Available at: http://www.ictp.it/~pub_off IC/2006/090

United Nations Educational, Scientific and Cultural Organization and

International Atomic Energy Agency

THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS

STRUCTURAL EVOLUTION AND SURFACE MAGNETISM IN Mg-SUBSTITUTED Li0.5Fe2.5O4 NANOPARTICLES

PREPARED BY BALL MILLING

Hisham M. Widatallah∗ Physics Department, Sultan Qaboos University, PO Box 36, 123 Muscat, Oman

and The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy

and

Abbasher. M. Gismelseed

Physics Department, Sultan Qaboos University, PO Box 36, 123 Muscat, Oman.

MIRAMARE – TRIESTE

December 2006

∗ Regular Associate of ICTP. Corresponding author: hishammw@squ.edu.om

1

Abstract

The structural evolution and magnetic properties of Mg-substituted-Li0.5Fe2.5O4

nanocrystalline particles prepared by ball milling are investigated. The average crystallite size is

found to decrease with increasing milling time approaching ~ 12 nm after 50 h of milling.

Rietveld refinement of the XRD data shows the cores of the nanoparticles and their surfaces to

have different cation distributions. The increase in the average lattice constant with milling time

up to 38 h and its subsequent decrease imply large strains and bond deformation, respectively.

The shifts of infrared spectral bands of the milled samples relative to those of the non-milled one,

suggest a milling-induced cation migration from the octahedral (B) to the tetrahedral (A) sites.

Superparamagnetism is found to be enhanced with increasing milling time. A simple two-sextet

fit for the 78.5 K Mössbauer spectrum of the nanoparticles and their core-to surface ratio, inferred

from XRD Rietveld refinement, enabled the estimation of Fe3+ population at the A- and B-sites in

the surface layers. While the measured magnetization of the nanoparticles reasonably agrees with

that calculated using the Néel’s collinear model it is, nonetheless, suggestive of a thermally-

induced spin reversal and/or a minor canting effect that is more pronounced for the A-sub-lattice.

2

I. INTRODUCTION

The spinel-related lithium ferrite of the composition Li0.5Fe2.5O4 and its cation-substituted

variants are of great importance in microwave and memory core applications owing to

their high Curie temperature, high saturation magnetization and excellent hysteresis loop

properties [1-5]. Li0.5Fe2.5O4 adopts an inverse spinel-related structure in which Li+ and

3/5 of all Fe3+ ions occupy the octahedral B-sites whilst the remaining Fe3+ occupy the

tetrahedral A-sites. The physical properties of the material, as those of other spinel-

related ferrites, are theoretically modelled by the super-exchange ionic interactions JAB,

JAA and JBB and are, therefore, determined by the type and distribution of their constituent

cations over the tetrahedral A- and octahedral B- sites [1-5].

The reduction of the ferrite particle size to the nanometre scale results in unusual

magnetic properties originating form changes in the A- and B-cationic populations

relative to those of the bulk counterparts [6-8]. Structurally, nanoparticles are modelled as

having a core that is isostructural with the bulk and a large volume fraction surface layer

with a different cationic distribution from that of the bulk. Indeed this “core-surface”

notion of a nanoparticle has satisfactorily been used to explain the magnetization

reduction (or enhancement) in spinel ferrite nanoparticles relative to that of the

corresponding bulk [7].

Conventional synthetic routes of spinel ferrite nanoparticles involve the use of

high temperature and include costly and technically-demanding methods such as the

radio-frequency inductively coupled plasma synthesis[8], hydrothermal synthesis [9],

electrochemical synthesis[10,11], coprecipitation [11] and microwave processing [11].

The elevated temperatures used in these methods often result in technological drawbacks,

such as the aggregation and coarsening of the particles or the inevitable precipitation of

impurity phases, whose presence poses a limit on the technological use of the material

[2,7,10]. Challenges of this nature have prompted the search for low-cost, simple and

low-temperature processing routes. An important technique, meeting these requirements,

which is being increasingly used to synthesize inorganic solid nanoparticles is ball

(mechanical) milling [4,6,7,13]. With this technique, nanoparticles can be prepared in

one- or two-step processes or simply via subjecting a bulk ferrite material to milling

[6,7,14].

3

In this work we present a detailed and systematic study of nanocrystalline

particles obtained by milling in air and for different times a pristine Mg-substituted-

Li0.5Fe2.5O4 sample prepared at 600 ºC. In particular we explore the evolution of the

structural and magnetic properties of the milled samples as a function of both milling

time and particle size using x-ray powder diffraction (XRD), Fourier transform infrared

spectroscopy (FT-IR), Mössbauer spectroscopy and magnetic measurements. We will

show how these techniques can be combined to infer the milling-activated magnetic

cation distribution in the surface layers of the nanoparticles and use that to interpret the

significant changes in their observed magnetic properties relative to those of he non-

milled sample..

II. EXPERIMENTAL

Mg-substituted corundum-related α-Fe2O3 prepared hydrothermally as described

elsewhere [15] was mixed in a molar ratio of 5: 1 with Li2CO3 and sintered in air at 600

°C for 12h. This led to the formation of a single-phased Mg-substituted Li0.5Fe2.5O4.

Chemical analysis showed the resulting ferrite to have a compositional formula of

Li0.41Fe2.41Mg0.17O4. This material was then dry-milled in air for 6.5 h, 15 h, 38 h and 50

h time intervals using a Retsch PM400 planetary ball mill with stainless steel vials (250

ml) and balls (20mm) at a milling speed of 200 rpm. The powder-to-ball weight ratio was

fixed at 1: 20. The morphology and particle size of the milled samples were investigated

with a JEOL 1234 transmission electron microscope (TEM). X-ray powder diffraction

(XRD) patterns were recorded with a Siemens D5000 diffractometer using CuKα

radiation. Rietveld refinement of the XRD data was performed using the program

WinProf [16]. Fourier transform infrared (FT-IR) spectra were recorded using KBr

pellets (~1 mg sample per 300 mg KBr) with a Nicollet Impact 400D Spectrometer at a

scan rate of 150 cm-1/min. 57Fe Mössbauer spectra were recorded at 298 K and 80K in

the transmission geometry using a 25 mCi 57Co/Rh γ-ray source. Chemical isomer shifts

are quoted relative to that of α-Fe at 298 K. The temperature dependence of the

magnetization was measured at a heating rate of 4 K/min using a Faraday balance in a

magnetic field of 1.5 T. The temperature was stabilized within 0.5K.

4

III. RESULTS AND DISCUSSION

A-Transmission electron microscopy

The TEM micrographs shown in Fig. 1 illustrate the influence of milling on the

morphology and size of the Mg-substituted Li0.5Fe2.5O4 particles. Fig. 1(a) shows that

most of the non-milled ferrite particles are cubic in shape with an average size of ~0.2

µm. Fig.1(b) shows that milling the material for 6.5 h results in irregular particles with a

broad particle size distribution extending from ~ 40 nm to ~ 0.3 µm. Further

fragmentation and shape irregularity are observed as the milling proceeds. The size

distribution narrows to the 20 nm - 0.2 µm range after 38 h of milling as shown in

Fig.1(c), while some particles start to agglomerate (presumably due their dipolar

magnetic fields). Fig.1(d) shows that after 50 h of milling, a mixture of nearly-spherical

and irregularly-shaped nanoparticles is obtained. The corresponding particle size

distribution is quite narrow, with most of the particles being in the 5 nm - 20 nm range.

An tendency of the nanoparticles to agglomerate forming grains that are 50nm-150 nm in

size is clearly observed.

B- X-ray Powder diffraction

The XRD patterns of the Mg-substituted-Li0.5Fe2.5O4 samples milled for different times

are given in Fig. 2. The XRD pattern of the non-milled sample (0 h) is characterized by

sharp reflection peaks that refine to a single inverse-spinel phase (space group: mFd 3 ).

The absence of superstructure peaks reveals that the Li+ and Fe3+ ions are randomly

distributed over the octahedral B-sites [3,4]. A careful Rietveld refinement of this pattern

has shown the impurity Mg2+ ions to substitute for tetrahedral Fe3+ ions whereas some of

the expelled Fe3+ ions partially replace Li+ ions at the octahedral B-sites [3] Fig. 2 shows

that the single spinel-related phase is preserved in all milled samples, as no new

reflection peaks appear in the XRD patterns. The decrease in the intensities of the peaks

and their broadening with increasing milling time reflect both structural disorder and a

decrease in the crystallite size. Accordingly, the XRD patterns of the milled samples were

Rietveld-refined with two spinel-related phases. One with sharp reflection peaks and a

similar cation distribution to the non-milled sample corresponds to the large particles in

each sample in addition to the nanoparticles’ cores. The second phase having broad

5

reflection peaks is associated with the progressively evolving surface layers of the

nanoparticles. Being aware that the short-range structural order in the nanoparticles

affects the resolving power of diffraction techniques significantly [7], we opted not to

refine the surface phase to a particular cation distribution as we did with that of core. The

intensity ratio for both phases, which is a measure of their relative abundance, varied

from 1: 0 for the non-milled sample to 1: 4 for the sample milled for 50 h suggesting for

the later a surface layer that amounts to ~ 80% of the total volume of the nanoparticle.

The variation of the average crystallite size (D) with milling time is shown in Fig 3. A

very rapid reduction of the crystallite size is observed in the early stages of the milling

process followed by a slow decrease leading to a value of ~12 nm after 50 h which is

almost similar to the average TEM-determined particle size (Fig. 1). Assuming a

spherical shape for these nanoparticles, the corresponding thickness (t) obtained of the

surface layer is ~ 2.5 nm (or 12-15 cationic layers). Fig. 4 shows the variation of the

average lattice constant (a) with milling time. The increase in a with decreasing

crystallite size down to ~15 nm (38 h) may be interpreted in terms of milling-induced

supersaturation of vacancies in the unit cells due to higher energetic configurations as

suggested by Liu et al [17]. This will disturb the cationic arrangement leading to large

strains within the particles that result in the observed lattice expansion [18]. The decrease

in the lattice constant following further milling (Fig. 4) is suggestive of some deformation

of bond angles induced by prolonged milling as proposed elsewhere [19]. Taken together,

these results reflect a different type of cation distribution and crystalline symmetry in the

nanoparticle relative to that of the non-milled material.

C- Fourier transform infrared spectroscopy

Additional information on the milling-induced changes in the crystalline symmetry and

cationic ordering can be obtained from the FT-IR spectra recorded from the Mg-

substituted-Li0.5Fe2.5O4 samples shown in Fig. 5. In spinel ferrites the IR active

vibrational bands around 600 cm-1 are attributed to stretching bonds at the tetrahedral A-

sites whereas those around 400 cm-1 are associated with octahedral sites [20,21]. Pure

Li0.5Fe2.5O4 is known to have active IR bands at 583 cm-1 and 470 cm-1 due to the

tetrahedral Fe3+-O2- and octahedral Li+- O2- groups, respectively [22].

6

For the non-milled Mg-substituted-Li0.5Fe2.5O4, the FT-IR spectrum shows the

tetrahedral band to shift negatively reaching 563 cm-1 and that of the octahedral bond to

shift positively becoming 481 cm-1. Noting that the IR band frequency shifts have an

inverse relation with the change in the ionic bond length [23], these results can easily be

reconciled with XRD results cited above. The substitution of Mg2+ (71 pm) for the

tetrahedrally-coordinated Fe3+ (63 pm) [24] expands the tetrahedral interstice (elongates

the bond length) resulting in the observed negative shift of the tetrahedral vibration band.

On the other hand, the substitution of Li+ (90 pm) by octahedrally-coordinated Fe3+ (69

pm) [24] contracts the octahedral interstice (shortens the bond length) leading to a

positive shift of the octahedral IR band as observed.

It is interesting to note that in all the FT-IR spectra of the milled samples, the

tetrahedral band broadens and shifts positively to higher wavenumbers (~ 605 cm-1).

Such a positive band shift implies an ionic bond shortening and is, thus, suggestive of an

increase in the cationic population of the tetrahedral sites. The octahedral vibration band,

on the other hand, significantly broadens and shifts negatively to wavenumbers that are

below the lowest limit of the measurement range (400 cm-1). Such a negative band shift

implies an increase in the ionic bond lengths (or bond weakening) that can be associated

with milling-induced movement of octahedral cations to tetrahedral sites. The band

broadening reflects a reduction in both size and crystallinity.

D- Mössbauer spectroscopy and magnetization measurements

The Mössbauer spectra recorded at 298 K for the Mg-Li0.5Fe2.5O4 samples milled at

different times are shown in Fig. 6. The spectrum of each sample is a six-line magnetic

pattern superimposed on a central doublet whose area increases progressively with

milling time. In the literature we note that some authors have used detailed models,

involving multiple (up to five) sets of magnetic sextets to model pure and cation-

substituted Li0.5Fe2.5O4 by explicitly taking into accounts the influence of super-

transferred hyperfine fields at both crystallographic sites [18,25]. The fact that the cation

distributions in the cores of the nanoparticles and their surfaces are different, suggests

that using such a detailed fitting model is impractical in the present case. Instead, we

adopt here a simple model to fit the magnetic part of each spectrum with two overlapping

7

sextets for Fe3+ in both tetrahedral A- and octahedral B-sites which is sufficient for

drawing general conclusions at this stage. The corresponding hyperfine parameters are

given in Table 1. The ratio of the spectral areas of the A- and B-sextets for the non-

milled Mg-substituted-Li0.5Fe2.5O4 is 1: 2 relative to that of pure Li0.5Fe2.5O4 (1: 1.5)

reflecting the substitution of Mg2+ ion for Fe3+ at the A-sites. The broadening of the

Mössbauer absorption lines with increasing milling time is a clear indication that the

magnetic (Fe3+) cationic distribution around the each Fe3+ nucleus is appreciably

disordered [6]. The quadrupole splitting values (not shown in the table) for both sextets

are negligible whereas their isomer shifts are slightly higher than those of the non-milled

sample which is probably due to more Fe atoms in or near the surface layer with a

different chemical coordination from that of the core. The reduction of the hyperfine

magnetic fields at both sides can be attributed to weak magnetic super-exchange

interaction in the nanoparticles, surface layers. The area of the central doublet increases

from 4% for the non-milled samples to 19% for the sample milled for 50 h. This doublet

is associated with superparamagnetic relaxation of particles having “effective” volumes

with blocking temperatures TB< 298 K [18,26,27]. Superparmagnetism can, also, lower

the average magnetic hyperfine field of the nanoparticles [27].

The 78.5 K Mössbauer spectra of the milled Mg-substituted Li0.5Fe2.5O4 samples

are shown in Fig. 7. It is clear that the superparamagnetic relaxation is almost suppressed

and the spectra reduce to broadened sextets superimposed on very weak unresolved

doublets. The doublet indicates that some residual relaxation effects are still present

which may be due nanoparticles whose blocking temperatures are lower than 78.5 K. In a

detailed study Dormann et al [25] showed that the relative occupation of the Fe ions in

the A- and B- sites derived from a 77 K zero-field Mössbauer spectrum of Li0.5Fe2.5O4 is

similar to that obtained from a 4.2 K in-field (6.5 T) spectrum. So, for the purpose of

determining the Fe distribution in our nanoparticles, it is sufficient to use the 78.5 K

Mössbauer spectra (Fig. 7). We also note that in fitting the Mössbauer spectra of spinel

ferrite nanoparticles, some authors have used four sub-spectra to cater for Fe3+ nuclei at

the A- and B- sites of both the core and the surface phases [7]. In doing so it was assumed

that the core has the same cation distribution of the bulk. Consequently fitting constraints

were imposed the hyperfine parameters of the core phase. Our fitting approach for the

8

78.5 K Mössbauer spectra of the nanoparticles will be different but essentially based on

the same reasoning. We use only two, easily-resolved, magnetic sextets due to Fe3+ at the

A- and B-sites. The central shift for each of the sextets and their spectral-area ratios

(Table 2) are the weighted averages values of the corresponding parameters of the core

and the surface phases. A particular hyperfine parameter for either phase can be obtained

algebraically using the core-surface ratio obtained previously from the XRD Rietveld

refinement under the assumption that core and the non-milled sample are isostructural.

We shall apply this fitting approach for the spectrum of sample milled for 50 h (which is

fully nanocrystalline) to find the A: B spectral area ratio of its surface layer knowing that

it has an average A: B spectral ratio of 45: 53 (or 1: 1.18) as shown in Table 2 . Using

the core to surface ratio of 1: 4 (inferred from XRD data) and the fact that the core has an

A: B spectral area ratio of 1: 2, it can easily be shown that the A: B spectral area ratio of

the surface layer of the nanoparticles is 1: 1.1. Thus per formula unit for these

Li0.41Fe2.41Mg0.17O4 nanoparticles there are 1.15 of the Fe3+ ions in the tetrahedral A-sites

whereas the rest, 1.26 Fe3+ ions, occupy the octahedral B- sites of the surface layer. As

there are 8 formula units in the spinel structure, such an occupation of more than 8 out of

the 64 of the available tetrahedral A-sites is unusual, but has previously been reported for

nanostructured Ni0.5Zn0.5Fe2O4 spinel ferrite [28]. This implies that the octahedral-to-

tetrahedral cationic migration inferred from the FT-IR spectra is mostly of the magnetic

Fe3+ ions. With the set of techniques used in the present study one can not elaborate on

whether the non-magnetic (Li+ and Mg2+) ions experience any milling-induced migration

or not.

To appreciate how the magnetic properties of Mg-substituted Li0.5Fe2.5O4 are

influenced by milling, we recall that according to the Néel’s collinear spin model, the

magnetic moments on the A- and B- sites are coupled antiferromagnetically, leading to a

net magnetization per formula unit at 0K (Ms) that is simply the numerical difference

between the two sub-lattice magnetizations [1-5]. Using the known magnetic moments of

Mg2+, Li+ and Fe3+ namely 0 Bµ , 0 Bµ and 5 Bµ respectively and the cation distribution

inferred from the XRD Rietveld refinement of the non-milled sample [3], the theoretical

magnetization at 0K of Mg-substituted Li0.5Fe2.5O4 per formula unit is given by: 227.10475.35)83.057.1( −==×−=−= kgAmMMM BBABCs µµ

9

Fig. 8 shows the measured thermal variation of magnetization for the milled Mg-

substituted Li0.5Fe2.5O4 samples starting from 300K. It is seen that throughout the

temperature range investigated, the magnetization of all the samples decreases

monotonically with increasing temperature. At 300K the magnetization decreases with

decreasing crystallite size from 60.3 Am2/kg for the non-milled sample to 35.6 Am2/kg

for the sample milled for 50 h. Using the Néel’s model and the surface magnetic (Fe3+)

cationic distribution inferred from the 78.5 K Mössbauer spectrum, the theoretical

magnetization per formula unit at 0K for the surface layer of the nanoparticle obtained

after 50 h of milling is given by: 224.1555.05)15.126.1( −==×−=−= kgAmMMM BBABSs µµ

Following Šepelák et al [7], the change in the magnetization for a spherical nanoparticle

relative to its bulk,∈ , can be estimated in the following relation:

3

34

2/

0

32/

2/3422

2

244

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛−+

∈=∫ ∫−

−

DM

DMdrrMdrrM

Cs

tD D

tDCsSsCs

π

πππ

where D is the particle size and t is the thickness of the surface layer of nanoparticle.

Thus for the nanoparticles obtained after 50 h of milling, using a core magnetization

(CsM = 104.7 Am2kg-2), the average particle size (D =12 nm), and a surface layer

thickness (t = 2.5 nm), the estimated relative change in the magnetization is 31.0∈= . This

corresponds to a magnetization per formula unit at 0K of 32 Am2kg-2 which is in

reasonable agreement with that observed at 300K (~35 Am2kg-2) as is seen in Fig. 8. The

slight discrepancy between the two values could be reconciled, if allowance is made

either for a minor spin thermal reversal and/or spin canting for the A-sub-lattice spins,

both of which can slightly increase the difference between the effective magnetizations of

the sub-lattices. Also, as seen from Fig. 1 the nanoparticles are not fully spherical as

assumed in the theoretical calculations. Fig. 8 also shows that the Curie temperature Tc of

the nanocrystalline samples is reduced to ∼ 840K (vs. ∼900K for non-milled S0). The

also could be due attributed to the different spin arrangement in the surface layer relative

to that of the core that weaken the magnetic super-exchange interactions.

10

IV. CONCLUSIONS

The structural evolution and magnetic properties of nanocrystalline Mg-substituted-

spinel-related Li0.5Fe2.5O4 particles prepared by ball milling have been investigated. Both

particle size and crystallite size were found to decrease progressively as milling proceeds

approaching ~ 12 nm after 50 h of milling. Rietveld refinement of the XRD data shows the

cores of the nanoparticles and their surface layers to have different cation distributions. The

lattice constant was found to increase with decreasing particle size and then decrease

implying large strains within the particles and bond deformation respectively. The

superparamagnetic behavior observed in the 298 K Mössbauer spectra is almost

suppressed at 78.5K. The infrared spectra of the milled samples reveal a cationic

migration from the B- to the A- sites in the spinel structure. A simple fit approach of the

78.5 K Mössbauer spectrum for the nanoparticles obtained after 50h of milling in

conjunction with the core-to-surface ratio inferred from the XRD Rietveld refinement

enabled the quantitative estimation of the Fe3+ distribution in the surface phase of the

nanoparticles. This constitutes a simple and reliable method for determining the magnetic

cation distribution without the need of using large magnetic fields at very low

temperatures. While the experimentally measured magnetization of the nanoparticles is

found to reasonably agree with that calculated using the Néel’s collinear model it,

nonetheless, suggests a thermal spin reversal and/or a minor canting effect which are

more pronounced for the A-sub-lattice spins.

Acknowledgments: We thank Mr. Issa Al-Amri for producing TEM micrographs. We

are also thankful to Dr. C. Johnson, Prof. F. Berry, Dr. M. Pekala and Mrs. I. Sirrour.

This work was done within the framework of the Associateship Scheme of the Abdus

Salam International Centre for Theoretical Physics, Trieste, Italy. Financial support from

the Swedish International Development Cooperation Agency is acknowledged.

11

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12

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Table 1: Mössbauer parameter derived from fitting the spectra recorded at 298 K for the Mg-substituted Li0.5Fe2.5O4 samples milled at the times indicated. Milling time (h) Parameter Sextet A Sextet B Central doublet

0 H(T) 48.4 50.2 δ (mms-1) 0.25 0.30 0.30 ∆(mms-1) 0.03 0.02 0.51 Area (%) 32 64 4 6.5 H(T) 48.4 50.4 δ (mms-1) 0.28 0.44 0.32 ∆(mms-1) 0.00 0.01 0.54 Area (%) 35 59 6 15 H(T) 46.0 48.9 (mms-1) 0.29 0.45 0.32 ∆(mms-1) 0.01 0.01 0.67 Area (%) 40 49 11 38 40.5 48.0 48.2 δ (mms-1) 0.28 0.40 0.32 ∆(mms-1) 0.00 0.01 0.77 Area (%) 43 55 16 50 H(T) 40.7 47.9 δ (mms-1) 0.29 0.40 0.32 ∆(mms-1) 0.02 0.01 0.80 Area (%) 36 45 19 Hyperfine field (H), isomer shift (δ), quadrupole splitting (∆) and relative spectral area (Area).

14

Table 2: Mössbauer parameter derived from fitting the spectra recorded at 78.5 K for the Mg-substituted Li0.5Fe2.5O4 samples milled at the times indicated. Milling time (h) Parameter Sextet A Sextet B Central doublet

0 H(T) 51.2 53.4 δ (mms-1) 0.34 0.40 0.33 ∆(mms-1) 0.03 0.02 0.48 Area (%) 32 65 3 6.5 H(T) 50.2 52.5 δ (mms-1) 0.37 0.44 0.27 ∆(mms-1) 0.00 0.02 0.59 Area (%) 36 61 3 15 H(T) 49.2 51.7 (mms-1) 0.40 0.45 0.32 ∆(mms-1) 0.03 0.01 0.63 Area (%) 41 57 2 38 H(T) 48.0 51.2 δ (mms-1) 0.37 0.40 0.34 ∆(mms-1) 0.00 0.01 0.49 Area (%) 43 55 2 50 H(T) 47.3 51.0 δ (mms-1) 0.37 0.40 0.36 ∆(mms-1) 0.02 0.02 0.49 Area (%) 45 53 2 Hyperfine field (H), isomer shift (δ), quadrupole splitting (∆) and relative spectral area (Area).

15

Fig. 1: The TEM micrographs of the (a) the Mg-substituted-Li0.5Fe2.5O4 samples milled for (a) 0 h; (b) 6.5 h; (c) 38 h and (d) 50 h. The scale bar for micrographs (a), (b), and (c) represents 0.2µm; for micrograph (d)

it represents 30 nm.

(a) (b)

(c) (d)

16

20 25 30 35 40 45 50 55 60 65 70 75 80

0 h

6 . 5 h

1 5 h

3 8 h

5 0 h

Inte

nsity

(arb

. uni

ts)

02253

3

620

440

333

42240

0

222

311

220

2 θ (o)

`

Fig. 2: The x-ray diffraction patterns of the Mg-substituted-Li0.5Fe2.5O4 samples milled for the times indicated.

17

0 5 10 15 20 25 30 35 40 45 50 550

5

10

15

20

25

30

35

40

45

50

aver

age

crys

tallit

e si

ze (n

m)

milling time (h)

Fig. 3: The variation of the average crystallite size Mg-substituted-Li0.5Fe2.5O4 samples with milling time.

0 5 10 15 20 25 30 35 40 45 508.340

8.342

8.344

8.346

8.348

8.350

8.352

Latti

ce c

onst

ant

(Ang

strö

m)

Milling Time (h)

Fig. 4: The variation of the average lattice parameter of the Mg-substituted-Li0.5Fe2.5O4 samples with milling time.

18

800 700 600 500 400

606

0 h

6.5 h

15 h

38 h

603

604

605

481

563

50 h

wavenumber / (cm-1)

Fig. 5: FT-IR spectra for Mg-substituted Li0.5Fe2.5O4 milled for the times indicated.

19

-9 -6 -3 0 3 6 9

2

2

2

3

4

5 0 h

3 8 h

1 5 h

6 . 5 h

0 h

Rel

ativ

e Tr

ansm

issi

on (%

)

V e l o c i t y / (m m s-1)

Fig. 6: The Mössbauer spectra of the Mg-substituted- Li0.5Fe2.5O4 samples at 298 K.

20

-9 -6 -3 0 3 6 9

2 . 5 %

3 %

3 %

4 %

4 .5 % 0 h

6 . 5 h

1 5 h

3 8 h

5 0 h

Rel

ativ

e tra

nsm

issi

on /

(%)

V e l o c i t y / (m m s-1)

Fig. 7: The Mössbauer spectra of the Mg-substituted- Li0.5Fe2.5O4 samples at 78.5 K.

21

300 400 500 600 700 800 9000

10

20

30

40

50

60 0 h 6.5 h 15 h 38 h50 h

Mag

netis

atio

n (A

m2 /k

g)

T e m p e r a t u r e / (K)

Fig. 8: The temperature variation of the magnetization of the Mg-substituted-Li0.5Fe2.5O4 samples milled for the times indicated.