Effect of 50 MeV Li3+ ion irradiation on mechanical characteristics of pure and Ga–In substituted M-type strontium hexaferrite

Nuclear Instruments and Methods in Physics Research B 222 (2004) 175–186 www.elsevier.com/locate/nimb

Effect of 50 MeV Li3þ ion irradiation on mechanical 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, India b 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 SrGax Iny Fe12
ðxþyÞ O19 (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, brittleness 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 applications in millimeter wave frequency devices, magnetic memories, high-density magnetic recording medium, etc. [1–4]. M-type compounds have a

*

Corresponding author. Tel./fax: +91-191-2453079. E-mail address: [email protected] (K.K. Bamzai).

general formula MeFe12 O19 or MeOÆ6Fe2 O3 , Me being either barium or strontium, exhibit a hexagonal symmetry, C6 /mmc with two formula units per unit cell [5]. Hexaferrites with the magnetoplumbite or related structures seem most promising because of their strong magnetic anisotropy [6,7]. The cell  and parameters for pure SrFe12 O19 are a ¼ 5:883 A  [8]. The lattice parameters of substic ¼ 23:046 A tuted compositions and their Curie temperature are

0168-583X/$ - see front matter
2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2004.01.222

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

reported by Rinaldi and Licci [1]. The low symmetry of the structure strongly affects the magnetic properties of this class of ferromagnetic oxides; in fact all of them have a large magnetocrystalline anisotropy, 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 SrFe12 O19 and BaFe12 O19 are also considered to be the most promising particulate media for perpendicular recording due to their chemical, morphological and magnetic characteristics such as mm-devices, master tapes, magnetic heads and several others [10]. For these applications, 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 significance. Only a few studies have been reported dealing with the effects of additives on mechanical properties 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 microstructure such 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 B2 O3 . However, little is known about the hard magnetic properties of substituted Srferrite particles. Kohmoto [14] studied the effect of substitution for Fe in SrFe12 O19 particles to obtain high coercive forces. The growth and characterization of Mn, Ti substituted hexaferrite crystals were reported by Licci et al. [15], whereas characterization like X-ray topography and etching of Ga/In substituted were reported by Raina et al. [16–18]. Turilli and Licci [19] reported the substitutional effects induced by Bi and Co on magnetic properties of SrFe12 O19 . Among the properties of the materials that affect microhardness, the main ones are its process of growth/preparation, chemical 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 polycrystalline form [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 two decades, the swift heavy ions (SHI) irradiation in magnetic oxides and ferrites have been studied to understand the damaged structure and the modifications 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 of dopants 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 on mechanical 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 irradiated pure and substituted strontium hexaferrite. The present paper reports a detailed study on mechanical characteristics of unirradiated (UIR) and irradiated (IR) pure and substituted Sr-hexaferrite 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 SrGax Iny Fe12
ðxþyÞ O19 (x ¼ 0, 5, 7, 9; y ¼ 0, 0.8, 1.3, 1.0)

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were grown using a flux technique by slow cooling (5–7.8 C/h) of the supersaturated high temperature solution (1350 C for 24 h) in platinum crucible using 70% molar concentrations of ferrite composition (SrCO3 , Ga2 O3 , In2 O3 , Fe2 O3 ) and 30% flux (Bi2 O3 ) [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 of ion in materials) calculations [29]. The range for pure Sr-hexaferrite and substituted Ga5 In0:8 , Ga7 In1:3 and Ga9 In1 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 both unirradiated 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 microhardness tester (mhp-100) equipped with diamond indenter attached to Optical microscope Neophot-2 of Carl Zeiss, Germany. The distance between consecutive indentations was kept more than five times the diagonal length of the indentation mark to avoid the surface effects. Precautions were taken

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to ensure that the axis of indenter was at right angle to the plane of crystals. At least five indentations were done for each load on each sample. Diagonal lengths of these marks were measured using filar micrometer eye piece at a magnification of ·500 and averages of these diagonal lengths were taken. The microhardness value was calculated using the equation [30,31] Hv ¼ 2 sin 68P =d 2 ¼ 1:8544 P =d 2 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 formula 2

2 1=2

DHv ¼ 1:8544½ð1=yDP Þ þ P 2 =y 4 ðDyÞ 

;

ð2Þ

where y ¼ d 2 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 considered and for a particular indentation mark, average 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 )

Table 1 Data on microhardness measurements and analysis for unirradiated (UIR) (Panel A) and irradiated (IR) (Panel B) pure and different compositions of Ga–In substituted strontium hexaferrite Sample

 



nk



nh

K1 (MN/m2 )

K2 (MN/m2 )

W (N)

Panel A SrFe12 O19 SrGa5 In0:8 Fe6:2 O19 SrGa7 In1:3 Fe3:7 O19 SrGa9 In1 Fe2 O19

1.78 ± 0.12 1.75 ± 0.12 1.72 ± 0.12 1.70 ± 0.12

1.92 ± 0.17 1.91 ± 0.17 1.90 ± 0.17 1.89 ± 0.18

7465.34 9328.67 11,151.67 12,989.12

4110.64 4868.07 5477.47 6043.19

0.031 0.034 0.039 0.043

Panel B SrFe12 019 SrGa5 In0:8 Fe6:2 O19 SrGa7 In1:3 Fe3:7 O19 SrGa9 In1 Fe2 O19

1.80 ± 0.12 1.77 ± 0.12 1.72 ± 0.12 1.70 ± 0.12

1.92 ± 0.16 1.91 ± 0.17 1.89 ± 0.17 1.88 ± 0.17

6483.35 7564.14 9226.98 10,322.62

3696.09 4046.06 4364.08 4567.75

0.029 0.033 0.041 0.045

nk represents the value of n on application of Kick’s law (P ¼ K1 d n ). nh represents the value of n on application of Hays and Kendall’s law (P
W ¼ K1 d n ).

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and yield strength (ry ) were determined using the relevant expressions.

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 Mtype hexaferrite under consideration. 3.1. Load dependence of hardness The load dependence of Hv has been extensively investigated and reported [32–37]. From the reports one can classify the materials on the basis of microhardness characteristics as follows: ii(i) i(ii) (iii) (iv)

Hv independent of load, Hv increases with increasing load, Hv decreases with increasing load, Hv increases in the low load region and decreases in the high load region, i(v) Hv shows complex dependence on load. It is interesting to see how pure and Ga–In substituted 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 SrFe12 O19 and (b) highly substituted SrGa9 In1 Fe2 O19 . 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) SrFe12 O19 and (b) SrGa9 In1 Fe2 O19 .

Fig. 2. A plot showing Vickers microhardness versus applied load for unirradiated and irradiated pure and substituted Srhexaferrite.

Fig. 2 is a graph showing the variation of hardness number with the applied load. For pure Sr-hexaferrite (UIR), the value ranges from (11,358.2 to 7814.2 MN/m2 ) and for highly substituted Srhexaferrite, 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 substituted 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 the material. Tagomori and Iwase [38] and Kuramoto Jr. et al. [39] associate the decrease in enamel microhardness 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

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

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crystals. This type of behaviour can be qualitatively explained on the basis of depth of penetration of the indenter [40–42]. This explanation is also favoured by Brookes [43] who associated the hardness 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 modification of Kick’s law [45]. According to Kick’s law P ¼ K1 d n ;

ð3Þ

where K1 is the standard hardness constant and n is 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 given as P
W ¼ K2 d 2 ;

Fig. 3. A plot showing log P versus log d for unirradiated and irradiated pure and substituted Sr-hexaferrite.

ð4Þ

where W is sample resistance pressure and represents 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
K2 d 2 : Substituting the value of (3) in above equation. We have W ¼ K1 d n
K2 d 2 or d n ¼ K2 =K1 d 2 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 is calculated from a graph between d n versus d 2 as shown in Fig. 4. The values of these constants have

Fig. 4. A plot showing d 2 versus d n for unirradiated and irradiated pure and substituted Sr-hexaferrite.

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been determined by using method of least square fitting using a software program in Fortran language. A plot of logðP
W Þ versus log d as shown in Fig. 5 yields the value of n ffi 2 thereby suggesting 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=d 2

ð6Þ

or Hv ¼ 1:8544  K2 :

ð7Þ

3.2. Effect of substitution The effect of substitution on hardness follows the equation [46,47]

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 )

SrGa5 In0:8 Fe6:2 O19 SrGa7 In1:3 Fe3:7 O19 SrGa9 In1 Fe2 O19

5.8 8.3 10

1415.34 1550.41 1668.07

39.35 50.47 83.40

DHv ¼ Kxð12
xÞ;

ð8Þ

where DHv is the deviation of the measured hardness 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 SrGa5 In0:8 Fe6:2 O19 , SrGa7 In1:3 Fe3:7 O19 and SrGa9 In1 Fe2 O19 , respectively. The value of K (as given in Table 2) increases 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 (standard hardness constant) calculated on application of Hays and Kendall’s law. Shrivastava [48] considered the effect of the presence of substituted ions on the dislocation mobility and on the hardness. 3.3. Effect of tetragonality and density Fig. 6 shows the variation of crystal tetragonality as a function of substitution. With increase in Ga + In content, the crystal tetragonality decreases because of shrinkage of lattice parameters along the c-axis. The density of the crystals is calculated by the formula [49] q ¼ ZM=N0 V ; 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 composition weight and V is the volume of the unit cell and is given by the formula (for regular hexagon) V ¼ 3 31=2 a2 c=2;

Fig. 5. A plot showing logðP
W Þ versus log d for unirradiated and irradiated pure and substituted Sr-hexaferrite.

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

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Fig. 7. A curve showing effect of Ga–In substitution on density and load independent hardness. Fig. 6. A curve showing effect of Ga–In substitution on crystal tetragonality and cell parameters.

The X-ray density of these crystals was found to increase with the substitution till Ga–In concentration becomes 8.3, thereafter, it almost remains the same (Fig. 7). This is explained on the basis of ionic radii where Fe is replaced by Ga–In, the ionic  radii for Fe in case of pure SrFe12 O19 is 7.68 A whereas for substituted Ga5 In0:8 Fe6:2 , Ga7 In1:3  Fe3:7 and Ga9 In1 Fe2 are 7.716, 7.761 and 7.67 A, respectively. As the ionic radius for highly substituted is comparable with pure strontium hexaferrite, so there is saturation in the density curve after concentration of Ga–In gets 8.3. Table 3 gives combined data of the density of pure and substituted Sr-hexaferrite, the number of Fe atoms substituted and cell parameter of each composi-

tion. Fig. 7 also shows the increase in load independent 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 unirradiated and irradiated crystals of pure as well as substituted Sr-hexaferrite. The rate of increase in crack length per unit increase in load is much higher for unirradiated SrFe12 O19 (i.e. higher concentration of Fe as against Ga and In), whereas the rate of increase for irradiated pure and

Table 3 Data shows number of Fe atoms substituted, their cell parameters and density of pure and substituted Sr-hexaferrite Sample

SrFe12 O19 SrGa5 In0:8 Fe6:2 O19 SrGa7 In1:3 Fe3:7 O19 SrGa9 In1 Fe2 O19

Hv (load independent) (MN/m2 ) 7622.8 9027.4 10,157 11,206

Number of Fe atoms substituted (Ga + In) Ga

In

x

Cell parameter  ‘c’ (A)

0 5 7 9

0 0.8 1.3 1

0 5.8 8.3 10

23.05 22.93 22.88 22.98

Cell parameter  ‘a’ (A)

c=a

Volume, V · 10
24 (cm3 )

Density, D (g/cm3 )

5.883 5.884 5.888 5.924

3.918 3.897 3.885 3.879

2069.81 2060.09 2058.76 2092.39

5.11 5.698 5.97 5.93

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Fig. 10. Indentation mark on SrGa9 In1 Fe2 O19 at a load of 0.882 N for (a) unirradiated (UIR) and (b) irradiated (IR).

ture; the property of a material which enable it to absorb energy while being stressed above its elastic limit but without being fractured. According to Ponton and Rawling [50] there are two modeling approaches to the crack systems, which can develop in a material as a result of indentation. These are

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 SrGa9 In1 Fe2 O19 at a load of 0.294 N for (a) unirradiated (UIR) and (b) irradiated (IR).

substituted strontium hexaferrite is almost uniform. The crack length increases after irradiation as is clearly seen in Figs. 9 and 10, thereby confirming 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 relative degree of resistance to impact without frac-

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 toughness 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 material and 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=a P 2:5, the cracks formed around the indentation take the form of median cracks and fracture toughness is calculated using the relation [50,53] Kc ¼ kP =c3=2 ;

ð9Þ

where 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

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

cracks and fracture toughness may be calculated using the relation [50] Kc ¼ kP =al1=2 ;

ð10Þ

where 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=a P 2:5 and the cracks developed are median cracks. Thus Eq. (9) is used to calculate the fracture 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

183

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 measured 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 appreciable deformation. The mathematical value of brittleness index, Bi , can be calculated by using the relation [52] Bi ¼ Hv =Kc :

ð11Þ

Fig. 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 Ga9 In1 (containing least Fe) composition decreases with increase in

Table 4 Values of half-diagonal length, crack length and nature of crack for unirradiated (UIR) (Panel A) and irradiated (IR) (Panel B) pure and substituted strontium hexaferrite crystals Load P (N)

a (lm)

c (lm)

Nature of crack

Ga0 In0

Ga5 In0:8

Ga7 In1:3

Ga9 In1

Ga0 In0

Ga5 In0:8

Ga7 In1:3

Ga9 In1

Panel A 0.098 0.196 0.294 0.392 0.49 0.588 0.686 0.784 0.882 0.98

2 3 3.875 4.625 5.25 5.812 6.375 6.75 7.25 7.625

1.75 2.6875 3.5 4.25 4.825 5.325 5.812 6.25 6.625 7

1.625 2.5 3.25 3.938 4.5 5 5.5 5.875 6.25 6.562

1.5 2.312 3.062 3.712 4.288 4.775 5.188 5.575 5.938 6.25

– – 7.25 9.14 10.69 12.42 13.99 15.27 16.7 18.05

– – 5.13 6.34 7.4 8.36 9.11 10.16 11 11.89

– 3.722 4.98 6.165 7.137 8.15 8.875 9.875 10.74 11.44

– – – – – – 6.71 7.4 8.056 8.67

Palmqvist Palmqvist Palmqvist Palmqvist Palmqvist Palmqvist Palmqvist Palmqvist Palmqvist Palmqvist

Panel B 0.098 0.196 0.294 0.392 0.49 0.588 0.686 0.784 0.882 0.98

2 3.1875 4.1 4.8325 5.526 6.152 6.66 7.15 7.612 8.056

2 3.0375 3.906 4.625 5.254 5.838 6.394 6.869 7.282 7.676

1.875 2.875 3.675 4.365 5.004 5.566 6.152 6.578 7.006 7.375

1.788 2.751 3.552 4.25 4.865 5.405 5.931 6.394 6.84 7.212

– – – – 14.4 16.1 17.5 19.3 21.3 23.3

– – – – – – – – – –

6.8 8.2 9.7 11.3 12.9 14.6 16.25 17.8 19.3 21.3

– 7 8.9 10.8 12.2 13.7 15.19 16.94 18.56 19.9

Median Median Median Median Median Median Median Median Median Median

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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)

Bi (m
1=2 )

Kc  106 (N/m3=2 ) Ga0 In0

ry (MN/m2 )

Ga5 In0:8

Ga7 In1:3

Ga9 In1

Ga0 In0

Ga5 In0:8

Ga7 In1:3

Ga9 In1

Ga0 In0

Ga5 In0:8

Ga7 In1:3

Ga9 In1

Panel A 0.098 – 0.196 – 0.294 5.898 0.392 5.696 0.49 5.714 0.588 5.62 0.686 5.569 0.784 5.682 0.882 5.651 0.98 5.684

– – 9.395 9.111 9.037 9.051 9.281 9.059 9.089 9.041

– 10.13 9.82 9.53 9.58 9.46 9.7 9.53 9.51 9.66

– – – – – – 15.3 14.87 14.57 14.39

– – 1539 1492 1442 1436 1405 1404 1377 1375

– – 1184 1104 1080 1062 1014 1027 1025 1026

–

– – – – – – 772.4 786.4 796.1 808.3

3786 3365 3026 2832 2747 2690 2608 2659 2593 2605

4945 4194 3709 3354 3253 3204 3138 3102 3105 3091

5735 4846 4301 3907 3739 3635 3504 3510 3489 3516

6731 5664 4844 4395 4119 3985 3939 3898 3866 3877

Panel B 0.098 – 0.196 – 0.294 – 0.392 – 0.49 1.28 0.588 1.30 0.686 1.34 0.784 1.32 0.882 1.28 0.98 1.24

– – – – – – – – – –

0.79 1.19 1.39 1.47 1.51 1.51 1.5 1.49 1.49 1.42

– 1.51 1.58 1.58 1.64 1.66 1.66 1.61 1.57 1.58

– – – – 5670 5540 5275 5347 5507 5626

– – – – – – – – – –

16,358 9238 7260 6488 6009 5827 5601 5638 5591 5882

– 7950 6835 6368 5852 5621 5446 5522 5567 5528

3354 2981 2703 2533 2420 2400 2353 2353 2352 2333

3786 3283 2977 2832 2743 2667 2593 2568 2570 2570

4308 3664 3364 3179 3024 2933 2801 2800 2777 2784

4740 4001 3600 3354 3199 3110 3013 2964 2913 2911

Fig. 11. Variation of fracture toughness with load for unirradiated and irradiated pure and substituted Sr-hexaferrite.

1435 1314 1230 1171 1153 1084 1105 1101 1092

Fig. 12. Brittleness index versus load for unirradiated and irradiated pure and substituted Sr-hexaferrite.

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load but has tendency to saturate at higher load (>0.9) whereas Bi for Ga9 In1 remains almost saturated at load >0.6 N. In case of irradiated crystals, the brittleness index shows remarkable increase 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 indentation impression can be characterized by one of the five standards of brittleness as reported in the literature [55].

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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 (SrGa9 In1 Fe2 O19 ) in which cracks get initiated at 0.68 N and show linear increase with load. Crack length increases in case of irradiated crystals due to amorphization. The irradiation 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 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
2Þg

n
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 SrFe12 O19 in case of UIR and IR crystals 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 defects in the material and also creates amorphization due to which the microhardness decreases as compared to unirradiated crystals. Irrespective of whether the material is irradiated or not, the microhardness decreases non-linearly up to 0.588 N and thereafter it attains saturation. This non-linear behaviour is explained on the basis of Hays and Kendall’s law. Effect of Ga–In substitution in pure SrFe12 O19 increases the microhardness which follows the law DHv ¼ Kxð12
xÞ, where K is a constant. The X-ray densities of unirradiated crystals increases whereas the crystal tetragonality

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 collaborative programme between MASPEC, Italy and the Crystal Growth and Materials Research Group, Department of Physics, University of Jammu.

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