effect of 50 mev li3+ ion irradiation on mechanical characteristics of pure and ga–in substituted...

Nuclear Instruments and Methods in Physics Research B 222 (2004) 175–186

www.elsevier.com/locate/nimb

Effect of 50 MeV Li3þ ion irradiation onmechanical characteristics of pure and Ga–In

substituted M-type strontium hexaferrite

Balwinder Kaur a, Monita Bhat a, F. Licci b, Ravi Kumar c,P.N. Kotru a, K.K. Bamzai a,*

a Crystal Growth and Materials Research Laboratory, Department of Physics and Electronics,

University of Jammu, Jammu 180006, Indiab Instituto MASPEC-CNR, Via Chiavari 18/A, 43100 Parma, Italy

c Nuclear Science Centre, New Delhi 110067, India

Received 25 September 2003

Abstract

The 50 MeV Li3þ ion irradiation induced modification on mechanical characteristics of flux grown strontium

hexaferrite crystals of the type SrGaxInyFe12�ðxþyÞO19 (where x ¼ 0, 5, 7, 9 and y ¼ 0, 0.8, 1.3, 1.0) have been studied.

Mechanical characteristics including Vicker’s microhardness, density, fracture mechanics, crack propagation, brittle-

ness index, yield strength of the crystals are assessed. Variation of microhardness with load is explained by using Hays

and Kendall’s law with the concept of Newtonian resultant pressure. The decrease in Vickers microhardness values of

irradiated crystals is explained because of amorphization in the material. The cracks developed are classified into

palmqvist and median types. Variation of load independent Hv and density with Ga–In concentration are discussed.

The average values of fracture toughness (Kc), brittleness index (Bi) and yield strength (ry) are also determined.

� 2004 Elsevier B.V. All rights reserved.

PACS: 61.80.Jh; 46.50.+a; 62.20.Mk

Keywords: Irradiation; Microhardness; Hexagonal ferrite; Crack propagation

1. Introduction

Hexaferrites find wide technological applica-

tions in millimeter wave frequency devices, mag-

netic memories, high-density magnetic recordingmedium, etc. [1–4]. M-type compounds have a

* Corresponding author. Tel./fax: +91-191-2453079.

E-mail address: [email protected] (K.K. Bamzai).

0168-583X/$ - see front matter � 2004 Elsevier B.V. All rights reser

doi:10.1016/j.nimb.2004.01.222

general formula MeFe12O19 or MeOÆ6Fe2O3, Me

being either barium or strontium, exhibit a hex-

agonal symmetry, C6/mmc with two formula units

per unit cell [5].

Hexaferrites with the magnetoplumbite or re-lated structures seem most promising because of

their strong magnetic anisotropy [6,7]. The cell

parameters for pure SrFe12O19 are a ¼ 5:883 �A and

c ¼ 23:046 �A [8]. The lattice parameters of substi-

tuted compositions and their Curie temperature are

ved.

mail to: [email protected]

176 B. Kaur et al. / Nucl. Instr. and Meth. in Phys. Res. B 222 (2004) 175–186

reported by Rinaldi and Licci [1]. The low sym-

metry of the structure strongly affects the magnetic

properties of this class of ferromagnetic oxides; in

fact all of them have a large magnetocrystallineanisotropy, partially due to the dipole–dipole

interaction and partially due to the spin orbit

coupling and crystalline field effects [9]. This kind

of application requires high quality single crystals.

Hexagonal hard ferrites, the prototype of which

is represented by SrFe12O19 and BaFe12O19 are also

considered to be the most promising particulate

media for perpendicular recording due to theirchemical, morphological and magnetic character-

istics such as mm-devices, master tapes, magnetic

heads and several others [10]. For these applica-

tions, the hardness or mechanical properties of

these materials should be known. The hardness of

ferrites with respect to breakage depends upon its

resistance to the expansion of cracks, and so the

study on propagation of cracks is of great signifi-cance.

Only a few studies have been reported dealing

with the effects of additives on mechanical prop-

erties in ferrites. It has been reported that addition

of impurity oxides to barium hexaferrite [11] and

strontium hexaferrite [12] can improve their

strength. In both cases, the improved mechanical

properties are related to changes in microstructuresuch as grain size, porosity, absence of flaws, etc.

Gray and Routile [13] observed that the magnetic

properties of strontium ferrites deteriorate on the

addition of B2O3. However, little is known about

the hard magnetic properties of substituted Sr-

ferrite particles. Kohmoto [14] studied the effect of

substitution for Fe in SrFe12O19 particles to obtain

high coercive forces. The growth and character-ization of Mn, Ti substituted hexaferrite crystals

were reported by Licci et al. [15], whereas char-

acterization like X-ray topography and etching of

Ga/In substituted were reported by Raina et al.

[16–18]. Turilli and Licci [19] reported the substi-

tutional effects induced by Bi and Co on magnetic

properties of SrFe12O19. Among the properties of

the materials that affect microhardness, the mainones are its process of growth/preparation, chem-

ical inhomogeneity, anisotropy of the specimen

influence of grain boundaries, defects and so on.

All these factors are reduced greatly in case of a

single crystal grain under controlled conditions.

The information obtained regarding mechanical

hardness/strength on a single crystal is very much

more reliable than that obtained on polycrystallineform [20].

It is well known that irradiation of solids with

energetic particle beams leads to creation of wide

variety of defect states [21]. Swift heavy ions,

which are in the range of MeV under different

conditions, can produce additional defects, create

phase transformations and give rise to anisotropic

growth to some materials. During the last twodecades, the swift heavy ions (SHI) irradiation in

magnetic oxides and ferrites have been studied to

understand the damaged structure and the modi-

fications on their physical properties [22–26].

During the irradiation, damage is produced in the

near surface region of the substrate leading to

stress and amorphization in structures causing

cracking, delamination, anomalous diffusion ofdopants and void formation [27,28]. The nature of

damaged structures depends upon the electronic

energy loss (Se) in these materials. It is well known

that to generate amorphization, certain threshold

value of electronic energy loss (Seth) is required.

If the Se is less than the Seth, then only the

point/clusters of defects will be generated in the

materials [25]. The study of radiation effects onmechanical characteristics of these materials is

relatively less developed field. For the present case,

we irradiated pure and substituted Sr-hexaferrite

with 50 MeV Li3þ ion, which can generate only the

point/clusters of defects. To the best of author’s

knowledge, there is no work reported on irradi-

ated pure and substituted strontium hexaferrite.

The present paper reports a detailed study onmechanical characteristics of unirradiated (UIR)

and irradiated (IR) pure and substituted Sr-hexa-

ferrite single crystal with the aim of investigating

the effect of irradiation on microhardness, fracture

toughness, brittleness index and yield strength of

these materials.

2. Experimental techniques

Single crystals of the composition SrGaxIny-

Fe12�ðxþyÞO19 (x ¼ 0, 5, 7, 9; y ¼ 0, 0.8, 1.3, 1.0)

B. Kaur et al. / Nucl. Instr. and Meth. in Phys. Res. B 222 (2004) 175–186 177

were grown using a flux technique by slow cooling

(5–7.8 �C/h) of the supersaturated high tempera-

ture solution (1350 �C for 24 h) in platinum cru-

cible using 70% molar concentrations of ferritecomposition (SrCO3, Ga2O3, In2O3, Fe2O3) and

30% flux (Bi2O3) [1]. Single crystals of pure and

substituted Sr-hexaferrites were irradiated with 50

MeV Li3þ ion with different fluence rates ranging

from 1 · 1012, 1 · 1013, 5 · 1013 and 1 · 1014 ions/

cm2 using 15 UD Pelletron Accelerator at Nuclear

Science Centre, New Delhi. The range of 50 MeV

Li3þ ion was calculated using TRIM (transport ofion in materials) calculations [29]. The range for

pure Sr-hexaferrite and substituted Ga5In0:8,

Ga7In1:3 and Ga9In1 comes out to be 0.159, 0.151,

0.148 and 0.150 mm, respectively. It was ensured

from TRIM calculations that the thickness of the

samples are comparable with the range of the ions.

The selected smooth cleavage surface of (0 0 0 1)

plane was subjected to indentation tests on bothunirradiated and irradiated crystals. On having

confirmed that hardness is independent of time of

indentation, loads ranging from 0.098 N to 0.98 N

were used for indentation for 10 s in all cases. This

indentation is done by using Vicker’s microhard-

ness tester (mhp-100) equipped with diamond in-

denter attached to Optical microscope Neophot-2

of Carl Zeiss, Germany. The distance betweenconsecutive indentations was kept more than five

times the diagonal length of the indentation mark

to avoid the surface effects. Precautions were taken

Table 1

Data on microhardness measurements and analysis for unirradiated (U

compositions of Ga–In substituted strontium hexaferrite

Sample �nk �nh

Panel A

SrFe12O19 1.78± 0.12 1.92± 0.17

SrGa5In0:8Fe6:2O19 1.75± 0.12 1.91± 0.17

SrGa7In1:3Fe3:7O19 1.72± 0.12 1.90± 0.17

SrGa9In1Fe2O19 1.70± 0.12 1.89± 0.18

Panel B

SrFe12019 1.80± 0.12 1.92± 0.16

SrGa5In0:8Fe6:2O19 1.77± 0.12 1.91± 0.17

SrGa7In1:3Fe3:7O19 1.72± 0.12 1.89± 0.17

SrGa9In1Fe2O19 1.70± 0.12 1.88± 0.17

�nk represents the value of n on application of Kick’s law (P ¼ K1dn)�nh represents the value of n on application of Hays and Kendall’s la

to ensure that the axis of indenter was at right

angle to the plane of crystals. At least five inden-

tations were done for each load on each sample.

Diagonal lengths of these marks were measuredusing filar micrometer eye piece at a magnification

of ·500 and averages of these diagonal lengths

were taken. The microhardness value was calcu-

lated using the equation [30,31]

Hv ¼ 2 sin 68�P=d2 ¼ 1:8544P=d2 N=m2; ð1Þ

where Hv is the Vicker’s hardness number, P is the

applied load and d is the average diagonal length

of indentation mark.

The error on Hv is calculated by using the for-mula

DHv ¼ 1:8544½ð1=yDP Þ2 þ P 2=y4ðDyÞ2�1=2; ð2Þ

where y ¼ d2 and Dy ¼ 2dDd; DP , Dy and Dd being

errors in P , y and d, respectively.A programme in Fortran 77 language using

method of least square was made and run on

computer to calculate the value of various

parameters as listed in Table 1.

For crack measurements, only well-defined

cracks developed during indentation were consid-ered and for a particular indentation mark, aver-

age crack length of all such cracks was taken. The

crack length was measured from the center of

indentation mark up to one tip of the crack.

Fracture toughness (Kc), and brittleness index (Bi)

IR) (Panel A) and irradiated (IR) (Panel B) pure and different

K1 (MN/m2) K2 (MN/m2) W (N)

7465.34 4110.64 0.031

9328.67 4868.07 0.034

11,151.67 5477.47 0.039

12,989.12 6043.19 0.043

6483.35 3696.09 0.029

7564.14 4046.06 0.033

9226.98 4364.08 0.041

10,322.62 4567.75 0.045

.

w (P �W ¼ K1dn).


and yield strength (ry) were determined using the

relevant expressions.

Fig. 2. A plot showing Vickers microhardness versus applied

load for unirradiated and irradiated pure and substituted Sr-

hexaferrite.

3. Results and discussion

Experiments were performed on irradiated (IR)

and unirradiated (UIR) single crystals of both

pure and Ga–In substituted strontium hexaferrite

under similar conditions. Following observations

were made on the mechanical behaviour of the M-

type hexaferrite under consideration.

3.1. Load dependence of hardness

The load dependence of Hv has been extensively

investigated and reported [32–37]. From the re-

ports one can classify the materials on the basis of

microhardness characteristics as follows:

ii(i) Hv independent of load,

i(ii) Hv increases with increasing load,

(iii) Hv decreases with increasing load,

(iv) Hv increases in the low load region and de-

creases in the high load region,

i(v) Hv shows complex dependence on load.

It is interesting to see how pure and Ga–Insubstituted strontium hexaferrite responds to

indentation.

Fig. 1 is the representative photomicrograph of

indentation impression on (0 0 0 1) basal plane at

an applied load of 0.98 N for (a) pure SrFe12O19

and (b) highly substituted SrGa9In1Fe2O19. With

the increase in the value of applied load, it can be

observed that size of indentation mark increases.

Fig. 1. Photomicrograph showing indentation mark at a load

of 0.98 N for (a) SrFe12O19 and (b) SrGa9In1Fe2O19.

Fig. 2 is a graph showing the variation of hardness

number with the applied load. For pure Sr-hexa-

ferrite (UIR), the value ranges from (11,358.2 to

7814.2 MN/m2) and for highly substituted Sr-

hexaferrite, the value ranges from (20,192.3 to

11,630.7 MN/m2) for loads ranging from 0.098 N

to 0.98 N, respectively. Whereas for irradiated(IR) the value ranges from 10,061.24 to 7000.09

MN/m2 for pure strontium hexaferrite and

14,219.27 to 8733.692 MN/m2 for highly substi-

tuted strontium hexaferrite in the load ranging

from 0.098 N to 0.98 N, respectively. Fig. 2 clearly

shows decrease in the value of microhardness for

irradiated samples and this decrease is attributed

to certain types of amorphization occurring in thematerial. Tagomori and Iwase [38] and Kuramoto

Jr. et al. [39] associate the decrease in enamel mi-

crohardness to the presence of deep cracks and to

surface fragility for laser irradiated enamel. The

graph of Fig. 2 shows that microhardness value

decreases non-linearly as the applied load increases

until about 0.588 N of applied load, thereafter it

almost attains saturation for both UIR and IR

Fig. 3. A plot showing log P versus log d for unirradiated and

irradiated pure and substituted Sr-hexaferrite.

Fig. 4. A plot showing d2 versus dn for unirradiated and irra-

diated pure and substituted Sr-hexaferrite.


crystals. This type of behaviour can be qualita-

tively explained on the basis of depth of penetra-

tion of the indenter [40–42]. This explanation is

also favoured by Brookes [43] who associated thehardness increase at low loads with the early stages

of plastic deformation. Since indenter penetrates

only surface layers at lower loads, the effect is

more pronounced at these loads. However, with

the increase in the depth of penetration, the effect

of inner layers becomes more and more prominent

and ultimately leading to saturation in the values

of hardness [43].

3.1.1. Application of Hays and Kendall’s law

This type of non-linear behaviour is explained

by Hays and Kendall’s law [44], which is a modi-

fication of Kick’s law [45]. According to Kick’s

law

P ¼ K1dn; ð3Þwhere K1 is the standard hardness constant and nis Meyer’s index, which is proposed to be equal to

2. However, in pure and substituted strontium

hexaferrite crystals of both UIR and IR, the value

of n was found to be less than 2.

For the materials which do not show n ¼ 2,

Hays and Kendall’s law is applied which is givenas

P � W ¼ K2d2; ð4Þwhere W is sample resistance pressure and repre-

sents the minimum applied load that causes an

indentation, K2 is a constant and n ¼ 2 is the

logarithmic index.

From (4) we have

W ¼ P � K2d2:

Substituting the value of (3) in above equation. We

have

W ¼ K1dn � K2d2

or

dn ¼ K2=K1d2 þ W =K1: ð5Þ

A graph of log P versus log d is shown in Fig. 3.

From its slope, n and K1 is calculated. K2 and W iscalculated from a graph between dn versus d2 as

shown in Fig. 4. The values of these constants have

Table 2

Values of constant K determined for substituted strontium

hexaferrite crystals

Sample x (number of

Fe atoms

substituted)

DHv

(MN/m2)

K(MN/m2)

SrGa5In0:8Fe6:2O19 5.8 1415.34 39.35

SrGa7In1:3Fe3:7O19 8.3 1550.41 50.47

SrGa9In1Fe2O19 10 1668.07 83.40


been determined by using method of least square

fitting using a software program in Fortran lan-

guage. A plot of logðP � W Þ versus log d as shown

in Fig. 5 yields the value of n ffi 2 thereby sug-gesting the validity of the theory involving concept

of resistance pressure (W ) as proposed by Hays

and Kendall. The data on n, K1, K2 and W thus

determined for unirradiated and irradiated is given

in Table 1.

The application of Hays and Kendall’s law

leads us to a modified formula of Eq. (1) which

gives load independent values of Hv:

Hv ¼ 1:8544ðP � W Þ=d2 ð6Þor

Hv ¼ 1:8544� K2: ð7Þ

3.2. Effect of substitution

The effect of substitution on hardness followsthe equation [46,47]

Fig. 5. A plot showing logðP � W Þ versus log d for unirradiated

and irradiated pure and substituted Sr-hexaferrite.

DHv ¼ Kxð12� xÞ; ð8Þ

where DHv is the deviation of the measured hard-

ness and K is a constant.

The value of K is obtained by fitting the

experimental data in Eq. (8). In case of substituted

strontium hexaferrite, the value of K comes out to

be 39.35, 50.47 and 83.40 for SrGa5In0:8Fe6:2O19,

SrGa7In1:3Fe3:7O19 and SrGa9In1Fe2O19, respec-

tively. The value of K (as given in Table 2) in-creases with the increase in substitution and is a

measure of maximum hardness. This value of K is

in agreement with the constant K1 and K2 (stan-

dard hardness constant) calculated on application

of Hays and Kendall’s law. Shrivastava [48] con-

sidered the effect of the presence of substituted

ions on the dislocation mobility and on the hard-

ness.

3.3. Effect of tetragonality and density

Fig. 6 shows the variation of crystal tetrago-nality as a function of substitution. With increase

in Ga+ In content, the crystal tetragonality de-

creases because of shrinkage of lattice parameters

along the c-axis. The density of the crystals is

calculated by the formula [49]

q ¼ ZM=N0V ;

where Z is the number of molecules in a unit cell (6

in case of hexagonal unit cell), N0 is Avogadro’s

number (6.02 · 1023 atoms/mol), M is the compo-

sition weight and V is the volume of the unit cell

and is given by the formula (for regular hexagon)

V ¼ 331=2a2c=2;

where ‘a’ and ‘c’ are the cell parameters in �A.

Fig. 6. A curve showing effect of Ga–In substitution on crystal

tetragonality and cell parameters.

Fig. 7. A curve showing effect of Ga–In substitution on density

and load independent hardness.


The X-ray density of these crystals was found to

increase with the substitution till Ga–In concen-

tration becomes 8.3, thereafter, it almost remains

the same (Fig. 7). This is explained on the basis ofionic radii where Fe is replaced by Ga–In, the ionic

radii for Fe in case of pure SrFe12O19 is 7.68 �Awhereas for substituted Ga5In0:8Fe6:2, Ga7In1:3-

Fe3:7 and Ga9In1Fe2 are 7.716, 7.761 and 7.67 �A,

respectively. As the ionic radius for highly substi-

tuted is comparable with pure strontium hexafer-

rite, so there is saturation in the density curve after

concentration of Ga–In gets 8.3. Table 3 givescombined data of the density of pure and substi-

tuted Sr-hexaferrite, the number of Fe atoms

substituted and cell parameter of each composi-

Table 3

Data shows number of Fe atoms substituted, their cell parameters an

Sample Hv (load

indepen-

dent)

(MN/m2)

Number of Fe atoms substituted

(Ga+ In)

Ga In x

SrFe12O19 7622.8 0 0 0

SrGa5In0:8Fe6:2O19 9027.4 5 0.8 5.8

SrGa7In1:3Fe3:7O19 10,157 7 1.3 8.3

SrGa9In1Fe2O19 11,206 9 1 10

tion. Fig. 7 also shows the increase in load inde-

pendent values of Hv with the number of Fe atoms

substituted in the composition.

3.4. General crack propagation

Fig. 8 shows the variation of crack length (lm)

versus applied load for unirradiated and irradiated

pure and substituted strontium hexaferrite. From

this, we observe that crack length shows linear

increase with increase in load in case of unirradi-

ated and irradiated crystals of pure as well as

substituted Sr-hexaferrite. The rate of increase in

crack length per unit increase in load is muchhigher for unirradiated SrFe12O19 (i.e. higher

concentration of Fe as against Ga and In),

whereas the rate of increase for irradiated pure and

d density of pure and substituted Sr-hexaferrite

Cell

parameter

‘c’ (�A)

Cell

parameter

‘a’ (�A)

c=a Volume,

V · 10�24

(cm3)

Density,

D (g/cm3)

23.05 5.883 3.918 2069.81 5.11

22.93 5.884 3.897 2060.09 5.698

22.88 5.888 3.885 2058.76 5.97

22.98 5.924 3.879 2092.39 5.93

Fig. 8. A curve showing effect of load on crack length for

unirradiated and irradiated pure and substituted Sr-hexaferrite.

Fig. 9. Indentation mark on SrGa9In1Fe2O19 at a load of 0.294

N for (a) unirradiated (UIR) and (b) irradiated (IR).

Fig. 10. Indentation mark on SrGa9In1Fe2O19 at a load of

0.882 N for (a) unirradiated (UIR) and (b) irradiated (IR).


substituted strontium hexaferrite is almost uni-form. The crack length increases after irradiation

as is clearly seen in Figs. 9 and 10, thereby con-

firming the decrease in microhardness due to the

presence of deep cracks and surface fragility of the

irradiated samples [38].

3.5. Fracture toughness

The term toughness may be defined as the rel-

ative degree of resistance to impact without frac-

ture; the property of a material which enable it to

absorb energy while being stressed above its elastic

limit but without being fractured. According toPonton and Rawling [50] there are two modeling

approaches to the crack systems, which can de-

velop in a material as a result of indentation. These

are

i(i) radial-median or ‘‘half penny’’ cracks, and

(ii) palmqvist cracks.

These cracks are described schematically in the

literature [42,50]. Calculations of fracture tough-

ness depend on the nature of cracks exhibited by

the crystal [50]. The fracture mechanics in the

indentation process have provided an equilibrium

relation [51] for a well-developed crack extending

under center loading conditions. The resistance to

the fracture indicates the toughness of a materialand the fracture toughness Kc determines how

much fracture stress is applied under uniform

loading. Transition from palmqvist to median

cracks occur at a well-defined value of c=a [52], ‘c’being the crack length measured from the centre of

indentation mark to the crack end and ‘a’ is the

half-diagonal length of the indentation mark.

For c=aP 2:5, the cracks formed around theindentation take the form of median cracks and

fracture toughness is calculated using the relation

[50,53]

Kc ¼ kP=c3=2; ð9Þwhere P is applied load in Newton, k is a constant

and k ¼ 1=7 for Vicker’s indenter.

For c=a < 2:5, the cracks formed during

indentation have the configuration of palmqvist


cracks and fracture toughness may be calculated

using the relation [50]

Kc ¼ kP=al1=2; ð10Þwhere l ¼ c� a is the mean palmqvist crack

length.In case of unirradiated pure and substituted

strontium hexaferrite the ratio c=a < 2:5 and the

cracks developed are palmqvist cracks. Thus Eq.

(10) is used to calculate the fracture toughness

(Kc). However, in case of irradiated pure and

substituted strontium hexaferrite the ratio

c=aP 2:5 and the cracks developed are median

cracks. Thus Eq. (9) is used to calculate the frac-ture toughness for median types of cracks. Tables

4 (Panels A and B) and 5 (Panels A and B) show

the details regarding crack length, nature of

cracks, fracture toughness for the crystals under

investigation. Fig. 11 shows the graph of fracture

toughness versus load in case of UIR and IR

crystals of pure and substituted Sr-hexaferrite. As

is clear from the graph, the values of fracture

Table 4

Values of half-diagonal length, crack length and nature of crack for u

and substituted strontium hexaferrite crystals

Load P(N)

a (lm) c

Ga0In0 Ga5In0:8 Ga7In1:3 Ga9In1 G

Panel A

0.098 2 1.75 1.625 1.5 –

0.196 3 2.6875 2.5 2.312 –

0.294 3.875 3.5 3.25 3.062

0.392 4.625 4.25 3.938 3.712

0.49 5.25 4.825 4.5 4.288 1

0.588 5.812 5.325 5 4.775 1

0.686 6.375 5.812 5.5 5.188 1

0.784 6.75 6.25 5.875 5.575 1

0.882 7.25 6.625 6.25 5.938 1

0.98 7.625 7 6.562 6.25 1

Panel B

0.098 2 2 1.875 1.788 –

0.196 3.1875 3.0375 2.875 2.751 –

0.294 4.1 3.906 3.675 3.552 –

0.392 4.8325 4.625 4.365 4.25 –

0.49 5.526 5.254 5.004 4.865 1

0.588 6.152 5.838 5.566 5.405 1

0.686 6.66 6.394 6.152 5.931 1

0.784 7.15 6.869 6.578 6.394 1

0.882 7.612 7.282 7.006 6.84 2

0.98 8.056 7.676 7.375 7.212 2

toughness considerably decreases after irradiation

because of increase in the crack length due to

amorphization.

3.6. Brittleness index

The property of breaking without perceptible

warning or without visible deformation is mea-

sured by brittleness index. It is an important

property that affects the mechanical behaviour of

a material and gives an idea about the fracture

induced in a material without any appreciabledeformation. The mathematical value of brittle-

ness index, Bi, can be calculated by using the

relation [52]

Bi ¼ Hv=Kc: ð11ÞFig. 12 shows the variation of brittleness index

versus load (N) for both UIR and IR crystals.From this curve we observe that brittleness index

for all compositions except Ga9In1 (containing

least Fe) composition decreases with increase in

nirradiated (UIR) (Panel A) and irradiated (IR) (Panel B) pure

(lm) Nature of

cracka0In0 Ga5In0:8 Ga7In1:3 Ga9In1

– – – Palmqvist

– 3.722 – Palmqvist

7.25 5.13 4.98 – Palmqvist

9.14 6.34 6.165 – Palmqvist

0.69 7.4 7.137 – Palmqvist

2.42 8.36 8.15 – Palmqvist

3.99 9.11 8.875 6.71 Palmqvist

5.27 10.16 9.875 7.4 Palmqvist

6.7 11 10.74 8.056 Palmqvist

8.05 11.89 11.44 8.67 Palmqvist

– 6.8 – Median

– 8.2 7 Median

– 9.7 8.9 Median

– 11.3 10.8 Median

4.4 – 12.9 12.2 Median

6.1 – 14.6 13.7 Median

7.5 – 16.25 15.19 Median

9.3 – 17.8 16.94 Median

1.3 – 19.3 18.56 Median

3.3 – 21.3 19.9 Median

Table 5

Values of fracture toughness, brittleness index and yield strength for unirradiated (UIR) (Panel A) and irradiated (IR) (Panel B) pure

and substituted strontium hexaferrite crystals

Load

P (N)

Kc � 106 (N/m3=2) Bi (m�1=2) ry (MN/m2)

Ga0In0 Ga5In0:8 Ga7In1:3 Ga9In1 Ga0In0 Ga5In0:8 Ga7In1:3 Ga9In1 Ga0In0 Ga5In0:8 Ga7In1:3 Ga9In1

Panel A

0.098 – – – – – – – – 3786 4945 5735 6731

0.196 – – 10.13 – – – 1435 – 3365 4194 4846 5664

0.294 5.898 9.395 9.82 – 1539 1184 1314 – 3026 3709 4301 4844

0.392 5.696 9.111 9.53 – 1492 1104 1230 – 2832 3354 3907 4395

0.49 5.714 9.037 9.58 – 1442 1080 1171 – 2747 3253 3739 4119

0.588 5.62 9.051 9.46 – 1436 1062 1153 – 2690 3204 3635 3985

0.686 5.569 9.281 9.7 15.3 1405 1014 1084 772.4 2608 3138 3504 3939

0.784 5.682 9.059 9.53 14.87 1404 1027 1105 786.4 2659 3102 3510 3898

0.882 5.651 9.089 9.51 14.57 1377 1025 1101 796.1 2593 3105 3489 3866

0.98 5.684 9.041 9.66 14.39 1375 1026 1092 808.3 2605 3091 3516 3877

Panel B

0.098 – – 0.79 – – – 16,358 – 3354 3786 4308 4740

0.196 – – 1.19 1.51 – – 9238 7950 2981 3283 3664 4001

0.294 – – 1.39 1.58 – – 7260 6835 2703 2977 3364 3600

0.392 – – 1.47 1.58 – – 6488 6368 2533 2832 3179 3354

0.49 1.28 – 1.51 1.64 5670 – 6009 5852 2420 2743 3024 3199

0.588 1.30 – 1.51 1.66 5540 – 5827 5621 2400 2667 2933 3110

0.686 1.34 – 1.5 1.66 5275 – 5601 5446 2353 2593 2801 3013

0.784 1.32 – 1.49 1.61 5347 – 5638 5522 2353 2568 2800 2964

0.882 1.28 – 1.49 1.57 5507 – 5591 5567 2352 2570 2777 2913

0.98 1.24 – 1.42 1.58 5626 – 5882 5528 2333 2570 2784 2911

Fig. 11. Variation of fracture toughness with load for unirra-

diated and irradiated pure and substituted Sr-hexaferrite.

Fig. 12. Brittleness index versus load for unirradiated and

irradiated pure and substituted Sr-hexaferrite.



load but has tendency to saturate at higher load

(>0.9) whereas Bi for Ga9In1 remains almost sat-

urated at load >0.6 N. In case of irradiated crys-

tals, the brittleness index shows remarkableincrease in its values and decreases with increasing

load.

According to published scale for estimating the

brittleness number of crystals, the cracks obtained

around any single indentation gives a comparative

measure of material brittleness [54]. Each inden-

tation impression can be characterized by one of

the five standards of brittleness as reported in theliterature [55].

3.7. Yield strength

From hardness value, the yield strength ry can

be calculated [56]. For Meyer’s index n > 2

ry ¼ Hv=2:9½1� ðn� 2Þ�

� f12:5ðn� 2Þ=1� ðn� 2Þgn�2: ð12Þ

If n < 2, then this equation is reduced to ry ¼ Hv=3[57]. In the present case, n being less than 2, the

equation ry ¼ Hv=3 is applied.

The values of fracture toughness Kc, brittleness

index Bi and yield strength ry for pure and

substituted SrFe12O19 in case of UIR and IRcrystals are compiled and is shown in Table 5

(Panels A and B).

4. Conclusions

The following broad conclusions can be drawn

from the above observations.The 50 MeV Li3þ ion irradiation produces de-

fects in the material and also creates amorphiza-

tion due to which the microhardness decreases as

compared to unirradiated crystals. Irrespective of

whether the material is irradiated or not, the mi-

crohardness decreases non-linearly up to 0.588 N

and thereafter it attains saturation. This non-linear

behaviour is explained on the basis of Hays andKendall’s law. Effect of Ga–In substitution in pure

SrFe12O19 increases the microhardness which fol-

lows the law DHv ¼ Kxð12� xÞ, where K is a

constant. The X-ray densities of unirradiated

crystals increases whereas the crystal tetragonality

decreases with increase in Ga–In substitution.

Cracks get initiated at a load of 0.294 N in pure

and substituted Sr-hexaferrite except for highly

substituted ones (SrGa9In1Fe2O19) in which cracksget initiated at 0.68 N and show linear increase

with load. Crack length increases in case of irra-

diated crystals due to amorphization. The irradi-

ation also affects the type of crack system. The

median type of crack system develops in irradiated

crystals whereas palmqvist crack system develops

in unirradiated crystals.

Acknowledgements

One of the authors B.K. is thankful to the

Nuclear Science Centre (NSC), New Delhi for

awarding project fellowship. This work is funded

by NSC, New Delhi under UFUP scheme no.

30312. This work is also a part of collaborativeprogramme between MASPEC, Italy and the

Crystal Growth and Materials Research Group,

Department of Physics, University of Jammu.

References

[1] S. Rinaldi, F. Licci, IEEE Trans. Magn. MAG-20 (5)

(1984) 1267.

[2] G. Turilli, F. Licci, S. Rinaldi, J. Magn. Magn. Mater. 59

(1986) 127.

[3] O. Kubo, T. Ido, H. Yokohama, IEEE Trans. Magn. 18

(1982) 1122.

[4] K. Haneda, A.H. Morrish, IEEE Trans. Magn. 25 (1989).

[5] P. Batti, Ceramurgia (Colloquio Nazionale Sugli Ossidi

Ferrimagnetici Esagonali Parma, 19–20 Giugno 1975)

Anno VI (1) (1976) 11.

[6] J. Nicolas, in: E.P. Wohlfarth (Ed.), Ferromagnetic Mate-

rials, North Holland, Amsterdam, 1980.

[7] A.H. Eschenfelder, Magnetic Bubble Technology, Springer

Verlag, Berlin, 1980.

[8] F. Licci, S. Rinaldi, T. Besagni, Mater. Lett. 1 (5) (1983)

163.

[9] G. Asti, S. Rinaldi, A.I.P. Conf. Proc. 34 (1976) 214.

[10] D. Speliotis, IEEE Trans. Magn. MAG-23 (1987) 25.

[11] H.E. Schuetz, H.W. Hennicke, Ber. Dtsch. Keram. Ges. 55

(1978) 308;

Chem. Abstr. 89 (1978) 8390q.

[12] D. Wills, J. Masiulanis, J. Can. Ceram. Soc. 45 (1976) 15.

[13] T.J. Gray, R.J. Routil, in: Symposium on Electricity and

Magnetism in Optical Ceramics, London, 13–14 December

1972, p. 91.


[14] O. Kohmoto, T. Tsukada, S. Sato, Jpn. J. Appl. Phys. 29

(1990) 1944.

[15] F. Licci, T. Besagni, J. Labar, Mater. Res. Bull. 22 (1987)

467.

[16] U. Raina, S. Bhat, P.N. Kotru, F. Licci, Mater. Chem.

Phys. 39 (1994) 110.

[17] U. Raina, S. Bhat, P.N. Kotru, P. Franzosi, F. Licci, Cryst.

Res. Technol. 31 (6) (1996) 783.

[18] U. Raina, S. Bhat, P.N. Kotru, F. Licci, J. Mater. Sci. 31

(1996) 3035.

[19] G. Turilli, F. Licci, J. Magn. Magn. Mater. 75 (1988) 111.

[20] N.A. Goryunova, A.S. Borshchevskii, D.N. Tretiakov, in:

R.K. Willardson, A.C. Beer (Eds.), ‘Hardness’, Semicon-

ductors and Semimetals, Academic Press, New York,

London, 1968, p. 3.

[21] M.W. Thompson, Defects and Radiation Damage in

Metals, Cambridge University Press, Cambridge, 1969.

[22] J.M. Costantini, F. Studer, J.C. Peuzin, J. Appl. Phys. 90

(2001) 126.

[23] J.M. Costantini, F. Brisard, J.L. Flament, D. Bourgault, L.

Sinopoli, J.L. Uzureau, Nucl. Instr. and Meth. B 59–60

(1991) 600.

[24] S. Meillon, F. Studer, M. Hervieu, H. Pascard, Nucl. Instr.

and Meth. B 107 (1996) 363.

[25] F. Studer, M. Toulemonde, Nucl. Instr. and Meth. B 65

(1992) 560.

[26] S. Furuno, N. Sasajima, K. Hojou, K. Izui, H. Ostu, T.

Muromura, T. Matsui, Nucl. Instr. and Meth. B 127–128

(1997) 181.

[27] C.A. Volkert, J. Appl. Phys. 70 (1991) 3521.

[28] J.P. Singh, R. Singh, D. Kanjilal, N.C. Mishra, V.

Ganesan, J. Appl. Phys. 87 (2000) 2742.

[29] J.F. Ziegler, J. Manoyan, Nucl. Instr. and Meth. B 35

(1988) 215.

[30] B.W. Mott, Microindentation Hardness Testing, Butter-

worths, London, 1966, p. 9.

[31] J. Dowman, M. Bevis, Colloid Polym. Sci. 255 (1977) 954.

[32] D. Townsend, J.E. Field, J. Mater. Sci. 25 (1990) 1347.

[33] U. Raina, S. Bhat, P.N. Kotru, B.M. Wanklyn, Mater.

Chem. Phys. 34 (1993) 257.

[34] P.N. Kotru, K.K. Raina, S.K. Kachroo, B.M. Wanklyn,

J. Mater. Sci. 19 (1984) 2582.

[35] P.N. Kotru, S. Gupta, S.K. Kachroo, B.M. Wanklyn, J.

Mater. Sci. 20 (1985) 3949.

[36] D.J. Clinton, R. Morell, Mater. Chem. Phys. 17 (1987) 461.

[37] S.R. Vadrabade, Ph.D. Thesis, Nagpur University, 1991.

[38] S. Tagomori, T. Iwase, Caries Res. 29 (1995) 513.

[39] M. Kuramoto Jr., E. Matson, M.L. Turbino, R.A.

Marques, J. Baz. Dent. 12 (1) (2001) 31.

[40] H. Buckle, Metall. Rev. 4 (1950) 13.

[41] J.R. Pandya, L.J. Bhagia, A.J. Shah, Bull. Mater. Sci. 5

(1983) 79.

[42] K.K. Bamzai, P.N. Kotru, B.M. Wanklyn, J. Mater. Sci.

Technol. 16 (4) (2000) 405.

[43] C.A. Brookes, in: Proceedings of the Second International

Conference on Science of Hard Materials (Rhodes), First

Physics Conference Series, Vol. 75, Hilger, Bristol, 1986

(Chapter 3).

[44] C. Hays, E.G. Kendall, Metallography 6 (1973) 275.

[45] F. Kick, Das gesetz der, Proportionalen Widerstande and

Siene Anwendung, Delipzig Felix 1885.

[46] T. Thirmal Rao, D.B. Sirdeshmukh, Cryst. Res. Technol.

26 (1991) K53.

[47] D.B. Sirdeshmukh, T.K. Swamy, P. Geetakrishna, K.G.

Subhadra, Bull. Mater. Sci. 26 (2) (2003) 261.

[48] U.C. Shrivastava, J. Appl. Phys. 51 (1980) 1510.

[49] L.M. Troilo, D. Damjanovic, R.E. Newnham, J. Am.

Ceram. Soc. 77 (3) (1994) 857.

[50] C.B. Ponton, R.D. Rawlings, Br. Ceram. Trans. J. 88

(1989) 83.

[51] B.R. Lawn, D.B. Marshall, J. Am. Ceram. Soc. 62 (1979)

347.

[52] K. Nihara, R. Morena, D.P.H. Hasselman, J. Mater. Sci.

Lett. 1 (1982) 13.

[53] B.R. Lawn, E.R. Fuller, J. Mater. Sci. 9 (1975) 2016.

[54] I.N. Frantsevich, A.N. Pilyankevich, Trans. Seminar on

Heat Resist Mat, No. 5, Ukr SSR, Kiev, 1960, p. 28.

[55] J.H. Westbrook, in: J.H. Westbrook, H. Conard, The

Science of Hardness Testing and its Research Applications,

Pub. Am. Soc. for Metal, Metal Park, OH, 1973, p. 492.

[56] J.P. Cahoon, W.H. Broughton, A.R. Katzuk, Metall.

Trans. 2 (1971) 1979.

[57] R. Wytt, Metals, Ceramica and Polymers, London, 1974

(Chapters 5 and 6).

effect of 50 mev li3+ ion irradiation on mechanical characteristics of pure and ga–in substituted...

Documents