Influence of High-Energy Ball Milling on Reaction Kinetics in the Ni–Al System: An Electrothermorgaphic Study

Abstract

A new electrothermographic method, viz. high-speed temperature scanning, was applied to kinetic studies of reactions taking place in the Ni-Al system, including those after mechanical activation in a planetary ball mill. Treatment of the temperature profiles taken at different heating rates in terms of the Kissinger-Akahira-Sunose (KAS) approximation gave activation energy E for non-activated mixtures: E = 155 kJ/mol (for temperature range 650–850°C). But for mechanically activated mixtures, the characteristic points (reaction onset temperature, temperature of maximum reaction rate) were found to decrease with increasing heating rate, which makes the KAS method inapplicable to these compositions. It has been concluded that mechanical treatment leads to significant changes in the reaction kinetics, possibly due to splitting the reaction route into two stages the first of which has very low activation energy.

Full text

ISSN 10613862, International Journal of SelfPropagating HighTemperature Synthesis, 2015, Vol. 24, No. 1, pp. 21–28. © Allerton Press, Inc., 2015.
21
1
INTRODUCTION
A variety of engineering technologies involve
chemical reactions under essentially nonisothermal
hightemperature conditions. It has been reported
that heating rates may have marked influence on dif
ferent processes, including chemical kinetics and
phase transformation mechanisms [1–5]. Thus it is
understood that under high heating rates, the kinetics
of interaction between the reactants may differ signif
icantly as compared to the kinetic laws obtained in
nearisothermal conditions. The problem becomes
even more complicated in the conditions typical of
various combustion and plasma syntheses or laser
induced processes where the rate of temperature
change reaches a value of 10
3
–10
5
K/s. In many cases,
the observed reaction rates appear to be greater than
those obtained in isothermal conditions. There are a
few techniques which allow monitoring the kinetics of
chemical reactions under such conditions, including
the socalled electrothermographic [6, 7] and electro
thermalexplosion analyses [8, 9]. In this work, a new
thermographic method based on the use of highspeed
temperature scanner (HSTS) [10–13] was used to
investigate the kinetics of chemical reactions in the
1
The article is published in the original.
Ni–Al system. The results of the HSTS experiments
are compared with those obtained by other tech
niques.
EXPERIMENTAL
Experiments were conducted with commercially
available powders of Al (ASD1, Russia, particle size
<30
μ
m) and Ni (PNK, mean particle size 20
μ
m).
The powders were mixed at 1 : 1 atomic ratio by two
methods. Nonactivated mixtures were prepared in an
alumina mortar by manual mixing for 10 min. Acti
vated mixtures were prepared by a short term (1–5 min)
high energy ball milling (HEBM) in a planetary ball
mill (Activator2S, Novosibirsk, Russia). The rotation
speed of a sun wheal was 694 rpm and ratio of the
speed of the milling jar to the speed of the sun wheal
was
K
= 1. A special locking device and jar lid afforded
to evacuate the vial and perform grinding operations in
an inert atmosphere (e.g., argon). The ball (6 mm steel
balls) to mill ratio was 40 : 1. The HEBM resulted in
formation of fine lamellar composite structure shown
in Fig. 1.The thickness of the Ni and Al layers varied
between tens of nanometers to one micron. Therefore,
the contact area between the reactants increases
approximately by a factor of 10
3
–10
4
as compared to
Influence of HighEnergy Ball Milling on Reaction Kinetics
in the Ni–Al System: An Electrothermorgaphic Study
1
A. A. Nepapushev
a
, K. G. Kirakosyan
b
, D. O. Moskovskikh
a
, S. L. Kharatyan
b
,
A. S. Rogachev
a
,
c
, and A. S. Mukasyan
a,d
a
Center of Functional Nanoceramics, National University of Science and Technology, Russia
b
Institute of Chemical Physics, National Academy of Sciences, Armenia
c
Institute of Structural Macrokinetics and Materials Science, Russian Academy of Sciences, Russia
d
Department of Chemical and Biomolecular Engineering, University of Notre Dame, USA
email: rogachev@ism.ac.ru, suren@ichph.sci.am
Received November 17, 2014
Abstract
—A new electrothermographic method, viz. highspeed temperature scanning, was applied to
kinetic studies of reactions taking place in the Ni–Al system, including those after mechanical activation in
a planetary ball mill. Treatment of the temperature profiles taken at different heating rates in terms of the
Kissinger–Akahira–Sunose (KAS) approximation gave activation energy
E
for nonactivated mixtures:
E
=
155 kJ/mol (for temperature range 650–850
°
C). But for mechanically activated mixtures, the characteristic
points (reaction onset temperature, temperature of maximum reaction rate) were found to decrease with
increasing heating rate, which makes the KAS method inapplicable to these compositions. It has been con
cluded that mechanical treatment leads to significant changes in the reaction kinetics, possibly due to split
ting the reaction route into two stages the first of which has very low activation energy.
Keywords
: heterogeneous hightemperature reaction, mechanical activation, kinetics, thermography, nickel
aluminide
DOI:
10.3103/S1061386215010082

22
INTERNATIONAL JOURNAL OF SELFPROPAGATING HIGHTEMPERATURE SYNTHESIS Vol. 24 No. 1 2015
NEPAPUSHEV et al.
nonactivated mixture, which should affect the kinet
ics of heterogeneous reaction.
The kinetic parameters of the hightemperature
heterogeneous reaction in activated and nonactivated
mixtures were studied with a HSTS device designed
and fabricated at the Institute of Chemical Physics
(Republic of Armenia). It is designed to investigate the
kinetics of chemical reactions of the reactive powder
mixtures under highheatingrate conditions. The
sequence of the experimental steps shown in Fig. 2 was
as follows: (
i
) reactive powder mixture
1
is placed into
an envelope made of metal (e.g. Ni) foil
2
; (
ii
) enve
lope
3
with the mixture (3) is enfolded and a thermo
couple is welded to the foil in area
4
of powder loca
tion; (
iii
) thus prepared envelope is placed between
electrodes
5
into reaction chamber
6
filed with argon
gas (1 atm) and preheated by passing electric current
through foil
5
with desired temperaturetime schedule
provided by PCassisted controller
7
. In this work the
linear preheating schedule was used at heating rate
ranging between 130 and 7800 K/min. The socalled
“inert” preheating of the envelope (after the reaction
was accomplished) is also conducted for calibration
purpose.
Typical temperature profiles for “reactive” and
“inert” experiments are shown in Fig. 3. It can be seen
that the inert experiment provides liner temperature
time profile, which defines the heating rate and coin
cides with the reactive Tprofile at the first heating
stage, when the reaction does not occur. The deviation
of the reactive profile from the inert one is seen to
begin at
T
0
, and this temperature (
T
0
) can be regarded
as a temperature of reaction onset.
A pronounced exothermic peak is observed at some
T
>
T
0
, and it attaining a maximum value (
T
max
) at
temperature
T
* on the inert profile. Thus the differ
ence (
Δ
T
) between
T
max
and
T
* defines a temperature
change owing solely to the heat release in reaction. At
some moment, electric current is switched off and the
sample is allowed to cool down. Note that our
approach is similar to that adopted in conventional
DTA method. However, HSTS provides much higher
heating rates (up to 10
4
K/min) which can be precisely
governed by PCassisted controller of power supply.
To determine kinetic parameters of the reaction,
the obtained data were processed in terms of the so
called isoconversion method suggested by Kissinger
[14] that is well known in thermography. In this
method, the activation energy is calculated based on
the shift of in the DTA curve as a function of
heating rate
V
h
:
(1)
where
V
h
is the heating rate (K/min), is the reac
tion temperature which corresponds to the position of
the maximum peak on the DTA curve (K),
A
is some
constant,
E
the effective activation energy of the pro
cess, and
R
the universal gas constant. It should be
noted that, in conventional DTA method, the differ
ence between
T
max
and
T
* is small, i.e. the prepro
grammed temperature of the furnace is close to real
temperature of the sample. Following this approach, it
(
)
DTA
max
T
()
h
DTA
DTA 2
max
max
1
ln ln ,
VE
ART
T
⎛⎞
⎛⎞
⎜⎟
=−
⎜⎟
⎜⎟
⎝⎠
⎝⎠
DTA
max
T
2
μ
m
Fig. 1.
Typical microstructure of the composite formed
after HEBM of Ni–Al powder mixture (white areas Ni,
dark areas Al).
(a) (b)
1
234
5
6
7
Fig. 2.
Samples used in experiments and overall view of the experimental setup: (a) metal envelopes containing reactive mixture
and (b) reaction chamber and controller:
1
reactive mixture,
2
boat of Ni foil,
3
powder mixture in the Ni boat,
4
envelope with
reactive mixture and thermocouple,
5
heated sample,
6
reaction chamber, and
7
PCassisted controller.

INTERNATIONAL JOURNAL OF SELFPROPAGATING HIGHTEMPERATURE SYNTHESIS Vol. 24 No. 1 2015
INFLUENCE OF HIGHENERGY BALL MILLING ON REACTION KINETICS 23
is also assumed (for conditions of rapid heating in
HSTS setup) that
≡
T
* (Fig. 3). However, this
temperature gap in the HSTS method (
V
h
= 10–
10000 deg/min) may be significantly larger than in
the conventional DTA/DSC technique (
V
h
= 1–
100 deg/min). This difference may influence the
results of kinetics analysis, as it will be shown below.
RESULTS AND DISCUSSION
The typical temperature profiles obtained for dif
ferent Ni–Al mixtures heated at a rate of 2600 K/min
are given in Fig. 4. As is seen in Fig. 5, the reaction
onset temperature (
T
0
) decreases with increasing
τ
DTA
max
T
(Fig. 5a). For nonactivated powders
T
0
= 730°C,
which is above the melting point of Al, while for acti
vated powders it gradually decreases down to ~300°C.
These data are in good agreement with those obtained
earlier by other experimental methods [15, 16]. The
characteristic values of
T
* also gradually decrease
(Fig. 5b). It is important that the
T
* values for the
samples pressed from the particles activated for more
than 1 min are below the melting point of Al, which
indicates that maximum heat release in these systems
is due solely to solidstate reactions. The overheating
(
Δ
T
max
=
T
max
–
T
*) which characterizes the amount
of energy released, first slightly increases with milling
time reaching maximum at
τ
= 3 min and then
1200
900
600
300
2416128
40 20
T
, °C
Stop heating
Cooling
part
Heating
part
Intensive
exotherm
T
max
T
0
T
*
T
inert heating
T
Iheating
Δ
T
t
, s
Fig. 3.
Typical “reactive” and “inert” temperature profiles with characteristic temperatures.
1200
600
16128
40 20
T
, °C
t
, s
1000
800
400
200
0 min
1 min
2 min
3 min
4 min
5 min
Fig. 4.
Reaction thermograms for different Ni–Al mixtures (
V
h
= 2600 deg/min). Indicated are durations
τ
of HEBM.

24
INTERNATIONAL JOURNAL OF SELFPROPAGATING HIGHTEMPERATURE SYNTHESIS Vol. 24 No. 1 2015
NEPAPUSHEV et al.
decreases (Fig. 5c). The former can be explained by a
higher extent of conversion during thermal explosion
due to intermixing of the reactants to a nano level dur
ing HEBM, while the former effect is due to possible
interaction between Ni and Al directly in the milling jar.
Thus these experiments confirmed results obtained
by relatively slow (up to 100 K/min) conventional
DTA method that HEBM leads to significant decrease
in
T
0
and that in mechanicallyinduced nanomixed
structures the reaction may proceed to a significant
extent at temperatures below the eutectics in the Ni–
Al system.
Dependencies of
T
0
,
T
*, and
Δ
T
max
on
V
h
for non
activated mixtures are shown in Figs. 6a–6c. It can be
seen that all three parameters increase with increasing
V
h
. Such a behavior of
T
0
and
T
* is typical of the exo
thermic systems with high activation energies, while
increase in
Δ
T
max
can be explained by the fact that the
onset reaction temperature is higher at higher preheat
ing rate.
Using Eq. (1) and the data presented in Fig. 6b we
plotted (Fig. 7) the Arrheniustype dependence, i.e.
= which was then used to obtain the
value of apparent activation energy
E
for the reaction
in nonactivated Ni–Al powders. For the temperature
range 650–850°C (which is above the eutectic tem
perature for the Ni–Al system)
E
was found to have a
value of 155 kJ/mol. This value fits well to that
obtained in [17] by DTA/TG method for chemically
activated mixture (159 kJ/mol) for the temperature
()
h
*
2
ln V
T
⎛⎞
⎜⎟
⎝⎠
(
)
1
,
*
FT
800
600
400
200
5432
10
(c)
Δ
T
max
, °C
τ
, min
900
600
300
5432
10
(b)
T
*, °C
900
600
300
5432
10
(a)
T
0
, °C
Fig. 5.
Parameters of thermal explosion—
T
0
(a),
T
* (b),
and
Δ
T
max
(c)—as a function of
τ
(
V
h
= 2600 deg/min).
Δ
T
max
, °C
V
h
, deg/min
T
*, °C
900
600
300
7500600045003000
15000
(a)
T
0
, °C
900
600
300
7500600045003000
15000
(b)
800
600
200
7500600045003000
15000
(c)
400
Fig. 6.
Parameters of thermal explosion in nonactivated
Ni–Al mixtures—
T
0
(a),
T
* (b), and
Δ
T
max
(c)—as a
function of heating rate
V
h
.

INTERNATIONAL JOURNAL OF SELFPROPAGATING HIGHTEMPERATURE SYNTHESIS Vol. 24 No. 1 2015
INFLUENCE OF HIGHENERGY BALL MILLING ON REACTION KINETICS 25
interval 650–750°C and is lower than that obtained in
[9] by electrothermal explosion method for nonacti
vated Ni–Al mixture (
∼
200 kJ/mol for
T
= 850–
1000°C). This result again confirms the durability of
our method.
The above data can be also compared with the
effective activation energy obtained in the combustion
experiments with Ni–Al mixtures. According to [18],
the temperature dependences of burning velocity for
mixtures with fine Ni powder gave
E
= 75–76 kJ/mol for
T
> 1455°C (melting point of Ni) and
E
= 140 kJ/mol for
T
< 1455°C. Mixtures with coarse Ni particles (41–
73
μ
m) showed
E
= 134 kJ/mol in the temperature
range 1200–1600°C. Thus, our data are in a satisfac
tory agreement with the combustion data obtained
below the melting point of Ni or in experiments with
coarse Ni powders.
Typical temperature profiles of reaction in
mechanically activated mixture (
τ
= 3 min) at differ
ent
V
h
are shown in Fig. 8. Statistical treatment of such
curves also allowed us to plot the values of
T
0
,
T
*
, and
Δ
T
max
as a function of
V
h
(Fig. 9).
It can be seen that the
T
0
and
T
* values, being
always below the eutectic temperature (639°C) for the
system, decrease with increasing
V
h
and such behavior
is different as compared to that of nonactivated mix
tures. Moreover, formal application of Eq. (1) under
conditions when
T
* decreases with increasing
V
h
leads
to negative apparent activation energy for the system.
These effects require a special discussion.
The Kissinger–Akahira–Sunose (KAS) method
belongs to socalled
p
(
y
)isoconversion approach
which is applicable under the assumption that param
eter
y
=
E
/
RT
1 [19]. Briefly, assuming that the reac
tion rate ( ) is the product of two functions, one
depending solely on temperature
T
and the other one
solely on extent of conversion
η,
we obtain:
(2)
The temperature dependent function is generally
assumed to be of the Arrhenius type:
(3)
From (2) and (3) it follows that
(4)
In case of linear heating rates,
V
=
dT
/
dt
= const,
we may rewrite (4) in the form:
(5)
and hence
E
can be determined form a slope of the
– 1/
T
plot.
Ⰷ
η

dη
dt
fη()kT().=
kk
0E
RT
–
⎝⎠
⎛⎞
.exp=
dη
dt
ln E
RT
 – fη()ln–const.+=
dη
dT
 V
⎝⎠
⎛⎞
ln E
RT
–fη()ln–=
(
)
ln d
V
dT
η
–ln(
V
h
,/
T
*
2
)
(1/
T
)
×
10
4
, K
–1
8
6
211.010.510.09.5
9.0
4
8.5
10
E
= 37.0 kcal/mol = 155 kJ/mol
Fig. 7.
Determination of apparent activation energy
E
for
nonactivated Ni–Al mixture.
1000
800
600
400
200
0100806040
20 120
t
, s
T
, °C 2600°/min
390°/min
260°/min
780°/min
Fig. 8.
Typical temperature profiles of reaction in mechanically activated mixtures (
τ
= 3 min) at different
V
h
(indicated).

26
INTERNATIONAL JOURNAL OF SELFPROPAGATING HIGHTEMPERATURE SYNTHESIS Vol. 24 No. 1 2015
NEPAPUSHEV et al.
With account of (3) and (2), we have:
(6)
where
y
=
E
/
RT
,
y
f
=
E
/
RT
f
, and
T
f
is the temperature
at an equivalent (fixed) state of transformation.
The temperature integral on the right side is the so
called Arrhenius integral
p
(
y
):
(7)
ηd
fη()

0
η
∫k0
V
E
RT
–
⎝⎠
⎛⎞
exp Td
0
Tf
∫
=
=
k0
V
E
R
y–()exp
y2
y,d
yf
∞
∫
y–()exp
y2
yd
yf
∞
∫py
f
().=
Assuming that
y
1, the following approximation
to (7) can be obtained:
(8)
The assumption
y
1 seems reasonable because
for the majority of solidstate reactions 15 <
y
< 60. By
taking the logarithm of Eq. (6) and using (8) one may
obtain:
(9)
And at constant extent of conversion
η
, we have:
(10)
which is exactly the formula (1) described above.
According to this equation, the ln( /
V
) – 1/T
f
plot
should represent a straight line with a slope equal to
E
/
R
.
Thus, the correct application of the KAS method is
based on the following assumptions: (a) the reaction is
onestage, (b) its rate depends on temperature accord
ing to Arrhenius law (3), (c)
y
=
E
/
RT
1; and (d) the
sample is heated linearly at constant rate
V
(5).
For nonactivated mixtures, E
≈
155 kJ/mol and
thus, for
T
~ 1000 K,
y
=
E
/
RT
~ 20, which fits the
assumption used in the Kissinger approximation.
However, it is known that mechanical treatment leads
to a significant decrease in E and thus the accuracy of
the method decreases, which may lead, taking also
into account the error of T* measurements, to nega
tive values of the activation energy.
On the other hand, close inspection of Fig. 8 sug
gests that the values of
T
max
increase with increasing
V
h
. If we assume that at
T
=
T
max
the full conversion
(
η
= 1) is achieved in all experiments with activated
samples, then we may use
T
f
=
T
max
as a reference tem
perature in Eq. (10). The plot based on such an
as sumpt ion is sho wn in F ig. 10. It can be see n that with
fitting accuracy of 95% we do have a straight line with
a slope corresponding to
E
of about 83 kJ/mol. This
value is twice less than that for the nonactivated mix
ture (see Fig. 7) and close to the data obtained by other
methods for activated Ni–Al mixtures [9, 16]. Note
that in this case parameter
y
is about 10.
In our previous work [20] it has been shown that
nanosized precursors of the reaction product appear
during the HEBM of Ni–Al mixtures; therefore, the
reaction splits into two stages. Part of the mixture,
fraction
x
, transforms into some highreactive nanoc
rystalline phase (reaction precursor) and reacts with
low activation energy
E
2
; the rest fraction, 1 –
x
, retains
initial reactivity and activation energy
E
1
;
E
2
<
E
1
. Then
Ⰷ
py() pky()≈y–()exp
y2
.=
Ⰷ
ηd
fη()

0
η
∫
ln k0E
R
ln 1
Vyf
2
ln yf.–+=
V
Tf
2
ln E
RTf
–C2,+=
f
2
T
Ⰷ
900
600
300
07500600045003000
1500
Δ
T
max
, °C
V
h
, min
T
*, °C
(a)
T
0
, °C
900
600
300
07500600045003000
1500
(b)
800
600
200
07500600045003000
1500
(c)
400
Fig. 9.
Parameters of thermal explosion—
T
0
(a),
T
* (b),
and
Δ
T
max
(c)—in activated (
τ
= 3 min) Ni–Al mixtures
as a function of
V
h
.

INTERNATIONAL JOURNAL OF SELFPROPAGATING HIGHTEMPERATURE SYNTHESIS Vol. 24 No. 1 2015
INFLUENCE OF HIGHENERGY BALL MILLING ON REACTION KINETICS 27
the reaction rate (
W
) at temperature
T
can be repre
sented in the form:
(11)
where
E
eff
is the effective activation energy for the
overall process. Assuming, for the sake of simplicity,
that
k
≈
k
1
≈
k
2
, the formula for evaluation of
E
eff
was
obtained [20]:
(12)
The effective energy of activation decreases with
increasing
x
. Therefore, we can assume here that the
unusually low or even negative values of the apparent
activation energy appear due to the twostage reac
tion, where the first stage is the lowactivated transfor
mation of nanocrystalline or amorphous precursors
into the crystalline phase.
CONCLUSIONS
It has been demonstrated that HSTC technique is a
powerful tool for investigating the kinetics of heteroge
neous gasless reactions in conditions similar to those
existing in a combustion wave, which cannot be
achieved by conventional DTA/TGA method. It has
also been confirmed that highenergy ball milling
leads to a significant decrease in reaction onset tem
perature as well as in apparent activation energy.
Wke
Eeff
RT

1x–()k1e–E1
RT
xk2e–E2
RT

,+==
Eeff E1RT 1xe
E1E2
–
RT

1–
⎝⎠
⎜⎟
⎛⎞
+.ln–=
ACKNOWLEDGMENTS
This work was supported by SCS RA and RFBR
joint Armenian Russian research Grant AR 13RF
057 // 130390604. The authors also gratefully
acknowledge the financial support of the Ministry of
Education and Science of the Federation in the frame
work of increase Competitiveness of NUST “MISIS”
(No. K22014001).
REFERENCES
1. Seebauer, V., Petek, J., and Staudinger, G., Effects of
particle size, heating rate and pressure on measurement
of pyrolysis kinetics by thermogravimetric analysis,
Fuel
, 1997, vol. 76, no. 13, pp. 1277–1282.
2. Kharatyan, S.L. and Chatilyan, H.A., Nonisothermal
kinetics and mechanism of tungsten siliconizing in gas
less combustion wave,
Int. J. Self.Prop. HighTemp.
Synth
., 1999, vol. 8, no. 1, pp. 31–42.
3. Thiers, L., Leitenberger, B., Mukasyan, A.S., and
Varma, A., Influence of preheating rate on kinetics of
hightemperature gas–solid reactions,
AIChE J.
, 2000,
vol. 46, no. 12, pp. 2518–2524.
4. Pinheiro, G.F.M., Lourenco, V.L., and Iha, K., Influ
ence of heating rate on thermal decomposition of
HMX,
J. Therm. Anal. Calorim
., 2002, vol. 67, no. 2,
pp. 445–452.
5. Kharatyan, S.L., Chatilyan, H.A., Mukasyan, A.S.,
Simonetti, D.A., and Varma, A., Influence of heating
rate on kinetics of rapid hightemperature reactions in
condensed heterogeneous media: Mo–Si system,
AIChE J
., 2005, vol. 51, no. 1, pp. 261–270.
6. Grigor’ev, Y.M., Gal’chenko, Y.A., and
Merzhanov, A.G., Investigation of the rate of the high
temperature reaction between aluminum and oxygen
using the ignition method,
Combust. Explos. Shock
Wav es
, 1973, vol. 9, no. 2, pp. 162–167.
7. Kharatyan, S.L., Grigor’ev, Y.M., and Merzhanov, A.G.,
Kinetics of heat release during hightemperature nitra
tion of titanium,
Izv. Akad. Nauk SSSR, Ser. Met
.,
1977, vol. 10, no. 2, pp. 178–181.
8. Shteinberg, A.S. and Knyazik, V.A., Macrokinetics of
hightemperature heterogeneous reactions: SHS
aspects,
Pure Appl. Chem
., 1992, vol. 64, no. 7, pp. 965–
976.
9. Shteinberg, A.S., Lin, Y.C., Son, S.F., and Mukasyan, A.S.,
Kinetics of high temperature reaction in Ni–Al Sys
tem: Influence of mechanical activation,
J. Phys.
Chem., Ser. A
, 2010, vol. 114, no. 20, pp. 6111–6117.
10. Hobosyan, M.A., Kirakosyan, Kh.G., Kharatyan, S.L.,
and Martirosyan, K.S., Study of dynamic features of
highly energetic reactions by DSC and highspeed tem
perature scanner (HSTS),
MRS Proc
., 2013, p. 1521,
MRSF121521000105; DOI:10.1557/opl.2013.144.
11. Hobosyan, M.A., Kirakosyan, Kh.G., Kharatyan, S.L.,
and Martirosyan, K.S., Reaction dynamics of
PTFE/Al
2
O
3
system at various heating rates,
Abstr. XII
Int. Symp. on SHS
, 2013, South Padre Island, TX
(USA), pp. 219–220.
12. Nepapushev, A.A., Moskovskikh, D.O.,
Kirakosyan, Kh.G., Kharatyan, S.L., Rogachev, A.S.,
8
7
6
50.00090.0008
0.0007
1/
T
max
–ln(
V
/
T
max2
)
Equation
Weight
Residual sum of
squares
Pearson’s r
Adj. RSquare
D
y
=
a
+
bx
No weighting
0.26902
0.97104
0.9315
Value Standard error
Intercept
Slope
–2.49229
11192.6646
1.00228
1231.56047
Fig. 10.
Determination of apparent activation energy
E
for
activated (
τ
= 3 min) Ni–Al mixtures.

28
INTERNATIONAL JOURNAL OF SELFPROPAGATING HIGHTEMPERATURE SYNTHESIS Vol. 24 No. 1 2015
NEPAPUSHEV et al.
and Mukasyan, A.S., Study of high temperature kinet
ics in mechanochemically activated Ni–Al system at
high heating rates,
Abstr. XII Int. Symp. on SHS
, 2013,
South Padre Island, TX (USA), pp. 57–58.
13. Kirakosyan, Kh.G., Kharatyan, S.L., Nepapushev, A.A.,
Moskovskikh, D.O., Rogachev, A.S., and Mukasyan, A.S.,
Some specific features at rapid heating of mecha
nochemically activated Ni–Al system,
Abstr. XIII Int.
Ceramics Congress CIMTEC 2014
, 2014, Montecatini
Terme (Italy), CB9.5:L03.
14. Kissinger, H.E., Reaction kinetics in differential ther
mal analysis,
Anal. Chem
., 1957, vol. 29, no. 11,
pp. 1702–1706.
15. Gasparyan, A.G. and Shteinberg, A.S., Macrokinetics
of reaction and thermal explosion in Ni–Al powder
mixtures,
Combust. Explos. Shock Waves
, 1998, vol. 24,
no. 3, pp. 324–330.
16. White, J.D.E., Reeves, R.V., Son, S.F., and
Mukasyan, A.S., Thermal explosion in Al–Ni system:
Influence of mechanical activation,
J. Phys. Chem.,
Ser. A
, 2009, vol. 113, no. 48, pp. 13541–13547.
17. Baghdasaryan, A.M., Hobosyan, M.A.,
Khachatryan, H.L., Niazyan, O.M., Kharatyan, S.L.,
Sloyan, L.H., and Grigoryan, Y.G., The role of chemi
cal activation on the combustion and phase formation
laws in the Ni–Al–promoter system,
Chem. Eng. J
.,
2012, vol. 188, pp. 210–215.
18. Itin, V.I. and Naiborodenko, Yu.S.,
HighTemperature
Synthesis of Intermetallic Compounds
, Tomsk: Izd.
Tomsk. Univ., 1989, pp. 85–87 (in Russia).
19. Starink, M.J., The determination of activation energy
from linear heating rate experiments: A comparison of
the accuracy of isoconversion methods,
Thermochim.
Acta
, 2003, vol. 404, nos. 1–2, pp. 163–176.
20. Rogachev, A.S., Shkodich, N.F., Vadchenko, S.G.,
Baras, F., Kovalev, D.Yu., Rouvimov, S., Nepapushev, A.A.,
and Mukasyan, A.S., Influence of high energy ball mill
ing on structure and reactivity of the Ni + Al powder
mixture,
J. Alloys Comp
., 2013, vol. 577, pp. 600–605.