Ijmsi Vol 1 Isuue 1 2013

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Editor in chief of IJMSIProfessor Dr. Hazizan MD AkilProfessor of Polymer Composites,Universiti Sains Malaysia,Penang ,Malaysia

Editorial Board of IJMSI

Prof. Dr. It-Meng (Jim) LowDepartment of Imaging & Applied Physics,

Curtin University of Technology,Australia

Prof. Dr. JAVIER NARCISOIUMA (Institute of Materials Science),

Aicante University,SPAIN

Prof. Dr.Laith Ahmed NajamNuclear Physics and Radiation Physics ,

Mosul University,IRAQ

Prof. Dr. Wesley CantwellDepartment of Engineering,

University of Liverpool,UK

Prof. Dr. Junhua DongInstitute of Metal Research,

Chinese Academy of SciencesChina

Assoc. Prof. Dr. Mokhtar Che IsmailCentre for Corrosion Research,Universiti Teknologi Petronas,

Malaysia

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Assoc. Prof. Dr. Sunday Joshua AojoloMechanical Engineering Department,

University of Lagos, Akoka, Lagos,Nigeria

Assoc. Prof. Dr. Cesare MalagùDepartment of Physics and Science of Earth,

University of Ferrara,Italy

Assis. Prof. Dr. Amir MaghsoudipourMaterials & Energy Research Center Karaj,

Alborz,Iran

Assis. Prof. Dr. Ali Sabea HammmodMaterials Engineering Department,

Faculty of Engineering,University of Kufa,

Iraq

Assoc. Prof. Dr. Tahar TouamLaboratoire des Semi-Conducteurs,

Département de Physique,Université badji Mokhtar-Annaba,

Algeria

Assis. Prof. Dr.zohreh hamnabardnuclear science & technology research center

Alborz,Iran

Assoc. Prof. Dr. Mustafa ToparliMechanical Engineering Department,

Dokuz Eylül University, Izmir,Turkey

Dr. Arash DehzangiInstitute of Microengineering and

Nanoelectronics (IMEN),Universiti Kebangsaan Malaysia,

Malaysia


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Dr. Martin Choirul FatahNo. 30, Blok B 11, Rt 07/09, Komplek LAPAN,

Pekayon13710 DKI Jakarta,

Indonesia

Assoc. Prof. Dr. GEORGE VARUGHESEPRINCIPAL

Catholicate College,Pathanamthitta - 689 645,Kerala,

INDIA

Dr. Alma Valor ReedCIDIM-ESIQIE-IPN

UPALM Edif. 7 1er piso.Col. Zacatenco. Del. GAM

Mexico DF 07738.Mexico.

Dr. Yuli Panca AsmaraCorrosion and Fracture Focus Group (CFRAC),

Universiti Malaysia PAHANG,Malaysia

Technical editorSaeid Kakooei, PhD candidateCentre for Corrosion Research,Universiti Teknologi Petronas,

Malaysia

Dr. Jalal RouhiSchool of physics,

Universiti Sainse Malaysia,Malaysia


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Table of content

Cover

Editorial Board I to III

Publication ethics IV

Table of content V

Rayleigh waves in electro-magneto-thermoelastic granular orthotropic non-homogeneousmedium of variable density subjected to gravity field and initial compressionRajneesh Kakar, Shikha Kakar PP.1-22

The Effect of Milling time on Phase Formation and Curie Temperature of Ultrafine Mn-ferriteSafoura Daneshfozoun, Esmaeil Mahdavi Ardakani, Jamshid Amighian, Morteza Mozafari PP.23-28

Download

Propagation of Torsional Surface Waves in Non-Homogeneous Viscoelastic Aeolotropic TubeSubjected to Magnetic FieldRajneesh Kakar, Shikha Kakar PP.29-44

Synthesis and Charactrization of Ni-Zn Ferrite Based Nanoparticles by Sol-Gel TechniqueMaryam Sharifi Jebeli, Norani Muti Binti Mohamed PP.45-53

Download

The Interaction Effects of Synthesis Reaction Temperature and Deposition Time on CarbonNanotubes (CNTs) YieldHengameh Hanaeia PP.54-61

Download

An overview of pH Sensors Based on Iridium Oxide: Fabrication and ApplicationSaeid Kakooei, Mokhtar Che Ismail, Bambang Ari-Wahjoedi PP.62-72

Download


International Journal of Material Science Innovations (IJMSI) Vol. 1 (1): 1-22, 2013ISSN xxxx-xxxx© Academic Research Online Publisher

1

Research Article

Rayleigh waves in electro-magneto-thermoelastic granular orthotropic non-homogeneous medium of variable density subjected to gravity field and initial

compression

Rajneesh Kakar a,*, Shikha Kakar b

a Principal, DIPS Polytechnic College, Hoshiarpur, Punjab, 146001, Indiab Faculty of Electrical Engineering, SBBSIET Padhiana, Jalandhar, 144001, India* Corresponding author. Tel.: +919915716560; fax: +911886237166E-mail address: [email protected]

ARTICLE INFO

Article historyRevised: 1 March 2013Accepted:10 March 2013

A b s t r a c tA mathematical model to show the effect of various inhomogeneities onpropagation of Rayleigh waves in prestressed elastic granular medium hasbeen presented. Inhomogeneities in electro-magneto and thermal fields havebeen assumed to vary exponentially with depth. Lame’s potential is used tosolve the problem. Some special cases have also been deduced. Dispersioncurves are computed numerically and presented graphically by usingMathCAD. The results indicate that on neglecting various effects of electricfield, magnetic field, initial stress and gravity, the calculations agrees withclassical theories.

© Academic Research Online Publisher. All rights reserved.

Keywords:InhomogeneityRayleigh wavesGravityInitial stress

1. Introduction

Rayleigh waves are a type of surface waves which are the combination of compression and shear waves.

These waves propagate with slightly lesser speed as compared to bulk shear waves. The study of surface

waves in granular medium is useful in the field of soil mechanics. Lot of literature on Rayleigh waves in

granular media is available in articles written by many authors such as Datta [2], Abd-Alla, El-Naggar

and Ahmed [3, 4, 5, 9] , Sharma JN and Kaur [6], Oshima [7], Paria [8]. Abd-Alla et al. [10] discussed

the effect of stress and gravity on propagation of Rayleigh waves in a magneto elastic material. Willson W

and Yu CP and Tang S [11, 12] investigated the problem of the propagation of magneto-thermo, elastic

plane waves. Gupta et al. [13] investigated surface waves in non-homogeneous granular material under

gravity. Roychoudhuri et al. [26] discussed thermoelastic wave. Recently, Xianhai Song et al. [14] studied

the application of particle swarm optimization to interpret Rayleigh dispersion curves. Kakar [15, 16, 17,

Rajneesh Kakar et al. / International Journal of Material Science Innovations (IJMSI) Vol.1 (1): 1-22,2013

2 | P a g e

18 and 27] has discussed Rayleigh waves in non-homogeneous granular media, viscoelastic and in elastic

media. Some problems on Love waves propagating in piezoelectric material under the effect of an electro-

elastic field were also discussed by Britan [19], Danoyan [20], Du et al. [21], Eskandari [22] and Du et al.

[23].

However, the combined effect of temperature, electric field and magnetic field on Rayleigh waves

propagating in non-homogeneous granular media has not been studied so far; therefore authors solved the

problem of Rayleigh waves propagating in a non- homogeneous granular medium under various

inhomogeneities particularly electro-magneto and thermo. In this paper, the effects of various types of non-

homogeneities in the form of magnetic field, electric field, gravity, temperature, initial compression on

Rayleigh waves is studied. The dispersion equation of Rayleigh waves is obtained with the help of method

of separation of variables. We have assumed that all the non-homogeneities are space dependent and vary

exponentially with depth. In our calculations, medium is taken to be discontinuous and consists of grains.

The motion of these grains is translatory as well as rotatory about its centre of gravity as shown in fig. 1.

The motion of these grains produce friction, therefore the concept of friction has taken in the governing

equations. Also, when the gravity, temperature, magnetic field, initial compression and non-homogeneity

are neglected, the frequency equation is in well agreement with the corresponding classical result. The

results are explained graphically by choosing standard parameters of the medium.

Fig. 1 Schematic of the problem

2. Governing equation and formulation of the problem

We consider Oxyz Cartesian co-ordinate system with O being any point on the free surface, here we

consider the free surface and interface of granular layer resting on non-homogeneous granular half space

bounded by two planes of different material given by z = 0 and z = H respectively. Also it is assumed that

oz being normal to half space and Rayleigh wave propagation in the positive direction of x-axis. Here it is

also assumed that at a great distance from centre of disturbance, the wave propagation is two dimensional

and is polarized in xz-plane. Therefore the displacement components along x and z-directions are non-zero


3 | P a g e

i.e. u1 and u3 are non-zero while u2 is zero. Also, it is assumed that, wave is surface wave as the

disturbance is extensively confined to the boundary. The parameters ( , , ) represent the rotation vector

of the grain about its centre of gravity. The non-symmetric stress tensor and non-symmetric stress couple

are given by ij ji and ij jiM M respectively.

The stress tensor ij is given by

/ij ij ij

(1)

Where ij and /ij are symmetric and anti-symmetric tensors and are

1 ( )2ij ij ji

/ 1 ( )2ij ij ji

(2)

Further symmetric strain tensor are given by relation

12

jiij ji

j i

uue ex x

(3)

The anti-symmetric stresses /ij are given by

/23 ,F

t

/31 ,F

t

/12 ,F

t/ / /

11 22 33 0. (4)

where F is the co-efficient of friction.

The stress couple ijM is given by

ij ijM M (5)

where M is the elastic constant,

11 ,x

22 0,33 ,

z23 0,

31 ,z

12 2( ),x 32 2( ),

z 13 ,x

21 0. (6)


4 | P a g e

where, components of rotation vector are

1 3, 2,1 ( ),2 y zu u 2 1, 3,

1 ( ),2 z xu u 3 2, 1,

1 ( ).2 x yu u

(7)

The state of initial stresses (function of z) are given by

;0 ;ij

i ji j

where i, j = 1, 2, 3

The Equation of equilibrium of initial stresses are

, 0,x , 0.z g (8)

The problem is dealing with magnetoelasticity. The basic equations will be electromagnetism and elasticity.

Therefore, the Maxwell equations of electromagnetic field in the absence of the displacement current (in

system-international unit) are

0, 0,,

t 0 0 .t

(9)

Where, , , 0 and 0 are electric field, magnetic field induction, permeability and permittivity of the

vacuum. For vacuum, 0 = 74 10 and 0 = 128.85 10 in SI units.

The value of magnetic field intensity is

00,0, i (10)

We have considered an elastic solid under constant primary magnetic field 0 acting on the y-axis, gravity

g, perturbation i and an initial stress P along the x-axis.

The dynamical equations of motion in the x and z dimensions of granular medium under gravity are

/ 213 3 3 3111 2 1

2 ,u ug Px z x y z z t

//23 3 2312 12 0,P

x z x x z/ 2

13 33 311 2 12 ,u ug P

x z x x x t

(11)

and

/ 311123 23 32 0,MM

x z


5 | P a g e

/ 321231 31 13 0,MM

x z

/ 13 3312 12 21 0.M M

x z

The problem deals with thermo viscoelastic solid, therefore, the thermal parameters are

(3 2 ) t (13)

where t is coefficient of linear expansion of solid.

3. Solution of problem

The stress components in presence of electric, magnetic and thermal field are given by2 2

11 11 1, 13 3, 0 0 ,x z e eC u C u H E T ,

2 233 13 1, 33 3, 0 0 ,x z e eC u C u H E T

11 44 3, 1,( ).x zC u u (14)

where, 33 11 13 442 , ,C C C C

Substituting Eq. (14), Eq. (5), Eq. (6) and Eq. (4) in Eq. (13) ; we get

( + 2 P) u1,xx + u1,zz + ( + P) u3,xz + u1,x x ( + 2 P) + u3,z x

( P)+ (u3,x + u1,z) z( )

– g u3,x – Ft

( ,z) – t z (F)–

2P

( u1,zz–u3,xz)20eH (2u1,xx u3,xz)

20eE (2u1,xx u3,xz)

Tx

=

u1,tt , (15)

(F ,t),z – (F ,t), x = 0, (16)

( + 2 ) u3,zz + u3,xx + ( + ) u1,xz + (u3,x + u1,z) x( ) + u1,x z

( ) + u3,z z ( + 2 )

2 20 0( )e eH E ( u1,xz–u3,xx) – 2

P ( u1,xz–u3,xx) +(u1,x + u3,z)

20eH 2

0eE (u1,x + u3,z) + g u1,xTz

+ Ft

( ,x) = u3,tt , (17)

Ft

+ M2

+ ,z z (M) = 0, (18)

Ft

+ M2 ( + w2) 2

Mwz z

= 0, (19)


6 | P a g e

Ft

+ M2

,z

Mz

= 0, (20)

where,

, are Lame’s constants and 311, 3,x z

uu u ux z

Now we assume the non-homogeneity of the granular half-space and co-efficient of friction are given by

= 0 emz

, = 0 emz

, = 0 emz

, F = F0 emz

, M = M0 emz

,

P = P0 emz

, e=( e)0 emz

e =( e )0 emz

, = 0 emz

(21)

Where, m, 0, 0, 0, F0, M0, P0, ( e)0, ( e )0 , 0 are dimensionless constants.

Inserting Inhomogeneities in Eq. (15-20), we get

( + 2 P0) u1,xx + u1,zz + ( + P0) u3,xz + u1,x x ( + 2 P0) + u3,z x

( P0)

+ (u3,x + u1,z) z( ) – g u3,x – F0

t ( ,z) – t z

(F0) 20 0( )e H (2u1,xx u3,xz)

20 0( )e E

(2u1,xx u3,xz) –0

2P

( u1,zz–u3,xz) 0Tx

= u1,tt, (22)

(F0 ,t),z – (F0 ,t), x = 0, (23)

( + 2 ) u3,zz + u3,xx + ( + ) u1,xz + (u3,x + u1,z) x( ) + u1,x z

( )– 0

2P

( u1,xz–u3,xx)

+ u3,z z ( + 2 ) 2

0 0( )e H ( u1,xz–u3,xx)2

0 0( )e E ( u1,xz–u3,xx) +(u1,x + u3,z)2

0 0( )e H 20 0( )e E

+ g u1,x 0Tz

+ F0t

( ,x) = u3,tt , (24)

0 tF + M0

2+ ,z z

(M0) = 0, (25)

0 tF + M0

2 ( + w2) 2

0wz z

M = 0, (26)

0 tF + M0

2,

0z

Mz

= 0, (27)

T can be calculated from Fourier’s law of heat conduction

p2T= 2

0 LTC T Gt t

, (28)


7 | P a g e

where, K be the thermal conductivity and obeys the law as given by K = K0 emz, p = 0

0

K and C is the

specific heat of the body at constant volume.

We introduce displacement potentials in terms of displacement components are given by

u1 = ,x – ,z , u3 = ,z + ,x (29)

Introducing Eq. (21), (29) into Eq. (22-27), we get2 2

– ,tt + g ,x + m '2 (2 ,z + ,x) – 2T = 0, (30)

t ( ,z – ,x) + m ,t = 0, (31)

2 2– ,tt + g ,x + s ,t + m ( 2

,x + 22

,z) = 0, (32)

–F0 ,t + M0

2+ M0 m ,z = 0, (33)

–s' ,t +2

–4

– m [ ,z –2 ( , z)] = 0, (34)

–s' ,t +2

+ m ,z = 0, (35)

where ,2 2

0 0 0 0 0 0 0

0

2 ( ) ( )e eP H E=

2,

2 = 0 0

0

22

P,

2 =

2 20 0 0 0 0

0

( ) ( )e eH E, s = 0

0

F, 2 = 0

0

K , s' = 0

0

FM

, '2=

2– 0

02P

. (36)

Eliminating from Eq. (32) and Eq. (34) ; we get

2 's mt z

[2 2

– ,tt + g ,x + m (2

,x + 22

,z)]+ s4 ( ,t) + ms

2 ( ,zt) = 0. (37)

To solve Eq. (30-35), we assume that

(x, z, t)= 1 (z) ei(lx–bt) , (38)

(x, z, t)= 1 (z) ei(lx–bt) , (39)

(x, z, t)= 1 (z) ei(lx–bt) , (40)

(x, z, t)= 1 (z) ei(lx–bt) , (41)

(x, z, t)= 1 (z) ei(lx–bt) . (42)

putting Eq. (38-42) in Eq. (30) and Eq. (37), we get

(2 D

2 – A) 1 – B 1 = 0, (43)

(A' D4 + B' D

3 + C' D

2 + d' D + E) 1 + (E' D

2 + F') 1 = 0, (44)


8 | P a g e

Where,

D=ddz

, A =2

l2 – b

2 – 2m

2, B = ilg – ilm

2 , A' =

2 – ibs, B' = 3m

2 – imsb,

C' = b (b + i2 s') – 2l

2 (B

2 – ibs) + 2m

2 2 , d' = (–2

2l2

m + 22 is'm – ml

2 2 + mb

2 + imsbl

2),

E= l4 (

2 – ibs) – bl

2 (b + i

2 s') + ib

3s', E' = (ilg + iml

2),

F'= (–ig l3 – gl bs' – iml

3 2 – ms'

2 b

2 + ilgm + il m

2 2). (45)

Therefore the solutions of Eq. (43) and Eq. (44) is of the form

1=j jz z

j jA e B e , (46)

1=j jz z

j jE e F e , j = 3, 4, 5 (47)

where, j (j = 3, 4, 5) are the real roots of the following equation

D6 + P1 D

5 + P2 D

4 + P3 D

3 + P4 D

2 + P5 D + P6 = 0, (48)

Where,

P1 =2

23m imsb

ibs,

2 2 2 2 2 2 2 2 2 2 2 2

2 2 2

' 2 2 2,

b b i s l ibs m ibs l b mP

ibs2 2 2 2 2 2 2 2 2 2 2 2 2

3 2 2

2 2 ' 2 3,

l is ml mb imsbl l b m m imsbP

ibs

P4 =2

2 2

' 'E AC BEibs

, P5 = 2 2

'Adibs

, P6 = 2 2

'BF AEibs

, (49)

where A', B', C', D', E', E, F, A, B are given by Eq. (45).

Further, the constants Aj, Bj (j = 3, 4, 5) are related with constants Ej, Fj respectively by means of Eq. (43).

Equating the coefficients of ejz, e– jz

(j = 3, 4, 5) to zero and using Eq. (43) and (44) ; we get

where,

Aj= j Ej and Bj = j Fj (j = 3, 4, 5), (50)

j=2

2 2 2 2 2 2lg

2i il m

j l b m (j = 3, 4, 5) (51)

Now solving Eq. (32) and Eq. (43) for 1 and 1, we get


9 | P a g e

(a1 D4 + a2 D

3 + a3 D

2 + a4 D + a5) 1 – isb (

2D

2 + a6) 1 = 0 (52)

Now eliminating 1 from Eq. (34) and Eq. (52), we get

[q1 D6 + q2 D

5 + q3 D

4+ q4 D

3 + q5 D

2 + q6 D + q7] = 0, (53)

Where,

q1= a1 – isb2, q = ma1 + a2 – isb

2 m, q3= a1 (is'b – l

2) + a2m + a3 – isba6 + 2isbl

2 2,

q4= a2 (is'b – l2) + a3m + a4 – isbma6 + isbml

2 2, q5= a3 (is' b – l

2) + a4m + a5 + 2isbl

2 a6 +

2l4 (–isb),

q6= (is'b – l2) a4 + ma5 + isb ml

2 a6, q7= a5 (is'b – l

2) – isbl

4 a6, a1=

2 2, a2= 2m

2 2,

a3=2 (–

2l2 – b

2 + 2m

2) + (b

2– l

2 2)

2, a4= 2m

2 (–

2l2 + b

2 + 2m

2),

a5 = (b2 – l

2 2) (–

2l2+ b

2 + 2m

2) + il (g + m

2) (ilg – ilm

2), a6= b

2 + 2m

2 –

2l2 . (54)

The solution of Eq. (53) is of the form

j=j jz z

j jE e F e j , (55)

Where,

j (j = 3, 4, 5) are the real roots of Eq. (33) and j=i

bs [

2 ( j

2 – l

2) + b

2 + (ilg + m i l

2) nj + 2m

2j],

Further substituting Eq. (38-42) into Eq. (31), Eq. (33) and Eq. (35), we get

(D + m) 1 – il 1 = 0, (56)

(D2 + mD + h

2) 1 = 0, (57)

(D2 + mD + h

2) 1 = 0, (58)

Where,

h2= is'b – l

2

The solutions of Eq. (58) and Eq. (58) are given by

1= A1 ez + Az e

– z, (59)

1= B1 ez + B2z e

– z, (60)

Where, =2 24

2m m h

, =2 24

2m m h

, m2 – 4h

2 > 0.

Substituting Eq. (59), Eq. (60) into Eq. (56), we get

(A1 + A1 m) ez + (–A2 + m A2) e

– z = il (B1 e

z+ B2 e

– z). (61)

Equating the co-efficients of e z and e– z to zero in Eq. (61), we get


10 | P a g e

A1=1i lBm

, A2 =2i lB

m. (62)

Let 0, 0, 0, F0, M0 are the characteristics of layer and 0 0 0 0 0, , , ,F M are the characteristics of

half-space, also for the lower half-space and description of surface wave propagation 1, 1, 1, 1, 1 goes

to zero as z , also the non-homogeneity constant m is replaced by constant m for lower granular half-

space also it is assumed that the real parts of (j = 3, 4, 5) are positive.

Thus for lower half-space

1 = j zj jF e , (63)

1 = j zjF e , (64)

1 = j zj jF e , (65)

1 = 2zi l B e

m, (66)

1 = 2zB e (j = 3, 4, 5). (67)

4. Boundary conditions and dispersion equation

Case-I The boundary conditions on interface z = H are

(i) u1 = 1u ,

(ii) u3 = 3u ,

(iii) = ,

(iv) = ,

(v) = ,

(vi) M33 = 33M ,

(vii) M31 = 31M ,

(viii) M32 = 32M ,

(ix) 33 = 33 ,

(x) 31 = 31 ,

(xi) 32 = 32 .

(xii)T=T


11 | P a g e

(xiii)T TT Tz z

(68)

Case-II The boundary conditions on free surface z = 0 are

(xii) M33 = 0,

(xiii) M31 = 0,

(xiv) M32 = 0,

(xv) 33 = 0,

(xvi) 31 = 0,

(xvii) 32 = 0, (69)

where

233 32 31, , ,M M M M M M

z z z2 2 2

2 2 2 233 13 33 13 33 0 02 2 ,e eC C C C H E T

x z x z

32 ,Ft

2 2 2

31 44 2 2 2 .C Fx z x z t

M31 (70)

From the boundary conditions (iii), (v), (vi) and (vii), we get

1 2H HB Be em m

= 2 HB em

, (71)

B1 eH + B2 e

– H = 2

HB e , (72)

M0 emH

[B1 eH – B2 e

– H] = 0 2

mH HM e B e , (73)

1 20

H HmH B e B eM e

m m= 2

0mH HBM e e

m. (74)

From Eq. (71) to Eq. (74), we have

B1= B2 = 2B = 0 (75)

i.e. = = = = 0. (76)

The other boundary conditions gives the following relations, conditions (xii) and (xiii) are identities due to

Eq. (76).

(xiv) gives,


12 | P a g e

i.e. K1E3 + K2E4 + K3E5 – K1F3 – K2 F4 – K3F5 = 0,

(xv) gives,

K4 E3 + K5E4 + K6 E5 + K7 F3 + K8 F4 + K9 F3 = 0,

(xvi) gives,

K10 E3 + K11 E4 + K12 E5 + K13 F3 + K14 F4 + K15 F5 = 0,

while condition (xviii) and (xi) is an identity,

(i) gives,

K163 5 34

3 17 4 18 5 19 3H H HHe E K e E K e E K e F

+ 5420 4 21 5

HHK e F K e F = 3 5419 3 20 4 21 5

H HHK e F K e F K e F ,

(ii) gives,

(il + n3 3)3He E3 + (il + n4 4)

4He E4 + (il + n5 5)5He E5

+ (il – n3 3)3He F3 + (il – n4 4)

4He F4 + (il – n5 5)5He F5

= 3 543 3 3 4 4 4 5 5 5

H HHil n e F il n e F il n e F ,

(iv) gives,

33He E3 + 4

4He E4 + 55He E5 + 3

3He F3

+ 544 4 5 5

HHe F e F = 3 543 3 4 4 5 5

H HHe F e F e F ,

(viii) gives,

M0 emH

3 5 341 3 2 4 3 5 1

H H HHK e E K e E K e E K e

543 2 4 3 5

HHF K e F K e F = 3 540 1 3 2 4 3 5

H HHmHM e K e F K e F K e F ,

(ix) gives,

emH 3 5 34

4 3 5 4 6 5 7 3H H HHK e E K e E K e E K e F

+ 548 4 9 5

HHK e F K e F = 3 547 3 8 4 9 5

H HHmHe K e F K e F K e F ,

(x) gives,

emH

3 5 3410 3 11 4 12 5 13 3

H H HHK e E K e E K e E K e F + 5414 4 15 5

HHK e F K e F

= 3 5413 3 14 4 15 5

H HHmHe K e F K e F K e F , (77)

where


13 | P a g e

Kj–2= j ( j – j

2 + l

2),

2jK = 2 2j j j l ,

Kj+1= nj [( j + 2 0) j2 – 0 l

2] + 2il 0 j,

1jK = 2 20 0 0 02 2j j jn l i l ,

Kj+4= nj [( j + 2 j) j2 – 0 l

2] – 2il 0 j,

4jK = 2 20 0 0 02 2j j jn l i l ,

Kj+7= ib F0 j + 2i l 0 n j j – 0 ( j

2 + l

2),

7jK = 2 20 0 02j j j jib F il n l ,

Kj+10= ibF0 j – 2i l 0 nj j – 0 ( j

2 + l

2),

10jK = 2 20 0 02j j j jib F il n l ,

Kj+13= ilnj – j,

Kj+16= ilnj + j,

16jK = j ji ln . (78)

Eliminating E3, E4, E5, F3, F4, F5, 3 4 5, ,F F F from Eq. (58),

We get 9 × 9 determinant, which gives wave-velocity equation,

1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8

2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8

3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8

4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8

5 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8

6 1 6 2 6 3 6 4 6 5 6 6 6 7 6 8

7 1 7 2 7 3 7 4 7 5 7 6 7 7 7 8

8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8

9 0 9 2 9

a a a a a a a aa a a a a a a aa a a a a a a aa a a a a a a aa a a a a a a aa a a a a a a aa a a a a a a aa a a a a a a aa a a

1 9

2 9

3 9

4 9

5 9

6 9

7 9

8 9

3 9 4 9 5 9 6 9 7 9 8 9 9

0

aaaaaaaa

a a a a a a

(79)

Equation (79) gives the dispersion equation of Rayleigh waves for a granular non-homogeneous medium

under the influence of gravity. The velocity of Rayleigh waves is given by the real part of the equation and

attenuation of the waves is due to granular nature of the medium given by imaginary part of the same

equation.

Where,

a11 =3

1HK e , a12 =

42

HK e , a13 =5

3HK e , a14 =

31

HK e , a15 =4

2HK e , a16 =

53

HK e ,


14 | P a g e

a17 = a18 = a19 = 0, a21 =3

4HK e , a22 =

45

HK e , a23 = 56

HK e , a24 =3

7HK e , a25 =

48

HK e ,

a26 =5

9HK e , a27 = a28 = a29 = 0, a31 =

310

HK e , a32 =4

11HK e , a33 =

512

HK e , a34 =3

13HK e ,

a35 =4

14HK e , a36 = K15

5He , a37 = a38 = a39 = 0, a41 = K16 ; a42 = K17, a43 = K18, a44 = K19, a45 = K20,

a46 = K47, a47 = 19K , a48 = 20K , a49 = 21K , a51 = il + n3 3 , a52 = il + n4 4, a53 = il + n5 5, a54 = il – n3 3,

a55 = il – n4 4, a56 = il – n5 5, a57 = 3 3il n , a58 = 4 4il n , a59 = 5 5il n , a61 = 3, a62 = 4, a63 = 5,

64 = 3, a65 = 4, a66 = 5, a67 = 3 , a68 = 4 , a69 = 5 , a71 = M0 emH

K1, a72 = M0 emH

K2, a73 = M0 emH

K3,

a74 = –K1 M0 emH

, a75 = –K2 M0 emH

, a76 = –K3 M0 emH

, a77 = 1 0mHK M e , a78 = 2 0

mHK M e ,

a79 = 3 0mHK M e , a81 = K4 e

mH, a82 = K5 e

mH, a83 = K6 e

mH, a84 = K7 e

mH, a85 = K8 e

mH, a86 = K9 e

mH,

a87 = 7mHK e , a88 = 8

mHK e , a89 = 9mHK e , a91 = K10 e

mH, a92 = K11 e

mH, a93 = K12 e

mH, a94 = K13 e

mH,

a95 = K14 emH

, a96 = K15 emH

, a97 = 13mHK e , a98 = 14

mHK e , a99 = 15mHK e . (80)

5. Particular cases

Equation (79) in determinant form gives the wave velocity equation of Rayleigh wave in granular non-

homogeneous medium under the influence of gravity, clearly from Eq. (79) we find that wave velocity

c =bl

not only depends on gravity, temperature ,magnetic field, electric field, initial stress but also on the

non-homogeneity of material.

Case-I In the absence of granular rotations, we get

0 0 jLt LtM s

= tj,

0 0 jLt Lt sM s

= j (j = 3, 4, 5), (81)

where

j=ib

[2 (tj

2 – l

2) + b

2 + (ilg + mil

2) j + 2m

2 tj]

and tj are the roots of the equation by using Eq. (33)2 2

tj

6 + (3m

2 2) tj

5 + b1 tj

4 + b2 tj

3 + b3tj

2 + b4tj + b5 = 0,

where

b1 = –32 2

l2 + 2m

2 2 2 + b

2 (

2 +

2) + 2m

4,

b2 = –6m2 2

l2 + mb

2 (

2 +

2) + 6m

2 4 + 2m

2 b

2,


15 | P a g e

b3= –l2 [–2l

2 2 2 + 2m

4 + (

2+

2) b

2] + 2m

2 2 (–

2l2+b

2+2m

2)

+ (b2 – l

2 2) (–

2l2 + b

2 + 2m

2) + il (g + m

2)+ (ilg – ilm

2),

b4 = –2ml2 2

(–2

l2 + b

2 + 2m

2) + (mb

2 – ml

2 2) + (–

2l2 + b

2+ 2m

2) + iml (g + m

2) (ilg – ilm

2),

b5 = –l2 [(b

2 – l

2 2) (–

2l2 + b

2 + 2m

2) + il (g + m

2) (ilg – ilm

2).

So Eq. (79) together with relation given by Eq. (81) forms the dispersion equation for the semi-infinite

elastic, isotropic and non-homogeneous medium overlain by a granular layer under the influence of gravity,

magnetic field, electric field and temperature.

Case-II In the absence of non-homogeneity, Eq. (79) gives the dispersion equation of Rayleigh waves for a

granular medium under the influence of gravity, magnetic field, electric field and temperature.

Where,

a71 = M0K1, a72 = M0K2, a73 = M0K3, a74 = –M0K1, a75 = –M0K2, a76 = –M0 K3, a77 = 1 0K M ,

a78 = 2 0K M , a79 = 3 0K M , a81 = K4, a82 = K5, a83 = K6, a84 = K7, a85 = K8, K86 = K9, a87 = 7K ,

a88 = 8K , a89 = 9K , a91 = K10, a92 = K11, a93 = K12, a94 = K13, a95 = K14, a96 = K15, a97 = 13K , a98 = 14K ,

a99 = 15K , (82)

and rest of aij’s are same as in Eq. (80).

Case-III In the absence of granular rotations and non-homogeneity, we get

0 0 0 jLt Lt Ltm M s

= xj,

0 0 0 jLt Lt Lt sm M s

= Wj (j = 3, 4, 5) (83)

where

Wj =2 2 2 2

j ji x l b il gnb

, j = 2 2 2 2 2j

i l gx l b

and xj are the roots of the equation2 2

xj

6 + [(

2 +

2) b

2 – 3

2 2l2] xj

4 + [2l

4 2 2 – b

2l2 (

2 +

2)

+ (b2 – l

2 2) (b

2– l

2 2) – l

2 g

2] xj

2 + [(b

2 – l

2 2) l

2 (

2l2 – b

2) + l

4 g

2] = 0

Thus the equation |aij| = 0, where i, j = 1, 2, ..... 9

where aij's are given by Eq. (82) gives the dispersion equation for the semi-infinite, elastic and isotropic

medium overlain by a granular layer under the influence of gravity.


16 | P a g e

Case-IV In the absence of gravity, magnetic field H0=0, electric field E0=0, temperature T0=0, initial stress

P0=0 and non-homogeneity, we get

5

2=

22

2

bl ,

( 32, 4

2) =

22 2 2 2 2 2 2

2

2 ' 2 ' 4 '

2

l b ib s i b l s b b i s b ss

ibs.

so by making 3, 4 0, the dispersion Eq. (79) reduces to

|bij|= 0 where i, j = 1, 2, ..... 9, (84)

where

b11 =3

1Hr e , b12 = – 3

1Hr e , b13 =

42

Hr e , b14 =4

2Hr e , b15 = b16 = b17 = b18 = b19 = 0, b21 =

33

Hr e ,

b22 =3

3Hr e , b23 =

44

Hr e , b24 =4

4Hr e , b25 =

55

Hr e , b26 =5

5Hr e , b27 = b28 = b29 = 0,

b31 =3

6Hr e , b32 =

36

Hr e , b33 =4

7Hr e , b34 =

47

Hr e , b35 =5

8Hr e , b36 =

58

Hr e ,

b37 = b38 = b39 = 0, b41 = – 3, b42 = 3, b43 = – 4, b44 = 4, b45 = il, b46 = il, b47 = 3 , b48 = 4 , b49 = il,

b51 = b52 = b53 = b54 = il, b55 = 5, b56 = – 5, b57 = b58 = il, b59 = – 5 , b61 = b62 = 3, b63 = b64 = 4,

b65 = b66 = 0, b67 = 3 , b68 = 4 , b69 = 0, b71 = M0 r1, b72 = –M0 r1, b73 = M0 r2, b74 = –M0 r2, b75 = b76 = 0,

b77 = 0 1M r , b78 = 0 2M r , b79 = 0, b81 = r3, b82 = –r3, b83 = r4, b84 = –r4, b85 = r5 = b86, b87 = 3r , b88 =

4r ,

b89 = 5r , b91 = r6 = b92, b93 = b94 = r7, b95 = r8, b96 = –r8, b97 = 6r , b98 = 7r , b99 = – 8r . (85)

and

r1 = 3 ( 3 – 3

2 + l

2), 1r = 2 2

3 3 3 l , r2 = 4 ( 4 – 4

2 + l

2), 2r = 2 2

4 4 4 l ,

r3 = 2il 0 3, 3r = 0 32 i l , r4 = 2il 0 4, 4r = 0 42 i l ,

r5 =2

20 22 bl , 5r =

22

0 22 bl , r6 = i b F0 3 – 0 ( 3

2 + l

2), 6r = ib 2 2

0 3 0 3F l ,

r7 = i b F0 4 – 0 ( 4

2 + l

2), 7r = ib 2 2

0 4 0 4F l , r8 = 2il 0 5, 8r = 0 52 i l . (86)

Eq. (84) gives the dispersion equation of Rayleigh waves for a granular medium in the absence of gravity

and non-homogeneity and is in complete agreement with that obtained by Bhattacharaya et al. [24].


17 | P a g e

Case-V In the absence of gravity, granular rotations, magnetic field H0=0, temperature T0=0, electric field

E0=0, initial stress P0=0 and non-homogeneity.

Now using Eq. (84) and (85) into Eq. (86), we get

2 23 4,

0 0 0Lt Lt Lt

m M s=

22 2

2, bl l

30 0 0Lt Lt Lt s

m M s= – ib

40 0 0Lt Lt Lt s

m M s= 0

40 0 0Lt Lt Lt

m M s= –

2

2b

60 0 0Lt Lt Lt r

m M s=

22

22 bl

70 0 0Lt Lt Lt r

m M s=

22

22 bl (87)

Similar results are also holds for lower medium.

Now using Eq. (87) into Eq. (86), then after some simplification we get 6 × 6 determinantal equation

|dij|= 0 where i, j = 1, 2, 3, ..... 6, (88)

where, d11 =4

42 Hl e , d12=2

222 bl 5He , d13=

442 Hl e , d14 =

22

22 bl 5He ,

d15= d16= 0, d21 =2

222 bl 4He , d22 =

552 Hl e , d23 =

22

22 bl 4He ,

d24 =5

52 Hl e , d25 = d26 = 0, d31 = – 4, d32 = – l, d33 = 4, d34 = –l, d35 = 4 ,

d36 = l, d41= –l, d42 = – 5, d43 = – l, d44 = 5, d45 = l, d46 = 5 , d51 =2

222 bl , d52 = 2l 5,

d53 =2

222 bl , d54 = –2l 5, d55 =

220

20

2 bl , d56 = 2l 0

05 , d61 = 2l 4,

d62 =2

222 bl , d63 = –2l 4, d64 =

22

22 bl , d65 =0

40

2l , d66 =2

202

0

2 bl . (89)


18 | P a g e

Thus Eq. (88) gives the dispersion equation of Rayleigh waves for semi-infinite elastic and isotropic

medium overlain by granular layer of thickness H in the absence of gravity and non-homogeneity is in

complete agreement with the equation obtained by Ewing et al. [25]

6. Numerical analysis

Numerical results have been obtained graphically to show the effect non-homogeneities and phase velocity

on initial stress and dimensionless wave number. The parameters for the material are taken in table 1.

Table 1Material properties

C11 C13 C44 C33 0

135 GPa 67.9 GPa 22.2 GPa 113 GPa 7500 Kg/m3

Various graphs are plotted with the help of MathCAD. Fig. 2 shows the effect of initial compression on the

Rayleigh Waves, it is obvious that Rayleigh wave velocity decreases with an increasing of the various

values of the initial stress P also with the wave number. Fig. 3 represents the variation of phase velocity

with dimensionless less wave number at different values of initial stress. The three modes of Rayleigh

waves have been plotted at two different values of initial stress i.e. at P = 1 and P = 0.1. The value of

magnetic field, electric field and temperature is fixed at 0.4 Tesla, 50 V/m and 293 K. It is clear from fig. 3

as the value of initial compression increases the phase velocity decreases sharply with dimension less wave

number. Fig. 4 is plotted to observe the effect of various non-homogeneities factor 'W in (%) on Rayleigh

waves velocity with respect wave number at P= 1and P= 0.1. In graph W represents the zeroth level of non-

homogeneities. Fig. 5 represents the effect of depth (dimensionless) on frequency (dimensionless) on

Rayleigh wave velocity.


19 | P a g e

Fig. 2 Variation of Rayleigh waves velocity respect to initial stress with the various values of the wave number,

H = 0.4 Tesla, g = 9.8 m/s2, T = 293 K, E=50 V/m, granular rotations =0.

Fig. 3 Variation of Rayleigh waves velocity respect wave number, H = 0.4 Tesla, E=50 V/m,

T = 293 K, g = 9.8 m/s2, P= 1, P= 0.1, granular rotations =0.


20 | P a g e

Fig. 4 Effect of coupled non-homogeneities (%) on Rayleigh waves velocity with respect wave number keeping

initial stress at P= 1and P= 0.1

Fig. 5 Variation of Rayleigh waves frequency with respect depth, H = 0.4 Tesla, E=50 V/m,

T = 293 K, g = 9.8 m/s2, P= 1, P= 0.1, granular rotations =0.


21 | P a g e

7. Conclusion

The frequency equation contains terms involving gravity and non-homogeneity, so the phase velocity not

only depends on gravity field but also on the non-homogeneity of the material medium, magnetic field,

electric field, temperature, initial stress and granular notations. The exact solution for inhomogeneous half-

space subjected to gravity field, electric field, magnetic field, temperature field and mechanical field is

obtained. All material coefficients are assumed to have the same exponent-law dependence on the depth of

the half space. The governing equations in Cartesian coordinates are recorded for future reference.

Acknowledgements

The authors are thankful to the referees for their valuable comments.

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International Journal of Material Science Innovations (IJMSI) 1 (1): 23-28, 2013ISSN xxxx-xxxx© Academic Research Online Publisher

23 | P a g e

Research Article

The Effect of Milling time on Phase Formation and Curie Temperature ofUltrafine Mn-ferrite

Safoura Daneshfozouna,c,* , Esmaeil Mahdavi Ardakanib,c , Jamshid Amighianc,Morteza Mozafaric

a Department of Chemical Engineering, Universiti Teknologi PETRONAS, Perak, Malaysiab Department of Fundamental and applied science, Universiti Teknologi PETRONAS, Perak, Malaysiac Nanophysics Research Group, Research Center for NanoSociences and nanoTechnology, The University ofIsfahan, Isfahan Iran* Corresponding author. Tel.: 0060175381750 fax: 006053688206E-mail address:[email protected]

ARTICLE INFO

Article historyReceived:01Feb2013Accepted:10Feb2013

A b s t r a c tNano sized MnFe2O4 powders were prepared via mechanochemical processing(MCP), using a refined domestic iron oxide (hematite) and manganese oxide asstarting materials. Milling was performed in a SPEX 8000D mixer/mill unit atdifferent milling times in air, Argon and oxygen atmospheres. In order toobtain a single-phase sample, the as-milled powders were annealed at differenttemperatures and in different atmospheres. Phase character of the as-milledand annealed powders was studied by a Bruker diffractometer, D8 model.Particle size of the powders was calculated, using Scherrer’s formula.Saturation magnetization of the samples was measured, using a sensitivepermeameter. Also curie temperature of samples was measured with a punctualLCR meter .The results show that milling in Argon and annealing in vacuumleads to a single-phase powder at lower annealing temperature in comparisonwith those annealed in conventional ceramic technique.


Keywords:mechanochemical processingNano sized MnFe2O4Saturation magnetizationCurie temperature

1. Introduction

In recent years, Magnetic nanoparticles are taken into interest of researchers due to theirspecific characteristics such as unique magnetic properties. The magnetic propertiesdifference between a bulk material and a nanomaterial is very evident, for example; muchgreater amount of magnetization and the magnetic anisotropy has been reported fornanoparticles. These reports also have stated that hundreds of degrees differences in the Curietemperatures between nanoparticle and the matching microscopic phases. The magneticproperties of nanoparticles is determined by using various factors such as chemicalcomposition, the type and the degree of defectiveness of the crystal lattice, the particle size

Daneshfozoun S. et al. / International Journal of Material Science Innovations (IJMSI) 1 (1): 23-28,2013

24 | P a g e

and shape, the morphology, interact the particle with their surrounding particles. So this canbe controlled by controlling some factors like nanoparticle size, shape, composition, andstructure. It must be mentioned that controlling these factors cannot always be possibleduring the synthesis of nanoparticles spatially when size and chemical composition ofsamples are nearly equal. Thus sometimes same type nanomaterials may have markedlydifferent properties. In addition, many unusual properties such as giant magnetoresistance,abnormally high magnetocaloric effect has been found in magnetic nanomaterials analyses[1,2].

Spinel ferrites are particularly attractive candidate for such studies due to their importanceboth in microwave devices and in soft magnetic applications where loss minimization isimportant [3]. Among the spinel ferrite, manganese ferrite has found a great interest due to itsmoderate Curie temperature and different cations distribution in tetrahedral (A) andoctahedral (B) sites, when different preparation techniques are used [4]. In most of thetechniques, the nanosize powders are prepared by wet chemical methods, e.g. coprecipitation[5]. The powders show magnetic properties different from those of the bulk samples preparedby standard ceramic technique [6]. Another method of preparing ferrite nanopowders ismechanical grinding of coarse powders, usually in dry condition and so many othertechniques [7].

In this work, we have prepared nano-sized MnFe2O4 powders by mechanochemicalprocessing (MCP), a process that makes use of chemical reactions activated by high-energyball milling. In this process high-energy collision from the balls transfer to a powder mixtureplaced in the ball mill. At first Benjamin and his co-workers developed this process at theInternational Nickel Company in 1960 and can produce fine, uniform dispersions of oxideparticles (Al2O3, Y2O3, and ThO2) in nickel-base superalloys by this simple method. Thistype of materials could not be made by more conventional powder metallurgy methods. It canbe said that synthesis and production of material has been changed by this Initiative.

Besides materials synthesis, high-energy ball milling is a way of varying the conditions inwhich chemical reactions usually take place either by changing the reactivity of as-milledsolids or by compelling chemical reactions within milling. It is, also, a way of inducing phasetransformations in starting powders with same chemical composition in their particles [8].We also studied the effect of milling time, atmosphere of milling and annealing process andtemperature of annealing on phase formation of ultrafine Mn-ferrite and investigated itsmagnetic properties.

2. Materials and Method

A refined domestic iron oxide (Fe2O3), which is a by-product of Mobarakeh Steel Complexand manganese oxide (MnO2) from E. Merck Co. were mechanically alloyed in a hardenedsteel vial using three 12.6 mm and four 6.3 mm hardened steel balls with a ball to powdermass ratio of 7:1. All the compositions were corrected for extra pick up of iron from ballmilling using iron deficient compositions. The mechanical alloying was performed either


25 | P a g e

under a pure argon atmosphere or in air in a SPEX 8000D mixer/mill unit, at different millingtimes. Annealing of the as-milled powders was carried out under vacuum or in air attemperatures between 700 and 1000 °C for 1h. Phase formation was studied for differentsamples with a Bruker D8 advance diffractometer (CuK =1.5405Å). Temperature of single-phase samples was measured by using a punctual LCR meter Mean particle size of eachsingle-phase sample was determined by Scherrer’s formula and XRD broadening peak. Formagnetic measurements, as-milled and annealed powders were cold pressed into about 10mm in diameter cylindrical specimens with a height of about 5 mm. Magnetic parameters ofthe samples were calculated from their hysteresis loops, using a sensitive permeameter with amaximum field of 1.2 kOe.

3. Results and discussion

Figure1 shows the X- ray diffraction patterns of the as-milled powder together with thoseannealed at different temperatures and different milling times, as indicated in the figure 1.

Fig.1. X-ray diffraction patterns of the as-milled powder together with those annealed atdifferent temperatures and different milling times.

As is clear, by increasing milling time, a decrease in annealing temperature is achieved. Thisis obvious because as the milling time is increased, the particle size of the powders willdecrease which leads to lower annealing temperature [9]. The maximum annealingtemperature of 850 °C, which obtained for the powder with 10 h milling time, is much lowerthan the annealing temperature of about 1250 °C associated to bulk MnFe2O4 observed inconventional ceramic technique. Variation of room temperature saturation magnetization ofthe single-phase samples with respect to milling time is shown in Figure 2.


26 | P a g e

Fig. 2. Variation of saturation magnetization versus milling time.

As can be seen the values of the saturation magnetization ( s) is smaller than those related tobulk MnFe2O4, about 80 emu/g, and decreases with the particle size. This decreasing can bediscussed in terms of a model in which it is assumed that each particle consists of aferromagnetic core surrounded by a spin-glass shell and the spins in the core and shell areexchange coupled [10]. Also another reason is that measurements were carried out on coldpressed samples, which have a low density and a high porosity and not on sintered ones witha high magnetic moment density. Table 1 shows the values of saturation magnetization ( s)coercive force (Hc) and the mean particle size of the samples.

Table 1. Values of (Hc), ( s) and the mean particle size of the samples.

Milling time (min) 20 45 90 300 360 600

s (emu/gr) 70.31 65.30 51.06 40.17 36.67 34.41Hc (Oe) 31.2 28.4 21.3 17.9 17.3 15Mean Particle size(nm)

34.52 32.38 26.36 21.81 20.62 19.8

Results show that, by reducing the particle size, both of saturation magnetization andcoercive force are decreased. The decrease of Hc with decreasing particle size has beendiscussed under the theory of single domain particles.

In Figure 3, Curie temperatures of the samples were measured by time-mill is shown. As youcan see, in the figure after a sharp decline in starts of fin curve, the Curie temperaturegradually decreases. This could be due to reduced nuclear magnetization resultant against theshell, because the Curie temperature is the temperature at which the intrinsic magnetizationdisappears and the smaller magnetization at the first needs lower temperature to eliminate[11].


27 | P a g e

Fig. 3. Curie temperatures of the samples versus milling time

4. Conclusions

In this work MnFe2O4 nanoparticles ranging from 19.8 to 36.3 nm were prepared viamechanochemical processing, using a refine domestic Fe2O3 and MnO2 from E. Merck Co. Inthis technique a lower annealing temperature with respect to conventional ceramic techniquewas achieved. Magnetic measurements of the powders (in the form of cold pressed cylinders)show that not only the saturation magnetization is smaller than those of bulk MnFe2O4, butalso decreases with reducing particle size. Also the results show that coercive force of thepowders is decreased with decreasing the particle size.

Acknowledgments

This study was started in Isfahan university and completed at The Universiti TeknologiPETRONAS and supported by The Office of Graduate studies. The authors are grateful to theoffice for their support.

References

1. Yong. -Kang Sun, Mingma, Ya Zhang and Ning Gu, Physicochem. Eng. Aspects ofColloids and Surfaces A: Synthesis of nanometer-size maghemite particles from magnetite ; (2004): 245:15


28 | P a g e

2. Lu, A.H., E.e.L. Salabas, and F. Schüth, Magnetic nanoparticles: synthesis, protection,functionalization, and application, Angewandte Chemie International Edition. 2007, 46(8):1222-1244

3. Töpfer, J., H. Kahnt, P. Nauber, S. Senz, and D. Hesse, Microstructural effects in low losspower ferrites, Journal of the European ceramic society. 2005, 25(12): 3045-3049

4. Frey, N.A., S. Peng, K. Cheng, and S. Sun, Magnetic nanoparticles: synthesis,functionalization, and applications in bioimaging and magnetic energy storage, ChemicalSociety Reviews. 2009, 38(9): 2532-2542

5. Gnanaprakash, G., S. Ayyappan, T. Jayakumar, J. Philip, and B. Raj, Magneticnanoparticles with enhanced -Fe2O3 to -Fe2O3 phase transition temperature,Nanotechnology. 2006, 17(23): 5851

6. Chen, J., C. Sorensen, K. Klabunde, G. Hadjipanayis, E. Devlin, and A. Kostikas, Size-dependent magnetic properties of MnFe2O4 fine particles synthesized by coprecipitation,Physical review B. 1996, 54(13): 9288

7. Rana, S., J. Philip, and B. Raj, Micelle based synthesis of cobalt ferrite nanoparticles andits characterization using Fourier Transform Infrared Transmission Spectrometry andThermogravimetry, Materials Chemistry and Physics. 2010, 124(1): 264-269

8. Takacs, L. International Journal of Self-Propagating High-Temperature Synthesis; (2009):18(4): 276-82

9. Nowosielski, R., R. Babilas, G. Dercz, L. Paj k, and J. Wrona, Structure and properties ofbarium ferrite powders prepared by milling and annealing, Archives of Materials Science andEngineering. 2007, 28(12): 735-742

10. Giri, S., A. Poddar, and T. Nath, Surface spin glass and exchange bias effect in Sm0.5Ca0. 5MnO3 manganites nano particles. 2011

11. Soleimani, R., M. Soleimani, M. Gheisari Godarzi, and A. Askari, Preparation of SoftManganese Ferrite and Inventional of its Magnetic Properties and Mn 55 Nuclear MagneticResonance, Journal of fusion energy. 2011, 30(4): 338-341


29 | P a g e

Research Article

Propagation of Torsional Surface Waves in Non-Homogeneous ViscoelasticAeolotropic Tube Subjected to Magnetic Field

Rajneesh Kakara,*, Shikha Kakarb

aPrincipal, DIPS Polytechnic College, Hoshiarpur, Punjab, 146001, IndiabFaculty of Electrical Engineering, SBBSIET Padhiana, Jalandhar, 144001, India* Corresponding author. Tel.: +919915716560; fax: +911886237166E-mail address:[email protected]

ARTICLE INFO

Article historyRevised:8 MarchAccepted:15March

A b s t r a c tThe effect of magnetic field on torsional waves propagating in non-homogeneous viscoelastic cylindrically aeolotropic material is discussed. Thedensity and elastic constant of the viscoelastic specimen are non-homogeneous. Bessel functions are taken to solve the problem and frequencyequations have been derived in the form of a determinant. Dispersion equationin each case has been derived and the graphs have been plotted showing theeffect of variation of elastic constants and the presence of magnetic field. Theobtained dispersion equations are in agreement with the classical result. Thenumerical calculations have been presented graphically by using MATLAB.


Keywords:Aeolotropic Material,Magnetic Field,Viscoelastic Solids,Non-Homogeneous,Bessel Functions

1 Introduction

A large amount of literature is available on surface wave in the monograph of Ewing [1]. But

there is a very few problems of cylindrically aeolotropic elastic material have been

considered so far because of the inherent difficulty in solving complicated simultaneous

partial differential equations. Kaliski [2], Narain [3] and many others have investigated the

magnetoelastic torsional surface waves. White [4] has investigated cylindrical waves in

transversely isotropic media. The elastic cylindrical shell under radial impulse was studied by

Mcivor [5]. Cinelli [6] has investigated dynamic vibrations and stresses in elastic cylinders

and spheres. Pan and Heyliger [7] have given the exact solutions for magneto-electro-elastic

Laminates in cylindrical bending. The wave propagation in non-homogeneous magneto-

electro-elastic plates has been solved by Bin et al. [8]. Kong et al. [9] solved the problem of

thermo-magneto-dynamic stresses and perturbation of magnetic field vector in non-

Rajneesh Kakaret al. / International Journal of Material Science Innovations (IJMSI) Vol.1 (1): 40-55,2013

30 | P a g e

homogeneous hollow cylinder. Recently, Kakar et al. [10, 11and 12] studied various surface

waves in elastic as well in viscoelastic media.

In this study, the torsional waves are investigated in non-homogeneous viscoelastic

cylindrically aeolotropic material subjected to a magnetic field. The problem is solved

analytically by using Bessel’s functions and numerically by using MATLAB.

2 Basic equations

The problem is dealing with magnetoelasticity. Therefore the basic equations will be

electromagnetism and elasticity. Therefore, the Maxwell equations of electromagnetic field in

the absence of the displacement current (in system-international unit) are [14]

0 , (1a)

0 , (1b)

t ,

(1c)

0 0 .t

(1d)

Where, , , 0 and 0 are electric field, magnetic field induction, permeability and

permittivity of the vacuum. For vacuum, 0 = 74 10 and 0 = 128.85 10 in SI units. Also,

the term Ohm's law is

,J E (2a)

Where, J is the current density and is a material conductivity.

The Lorentz force on the charge carriers is [14].

( ) ( ).vJ E V B E Bt

(2b)

The homogeneous form of the electromagnetic wave equation is [14]

22

0 0 2 0t

ò ,(3a)


31 | P a g e

22

0 0 2 0t

ò .(3b)

Where,2 2

22 2 2

1 1r r r r

The dynamical equations of motion in cylindrical coordinate , ,r z are (Love [13, 18])

Where, , , , . , ,rr r rz rr z zzs s s s s s s are the respective stress components, , ,R ZT T T are the

respective body forces and , ,u v w are the respective displacement components.

The stress-strain relations are [18]

0 0 011 12 13 ,rr rr zzs e e e (5a)

0 0 021 22 23 ,rr zzs e e e (5b)

0 0 031 32 33 ,zz rr zzs e e e (5c)

044 ,rz rzs e (5d)

055 ,z zs e (5e)

066 .r rs e (5f)

Where, ij elastic constants ( ij = 1, 2……6).

The elastic constants of viscoelastic medium are [21]

20 / / /

2ij ij ij ijt t( ij = 1, 2……6).

(6)

Where, /ij and / /

ij are the first and second order derivatives of .ij

The strain components are [20]

2

2

1 1 ( ) ,rrr rzrr R

ss s us s Tr r z r t (4a)

2

2

21 ,r z rs s s s vTr r z r t (4b)

2

2

1 .zrz zz rzZ

ss s s wTr r z r t (4c)


32 | P a g e

1 ,2rr

uer

(7a)

1 1 ,2

v uer r

(7b)

1 ,2zz

wez

(7c)

1 1 ,2z

w ver r z

(7d)

1 ,2rz

w uer z

(7e)

1 ,2zz

wez

(7f)

The rotational components are [20]

1 1 ,2r

w vr z

(8a)

1 1 ,2

u wr z r

(8b)

1 ( ) .zrv u

r r(8c)

Equations for the propagation of small elastic disturbances in a perfectly conductingviscoelastic solid will have the body force in terms of electromagnetic force J (using

Eq. (4)) and are

2

2

1 1 ( ) ,rrr rzrr R

ss s us s Jr r z r t

(9a)

2

2

21 ,r z rs s s s vJr r z r t

(9b)

2

2

1 .zrz zz rz

Z

ss s s wJr r z r t

(9c)

Let us assume the components of magnetic field intensity are 0r and z

constant. Therefore, the value of magnetic field intensity is

00,0, i (10)


33 | P a g e

Where, 0 is the initial magnetic field intensity along z-axis and i is the perturbation in the

magnetic field intensity.

The relation between magnetic field intensity and magnetic field induction is

0 (For vacuum, 0 = 74 10 SI units.)(11)

From Eq. (1), Eq. (2), Eq. (3) and Eq. (10), we get

20

vt t

(12)

The components of Eq. (12) can be written as

2,

0

1rrt

2,

0

1t

2

0

1 .z

t

(13a)

(13b)

(13c)

3 Formulation of the problem

Let us consider a semi-infinite hollow cylindrical tube of radii and . Let the elastic

properties of the shell are symmetrical about z-axis, and the tube is placed in an axial

magnetic field surrounded by vacuum. Since, we are investigating the torsional waves in an

aeolotropic cylindrical tube therefore the displacement vector has only v component. Hence,

0,u (14a)

0w (14b)

( , ).v v r z (14c)

Therefore, from Eq. (14) and Eq. (7), we get,

0,rr zz zre e e e

1 ,2z

vez

(15a)

(15b)


34 | P a g e

1 .2r

v ver r

(15c)

From Eq. (14) and Eq. (8), we get,

1 ,2r

vz

(16a)

0, (16b)

.zv vr r

(16c)

Using Eq. (14), Eq. (15) and Eq. (6), the Eq. (5) becomes

0,rr zz rzs s s s (17a)

2/ / /

66 66 66 2

1( ) ( ),2r

v vst t r r

(17b)

2/ / /

55 55 55 2

1( )( ).2z

vst t r

(17c)

Where, /ij and / /

ij are the first and second order derivatives of .ij

For perfectly conducting medium, (i.e. ), it can be seen that Eq. (2) becomes

0 ,0,0vc t

(18)

Eq. (1) and Eq. (18), the Eq. (13) becomes,

0, ,0ivz

(19)

From the above discussion, the electric and magnetic components in the problem are relatedas

0 ,0,0 0, ,0v vc t z

(20)

Using Eq. (19) and Eq. (1) to get the components of body force in terms of Gaussian systemof units as:

2

20, ,04

vz

(21)

Eq. (17) and Eq. (20) satisfy the Eq. (4a) and Eq. (4c), therefore, the remaining Eq. (4b)becomes


35 | P a g e

2 2/ / / / / /

266 66 66 55 55 552 2

22 2 2/ / /

66 66 66 2 2

1 1( ) ( ) ( )( )2 2

2 1( ) ( )2 4

v v vvr t t r r z t t r

tv v H vr t t r r z

(22)

Let / / / / / /, ,l l lij ij ij ij ij ijC r C r C r and 0

mr (23)

Where, ij , /ij , / /

ij and 0 are constants, r is the radius vector and ,l m are non-homogeneities.

From Eq. (23), we get Eq. (17) as

2/ / /

66 66 66 2

1( ) ( ),2

lr

v vs rt t r r

(24a)

2/ / /

66 66 66 2

1( ) ( ),2

lr

v vs rt t r r

(24b)

Using Eq. (23), the Eq. (22) becomes

2 2/ // / //

266 66 66 55 55 552 2

0 22 2 2/ //

66 66 66 2 2

1 1( ) ( ) ( ) ( )2 2

2 1( ) ( )2 4

l l

m

l

v v vr r vr t t r r z t t r rtv v H vr

r t t r r z

(25)

4 Solution of the problem

Let ( )( ) i z tv r e [16] be the solution of Eq. (25). Hence, Eq. (25) reduces to

22 21 22 2

( 1) ( 1) 0l

l lr r r r r

(26)

Where,

2 / / / 2 22 0 55 55 551 / / / 2

66 66 66

2 ( ) ,ii

(27a)

2 222 / / / 2

66 66 66

.2 ( )

Hi

(27b)

Eq. (26) is in complex form, therefore we generalize its solution for 0l and 2l

4.1 Solution for 0l

For, 0l the Eq. (26) becomes,

22

2 2

1 1( ) 0r r r r

(28)


36 | P a g e

Where,

2 2 21 2

(29)

The solution of Eq. (28) is

( )1 1{ ( ) ( )} i z tv PJ Gr QX Gr e (30)

From Eq. (24) and Eq. (30)

/ // 2 ( )66 66 66 0 1 0 1

2 2{ } { ( ) ( ) { ( ) ( )2 2

i z tr

P Qs i GJ Gr J Gr GX Gr X Gr er r

(31)

5 Boundary conditions and frequency equation

The boundary conditions that must be satisfied are

B1. For r , ( is the internal radius of the tube)

0( )r r rsB2. For r , ( is the external radius of the tube)

0( )r r rsWhere r and

0( )r are the Maxwell stresses in the body and in the vacuum, respectively.

There will be no impact of these Maxwell stresses. Hence,

0( ) 0r r (32)

On simplification, Eq. (18) and Eq. (30) gives( )0

1 1{ ( ) ( )} i z ti PJ Gr QX Gr ec

(33)

Let , ( )0

i z teHence, Eq. (3) becomes

22

2

1 0r r r

(34)

Where,2

2 22c

(35)

The solution of the Eq. (34) becomes

0 0( ) ( )RJ r SX r (36)

Where 0J and 0X are Bessel functions of order zero. R and S are constants.

From Eq. (37) and Eq. (40)

( )0 0{ ( ) ( )} i z tRJ r SX r e (37)


37 | P a g e

The boundary conditions B1 and B2with the help of the Eq. (31) and (32) turn into:

0 1 0 1{ ( ) 2 ( )} { ( ) 2 ( )} 0P G J G J G Q G X G X G (38)

0 1 0 1{ ( ) 2 ( )} { ( ) 2 ( )} 0P G J G J G Q G X Ga X G (39)

Eliminating P and Q from Eq. (38) and Eq. (39)

0 1 0 1

0 1 0 1

( ) 2 ( ) ( ) 2 ( )0

( ) 2 ( ) ( ) 2 ( )G J G J G G X G X GG J G J G G X Ga X G

(40)

On solving Eq. (40), we get the obtained frequency equation

0 1 0 1

0 1 0 1

( ) 2 ( ) ( ) 2 ( ) 0( ) 2 ( ) ( ) 2 ( )

G J G J G G X G X GG J G J G G X Ga X G

(41)

On the theory of Bessel functions, if tube under consideration is very thin i.e. and

neglecting 2 3, ........ , the frequency equation can be written as (Watson [16])

3 2 1 0 (42)

Where,

22 / / / 2 2 2

0 55 55 552

/ / / 266 66 66

2 ( )2Hi

i

(43)

Putting the value of in Eq. (42), the frequency of the wave can be found. Clearly,

frequency is dependent on magnetic field.

Put , (44)

The phase velocity 1 /c can be written as

2

2221

2 / / / 20 66 66 66

42

Hcc i

(45)

Where,

2 ,k

/ / / 255 55 55

/ / / 266 66 66

,ii

/ / / 22 66 66 660

02ic

(46)

The term i.e. magnetic field is negative in Eq. (45) which reduces the phase velocity oftorsional wave.

Case 1


38 | P a g e

Since the pipe under consideration is made of an aeolotropic material, then

/ / / 0ij ij (47)

Hence, from Eq. (42), Eq. (44) and Eq. (47) the frequency equation becomes

30 0 0 (48)

Using Eq. (45) and Eq. (46), the phase velocity is

2 22 266 552 0

0 66 662 2 2Hc

(49)

1220

2552

20 66 66

[ ]2

2[ ]

c Hc

(50)

Where, 20 66 02c

The term i.e. magnetic field is negative in Eq. (49) which reduces the phase velocity of

torsional wave. This is in complete agreement with the corresponding classical results [15]

Case 2

If the pipe under consideration is made of an isotropic material, then

/ //55 660,ij ij

(51)

Using Eq. (49) and Eq. (50), the phase velocity is

2 22 22 0

0

12 2 2

Hc(52)

This is in complete agreement with the corresponding classical results [3]

5.1Solution for l=2

For, 2l the Eq. (26) becomes,

222 212 2

(3 )3 ( 0r r r r

(53)

Putting 1 ( )rr

in Eq. (53), one get


39 | P a g e

2 2212 2

1 0r r r r

(54)

Where, 2 223 (55)

Solution of Eq. (54) will be (Watson [16])

1 2( ) ( )RJ r SX r (56)

Putting the value of and in Eq. (55), we get

( )1 1

1{ ( ) ( )} i z tRJ r SX r er

(57)

From the Eq. (24) and Eq. (56)

1 1 1 1/ / / 2 ( )

66 66 66

1 1 1 1

{ ( ) ( 2) ( )}2( ) 0

{ ( ) ( 2) ( )}2

i z tr

R rJ r J rs i e

S rX r X r(58)

With the help of Eq. (32), Eq. (56) and boundary conditions B1 and B2, we get

1 1 1 1 1 1 1 1{ ( ) ( 2) ( )} { ( ) ( 2) ( )} 02 2R SJ J X X

1 1 1 1 1 1 1 1{ ( ) ( 2) ( )} { ( ) ( 2) ( )} 02 2R SJ J X X (59)

Eliminating R and S from Eq. (58) and Eq. (59)

1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1

{ ( ) ( 2) ( )} { ( ) ( 2) ( )}0

{ ( ) ( 2) ( )} { ( ) ( 2) ( )}J J X XJ J X X

(60)

On solving Eq. (60), we get

1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1

{ ( ) ( 2) ( )} { ( ) ( 2) ( )}{ ( ) ( 2) ( )} { ( ) ( 2) ( )}

J J J JX X X X

(61)

If 1 is the root of the above equation, then

1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1

{ ( ) ( 2) ( )} { ( ) ( 2) ( )}{ ( ) ( 2) ( )} { ( ) ( 2) ( )}

J J F J F J FX X F X F X F

(62)

Where, 1F

On the theory of Bessel functions, if tube under consideration is very thin i.e. andneglecting 2 3, ........ , the frequency equation can be written as (Watson [18])


40 | P a g e

2 2 21

1

1( 2) 2 1 ( 2) 0(63)

Where,2 2

2 2 22 / / / 2

66 66 66

3 3 ,2 ( )

Hi

(64a)

2 / / / 2 22 0 55 55 551 / / / 2

66 66 66

2 ( ) .ii

(64b)

From the Eq. (62), Eq. (63) and Eq. (64), the phase velocity can be written as (same as aboveEq. (45) and Eq. (46))

2 / / / 222 55 55 55

2 / / / 20 66 66 662

icc i (65)

Case 1

Since the pipe under consideration is made of an aeolotropic material, then

/ / / 0ij ij(66)

The frequency equation is given by

1 1 1 1

1 1 1 1

3 1 3 3 3 1 3 3

3 1 3 3 3 1 3 3

{ ( ) ( 2) ( )} { ( ) ( 2) ( )}{ ( ) ( 2) ( )} { ( ) ( 2) ( )}

J J J JX X X X (67)

32 26 3 0 (68)

2 221

66

3 ,2H 2 2

2 0 553

66

2 , 2 3 at 1 1(69)

Using Eq. (65), Eq. (66), Eq. (67) and Eq. (69), we get (calculations are done in the similarmanner as for the Eq. (48) to Eq. (50) for 0l case)

12 2

2

3 552

01 66

2cc

(70)

Where,2

01 66 0/ 2c

Case 2

If the pipe under consideration is made of an isotropic material, then


41 | P a g e

/ //55 660,ij ij

(71)

The frequency equation (calculations are done as for the l=0 case) is

2 2 2 2

2 2 2 2

4 1 4 4 4 1 4 4

4 1 4 4 4 1 4 4

{ ( ) ( 2) ( )} { ( ) ( 2) ( )}{ ( ) ( 2) ( )} { ( ) ( 2) ( )}

J J J JX X X X

Where,

2 222 3 ,H

2 22 04

2 . (72)

Using Eq. (71) and Eq. (72), the phase velocity for this case is (same as above Eq. (45) andEq. (46)

02

22

24

222 1c

c

(73)

Where,

02

202c

6 Numerical analysis

The effect of non-homogeneity on torsional waves in an aeolotropic material made of

viscoelastic solids has been studied. The numerical computation of phase velocity has been

made for homogeneous and non-homogeneous pipe. The graphs are plotted for the two cases

(l=0 and l=2). Different values of (diameter/wavelength) for homogeneous in the

presence of magnetic field and non homogeneous case in the absence of magnetic field are

calculated from Eq. (49) and Eq. (65) with the help of MATLAB. The variations elastic

constants and presence of magnetic field in two curves have been obtained by choosing the

following parameters for homogeneous and non-homogeneous aeolotropic pipe. The

dispersion equations for both cases are solved numerically with the help of parameters.

Table 1.Material propertiesl

0

HomogeneousPipe

0 2.333 10

Inhomogeneous 2 2.333 10


42 | P a g e

Pipe

The curves obtained in Figure 1 clearly show that the phase velocity for homogeneous as

well as non-homogeneous case decreases inside the aeolotropic tube. The presence of

magnetic field also reduces the speed of torsional waves in viscoelastic solids. These curves

justify the results obtained in Eq. (50) and Eq. (52) mathematically given by Narain [3] and

Chandrasekharaiahi [15]. We see that for homogeneous case when magnetic field is present

and for non-homogeneous case when magnetic field is not present the variation i.e. shape of

the curves is same. For non-homogeneous case, the elastic constants and the density of the

tube are varying as the square of the radius vector.Table 2.Material properties

l H (Gauss) 5 5 6 6/

HomogeneousPipe

0 0.32 0.8

InhomogeneousPipe

2 0 0.8

Fig.1 Torsional wave dispersion curves

7 Conclusion

The above problem deals with the interaction of elastic and electromagnetic fields in a

viscoelastic media. This study is useful for detections of mechanical explosions inside the

earth. In this study an attempt has been made to investigate the torsional wave propagation in

non-homogeneous viscoelastic cylindrically aeolotropic material permeated by a magnetic

field. It has been observed that the phase velocity decreases as the magnetic field increases.

Acknowledgements

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.5

1

1.5

2

2.5

3

3.5

4

Diameter/Wavelength

Phas

e V

eloc

ity

l=0

l=2


43 | P a g e

We are thankful to Dr. K. C. Gupta for his valuable comments.

References

1. Ewing WM, Jardetzky, Press F. Elastic waves in layered media. McGraw-Hill, New

York 1957.

2. Kaliski S, Petykiewicz J. Dynamic equations of motion coupled with the field of

temperatures and resolving functions for elastic and inelastic bodies in a magnetic

field.Proceedings Vibration Problems1959; 1(2): 17-35.

3. Narain S.Magneto-elastic torsional waves in a bar under initial stress. Proceedings

Indian Academic Science1978; 87 (5): 137-45.

4. White JE, Tongtaow C. Cylindrical waves in transversely isotropic media.Journal of

Acoustic Society1981;70(4):1147-1155.

5. Mcivor IK. The elastic cylindrical shell under radial impulse. ASME J. Appl. Mech.

1966;33:831–837.

6. Cinelli G. Dynamic vibrations and stresses in elastic cylinders and spheres.ASME J.

Appl. Mech. 1966;33:825–30.

7. Pan E, Heyliger PR. Exact solutions for Magneto-electro-elastic Laminates in

cylindrical bending.Int. J. of Solid and Struct. 2005; 40: 6859-6876.

8. Bin W, Jiangong Y, Cunfu H. Wave propagation in non-homogeneous magneto-

electro-elastic plates.J. of Sound and Vib. 2005; 317: 250-264.

9. Kong T, Li DX, Wang X. Thermo-magneto-dynamic stresses and perturbation of

magnetic field vector in non-homogeneous hollow cylinder.Appl. Mathematical

Modeling2009; 33: 2939-2950.

10. Kakar R, Kakar S. Propagation of Rayleigh waves in non-homogeneous orthotropic

elastic media under the influence of gravity, compression, rotation and magnetic

field.Journal of Chemical, Biological and Physical Sciences 2012; (1): 801-819.

11. Kakar R, Kakar S.Influence of gravity and temperature on Rayleigh waves in non-

homogeneous, general viscoelastic media of higher order.International Journal of

Physical and Mathematical Sciences 2013;4(1): 62-70.

12. Kakar R, Kakar S. Rayleigh waves in a non-homogeneous, thermo, magneto,

prestressed granular material with variable density under the effect of

gravity.American Journal of Modern Physics 2013; 2(1): 7-20.

13. Love AEH. Some Problems of Geodynamics. Cambridge University press 1911.

14. Thidé B.Electromagnetic Field Theory. Dover Publications1997.


44 | P a g e

15. Chandrasekharaiahi DS. On the propagationof torsional waves in magneto-

viscoelastic solids. Tensor, N.S. 1972;23: 17-20.

16. Watson GN. A treatise on the theory of Bessel functions. Cambridge University Press,

Second Edition 1944.

17. Green AE. Theoretical Elasticity. Oxford University Press 1954.

18. Love AEH. Mathematical Theory of Elasticity. Dover Publications. Forth Edition

1944.

19. Timoshenko S. Theory of Elasticity, McGraw-Hill Book Company. Second Edition

1951.

20. Westergaard HM. Theory of Elasticity and Plasticity. Dover Publications1952.

21. Christensen RM. Theory of Viscoelasticity. Academic Press1971.


45 | P a g e

Research Article

Synthesis and Charactrization of Ni-Zn Ferrite Based Nanoparticles bySol-Gel Technique

Maryam Sharifi Jebeli*, Norani Muti Binti Mohameda Department of Fundamental & Applied Science, Universiti Teknologi,PETRONAS,Bandar Seri Iskandar, 31750 Tronoh, Perak.* Corresponding author. Tel.: 0060173151040E-mail address: [email protected]

ARTICLE INFO


A b s t r a c tA series of Ni-Zn ferrite based naoparticles (Ni0.76-xZn0.04+xTi0.0025Co0.1Cu0.075Mg0.04Fe1.96O3.96) in which x is varied from 0.01 to 0.04,were prepared by sol-gel technique. Characterization of the samples wasPerformed by X-Ray Diffraction (XRD), Raman Spectroscopy, and FieldEmission Scanning Electron Microscope (FESEM). The XRD results show themajor peak (311) of the spinel cubic structure for Ni-Zn ferrites. FESEMresults show that single phase Ni-Zn ferrite nanoparticles with averagediameters 17-45 nm can be obtained by sol gel technique. Initial permeabilityand Q factor for all samples were measured and the magnetic measurements ofthe nano ferrites show that it can be used as a magnetic feeder for thetransmitter.


Keywords:Sol Gel techniqueNanoparticlePermeabilityQ- factor

1. Introduction

Ferrites represent an important category of materials, which are largely used, due totheir numerous practical applications, as for example magnetic devices in electronic,optical and microwave installations [1-2].Substituted Ni-Zn ferrites have wide applicationsin radio frequency (RF) electronic devices due to the high initial permeability in combinationwith giant resistivity [3-5]. Most of the physical properties of these materials, especiallythe magnetic ones (coercivity, saturation magnetization, losses) dramatically change withthe decrease of the particle size, especially at nano-size range [3-4]. Thus, specialinterests have been paid to the synthesis that leads to formation of nanoferrites. In thiscontext, unconventional synthesis methods [5-8] have advantages over the conventionalmethods [9-10]. One of the most popular unconventional synthesis methods that recentlyhave been extensively used is the sol-gel method [11-13]. This method was successfully wasused in obtaining nanomaterials, especially magnetic nanoparticles that lead to formation offerrite particles having sizes between 10 to 100 nm [1- 4].

Jebeli M.S. et al. / International Journal of Material Science Innovations (IJMSI) 1 (1): 45-53, 2013

46 | P a g e

Some new techniques have been tried to reduce the sintering temperature of Ni-Zn basedferrites: such as addition of CuO and some sintering aids [1-8]. Moreover, the reduction ofthe particle size of the raw materials was also favorable for decreasing sintering temperature[14].

In this paper Ni-Zn ferrite based nanoparticles were prepared using a sintering temperatureof 5000C. Due to the CuO addition also another decrease of the sintering temperature wasobtained which is due to low melting point of CuO compared to other oxides. So a decreasein sintering temperature from 1200 °C (Conventional method) to 500 °C was obtained.


2.1. Materials and mix design

The samples were synthesized using Ni, Mg, Co ,Cu ,Zn ,Ti and Fe nitrates and citric acid asprecursors, by dissolving them in distilled water while stirring at room temperature. Thesolutions were evaporated by heating at 75oC with continuous stirring until a viscous gelformed. After the gel formed, the powders were dried at 110 C in an oven for 24 hours anddried powders were crushed by using mortar for 1 hour. Then, the samples were annealed at500 C with holding time of 4 hours [8].

2.2. Experimental test

PVA (Polyvinyl alcohol) was added into them for their granulation and pressed into toroidalshapes. The green bodies were sintered at 700 °C in air for 5 h [7]. The resultant toroidalcores had 10 mm outer diameter, 5mm inner diameter and 2 mm thickness. Initialpermeability and Q factor were carried out after each toroid was wound with 25 turns of0.3mm diameter insulating copper wire. The wire ends were scraped by using a sand paper.The sample was then connected to a Hewlett Packard 4284A Precision LCR meter. A seriesof inductance, LS, and Q factor values were recorded from the lowest frequency to resonancefrequencies. The initial permeability values were calculated by introducing Ls to the equationbelow [14]:

i=)(

2

1

00

2

DDtInN

Ls

where LS is the parallel inductance, N is the number of turns, 0 is the permeability of freespace (4 x10-7 m/A), t is the thickness, D0 is the outer diameter, and Di is the inner diameterof the toroid, respectively. The magnetic measurements of the component ferritesdemonstrated that it can be used as a magnetic feeder for the transmitter [15].


47 | P a g e

The phase identification of the calcined powders was performed by X-ray diffraction(XRD)on a Philips PW-1730 X-ray diffractometer using Cu K radiation ( =1.54 A0).The averagecrystallite sizes of the synthesized powders were determined by using the XRD patterns, viathe well-known Scherrer equation [16]. The morphology of the powders was investigated byField Emission Scanning Electron Microscope (FESEM).

3. Results and discussion

3.1 X-Ray Diffraction (XRD)

Figure 1 shows X-ray diffraction pattern of the samples prepared by sol-gel method. The X-ray diffraction patterns show well developed diffraction lines assigned to pure spinel phase,with all major peaks matching with the standard pattern of Ni-Zn ferrite, JCPDS 8-0234. Theaverage crystallite sizes of the ferrites calculated from the broadening of the (311) X-raydiffraction peak by the Scherrer equation [16] were about 15-20 nm.

Fig.1. X -ray diffraction Pattern of Ni0.76-x Zn0.04+x Ti0.0025Co0.1Cu0.075Mg0.04Fe1.96O3.96 after annealing at500oC for 4 hours which shows the major peaks of all samples is in [311].

3.2 Raman Spectra

The purpose of Raman Spectroscopy is to see the vibrations of the atoms in Ni0.76-xZn0.04+x

Ti0.0025Co0.1Cu0.075Mg0.04Fe1.96O3.96 samples after annealing at 500 C for 4 hours. Figure 2shows the major peaks of five samples is in range 486 to 698.392 cm 1. These ranges formajor Peaks of Raman shift were confirmed as Raman shift for Ni-Zn ferrite [3].


48 | P a g e

Fig.2. Raman pattern of Ni0.76-x Zn0.04+x Ti0.0025Co0.1Cu0.075Mg0.04Fe1.96O3.96 after

annealing at 500oC for 4 hours which shows the major peaks of five samples

is in range 486 to 698.392 cm 1.

3.3 FESEM results

(FESEM) is used to identify the morphology, dimension for grain size of the bulk and nano-sized particles [11].Figure 3a-3d ( for samples prepared by sol gel methods) show nearlyuniform spherical ferrite particles having a distribution size of 17-45nm. The ED pattern(inset) reflects that these nanoparticles are well crystallized, the d values calculated from thering diameters correspond well to the spinel structure and are consistent with the XRDpattern. The EDX spectrum revealed that the darker particles contain Zn, Ti, Mg, Cu, Ni andFe.

3.4 Initial permeability and Q factor

It is obvious that the increase of frequency has led to an increased initial permeability and Q

factor up to resonance frequency [7 and 12]. From figure 4, it was observed that a fall of

initial permeability with increasing Zn content. A probable explanation is that it was highly

difficult to disperse the Zn powder particles which tend to agglomerate, during the mixing

stage of the raw materials [17].


49 | P a g e

Fig. 3. Show nearly uniform spherical ferrite particles having a distribution size of 17-45 nm:

a) Ni0.75Zn0.05 Ti0.0025Co0.1Cu0.075Mg0.04Fe1.96O3.96 (sample No.1)

b)Ni0.74Zn0.06Ti0.0025Co0.1Cu0.075Mg0.04Fe1.96O3.96 (sample No.2)

c) Ni0.73Zn0.07Ti0.0025Co0.1Cu0.075Mg0.04Fe1.96O3.96, (sample No.3)

d) Ni0.72Zn0.08Ti0.0025Co0.1Cu0.075Mg0.04Fe1.96O3.96 (sample No.4)

e) Ni0.71Zn0.09Ti0.0025Co0.1Cu0.075Mg0.04Fe1.96O3.96 (sample No.5)

a b

c d

e


50 | P a g e

Table 1. EDX result for five samples prepared by sol –gel methodElement Weight

%

Sample

No: 1

Atomic

%

Sample

No: 1

Weight

%

Sample

No: 2

Atomic

%

Sample

No: 2

Weight

%

Sample

No: 3

Atomic

%

Sample

No: 3

Weight

%

Sample

No: 4

Atomic

%

Sample

No: 4

Weight

%

Sample

No: 5

Atomic

%

Sample

No: 5

Zn K 2.22 7.81 1.29 55.59 5 12.25 4.76 11.50 5.30 23.83

O K 32.06 55.20 26.23 0.83 32.91 56.94 30.20 54.79 21.95 36.66

Mg K 0.44 0.88 0.59 30.65 0.83 0.59 1.53 1.13 2.43 1.42

Fe K 43.59 26.47 50.48 11.02 41.88 0.73 44.09 22.91 52.36 30.83

Ni K 20.09 8.98 19.8 1.00 16.78 20.76 16.73 8.47 16.53 11.02

Cu L 1.40 0.43 2.00 0.67 1.87 7.91 2.06 0.94 2.15 1.11

Ti K 0.2 0.23 0.33 0.24 0.74 0.82 0.94 0.42 1.16 0.53

Totals 100.00 100.00 100.00 100.00 100.00

Fig.4. Initial Permeability of the toroids prepared by Ni-Zn ferrite based nanoparticles.

Fig.5. LCR meter and the toroids prepared by Ni-Zn ferrite based nanoparticles.


51 | P a g e

There is a marked shift (to the left) of resonance frequency due to the increment of Zn. Thus

nano-regions of badly non-stoichiometric compositions would be created, give rise, for

instance to Fe+2 ions which could contribute to eddy current through eFeFe 32

reaction [17]. Thus by adding more Zn, the lower the resonance frequency and thus the lower

initial permeability and Q factor are obtained (Figure 6).

Fig.6. Q factor of the samples prepared by sol- gel method

Initial permeability and Q factor of the samples were measured (Figure 4 and Figure 6) and

the sample No 1 has the most resonance frequency and initial permeability and we can used it

as a magnetic feeder for the transmitter (Figure 7).

Figure 7 shows comparison of aluminum transmitter with and without ferrites. We can see

magnetic field for aluminum transmitter with sample No:1 is 41% higher than the magnetic

field obtained without ferrite.

4. Conclusions

Ni-Zn ferrite based nanoparticles (Ni0.76-x Mg0.04+x Ti0.0025 Co0.1 Cu0.075 Zn0.04Fe1.96O3.96)

prepared by sol-gel method and single phase for this compound obtained at 5000C.

Nanocrystalline size for samples prepared by this method is about 15-20 nm. Initial

permeability and Q factor measured and investigated. Magnetic field of aluminum transmitter

with sample No:1 is 41% higher than aluminum transmitter without ferrite.


52 | P a g e

Fig.7. Comparison of aluminum transmitter with and without ferrite.

References

1. Anil Kumar PS, Shrotri JJ, Deshpande CE, Date SK. Systematic study of magnetic

parameters of NiZn ferrites synthesized by soft chemical approaches. Journal of Applied

Physics. 1997; 81(8):4788–4790.

2. Burke JE. Ceramic Fabrication Process. New York: Wiley; 1958.

3. Rezlescu E, Sachelarie L, Popa PD, Rezlescu N. Effect of substitution of divalent ions on

the electrical and magnetic properties of Ni-Zn-Me ferrites. IEEE Trans Magn. 2000;

36:3962–3967.

4. Goldman A. Modern Ferrite Technology. New York: Van Nostrand Reinhold. 1990.

5. Hsu JY, Ko WS, Chen CJ. The effect of V2O5 on the sintering of NiCuZn ferrite. IEEE

Trans Magn. 1995; 31:3994–3996.

6. Hsua WC, Chen SC, Kuo PC, Lie CT, Tsai WS. Preparation of NiCuZn ferrite

nanoparticles from chemical co-precipitation method and the magnetic properties after

sintering. Mater SciEng B-solid. 2004; 111:142–149.

7. Jankovskis J. Modelling the Frequency Dependence of Complex Permeability Based on

Statistics from Polycrystalline Ferrites Microstructure. Ferrites proceedings of the Eight

International Conference on Ferrites (ICF’8); Kyoto and Tokyo. 2000. p. 319.

8. Kim CW, Koh JG. A study of synthesis of NiCuZn-ferrite sintering in low temperature by

metal nitrates and its electromagnetic property, Journal of Magnetism and Magnetic

Materials. 2003; 257:355–368.


53 | P a g e

9. Kim CS, Kim WC, An SY, Lee SW. Structure and Mossbauer studies of Cu doped NiZn

ferrite. J MagnMagn Mater. 2000; 215-216:213–216.

10. Kondo K. The Digest Edition of Tokin Technical Revi. Vol. 26. Sendai, Japan: Tokin

Corporation; 1999. p. 1.

11. Kondo K, Chiba T, Yamada S, Otsuki E. Analysis of power loss in Ni-Zn ferrites. Journal

of Applied Physics. 2000; 87(9):6229–6231.

12. Caltun OF, Spinub L, Stancua AL, Thungb LD, Zhou W. Study of the microstructure and

of the permeability spectra of NiZnCu ferrites. Journal of Magnetism and Magnetic

Materials. 2002;242-245:160–162.

13. Lebourgeois R. Low Losses NiZnCu Ferrites’, Ferrites proceedings of the Eight

International Conference on Ferrites (ICF’8). Kyoto and Tokyo. 2000. p. 576.

14. Nakamura T. Low-temperature sintering of Ni-Zn-Cu ferrite and its permeability spectra.

Journal of Magnetism and Magnetic Materials. 1997;168:285–291.

15. Seo SH, Oh JH. Effect of MoO3 addition of sintering behaviors and magnetic properties

of NiCuZn ferrite for multilayer chip inductor. IEEE Trans Magn. 1999;35(5):3412–3414.

16. Shrotri JJ, Kulkarni SD, Deshpande CE, Mitra A, Sainkar SR, Anil Kumar PS, Date SK.

Effect of Cu substitution on the magnetic and electrical properties of Ni-Zn ferrite

synthesised by soft chemical method. Materials Chemistry and Physics. 1999; 59:1–5.

17. Zhang H, Ma ZW, Zhou J, Yue ZX, Li Lt, Gui ZL. Preparation and investigation of

(Ni0.15Cu0.25Zn0.60)Fe1.96O4 ferrite with very high initial permeability from self-propagated

powders. Journal of Magnetism and Magnetic Materials. 2000;213:304–308.


54 | P a g e

Review Article

The Interaction Effects of Synthesis Reaction Temperature and DepositionTime on Carbon Nanotubes (CNTs) Yield

Hengameh Hanaeia,b

a Institute of Advanced Technology (ITMA), University Putra Malaysiab Chemical Engineering Department, Universiti Teknologi PETRONAS* Corresponding author. Tel.:006014257185E-mail address: [email protected]

ARTICLE INFO


A b s t r a c tThis research focused on investigation of interaction effects of reactiontemperature and deposition time on FBCVD growth of CNTs. In present study,Fluidized Bed Chemical Vapor Deposition (FBCVD) has been introduced as apromising method for carbon nanotubes (CNTs) synthesis because of its largescale, low cost and high yield production. However, there is no clear relationbetween synthesis parameters and CNTs growth; therefore more datainvestigations are required for FBCVD synthesis of CNTs. Scanning ElectronMicroscopy (SEM), Transmission Electron Microscopy (TEM), ThermoGravimetric Analysis (TGA) and Energy Dispersive X-ray spectroscopy(EDX) were used in this work. The results demonstrated that the ideal reactiontemperature was 750°C and the deposition time was 40min.


Keywords:Carbon nanotubes; synthesis;Fluidized bed;Chemical vapor deposition;CNTs;

1. Introduction

Carbon nanotubes (CNTs) are present as a one-dimensional novel form of fullerenes. CNTs

are constructed from sp2 orbital hybridization of carbon atoms, with a few nanometers in

diagonal diameter and many microns in lengths. Carbon atoms are covalently bonded to each

other. This structure of carbon nanotubes makes it stronger than Sp3 bonds structure of

diamond. There are two categories of CNTs; multiwall carbon nanotubes (MWNTs) and

single wall carbon nanotubes (SWNTs) [1-3]. The most attractive and simple method is

chemical vapor deposition (CVD). It has been successfully scaled up to large quantities as

lower temperature and ambient pressure is needed. Compared to other methods, CVD is an

economical technique. CVD was first used for synthesis of CNTs by Endo and coworkers

Hanaei H. / International Journal of Material Science Innovations (IJMSI) 1 (1): 54-61, 2013

55 | P a g e

[4]. In this process, carbon nanotube is produced by heating a metal catalyst (e.g., iron,

nickel, or cobalt) to desired temperature (500°C - 1000°C) under a carrier gas. Then, a

hydrocarbon source is heated at desired temperature in a tube furnace over a period of time.

In this technique, thermal energy is used to break off the hydrocarbon in the presence of

catalyst. The mechanism of this process involves the separation of hydrocarbon molecules

deposited on metal catalyst particles [5-7].


There are two steps in FBCVD technique for synthesis of CNT: catalyst preparation and

actual reaction. Catalysts are usually prepared on a substrate, in this study Al2O3 as a

substrate and Fe-Mo as a catalyst were used. The right amount of alumina powder was added

to a solution of iron nitrate (Fe (NO3)3•9H2O) and (NH4)6Mo7O24•4H2O ammonium

molybdate. The weight ratio of Iron to molybdenum to alumina Fe: MO: Al2O3 is 9: 1: 5

[8]. In our experiments, catalyst was placed into the reactor and argon gas with 1.4 l/min ratio

was introduced into the bottom vessel of the reactor, and then passes through the gas

distributor, and finally flows out into the atmosphere. Acetone vapor was injected by the flow

of argon into the reactor. As a result the acetone was decomposed over the catalyst to form

carbon nanotubes. After reaction, the morphology and microstructure of the CNTs were

observed using SEM. The exact amount of carbon deposit formed during the reaction is

determined by weighing the catalyst before and after reaction. The yield of deposited carbon

is obtained from the total weight of the catalyst after the reaction by subtracting the initial

weight of the catalyst before reaction. Process carbon yield based on the amount of deposited

carbon during the reaction is obtained from the following formula:

Carbon Yield (%) = [(mtot-mcat)/mcat] * 100

where mcat is the initial amount of the catalyst before reaction) and mtot is the total weight of

the product after reaction [9].


56 | P a g e

3. Statistical Analysis

Two-way analysis of variance (ANOVA) was used to determine the difference between

samples, using SPSS software. Duncan test was used to carry out the difference of means

between pairs. And Hsu’s test was used to determine the best level of sample with p<0.05.

4. Result and Discussion

5g catalyst was used for this part of experiment the interaction effect of reaction temperature

and deposition time on CNTs growth was examined. The values applied in this set of

experiment were: 5g catalyst (Fe-Mo/Al2O3), acetone as a carbon source with rate of 1.5

mL/min and one carrier gas (Argon) with rate of 1.4 L/min. The carbon yield for each

condition was calculated using the above Equation. Table 1 indicates the carbon yield at

different deposition time and different reaction temperature condition. Based on the results of

the experiments presented in Table 1, the carbon yield rate at 550°C, 650°C, 750°C, 850°C

and 950°C reaction temperature is different for 30min to 50min deposition time. As described

in the previous section, the carbon yield reaches a maximum carbon yield at 40min and

50min deposition time. In addition, the carbon yield rate for 40min and 550°C is 50%, 650°C

is 78% and for 750°C is 98.19%. It can be seen that there is a linear trend between reaction

rate and reaction temperature from 550°C to 750°C and the carbon yield rate increased with

the increased of synthesis temperature from 550 °C to750 °C.

Table 1. The interaction effect of Temperature and Time on carbon yield

Temperature °C 550°C 650°C 750°C 850°C 950°C

weight 6.6 7.2 8.5 6.37 8.630min

Carbon yield(%) 32 44 70 27.4 72

weight 7.5 8.9 9.91 8.7 9.9040min

Carbon yield(%) 50 78 98.19 74 98.06

weight 7.75 9 9.97 8.9 9.9050min

Carbon yield(%) 55 80 99.5 78 98.1


57 | P a g e

Therefore, at low temperature, the decomposition rate of acetone is low and very little of

active catalytic sites led to the low carbon yield rate before 750°C. Beyond 750 °C, some

parasitic phenomena occurs which are responsible for deactivation of the catalyst and the

carbon yield decreased with the increase of synthesis temperature from 750°C to 850°C, at

850°C the carbon yield rate for 40min deposition time is 74%. When the reaction temperature

is greater than 850°C, the deposit is included in encapsulated iron particles and uncatalyzed

acetone. Supported catalyst at high temperature partial to sintering so, larger particle sizes

was obtained. The carbon yield at 950°C and 40min is 98.06%. Also for 50min deposition

time, carbon yield at 550, 650, 750, 850 and 950°C are 55%, 80%, 99.5%, 78% and 98.1%

respectively. Based on the above result, it can be concluded that the reaction temperatures at

750°C and 950°C for 40 min and 50min deposition time is good for carbon yield and at

750°C and 40min is favorable for high purity in the synthesis of CNTs according to SEM

images in Figure 2.

Also, same process occurred for 30min by changing the temperature. According to Table 1

the carbon yield reported for 30 min deposition time and at 550°C, is 32%, at 650°C is 44%,

at 750°C is 70%, at 850 °C is 27.4% and for 950°C is 72%. By comparing these results it can

be concluded that at 30, 40 and 50min deposition time, the carbon yield increased from

550°C to 750°C and after that at 850°C a decrease is observed because of deactivated catalyst

and at 950°C there is many uncatalyzed acetone. The highest carbon yield at all temperatures

is at 50min deposition time but 40min deposition time is favorable for high purity in the

synthesis of CNTs according to SEM images in Figure 2.

To make the comparison more understandable, Figure 1 demonstrates the effect of reaction

temperature and deposition time on carbon yield. As it is shown in the diagram of Figure 1 it

can be seen that, for constant amount of catalyst loading 5g, the effect of reaction temperature

on carbon yield depends on the time of deposition and vice versa. At different temperature

and time deposition different carbon yield percentage is observed.

It can be seen that, although the trend of changes is similar for each independent effect but at

different temperature and time deposition we can see different carbon yield percentage. The

effect of reaction temperature on carbon yield depends on the time of deposition and vice


58 | P a g e

versa. It can be concluded that the interaction of reaction temperature and deposition time is

significant. The result from statistical analysis confirmed the above results.

Fig.1. The interaction Effect of Temperature and Time on carbon yield

Results from two way analysis of variance (ANOVA) at a 95% confidence interval indicate

that temperature and time has a significant effect on the carbon yield. A p-value (0.001)

<0.05 shows a statistically significant effect, so we concluded that at constant amount of

catalyst, reaction temperature and deposition time has an effect on carbon yield during carbon

nanotube growth.

Qualitative characterization of the carbon deposits formed using the FBCVD process at

different deposition time and reaction temperature was performed by scanning electron

microscope (SEM). Figure 2 illustrates representative images of those samples that had high

carbon yield, (750°C, 40min), (750°C, 50min), (950°C, 40min) and (950 °C, 50 min). The

SEM images indicate that the trend toward CNTs formation at 950 °C with a deposition time

of 40 min and 50 min is almost low. It also shows that the product included amorphous

carbon and tubes with the diameter about 0.5 m. The product obtained at 750 °C and 50 min

also did not show significant formation of CNTs formation that could be attributed to the

deactivation of catalyst.

It can be seen that at 750°C and 40min deposition time, most of the CNTs were regularly

arranged with uniform and similar shapes. These results confirmed the TGA analysis as

attributed Figure 3 shows the TGA graphs of synthesized CNTs at (750°C, 40min), (750°C,

50min), (950°C, 40min) and (950°C, 50min). It can be seen that the amount of oxidization


59 | P a g e

temperature at 750°C, 40min is higher than 500°C and for another samples the oxidization

temperature is lower than 450°C so, this result indicates that the trend toward CNTs

formation at 750°C, 40min is the best. The TGA graph of reaction temperature at 950°C,

illustrated that the oxidization temperature is less than 420°C and it can be concluded that

more amorphous carbon is present. Amorphous carbon usually started to burn in temperature

of less than 420°C. This conclusion is consistent with the observation from SEM.

Fig.2. SEM image of CNT at: A) 750°C and 40min ,B) 750°C and 50min, C) 950°C and 40min, D 950°C and

50min


60 | P a g e

Fig.3. TGA Graph of all the samples in this set of experiments.

4. Conclusion

Our work was done in the fluidized-bed reactor with good heat and mass transfer coefficients

that allows uniform temperatures within the bed and rapid gas-solid interactions. Also in this

fluidized bed reactor, before the introducing acetone into the reactor, liquid form of acetone

was transformed to its vapor by the argon flow. That argon gas was preheated with using the

main body of furnace. Therefore, acetone vapor was injected by the flow of argon introduced

into reactor. So, these unique properties of fluidized bed make low cost and large scale

synthetic production. Present work demonstrates the interaction effect of synthesis

temperature and deposition time on carbon and CNTs yield in FBCVD. CNTs were

synthesized on a Fe-Mo bi-metallic catalyst system supported on Al2O3. The product was

analyzed by SEM, TGA. The results demonstrated that the ideal reaction temperature and

deposition time was about 750°C, 40min.

References

1. Ajayan, P., Nanotubes from carbon. Chem. Rev, 1999. 99(7): 1787-1800.

2. Baker, R., et al., Nucleation and growth of carbon deposits from the nickel catalyzeddecomposition of acetylene, in Journal of catalysis. 1972:51-62.

3. Iijima, S., Helical microtubules of graphitic carbon. Nature, 1991. 354(6348): 56-58.


61 | P a g e

4. Endo, M., et al., The production and structure of pyrolytic carbon nanotubes (PCNTs).Journal of Physics and Chemistry of Solids, 1993. 54(12): 1841-1848.

5. See, C. and A. Harris, A review of carbon nanotube synthesis via fluidized-bed chemicalvapor deposition. Industrial & Engineering Chemistry Research, 2007. 46(4): 997-1012.

6. Wei, F., et al., The mass production of carbon nanotubes using a nano-agglomerate fluidizedbed reactor: A multiscale space-time analysis. Powder Technology, 2008. 183(1): 10-20.

7. Venegoni, D., et al., Parametric study for the growth of carbon nanotubes by catalyticchemical vapor deposition in a fluidized bed reactor. Carbon, 2002. 40(10): 1799-1807.

8. Qian, W., et al., Synthesis of carbon nanotubes from liquefied petroleum gas containingsulfur. Carbon, 2002. 40: 2968-72.

9. Hernadi, K., et al., Fe-catalyzed carbon nanotube formation. Carbon, 1996. 34(10): 1249-1257.


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Review Article

An overview of pH Sensors Based on Iridium Oxide: Fabrication andApplication

Saeid Kakooei*, Mokhtar Che Ismail, Bambang Ari-Wahjoedi

Centre for Corrosion Research, Department of Mechanical Engineering, Universiti Teknologi PETRONAS,Tronoh31750, Malaysia* Corresponding author. Tel.: +60174958196;E-mail address: [email protected]

ARTICLE INFO


A b s t r a c tIn recent years, there has been an increasing interest in the adoption ofemerging sensing technologies for instrumentation within a variety ofstructural systems. Iridium oxide as an stable and interesting material for pHsensor in variuse temperature and pressure was paid attention by a lot ofresearchers. In this study an overview of different methods for fabrication ofIrO2 pH sensors and their application are presented.


Keywords:pH Sensor;Iridium Oxide;Electrodeposition;Sputtering;Sensor Fabrication

1. Introduction

During the past decades IrO2 became a superior material for reference electrode[1, 2] and pH

measurements in different fields such as biological media [3, 4], food industry [5], nuclear

field [6, 7], and oil and gas industry [8-10]. Iridium oxide can provide a rapid and stable

response in different media because of its high conductivity and low temperature coefficient.

Potentiometric response of the Iridium oxide to pH is a function of transition effect between

two oxidation states Ir(III) oxide and Ir(IV) oxide, which can be shown as follow[11]:

Ir(IV)oxide + qH+ + ne- Ir(III)oxide + rH2O

In 1996, Roe et al.[12] measured dissolved oxygen, pH, and ion currents on mild steel

corroded surface using three closely spaced microelectrodes. They proposed a real time

mapping of the pH distribution on the mild steel corroded surface.

Kakooei S. et al. / International Journal of Material Science Innovations (IJMSI) 1 (1): 62-72, 2013

63 | P a g e

Two properties of biocompatibility and corrosion resistance of iridium oxide electrodes are

noticeable [13]. This fact made iridium oxide electrodes as a potential candidate for

Microbial induced corrosion investigation. A crystal structure of stoichiometric iridium oxide

is shown in Figure 1.

Figure 1: Crystal structure of IrO2 [14]

The difference between IrOx pH sensor and traditional glass pH sensor is related to their

mechanism for pH measuring. Glass pH electrode depends on solution-phase activities of the

relevant electrode whereas IrOx is dependent on H+ activity and oxidation state of IrOx. The

proposed reaction at the anhydrous Iroquois electrode shown as[15]:

2IrO2 + 2H+ + 2e- Ir2O3 + H2O (1)

And for a hydrous IrOx electrode as follows reaction:

2[IrO2 (OH)2·2H2O]2- + 3H+ + 2e- [Ir2O3(OH)3·3H2O]3- + 3H2O

(2)

Hence the Nernstian response slopes for electrodes prepared by different methods can range

between 59 and 88.5 mV/pH. Moreover, proposed Nernst equations are as follows:

E=E0 - 2.3RT/2F log[Ir2O3]/[IrO2]2[H+]2 (3)

and

E = E0 - 2.3RT/2F log[Ir2O3]/[IrO2]2[H+]3 (4)

It be proposed that any variation in the Ir3+/Ir4+ ratio, IrOx electrode preparation, IrOx

electrodes age, and deliberate exposure to redox agents such as Fe(CN)63-/4- have been shown

to affect the pH response [15, 16].

Cathodic storage charge capacities (CSCC) of the test samples will be calculated by

integrating the cathodic area in cyclic voltammograms. The CSCC data generally be used in

the characterization of neural stimulation electrodes [17-19], although in some research work

CSCC calculated like this is approximately equal to the amount of Ir4+ on the substrate in thin


64 | P a g e

electrodeposited layers. The calculated area above-mentioned is presented by the CV of an

EIROF on Au in Figure 2 [20].

Fig. 2. CV of iridium oxide in PBS at 50 mV/s showing the area used to calculate the CSC of the film [20].

2- Iridium oxide pH sensor fabrication:

It is clear that preparation methods play the main role in the pH response of the iridium

oxide-based electrodes. Anhydrous iridium oxides were achieved by thermal oxidation or

sputtering Methods which showed pH response of 59 mV/pH, whereas iridium oxides

fabricated by electrochemically technique are predominantly hydrated iridium oxides such as

IrO2·4H2O, Ir(OH)4·2H2O which present a super-Nerntian response 90 mV/pH unit [21].

2-1. Sol–gel processes

Sol-gel method was used to fabricated IrO2 pH sensor on flexible substrate [22, 23]. Three

different groups of pH sensors fabricated by the sol-gel process indicated similar near super-

Nernstian response, good reversibility, and similar response times, which show better

reproducibility and repeatability in this fabrication technique.

The sol-gel technique is well-known as a cheap method for advance material fabrication. Da

Silva et al.[24] used a polymeric precursor approach to fabricate a low-cost pH sensor with

substitution of IrOx by TiO2. The best result was related to 70 % (IrOx)-30% (TiO2).


65 | P a g e

The challenge in sol-gel method is related to the drying process, which led to creating cracks

in iridium oxide film due to its dehydration. This phenomenon can be decreased by using

proper additives.

2-2. Electrochemical or thermal oxidation of iridium and iridium salts

Song et al. [13] fabricated an Ir/IrO2 pH sensor by using the potentiodynamically cycling

method on an Ir electrode in 0.5 M H2SO4 aqueous solution at a 50 mV/s scan rate with

different exposure time ( 2, 4, 8, and 24 hr). According to Figure 3, they found that pH

sensor fabricated by 2-hr and 4-hr treatment showed more drift than those fabricated by 8-hr

and 24-hr treatment.

Fig 3. Stacked voltammograms of iridium potentiodynamically cycled between –0.25 VSCE and 1.27 VSCE at 50

mV/s for 2, 4, 8, and 24 hr in deaerated 0.5 M H2SO4 aqueous solution [13].

Song et al. investigated the effect of bisulfite and thiosulfate ions on the Ir/IrO2 pH sensor.

The calibration of pH sensor significantly changed when exposed in solution test containing

aforementioned ions.

2-3. Sputtering

Sputtering method was used in most IrO2 film fabrication for neural stimulation electrods

[17, 25-27]. Kreider [28] in 1991 used sputtered iridium oxide as pH-sensing electrodes in

high-temperature high-pressure saline solutions. Sputtered iridium oxide films was fabricated

in mixed Argon and oxygen environment in a 1:l ratio at a total pressure of ~0.40 Pa. The

thickness of 0.5-0.7 µm thick depositions were made primarily on alumina circuit board at


66 | P a g e

30-40 °C and at 240 °C. He found that with increasing exposure time in saline solutions, pH

sensitivity decreased at high temperature. The main disadvantage of sputtering method is

expensive price of its target price which is not also available for some rare material.

2-4. Anodic or cathodic electrodeposition

Yamanaka [29] proposed electrodeposition of iridium oxide for the first time for fabrication

of display device. His suggested solution was based on a complex of IrCl4 and oxalate

component. After that a lot of researcher improved this solution or used it as described by

Yamanaka [18, 30-32].

Ryynänen et al. for first time used atomic layer deposition (ALD) for iridium oxide (IrOx)

fabrication as the pH sensitive layer with an average sensitivity of -67 mV/pH at 22 °C. They

could coat 110 nm IrOx layer on a glass substrate consists of 300 nm thick titanium

electrodes. Their pH sensor was able to detect pH in a range from pH 4 to pH 10 [33].

Various metals have been used as substrate for IrO2 coating such as Au, Pt, Ir, PtIr, stainless

steel, tin-doped indium oxide (ITO) [29, 34, 35]. Marzouk [36] in a valuable work

investigated various substrate pure metals such as Au, Ag, Ti, Cu, Ni, W, Zr, and Co and

some alloys such as nickel-chrome, Hastelloy and stainless steel. The blue layer of deposit,

proper adhesion of deposit to surface, and stability of the cyclic voltammogram were the

most important factor for substrates comparing. Mayorga et al. [35, 37] described a simple

pH sensor fabrication through IrO2 electrodeposition on stainless steel substrate. The

fabricated sensor had fast response time and good repeatability.

Most of researchers followed original Yamanaka solution[29], although some others

attempted the modification of his solution[38, 39].

Marzouk approved that using (NH4)2[IrCl6] instead of IrCl4 was wrong since the solution did

not develop to dark greenish-blue color for up to 7 days at room temperature [36]. Marzouk

was successful to reduce the development time of solution from 3 days to 10 minutes by

heating the solution to 90 °C. Petit et al. [38] replaced IrCl4 with K3IrCl6. The required time

for solution development was 4 days at 35 °C. This solution did not offer any highlighted

merit. Lu et al. [18] attempted to use H2IrCl6.6H2O for electrodeposition solution. Their

solution was developed from light yellow to dark blue after 5 days.


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Table 1. Application and characterization of IrO2 electrodes fabricated by electrodeposition technique.

Substrate Precursormaterials

Oxidethickness

Sensitivity(NernstianbehaviormV/pH)

Application References

Platinum wire --------- --------- 70.2 Interfacial pHmeasurement

[39]

Au, Pt, Ir, PtIr,and

316LVMstainless steel

wires

IrCl4, oxalicacid, andK2CO3

100 nm---------

Neural stimulation andrecording

[34]

Tin-dopedindium oxide

(ITO)


--------- --------- Electrochromic displaydevices

[29]

Platinum IrCl4, oxalicacid, andK2CO3

--------- -68 to -77 Glucose sensor [1]

Au, Ag, Ti, Cu,Ni, W, Zr, Co,nickel-chrome,Hastelloy andstainless steel


--------- -73 pH measurementas a detector in a flow

injection analysis (FIA)system

[36]

Platinum H2IrCl6·6H2O,oxalic acid,and K2CO3

--------- 75.51 pH measurement as aNeural sensor

[18]

Stainless steel IrCl4, oxalicacid, andK2CO3

20-30 nm --------- pH measurement as abiosensor

[35, 37]

SnO2-coatedglass

K3IrC16,oxalic acid,and K2CO3

-------- --------- --------- [38]

Polyimide-Cr-Au


-------- 77 pH measurementin brain tissues

[40]

ITO-coatedglass


-------- 64.5 ---------- [11]

Carbon fiber Na3IrCl6, HCl,NaOH

-------- --------- Scanningelectrochemical

microscope (SECM)

[41]

SputteredPlatinum on

flexibleKapton films


-------- -63.5 pH measurement ofextracellular MyocardialAcidosis during Acute

Ischemia

[42]

Platinum IrCl4, oxalicacid, andK2CO3

-------- 77.6 pH measurement ofmicrofluidic-based

microsystems

[32, 43]

SputteredGold on Siwafer


-------- -68 Monitoring of waterquality

[15]

Stainless steel IrCl4, oxalicacid, andK2CO3

-------- -73 Corrosion monitoring [44]

Nguyen et al. [40] observed a 12 mV/pH as drift of sensitivity after 8 days sensitivity test

repeating. They explained that this change in sensitivity is due to dehydration phenomenon of

hydrated iridium oxide, which can be minimized by keeping IrO2 pH sensor in phosphate

buffered saline (PBS) solution.


68 | P a g e

Wipf et al.[41] produced a pH microelectrode via electrodeposition of IrO2 on carbon fiber.

They used this pH sensor in development of the scanning electrochemical microscope

(SECM). The fabricated pH sensor was able to measure pH near a surface. The result was

shown as a vertical pH map or image.

As Lu et al.[18] reported there is an optimum thickness for IrO2 electrodeposited coating.

Coating electrochemical performance increase when its CSCc and thickness increase, but

when CSCc approach to ~45mC/cm2 delamination of IrO2 coating was detected. Their

demonstarated iridium oxide electrode showed a pH sensitivity -75.51 mV/pH in broad pH

range of 1-13. More research works are presented in Table 1 with electrode application and

other characterization.

2-5. Other methods

A surface renewable IrO2 pH sensor or hydrogen ion-selective electrode can be made by

using composite electrode technique. Quan et al.[21] used carbon black, polyvinyl chloride

and ammonium hexachloroiridate to fabricate an IrO2 based composite electrode. Increasing

IrO2 content up to 40 wt% showed an increasing on the pH response. They also investigated

the effect of different ions on pH electrode efficiency that resulted that Fe(CN)63- , Fe(CN)6

4-,

I-, and H2O2 affected by electrode result. Similar results for IrO2 pH sensor were also reported

in other research [45].

Park et al.[46, 47] fabricated an iridium oxide-glass composite electrode by mixing

ammonium hexachloroiridate and glass powder, pressing, and sintering under oxygen

atmosphere. The mention electrode was renewable by using 2000 grit SiC emery paper

whenever it becomes fouled or deactivated. They observed many microscopic voids in the

electrode surface after sintering at high temperature. pH response in these electrodes was

dependent on the size and population of voids. Surface voids can be reduced by hot press

sintering technique.

3. Applications

3.1. Biomedical and Biological applications

Marzouk et al.[48] in 2002 measured extracellular pH in ischemic rabbit papillary muscle for

the first time. They used a pH sensor based on an IrO2 film electrodeposited on a planar

sputtered platinum electrode fabricated on a flexible Kapton substrate.


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Fast response time of pH sensor is very important for biological application. Iridium oxide

pH microsensors were used to measure the acidification rate of CHO and fibroblast cells in a

cell culture with microfluidic control [32]. This approach can also be used in bioanalytical

filed or biosensor [32, 43].

Iridium oxide sensors are widely used in neural stimulation and recording electrodes

regarding to their low impedance, high charge storage capacity [34].

Iridium oxide based pH sensor is a reliable and robust approach for biological application.

O’Hare et al. [4] investigated application of IrO2 electrode fabricated by thermal oxidation

and anodization as a pH sensor in the cultured intervertebral disc. Their electrodes were

tending to be unstable in physiological media. Also dissolution of the hydrated oxide film

happened in higher concentrations of chloride. They reduced the effect of chloride by using

thermally annealed Nafion films. Although Nafion film caused an increase in response time,

it could protect iridium oxide film against the aggressive nature of biological media [32, 42].

3.2. Industrial applications

Zhang et al.[39, 49] used IrO2 pH sensor for measuring pH in electrode/solution interface in

electrodeposition process. They found that by increasing the applied potential, interfacial pH

increased. Marzouk [36] fabricated a tubular IrO2 pH sensor for using in a flow injection

analysis (FIA) system as a detector.

The pH of a solution is one of the most important parameters used for characterizing an

electrolyte during corrosion processes [5, 8, 10]. For this purpose, some researcher used

iridium oxide microelectrode to study the effect of local pH near the surface on corrosion on

steel surfaces [9, 50].

4. Conclusion

In this study various techniques for fabrication of IrO2 electrode was presented. Iridium oxide

pH sensor are able to measure pH changes in real-time which enablae researchers to use it in

variouse industrial field. More attention was paid to electrodeposition method due to cheaper

fabrication process, low-temperature process, potential for using cheaper substrates, and

versatility of sensor shapes and designs.


70 | P a g e

Acknowledgements

We are gratefully acknowledge the financial support from Ministry of Higher Education(ERGS Grant No: 158200327) and Universiti Teknologi PETRONAS that has made thiswork possible.

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L i s t o f A R O P U B J o u r n a l s :

I n t e r n a t i o n a l J o u r n a l o f P e t r o l e u m a n d G e o - s c i e n c eE n g i n e e r i n g ( I J P G E )

I n t e r n a t i o n a l J o u r n a l o f M a t e r i a l S c i e n c e I n n o v a t i o n s( I J M S I )

I n t e r n a t i o n a l J o u r n a l o f C i v i l a n d E n v i r o n m e n t a l R e s e a r c h( I J C E R )

I n t e r n a t i o n a l J o u r n a l o f E l e c t r o n i c E l e c t r i c a l E n g i n e e r i n gI n n o v a t i o n s ( I J E E E I )

I n t e r n a t i o n a l J o u r n a l o f E n g i n e e r i n g & T e c h n o l o g y S c i e n c e s( I J E T S )

I n t e r n a t i o n a l J o u r n a l o f C o m p u t e r E n g i n e e r i n g &I n f o r m a t i o n T e c h n o l o g y R e s e a r c h ( I J C E I T R )

Academic Research Online Publisher Sdn. Bhd. is aninternational publisher of a series of fast-track, peer-reviewed, open access international journals and bookscovering a wide range of academic disciplines. It aims toprovide fast peer review process for all submittedmanuscripts. The editorial model of AROPUB journalsaims to ensure that only manuscripts that are bothrigorous and provide a useful contribution to their field ofresearch are accepted for publication. Every journal iscollaboratively run by relatively large, internationalexperts.

Ijmsi Vol 1 Isuue 1 2013

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