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ISSN 10613862, International Journal of SelfPropagating HighTemperature 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 nonisothermal

hightemperature 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

nearisothermal 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 socalled electrothermographic [6, 7] and electro

thermalexplosion analyses [8, 9]. In this work, a new

thermographic method based on the use of highspeed

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 (ASD1, 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. Nonactivated 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 (Activator2S, 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 HighEnergy 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

email: rogachev@ism.ac.ru, suren@ichph.sci.am

Received November 17, 2014

Abstract

—A new electrothermographic method, viz. highspeed 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 nonactivated 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 hightemperature reaction, mechanical activation, kinetics, thermography, nickel

aluminide

DOI:

10.3103/S1061386215010082

22

INTERNATIONAL JOURNAL OF SELFPROPAGATING HIGHTEMPERATURE SYNTHESIS Vol. 24 No. 1 2015

NEPAPUSHEV et al.

nonactivated mixture, which should affect the kinet

ics of heterogeneous reaction.

The kinetic parameters of the hightemperature

heterogeneous reaction in activated and nonactivated

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 highheatingrate 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 temperaturetime schedule

provided by PCassisted controller

7

. In this work the

linear preheating schedule was used at heating rate

ranging between 130 and 7800 K/min. The socalled

“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 Tprofile 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 PCassisted controller of power supply.

To determine kinetic parameters of the reaction,

the obtained data were processed in terms of the so

called isoconversion 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 prepro

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

PCassisted controller.

INTERNATIONAL JOURNAL OF SELFPROPAGATING HIGHTEMPERATURE SYNTHESIS Vol. 24 No. 1 2015

INFLUENCE OF HIGHENERGY 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 nonactivated 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 solidstate 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

Iheating

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 SELFPROPAGATING HIGHTEMPERATURE 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 mechanicallyinduced nanomixed

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 Arrheniustype dependence, i.e.

= which was then used to obtain the

value of apparent activation energy

E

for the reaction

in nonactivated 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 nonactivated

Ni–Al mixtures—

T

0

(a),

T

* (b), and

Δ

T

max

(c)—as a

function of heating rate

V

h

.

INTERNATIONAL JOURNAL OF SELFPROPAGATING HIGHTEMPERATURE SYNTHESIS Vol. 24 No. 1 2015

INFLUENCE OF HIGHENERGY BALL MILLING ON REACTION KINETICS 25

interval 650–750°C and is lower than that obtained in

[9] by electrothermal explosion method for nonacti

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 nonactivated 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 socalled

p

(

y

)isoconversion 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

nonactivated 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 SELFPROPAGATING HIGHTEMPERATURE 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 solidstate 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

onestage, (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 nonactivated 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 nonactivated 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

nanosized 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 highreactive 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 SELFPROPAGATING HIGHTEMPERATURE SYNTHESIS Vol. 24 No. 1 2015

INFLUENCE OF HIGHENERGY 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 twostage reac

tion, where the first stage is the lowactivated 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 highenergy 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 // 130390604. 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. K22014001).

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6

50.00090.0008

0.0007

1/

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Equation

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Pearson’s r

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0.9315

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Slope

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1.00228

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E

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