaisseur de la couche Fe2B en fonction du
temps pour différentes températures.
Table 1. The experimental values of parabolic growth
constants at the (Fe2B/substrate) interface along with the
corresponding boride incubation times.
Tableau 1. Valeurs expérimentales des constantes de
croissance parabolique à l’interface (Fe2B/substrat) avec
les temps d’incubation de borure correspondants.
T(K) Experimental parabolic
growth constant k (mm · sÀ0.5
)
Boride incubation
time tFe2B
0 ðTÞ (s)
1123 0.3224 2002
1173 0.5239 1995.9
1223 0.8184 1994
1273 1.2344 1997.1
Fig. 11. Temperature dependence of the boron diffusion coeffi-
cients in the Fe2B layers.
Fig 11. Dépendance en température des coefficients de diffusion
du bore dans les couches Fe2B.
8 M. Ortiz-Domínguez et al.: Metall. Res. Technol. Vol, No (2018)

9. UNCORRECTEDPROOF
444 5 Conclusions
445 In the present work, the AISI T1 steel was hardened by
446 pack-boriding treatment in the temperature 1123–1273 K
447 with an exposure time varying from 2 to 8 h.
448 A single Fe2B layer was produced for all boriding
449 conditions at the surface of AISI T1 steel exhibiting a less
450 pronounced saw tooth morphology.
The kinetics of formation of Fe2B layer obeyed the
451parabolic growth law with the presence of a constant
452boride incubation time independent of the boriding
453temperature.
454The interfacial cohesion of Fe2B layers on AISI T1 steel
455obtained at 1173 K for 2 h was related to HF3 category
456whereas for the Fe2B layer produced at 1173 K for 8 h, its
457cohesive quality followed HF2 category according to the
458VDI 3198 norm.
459The average value of friction coefficient for the borided
460sample (at 1223 K for 8 h) was found to be lower than that
461of untreated sample. Thus, the boriding treatment
462improved the wear behaviour of AISI T1 steel.
The value of activation energy for boron diffusion in
463AISI T1 steel was estimated as 212.76 kJ molÀ1
using an
464analytic solution of a diffusion model based on the
465integral method. The obtained value of boron activation
466energy was compared to other data available in the
467literature.
468The set of differential algebraic equations, derived from
469the integral method, has been solved numerically for an
470experimental validation of this diffusion model by using
471two additional boriding conditions.
472A satisfactory concordance has been observed when
473comparing the experimental values of Fe2B layers’
474thicknesses with the predicted results.
Table 2. Comparison of activation energy for boron diffusion in AISI T1 steel with other borided ferrous alloys and
borided Armco iron.
Tableau 2. Comparaison de l’énergie d’activation pour la diffusion du bore dans l’acier AISI T1 avec d’autres alliages
ferreux borurés et le fer Armco boruré.
Material Boriding
method
Boron activation
energy (kJ molÀ1
)
Temperature
range (°C)
Method of calculation References
Armco iron Gaseous 73.08 (FeB) 120.65 (Fe2B) 800–1000 Diffusion model [54]
Armco iron Paste 157 950–1050 Diffusion model [19]
AISI M2 steel Paste 257.5 (FeB) 210.0 (Fe2B) 920–1000 Diffusion model [50]
AISI 1018 steel Electrochemical 172.75 ± 8.6 850–1000 Parabolic growth law [55]
AISI 8620 steel Plasma paste
boriding
124.7–138.5 700–800 Parabolic growth law [56]
AISI 4340 Steel Salt bath 234.0 800–1000 Parabolic growth law [57]
AISI D2 steel Salt bath 170.0 800–1000 Parabolic growth law [57]
Armco Iron Powder 157.5 (Fe2B) 850–1000 Diffusion model [14]
AISI 1018 Steel Powder 159.3 (Fe2B) 850–1000 Diffusion model [11]
AISI D2 steel Powder 201.5 (Fe2B) 850–1000 Diffusion model [13]
AISI P20 steel Powder 200 (FeB + Fe2B) 800–950 Parabolic growth law [58]
AISI 1045 steel Powder 154 ± 7 (FeB) 141 ± 9 (Fe2B) 900–1000 Diffusion model [59]
Ductile cast iron Powder 212.28 (FeB + Fe2B) 900–1000 Parabolic growth law [60]
C35 steel Powder 153.1 (FeB + Fe2B) 800–1000 Parabolic growth law [61]
AISI T1 steel Powder 212.76 (Fe2B) 850–1000 Integral method This work
Table 3. Comparison between the experimental values of
Fe2B layer thickness obtained at 1253 K for two treatment
times and the predicted values using the numerical solution
of integral method.
Tableau 3. Comparaison entre les valeurs expérimentales
de l’épaisseur de la couche Fe2B obtenues à 1253 K pour
deux temps de traitement et les valeurs prédites en utilisant
la solution numérique de la méthode intégrale.
Boriding
conditions
Experimental
Fe2B layer
thickness (mm)
Simulated Fe2B
layer thickness (mm)
by numerical solution
1253 K for 1.5 h 62.43 ± 11.44 61.32
1253 K for 2.5 h 87.80 ± 21.34 87.96
M. Ortiz-Domínguez et al.: Metall. Res. Technol. Vol, No (2018) 9

10. UNCORRECTEDPROOF
475
476 List of symQ6 bols
478 u(t)479 Boride layer thickness (mm)
480 a(t) and b(t)481 Time-dependent parameters
482 k483 Parabolic growth constant of the Fe2B layer
484 (mmsÀ0.5
)
485 t486 Treatment time (s)
487 tFe2B
0 ðTÞ488 Boride incubation time (s)
489 CFe2B
up490 Upper limit of boron content in Fe2B
491 (= 9 wt.%)
492 CFe2B
low493 Lower limit of boron content in Fe2B
494 (= 8.83 wt.%)
495 Cads496 Adsorbed boron concentration in the boride
497 layer (wt.%)
498 C0499 Boron solubility in the matrix (≈ 0 wt.%)
500 CFe2B½x; tŠ501 Boron-concentration profile in the Fe2B
502 layer (wt.%)
503 DFe2B504 Diffusion coefficient of boron in the Fe2B
505 phase (m2
sÀ1
)
506507Acknowledgements. The work described in this paper was
508supported by a grant of PRDEP and CONACyT México
509(National Council of Science and Techonology). Likewise, FCS
510reconoce los fondos del Departamento de Física y Matemáticas y
511de la División de Investigación de la UIA. The authors wish to
512thank to the Laboratorio de Microscopía de la UIA.
513References
5141. A.K. Sinha, J. Heat Treat. 4, 437 (1991)
5152. M.G. Krukovich, B.A. Prusakov, I.G. Sizov, The use of
516boriding processes in the industrial treatment of details and
517tools. In: Plasticity of boronized layers. Springer Series in
518Materials Science, Springer, Cham, 2006, Vol. 237
5193. S. Sahin, J. Mater. Process. Technol. 209, 1736 (2009)
5204. J. Ptačinová, M. Drienovsky, M. Palcut, R. Čička, M. Kusy,
521M. Hudáková, Kovove Mater. 53, 175 (2015)
5225. M. Keddam, M. Elias-Espinosa, M. Ortiz-Domínguez, I.
523Simón-Marmolejo, J. Zuno-Silva, Int. J. Surf. Sci. Eng. 11,
524563 (2017)
5256. O.A. Gómez-Vargas, M. Keddam, M. Ortiz-Domínguez,
526High Temp. Mater. Process. 36, 197 (2017)
5277. M. Ortiz-Domínguez, O.A. Gómez-Vargas, M. Keddam, A.
528Arenas-Flores, J. García-Serrano, Protect. Met. Phys. Chem.
529Surf. 53, 534 (2017)
5308. M.A. Flores-Rentería, M. Ortiz-Domínguez, M. Keddam, O.
531Damián-Mejía, M. Elias-Espinosa, M.A. Flores-González, S.
532A. Medina-Moreno, A. Cruz-Avilés, M. Villanueva-Ibañez,
533High Temp. Mater. Process. 31, 1 (2015)
5349. B. Mebarek, D. Madouri, A. Zanoun, A. Belaidi, Matériaux
535Techniques 103(7), 703 (2015)
53610. J. Zuno-Silva, M. Ortiz-Domínguez, M. Keddam, M. Elias-
537Espinosa, O. Damián-Mejía, E. Cardoso-Legorreta, M.
538Abreu-Quijano, J. Min. Metall. Sect. B-Metall. 50, 101
539(2015)
54011. M. Ortiz-Domínguez, J. Zuno-Silva, M. Keddam, O.
541Damián-Mejía, M. Elias-Espinosa, Int. J. Surf. Sci. Eng. 9,
542281–297 (2015)
54312. R. Kouba, M. Keddam, M. Kulka, Surf. Eng. 31, 563 (2015)
54413. M. Ortiz-Domínguez, M. Elias-Espinosa, M. Keddam, O.A.
545Gómez-Vargas, R. Lewis, E.E. Vera-Cárdenas, J. Zuno-Silva,
546Indian J. Eng. Mater. Sci. 22, 231 (2015)
54714. M. Elias-Espinosa, M. Ortiz-Domínguez, M. Keddam, M.A.
548Flores-Rentería, O. Damián-Mejía, J. Zuno-Silva, J. Her-
549nández-Ávila, E. Cardoso-Legorreta, A. Arenas-Flores, J.
550Mater. Eng. Perform. 23, 2943 (2014)
55115. M. Ortiz-Domínguez, M. Keddam., M. Elias-Espinosa, O.,
552Damián-Mejía, M.A. Flores-Rentería, A. Arenas-Flores, J.
553Hernández-Ávila, Surf. Eng. 30, 490 (2014)
55416. M. Ortiz-Domínguez, M.A. Flores-Rentería, M. Keddam, M.
555Elias-Espinosa, O. Damián-Mejía, J.I. Aldana-González, J.
556Zuno-Silva, S.A. Medina-Moreno, J.G. González-Reyes,
557Mater. Technol. 48, 905 (2014)
55817. Z. Nait Abdellah, M. Keddam, A. Elias, Int. J. Mater. Res.
559104, 260 (2013)
56018. Z. Nait Abdellah, M. Keddam, R. Chegroune, B. Bouarour,
561H. Lillia, A. Elias, Matériaux et Techniques 100, 581
562(2012)
56319. Z. Nait Abdellah, M. Keddam, A. Elias, Defect Diffus. Forum
564323–325, 401 (2012)
56520. I. Campos-Silva, M. Ortiz-Domínguez, H. Cimenoglu, R.
566Escobar-Galindo, M. Keddam, M. Elías-Espinosa, N. López-
567Perrusquia, Surf. Eng. 27, 189 (2011)
Fig. 12. SEM micrographs of Fe2B layers formed on AISI T1
steel at 1253 K for two treatment times a) 1.5 h and b) 2.5 h.
Fig 12. Micrographies MEB des couches Fe2B formées sur l’acier
AISI T1 à 1253 K pour deux temps de traitement a) 1,5 h et b) 2,5 h.
10 M. Ortiz-Domínguez et al.: Metall. Res. Technol. Vol, No (2018)

11. UNCORRECTEDPROOF
568 21. M. Keddam, R. Chegroune, Solid State Phenom. 170, 185
569 (2011)
570 22. M. Ortiz-Domínguez, E. Hernandez-Sanchez, J. Martínez-
571 Trinidad, M. Keddam, I. Campos-Silva, Kovove Mater. 48,
572 285 (2010)
573 23. M. Keddam, R. Chegroune, Appl. Surf. Sci. 256, 5025
574 (2010)
575 24. M. Keddam, Defect Diffus. Forum 297–301, 269 (2010)
576 25. M. Keddam, M. Ortiz-Domínguez, I. Campos-Silva, J.
577 Martínez-Trinidad, Appl. Surf. Sci. 256, 3128 (2010)
578 26. I. Campos-Silva, M. Ortiz-Domınguez, N. Lopez-Perrus-
579 quiaa, A. Meneses-Amador, R. Escobar-Galindo, J. Marti-
580 nez-Trinidad, Appl. Surf. Sci. 256, 2372 (2010)
581 27. I. Campos-Silva, M. Ortiz-Dominguez, Int. J. Microstruct.
582 Mater. Prop. 5, 26 (2010)
583 28. M. Ortíz-Domínguez, I. Campos-Silva, J. Martínez-Trinidad,
584 M. Elías-Espinosa, E. Hernández-Sánchez, D. Bravo-Bárce-
585 nas, Defect Diffus. Forum 297–301, 294 (2010)
586 29. I. Campos-Silva, M. Ortiz-Dominguez, M. Keddam, N.
587 López-Perrusquia, A. Carmona-Vargas, M. Elias-Espinosa,
588 Appl. Surf. Sci. 255, 9290 (2009)
589 30. I. Campos-Silva, M. Ortíz-Domínguez, C. VillaVelázquez, R.
590 Escobar, N. López, Defect Diffus. Forum 272, 79 (2007)
591 31. M. Keddam, Appl. Surf. Sci. 253, 757 (2006)
592 32. I. Campos, O. Bautista, G. Ramirez, M. Islas, J. De La Parra,
593 L. Zuniga, Appl. Surf. Sci. 243, 429 (2005)
594 33. M. Keddam, Appl. Surf. Sci. 236, 451 (2004)
595 34. I. Campos, J. Oseguera, U. Figueroa, J.A. Garcia, O.
596 Bautista, G. Kelemenis, Mater. Sci. Eng. A352, 261
597 (2003)
598 35. C.M. Brakman, A.W.J. Gommers, E.J. Mittemeijer, J.
599 Mater. Res. 4, 1354 (1989)
600 36. L.G. Yu, X.J. Chen, K.A. Khor, G. Sundararajan, Acta
601 Mater. 53, 2361 (2005)
602 37. H. Okamoto, J. Phase Equilib. Diffus. 25, 297 (2004)
603 38. Z. Nait Abdellah, R. Chegroune, M. Keddam, B. Bouarour,
604 L. Haddour, A. Elias, Defect Diffus. Forum 322, 1 (2012)
605 39. T.R. Goodman, Adv. Heat Transf. 1, 51 (1964)
606 40. U. Ascher, L. Petzold, Computer methods for ordinary
607 differential equations and differential-algebraic equations,
608 SIAM, Philadelphia, 1998
60941. I. Campos-Silva, D. Bravo-Bárcenas, A. Meneses-Amador,
610M. Ortiz-Dominguez, H. Cimenoglu, U. Figueroa-López, R.
611Tadeo-Rosas, Surf. Coat. Technol. 237, 402 (2013)
61242. I. Campos-Silva, M. Ortiz-Domínguez, O. Bravo-Bárcenas,
613M.A. Doñu-Ruiz, D. Bravo-Bárcenas, C. Tapia-Quintero, M.
614Y. Jiménez-Reyes, Surf. Coat. Technol. 205 (2010) 403
61543. N. Vidakis, A. Antoniadis, N. Bilalis, J. Mater. Process.
616Technol. 143–144, 481 (2003)
61744. S. Taktak, Mater. Des. 28, 1836 (2007)
61845. T.S. Eyre, Wear 34, 383 (1975)
61946. M. Carbucicchio, G. Palombarini, J. Mater. Sci. Lett. 10,
6201147 (1987)
62147. C. Badini, D. Mazza, J. Mater. Sci. 23, 3061 (1988)
62248. I. Ozbek, C. Bindal, Vacuum 86, 391 (2011)
62349. I. Campos, M. Farah, N. Lopez, G. Bermudez, G. Rodrıguez,
624C. VillaVelazquez, Appl. Surf. Sci. 254, 2967 (2008)
62550. I. Campos, G. Ramırez, U. Figueroa, J. Martınez, O. Morales,
626Appl. Surf. Sci. 253, 3469 (2007)
62751. S. Taktak, Mater. Des. 28, 1836 (2007)
62852. G.A. Rodríguez-Castro, L.F. Jiménez-Tinoco, J.V. Méndez-
629Méndez, I. Arzate-Vázquez, A. Meneses-Amador, H. Martí-
630nez-Gutiérrez, I. Campos-Silva, Mater. Res. 18, 1346 (2015)
63153. E.E. Vera-Cardenas, R. Lewis, A.I. Martınez-Perez, J.L.
632Bernal-Ponce, F.J. Perez-Pinal, M. Ortiz-Domınguez, E.D.
633Rivera-Arreola, Adv. Mech. Eng. 8, 1 (2016)
63454. M. Keddam, M. Kulka, N. Makuch, A. Pertek, L. Małdzinski,
635Appl. Surf. Sci. 298, 155 (2014)
63655. G. Kartal, O. Eryilmaz, G. Krumdick, A. Erdemir, S. Timur,
637Appl. Surf. Sci. 257, 6928 (2011)
63856. I. Gunes, S. Taktak, C. Bindal, Y. Yalcin, S. Ulker, Y. Kayali,
639Sadhana 38, 513 (2013)
64057. S. Sen, U. Sen, C. Bindal, Surf. Coat. Technol. 191, 274 (2005)
64158. I. Uslu, H. Comert, M. Ipek, O. Ozdemir, C. Bindal, Mater.
642Des. 28, 55 (2007)
64359. I. Campos-Silva, M. Flores-Jiménez, D. Bravo-Bárcenas, H.
644Balmori-Ramírez, J. Andraca-Adame, J. Martínez-Trinidad,
645J.A. Meda-Campaña, Surf. Coat. Technol. 309, 155 (2017)
64660. O. Azouani, M. Keddam, O. Allaoui, A. Sehisseh, Protect.
647Met. Phys. Chem. Surf. 53, 306 (2017)
64861. B. Bouarour, M. Keddam, O. Allaoui, O. Azouani, Metall.
649Res. Technol. 111, 67 (2014)
650 Cite this article as: Martin Ortiz-Domínguez, Mourad Keddam, Milton Elias-Espinosa, Marius Ramírez-Cardona, Alberto
651 Arenas-Flores, Juno Zuno-Silva, F. Cervantes-Sodi, E. Cardoso-Legorreta, Characterization and boriding kinetics of AISI T1 steel,
652 Metall. Res. Technol. Vol, 170218 (2018)
M. Ortiz-Domínguez et al.: Metall. Res. Technol. Vol, No (2018) 11

12. UNCORRECTEDPROOF
Author Queries
Q1 Please provide the full given names of the authors [Cervantes-Sodi; Cardoso-Legorreta].
Q2 Please check this sentence for correctness.
Q3 We have replaced [identidad] by [identified]. Please check for correctness.
Q4 We have inserted subheadings in this part. Please check for correctness.
Q5 We have replaced [during for] by [for]. Please check for correctness.
Q6 Please check the edit(s) made in this section, and correct if necessary.